Hydrogen and fundamental
defects in electron-irradiated
high-purity silicon
Jan Håvard Bleka
March 2008
Thesis submitted in partial fulfilment of the requirements
for the degree of Philosophiæ Doctor (Ph.D.)
at the University of Oslo
Abstract
The dynamics of various fundamental defects in electron-irradiated high-purity silicon
detectors (diodes) were investigated by deep-level transient spectroscopy (DLTS). Samples with various oxygen concentrations were used and hydrogen was intentionally introduced into some samples. The defect dynamics was investigated by first creating
defect centres by irradiating the diodes with 6-MeV electrons and subsequently annealing the samples, isochronally or isothermally, at increasingly higher temperatures up to
400 °C while measuring the concentration of the various electrically active defects by
DLTS. Based on the temperature- and time-dependent changes of the concentration of
the defects, models explaining the observations were suggested.
In one study, the annealing of the di-vacancy–oxygen (V2 O) centre was investigated
and modelled, and it was concluded that this centre anneals out through a dissociation
resulting in a vacancy–oxygen (VO) centre. The binding energy between the vacancy
and the VO centre was estimated to be ∼1.7 eV.
In another investigation, a defect centre annealing out after a few weeks at room
temperature was found to have two energy levels in the band gap: one, labelled E4,
0.37 eV below the conduction-band edge (Ec ) and the other, labelled E5, 0.45 eV
below Ec . Comparison with annealing studies performed with Fourier-transform infrared spectroscopy (FTIR) suggested that the defect may be a di-interstitial–oxygen (I2 O)
complex. E5 is known to correlate with the leakage current of silicon detectors, and it
was suggested that the oxygen concentration should be minimised to reduce the formation of I2 O centres and thus reduce the leakage current.
Several annealing studies with hydrogenated samples were performed. These resulted in the identification of a hydrogen-related level at Ec − 0.37 eV as a vacancy–
oxygen–hydrogen centre, which was labelled VOH∗ . This centre was seen to form
when positively charged hydrogen diffused in from the surface of the silicon diodes and
reacted with the VO centre at depths with locally high hydrogen concentration. VOH∗
was seen to break up when the hydrogen diffusion had resulted in a lower, more uniform
hydrogen concentration. Possible identification of other hydrogen-related defect levels
were also put forward; in particularly a hole trap located 0.23 eV above the valenceband edge which is suggested to be a di-vacancy–hydrogen (V2 H) centre.
i
ii
Abstract
Secondary-ion mass spectrometry (SIMS) was used to measure the depth profile of
hydrogen in some of the samples.
Acknowledgements
This chapter could, and should, have been much longer, but I will save some space
here and instead try to show my gratitude in real life to those that were not included in
writing.
My gratitude goes first of all to my main supervisor Bengt Gunnar Svensson who has
let me do things my own way and at my own pace, even though this has rarely been the
shortest way to the goal. Bengt has, with his decades of experience, shaped our articles
into what they are – at times by extensive rewriting – at times just by adding a magic
word. Especially rewarding has it been to sit down and compose articles together with
him – he has always listened carefully when I have disagreed and even quite often
understood and taken into account my concerns. A large thank you to my second
supervisor Edouard V. Monakhov who has had the undesirable task of making the initial
corrections to our articles to prepare them for Bengt’s scrutiny. Also, his experimental
experience has been invaluable when my experimental methods and brain have failed.
My sincere gratitude goes to Mayandi Jeyanthinath – for being a reliable friend, for all
the curry and for keeping a desk so overloaded with scientific papers that it has attracted
some attention away from my own desk. To Ulrike Grossner, for the laughs, the mentor
services, the lab collaboration and the smell of real beer. Lasse Vines, Mads Mikelsen
and Lars Sundnes Løvlie, for helping me out in many an existential crisis concerning
DLTS and related topics. Lars in particular, for never trusting other people’s calculation
and thus being valuable for consistency verifications; Mads, for making me question
opinions I took for granted.
I am grateful to Simen Bræck and Knut Johan Øen who were my flatmates during my
whole Ph.D. period; all those discussions in the middle of the night has taught me more
than what can be put down in text. To Thomas Bryhn and Jørnar Heggsum Hubred, for
providing me with much of the trash and entertainment required for the completion of
my project.
Thank you, Aleksander Ulyashin, for spending many late hours patiently trying to
cure my persistent naivety. Thank you, Terje Finstad, for patiently explaining me why
my self-made circuits have been shooting sparks when my attitude has been that they
should not. Thank you, David Wormald and it-hjelp, for the much valued help in times
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Acknowledgements
of broken pipes and low computing power.
I feel deeply indebted to Danie Auret and Ioana Pintilie who took very good care of
me during my two-week-long research stays in Pretoria (2005) and Hamburg (2007),
respectively – thank you!
To all the rest of my present and former colleagues: It is sad to abandon my messy
desk and not attend the cherished MiNaLab lunches any more; experience shows that it
is difficult to keep contact, but I choose to be optimistic and hope to maintain the contact
with you also in the following.
Last, but unfortunately most important of all: Sorry everyone that I have so many
times ”had to” be at MiNaLab instead of being out in the real world as a good friend. Let
us see if this can change in the coming years.
Yes, and I am not able to leave out a warm thank you to the developers of free
software who just out of good will provide the world with phenomenal applications which
allow me to materialise my ideas (and documents such as the present one). These
people make life with computers more enjoyable.
Contents
Abstract
i
Acknowledgements
iii
List of publications
vii
1 Introduction
1
2 Basic concepts
3
2.1
Semiconductors . . . . . . . . . . . .
2.1.1 Electrical properties of crystals
2.1.2 Doping semiconductors . . . .
2.1.3 pn junctions . . . . . . . . . .
2.1.4 Applications of pn junctions .
2.1.5 Radiation defects . . . . . . .
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2.2
Characterisation techniques . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 CV measurements . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Deep-level transient spectroscopy (DLTS) . . . . . . . . . . . .
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3 Experimental details
15
3.1
Sample structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3.2
Hydrogenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
3.3
Connecting electrically to the samples . . . . . . . . . . . . . . . . . .
17
3.4
Experimental set-ups . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Hydrogen-concentration measurements
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5 Fitting and modelling
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5.1
Fitting algorithms (general aspects)
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5.2
Fitting of DLTS spectra . . . . . . . . . . . . . . . . . . . . . . . . . .
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v
vi
Contents
5.3
Modelling of reaction equations . . . . . . . . . . . . . . . . . . . . . .
6 Summary of results
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31
6.1
Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
6.2
Paper II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.3
Paper III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.4
Paper IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.5
Paper V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.6
Paper VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
7 Concluding remarks
35
A User guides on software
37
A.1 Asterix how-to . . . . . . . . . . . . . . . . . . . . . . .
A.1.1 CV measurements . . . . . . . . . . . . . . . .
A.1.2 DLTS measurements . . . . . . . . . . . . . . .
A.1.3 Depth-profile measurements . . . . . . . . . . .
A.1.4 PID control that keeps the temperature constant
A.1.5 Temperature logger . . . . . . . . . . . . . . . .
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A.2 DLTS-transient analyser . . . . . . . . . . . . . . . . . . . . . . . . .
A.2.1 Feature overview . . . . . . . . . . . . . . . . . . . . . . . . .
A.2.2 Description of each of the features . . . . . . . . . . . . . . . .
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A.3 Defect-reaction modeller . . . . . . . . . . . . . . . . . . . . . . . . .
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A.4 Depth-dependent defect-reaction modeller . . . . . . . . . . . . . . . .
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A.5 DLTS-movie maker . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
B User guides on hardware
65
B.1
Lift for automatically controlling the nitrogen level on the Asterix set-up
B.1.1 Trouble shooting . . . . . . . . . . . . . . . . . . . . . . . .
B.1.2 Relevant LabView programs . . . . . . . . . . . . . . . . . .
B.1.3 Spare parts . . . . . . . . . . . . . . . . . . . . . . . . . . .
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B.2
Controllable mains switch on Tiffy . . . . . . . . . . . . . . . . . . . .
B.2.1 Relevant LabView programs . . . . . . . . . . . . . . . . . . .
B.2.2 Spare parts . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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B.3
Power amplifier for the heating elements on the Obelix set-up . . . . . .
B.3.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.2 Spare parts . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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C Example input file for the DLTS-transient analyser
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D Example input file for the defect-reaction modeller
83
Bibliography
89
List of publications
I
Defect behaviour in deuterated and non-deuterated n-type Si
J. H. Bleka, E. V. Monakhov, A. Ulyashin, F. D. Auret, A. Yu. Kuznetsov,
B. S. Avset and B. G. Svensson
Sol. St. Phen. 108–109, 553 (2005)
II
Annealing of the divacancy-oxygen and
vacancy-oxygen complexes in silicon
M. Mikelsen, J. H. Bleka, J. S. Christensen, E. V. Monakhov,
B. G. Svensson, J. Härkönen and B. S. Avset
Phys. Rev. B 75, 155202 (2007)
III
Room-temperature annealing of
vacancy-type defect in high-purity n-type Si
J. H. Bleka, E. V. Monakhov, B. S. Avset and B. G. Svensson
Phys. Rev. B 76, 233204 (2007)
IV
On the identity of a crucial defect contributing to
leakage current in silicon particle detectors
J. H. Bleka, L. Murin, E. V. Monakhov, B. S. Avset and B. G. Svensson
Appl. Phys. Lett. 92, 132102 (2008)
V
Rapid annealing of the vacancy-oxygen center and
the divacancy center by diffusing hydrogen in silicon
J. H. Bleka, I. Pintilie, E. V. Monakhov, B. S. Avset and B. G. Svensson
Phys. Rev. B 77, 073206 (2008)
VI
Dynamics of irradiation-induced defects in high-purity
silicon in the presence of hydrogen
J. H. Bleka, E. V. Monakhov, B. S. Avset and B. G. Svensson
To be published
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List of publications
Relevant publications not included
DLTS Study of Room-Temperature Defect
Annealing in High-Purity n-Type Si
J. H. Bleka, E. V. Monakhov, B. S. Avset and B. G. Svensson
ECS Trans. 3(4), 387 (2006)
Charge carrier removal in electron irradiated 4H and 6H SiC
M. Mikelsen, U. Grossner, J. H. Bleka, E. V. Monakhov, R. Yakimova,
A. Henry, E. Janzén and B. G. Svensson
To be published
Alignment of intrinsic defect levels in
the electronic band gap of 4H and 6H SiC
U. Grossner, M. Mikelsen, J. H. Bleka, E. V. Monakhov and B. G. Svensson
To be published
Chapter
1
Introduction
Silicon is still the material playing the central role in the fabrication of electronic devices.
It is a material with many advantageous properties and since the fabrication processes
in the silicon industry have matured for several decades, silicon devices are generally
cheaper to produce than devices from other materials. In addition, device fabrication
has not been proven in all types of semiconductor materials and in general, the complexity increases in compound materials. Silicon is, however, not perfect in all aspects.
It is not especially well suited for optical devices, as it does not have a direct band
gap; several other materials have larger band gaps than silicon – something which is
advantageous in many applications; and some materials, for instance SiC, or even better: diamond (effective n-doping is, however, a major problem with this material), can
withstand more irradiation by high-energy particles than silicon before the devices become unusable (Adam et al. 2003 [1]). In the construction of the Large Hadron Collider
(LHC) (at CERN, close to Geneva), which is currently scheduled to start operation in
May 2008, the radiation hardness of the particle detectors is a great concern and a major research-and-development challenge. For instance, in the Compact Muon Solenoid
(CMS), the fluence of fast hadrons will during the expected lifetime of the LHC reach
∼5 × 1015 cm−2 at a distance of 7 cm from the beam centre. If the radiation hardness
of the detectors is not significantly improved, the inner tracking detectors will have to
be moved further away from the collision point for the proposed upgrade to the Super
Large Hadron Collider (SLHC) around year 2015 (Gianotti et al. 2005 [2] (p. 318)),
an upgrade which will, hopefully, give an increase in the luminosity by a factor of ten
(URL [3], Gianotti et al. 2005 [2]).
Hydrogen is known to passivate, i.e. make electrically inactive, or shift the energy
levels of many of the radiation defects in silicon (Pearton 1986 [4], Coutinho et al.
2003 [5], Bonde Nielsen et al. 1999 [6], Pellegrino et al. 2001 [7], Monakhov et al.
2004 [8]). It has, therefore, been important to investigate the defect dynamics in the
presence of an increased hydrogen concentration. With sufficient knowledge, it may
be possible to introduce hydrogen such that detrimental defects, i.e. those that cause
an increased leakage current or that trap electrons, are transformed into defects with
1
2
1. Introduction
less harmful properties. This is the background for the investigations of hydrogenated
samples in the present project. In particular, the interaction between hydrogen and
vacancy-type defects has been addressed.
Hydrogen is, however, not a simple substance to investigate. It reacts easily with
many defects and impurities/dopants (Pearton 1986 [4], Zundel and Weber 1989 [9])
and it can, thus, be difficult to isolate and focus on one particular reaction. The diffusivity of hydrogen, and thus also the reaction rates, depend on the charge state of the
hydrogen atoms (Markevich and Suezawa 1998 [10], Weber et al. 2003 [11], Huang
et al. 2004 [12]); the doping and temperature of the material will, therefore, affect the
defect dynamics.
Chapter
2
Basic concepts
2.1
2.1.1
Semiconductors
Electrical properties of crystals
Let us start with the atom (figure 2.1); an atom consists of a heavy, positively charged
nucleus (built from protons and neutrons) with, if the atom is neutral, as many bound
electrons as there are protons in the nucleus. As the electrons have negative charge,
they repel each other, while they are attracted to the positively charged nucleus. Quantum physics allows electrons to be situated only at a few discrete distances from the
nucleus and also puts restrains on how many electrons can reside at a each of these
distances. This causes the electrons to organise themselves in these shells with given
energies, filling up from the lowest energy closest to the nucleus.
If several atoms are put closely together, the energy landscape of the electrons
changes, and for electrons at certain energy levels, paths over to neighbouring atoms
may open, enabling some of the electrons to move freely from one atom to the next. If
atoms are placed in a regular pattern, there are several possible outcomes depending
on the properties of the atoms and the pattern in which they are organised. If the
structure allows many electrons to move freely in the lattice, we have a metal – if no
electrons are free to move between the atoms, we have an insulator. A semiconductor is
Figure 2.1: Illustration of a lithium atom (Wikipedia).
3
4
2. Basic concepts
Figure 2.2: Illustration of the two filled and the one partly filled electron shells in a neutral silicon
atom.
in-between these two scenarios; in a perfect semiconductor lattice, no electrons are free
to move at low temperatures, but many electrons are bound so weakly to the nucleus
that their thermal energy is occasionally large enough to let them escape the energy
well and allow them to move freely in the lattice.
Silicon atoms have 14 protons in the nucleus and the surrounding 14 electrons are
organised in shells of two, eight and four electrons with room for four more electrons
in the outermost shell (figure 2.2). Silicon atoms naturally organise themselves in the
same lattice structure as that of the carbon atoms in diamond. A unit cell of the diamond
structure is shown in figure 2.3. When silicon atoms are put into a diamond structure,
four of the states of the outermost electron shell will be shifted to a higher energy which
will have a low electron occupancy, since the electrons will first populate the states
with lower energies – the ensemble of all these states will form the conduction band
of the crystal – while the remaining four states will get a reduction in the energy level
– the these states will form the valence band. As nature tries to lower its energy, the
four electrons in what used to be the outermost shell of the individual silicon atoms
will normally reside in the valence band and exactly fill this. Thus, an electron in the
valence band will not be free to move to a neighbouring atom, as there are usually
no vacant energy states there without going to higher energies. For electrons to move
freely between neighbouring silicon atoms, they must somehow acquire enough energy
to lift it up across the forbidden band gap (1.12 eV for silicon) and into the conduction
band where there are many available energy states.
2.1.2
Doping semiconductors
Ideal, flawless semiconductors (intrinsic semiconductors) have little value for practical
applications, because these systems are rather rigid with limited response at room temperature (as nearly all electrons are in the valence band, there are no available states
in the neighbouring atoms into which the electron can move, unless it gets excited up to
the free states in the conduction band). To make the material more exciting, free charge
carriers are introduced. Since the number of intrinsic electrons is exactly enough to fill
the electron states in the valence band, in principle, any additional electrons introduced
2.1. Semiconductors
5
Figure 2.3: A unit cell of a lattice with diamond structure (H. K. D. H. Bhadeshia).
into the lattice will have no state in the valence band into which to fall and will, therefore,
float freely around in the conduction band. A semiconducting material with an excess of
free electrons is called n-type material. A silicon crystal can be made n-type by replacing some of the silicon atoms by phosphorous atoms. The phosphorous atom has one
proton and one electron more than the silicon atom. In a silicon lattice, this additional
electron becomes very loosely bound and the thermal energy at room temperature is
enough to make it escape the host atom and jump up to the conduction band.
Another way of increasing the mobility in an intrinsic semiconductor is to remove
some of the electrons in the valence band such that the band is no longer completely
filled. When an electron is removed from the valence band, a hole is created in its
place. This hole can move around in the valence band just as freely as electrons in
the conduction band. Materials with an excess concentration of holes, compared with
intrinsic material, is said to be p-doped. In silicon, holes can be introduced by doping
with boron atoms, which have one electron less in their outer shell than the silicon
atoms.
2.1.3 pn junctions
Something very interesting happens when n-type and p-type material are put in contact
with each other. Since the n-type side has more electrons than the p-type side, the
thermal motion of electrons will cause a diffusion of electrons over to the p-type side.
Similarly, the higher hole concentration in the p-type material will cause diffusion of
holes over to the n-type side. This exchange of charge carriers will cause a positive
net charge on the n-type side of the junction, and a negative net charge on the p-type
side – thus, an electric field is building up. This electric field will work against the net
diffusion of charge carriers, and a stationary situation will be reached when the diffusion
is balanced by this internal electrical field. The electric field will cause a net force on
any free charge carriers, and there is, therefore, close to no free charge carriers in
the volume with the electrical field – this volume is the depletion zone. The energy
landscape of an electron in the proximity of the pn junction is illustrated in figure 2.4 –
6
2. Basic concepts
p+
~
E
n−
W
Figure 2.4: Band diagram for a pn junction. The Fermi level is shown as the blue line.
p+
p+
~
E
n−
~
E
n−
W
W
Figure 2.5: Band diagram for a pn junction with forward (left) and reverse (right) bias. Here, the
blue line is the quasi Fermi level.
this is usually how the band diagram for a pn junction is shown. In this situation there is
a small possibility of an electron in the conduction band having enough energy to climb
the hill caused by the electric field, but this is balanced by the small possibility of an
electron in the p-type material being excited to the conduction band and sliding down
the hill to the n-type side.
2.1.4
Applications of pn junctions
A pn junction is a rectifying diode – only voltage applied in the forward direction of the
diode will cause an electric current. If the positive pole of a battery is connected to the
p-type side of the diode and the negative pole to the n-type side, the electric field in
the diode will be reduced (left side of figure 2.5). In this case, electrons will again start
diffusing from the n-type material over to the p-type. The larger the applied bias, the
larger the flow of electrons. If the voltage is applied in the opposite direction, the energy
barrier for the electrons will be very high and the diffusion of electrons even smaller
than in an unbiased diode. On the p-type side, there are still very few electrons free to
move and there is, therefore, close to no current flowing across the reverse-biased pn
junction.
2.1. Semiconductors
7
A pn junction also has a photovoltaic effect – it may be used as a solar cell. When
photons with sufficient energy hits a semiconductor, electrons may be excited from the
valence band to the conduction band such that electron–hole pairs are formed. If this
happens sufficiently close to, or inside, the depletion zone, there is a substantial probability of the minority carrier being swept across the depletion zone (e.g., electrons are
minority carriers in p-type material). As this process continues, there will be an accumulation of holes on the p-type side and electrons on the n-type side of the junction. The
resulting charges will cause an electric field opposite to the internal one, and the barrier
height of the pn junction will be reduced. This will cause a situation similar to the one
in a junction with forward bias (see figure 2.5), where the quasi Fermi level is higher on
the n-type side than on the p-type side. This difference in the quasi Fermi level is the
voltage across a photovoltaic cell that can perform work in an electrical circuit.
The last application I will mention is the one that has been most relevant for this
project. When a pn junction is reverse biased, it can be used to detect particles or
photons that hit the diode, given that they cause a certain amount of electrons to be
excited to the conduction band. For this application it is often desirable to keep the
reverse bias strong and the doping low to get the depletion region as large as possible,
because when an ionisation even occurs in the depletion region, the excited electrons
and holes will be swept out of the depletion zone in opposite directions and cause a
measurable charge pulse.
2.1.5
Radiation defects
Low-energy radiation does not cause degradation of the detectors, but when the energy
of the incident particles is sufficiently high, they will start displacing silicon atoms from
their position in the crystal lattice. At the LHC at CERN, an enormous amount of particle
detectors will be used, in layer upon layer, to track different particles created in the
proton–proton collisions that are scheduled to begin in May 2008 (Wikipedia [15]). The
innermost pixel detectors will be as close as 7 cm from the centre of the proton beam;
here, the fluence of fast hadrons will reach ∼5 × 1015 cm−2 during the expected lifetime
of LHC (Gianotti et al. 2005 [2]).
Figure 2.6 shows an example of what may happen when a silicon atom is displaced
and becomes a self-interstitial. Now two defects have been created in the lattice, and
the energy landscape of the nearby electrons is modified. In this example, the vacancy
that is left after the silicon atom may easily move around and attach to an oxygen atom
to form the vacancy–oxygen centre (VO) (Brotherton and Bradley 1982 [16], Song et al.
1990 [17], Keskitalo et al. 1997 [18]). This centre has place for an electron. The problem is that the electron that fills this state will neither have the energy of electrons in
the valence band, nor that of electrons in the conduction band – its energy level will
be in-between: 0.18 eV below the conduction band edge (or 0.95 eV above the valence band edge). This is undesirable in several ways: Charge-carrier traps, such as
the VO centre, will reduce the concentration of free charge carriers, because electrons
in the conduction band can fill these states at lower energies and thus become immobile (figure 2.7 illustrates the energy landscape in such a conduction band). A more
8
2. Basic concepts
important problem, yet, arises with energy levels close to the middle of the band gap
– then valence-band electrons can rather easily be thermally excited up to the energy
needed to fill the defect state, and from this state it can get excited further up to the
conduction band. Hence, such defect levels in the middle of the band gap may act as
electron–hole pair generators – they make it easier for electrons to be excited from the
valence band to the conduction band. They may also act as recombination centres at
which a conduction-band electron and valence-band holes meet and annihilate. In the
case of the particle detectors, such generation centres and recombination centres will
increase the noise in the circuit and thus reduce the signal-to-noise ratio.
In addition to the creation of detrimental generation centres, operation in a radiationhard environment causes a steady increase in the concentration of acceptor-like defects (Moll 1999 [19], Lindström et al. 2001 [20], URL [21]). For detector applications,
p+ –n− –n+ structures, i.e. the bulk is weakly n-doped, are normally used. As the operation causes generation of acceptors, the effective concentration of free carriers (Neff )
in the bulk will first decrease, before the concentration of holes exceeds that of free
electrons and the bulk becomes more and more p-type. In this situation, the depletion
zone will have shifted from the p+ –n junction over to what is now the n+ –p junction on
the back side (URL [21]).
As the radiation dose to which a particle detector has been exposed increases, the
leakage current, and thus also the noise, increases (due to the electron–hole generation
centres), the relative strength of the ionisation signal decreases (due to the increase
in the acceptor concentration), the full-depletion voltage increases (also due to more
acceptors), resulting in an even smaller signal if the bias is not increased. All these
effects degrade the detection sensitivity of the structure. The leakage current can even,
in the worst case, cause thermal runaway due to ohmic heating (Gianotti et al. 2005 [2]).
How much high-energy radiation a material can withstand before being rendered
unusable as a detector, is referred to as radiation hardness and radiation tolerance. As
it is very costly and time consuming to install a new set of detectors in the detector
set-ups at CERN, considerable research has been made to engineer more radiationhard detectors (see, e.g., the report of the CERN RD50 collaboration and references
therein (URL [22])). One method is to search for materials where a certain radiation
dose causes less permanent damage; epitaxial-grown (EPI) silicon is suggested to be
an example of this (Kramberger et al. 2003 [23]). Other methods can be to introduce
lattice defects that can trap radiation defects in places where they cause less damage
(gettering) or to introduce defects that can combine with the harmful radiation defects
to alter the energy level of the electron states and thus make them less harmful to
the application. Hydrogen is one such impurity that is known to easily react with many
different defects and alter their electron states. The present project was initiated to shed
more light on the different reactions that hydrogen can cause in radiated silicon.
2.2. Characterisation techniques
9
Figure 2.6: Illustration of a silicon atom being knocked out of position, leaving behind a vacancy
and becoming a self-interstitial in its new position.
Figure 2.7: Illustration of the energy landscape experienced by an electron in the conduction
band close to a p+ –n junction with the presence of lattice defects.
2.2
Characterisation techniques
2.2.1 CV measurements
A simple and very useful measurement technique is to measure the change in capacitance as a function of the reverse voltage applied across a diode to determine the doping
concentration. When the reverse bias is increased slightly, the electric field, whose gradient is given by the concentration of fixed net charges (i.e. doping atoms), will increase
and cause the depletion zone to be extended. As capacitance is defined as the change
in the amount of charge as a function of the voltage, a depletion zone works as a nonlinear capacitor – a change in the voltage causes a change in the amount of charge in
the depletion region. Given uniform doping concentrations and abrupt interfaces, this
relationship easily enables us to find the doping concentration of asymmetrical pn junctions (i.e. p+ –n or p–n+ ) and Schottky diodes (p-type or n-type material coated with a
suitable metal). The capacitance C relates to the width of the depletion region W by
C=
εA
W
,
(2.1)
10
2. Basic concepts
where ε is the permittivity of the material and A the effective area of the diode. The
depletion width is
s
W=
2ε(V0 − V)
q
1
1
+
Na
Nd
,
(2.2)
where V0 is the potential barrier when no external bias is applied, V the applied bias,
q the elementary charge, Na the net acceptor concentration (the doping concentration)
in the p-type material and Nd the net donor concentration in the n-type material. If, for
instance, the p-type side is doped much stronger than the n-type, Na−1 can be neglected
and equations 2.1 and 2.2 can be combined into
1
2
(V0 − V) .
(2.3)
2
q
ε
A
Nd
C
This expression describes a straight line of the form y = mx + b, as the left side equals
a constant multiplied with the variable V in addition to the constant where V0 is included.
Thus, to find Nd we plot 12 as a function of V, which ideally gives a straight line, to find
C
the slope m, and from
2
=
m=−
2
(2.4)
εA2 qNd
we get
Nd = −
2.2.2
2
2
εA qm
.
(2.5)
Deep-level transient spectroscopy (DLTS)
It is helpful to look at the Fermi level when measuring DLTS. If a system is cooled
slowly to absolute zero (0 K), all the electrons will be as low as possible in the energy
landscape. All the electron states will then be occupied from the lowest energies up to a
level where there are no more electrons – this is the Fermi level. At absolute zero, there
are no electrons above the Fermi level.
When measuring DLTS, we first fill the electron traps by dipping them into the Fermi
sea; after they have been pulled out again, the electrons will, because of their thermal
energy, escape the traps again as the system attempts to establish equilibrium. The
deeper the trap – i.e. the higher the electron is required to jump to escape from its trap
and reach the conduction band – the more time it will take for the escape to be probable.
I will describe one cycle in the measurement routine – this cycle will result in one
data point in the DLTS spectrum. The sample is reverse biased most of the time during
the measurement, and this is where the cycle starts (figure 2.8): A few electrons occasionally acquire enough energy to jump up to the conduction band, just to reside there
for a while before falling back into a vacant trap either above or under the Fermi level.1
1
The Fermi level is not defined when the system is not in equilibrium – as is the case when we apply a bias
– so this is actually just the quasi-Fermi level.
2.2. Characterisation techniques
11
p+
U
U
U
n−
~
E
U
U
U
U
U
UU
U
U
U
U U
U
U
U
U
U
U
U U
U
Figure 2.8: The steady state before measuring a data point to add to the DLTS spectrum. The
blue haze on the left is an illustration of the Fermi sea at finite temperature, where the intensity
indicates to probability of finding an electron at a certain energy.
To start the measurement cycle, the reverse bias is removed for a short moment.
Figure 2.9 shows the band diagram in this unbiased state. Some of the traps that used
to be empty, due to their large energy distance to the Fermi sea, become filled as they
are now below the Fermi level.
When we have waited sufficiently long to allow all the submerged traps to capture
an electron (typically milliseconds), we reapply the reverse bias and immediately start
measuring the capacitance of the sample (figure 2.10). As always at finite temperatures,
the electrons will shake and wiggle violently around in their respective traps and they will
all, eventually, be able to free themselves from the potential well surrounding the trap.
The electrons in the shallow traps escape at a higher rate, but the electrons escape
also the deep traps, eventually. Had one of these electrons escaped its trap where the
conduction band is flat, it would soon be captured by another trap (or the same one
for that matter), but in the depletion region this is unlikely because the electric field will
immediately sweep the electron out of the region.
As the electrons escape and flow back into the non-depleted n-type side, there
is a change in the measured capacitance. After the reverse bias was reapplied, the
capacitance has increased with time in the manner shown in the graph in the upper
left corner of figure 2.11. The time required for an electron to escape a trap does not
only depend on the depth of the trap, but also the temperature of the sample, as this
will determine how violently the electrons wiggle. Therefore, if we assume that we have
only one kind of defect, with a certain trap energy, the capacitance transient will saturate
exponentially, like for instance the capacitance curve marked T2 in figure 2.11. Had
the sample been warmer, the electrons would have had more energy and they would
escape the traps in a shorter time; the capacitance transient would then look more like
the curve marked T3 , and vice versa if the measurement had been performed with a
cooler sample.
12
2. Basic concepts
p+
U
U
U
n−
~
E
U
U
U
U U
U
U
U
U
U U U U
U
U
U
U
U
U U
U
Figure 2.9: Unbiased p+ –n junction.
So the electrons escaped their traps at a certain rate and resulted in an exponential
capacitance transient with corresponding time constant. To construct a DLTS spectrum,
a weighting function (also known as a correlation function) is applied to the capacitance
transient. A time constant is chosen for this weighting function, and the result of the
mathematical operation performed gives the maximum amplitude when the time constant of the capacitance transient matches that of the weighting function. One weighting
function that can be used is the lock-in type shown in figure 2.11. If the time window of
the lock-in type weighting function is 320 ms, it will have the value 1 for the first 160 ms
of the capacitance transient and −1 for the next 160 ms. Multiplying the weighting
function with the capacitance transients gives the desired result: For slow and fast transients, such as T1 and T4 , respectively, the output value of the operation is small, while
for the transients with time constants matching the weighting function, such as T2 and
T3 , the multiplication gives a larger value.
When the whole operation is repeated at a higher and higher temperature, the
weighting function will cause a peak at the temperatures where the electrons have the
correct thermal energy to escape their traps with a rate that matches the weighting function. If we get two peaks in the scanned temperature region, it means that the electrons
are emitted from traps with two different energy levels. When measuring the peak of the
deepest trap, there will also be a contribution to the capacitance transient from the shallow trap, but this change in the capacitance is so fast that the weighting function will not
be influenced by it. The amplitude of a DLTS peak is proportional to the concentration
of the electron trap causing it; intuitively, many traps will emit many electrons and many
electrons will cause a large transient.
If weighting functions with different time constants are applied to the capacitance
transients, each resulting in a separate DLTS spectrum, it is possible to collect, from
the peak position of a given defect in each of the spectra, a set of data giving the emission rate versus temperature. Subsequently, an Arrhenius plot yielding the activation
enthalpy (approximately the energy difference between the conduction band and the
2.2. Characterisation techniques
13
p+
U
U
U
n−
~
E
U
U
U
U
U
UU
U
U
U
U U
U
U
U
U
U
U
U U
U
Figure 2.10: Reverse bias is again applied to the p+ –n junction and the electron traps above the
quasi Fermi level emit the captured electrons and remain empty.
defect level) and apparent capture cross section of the electron trap can be made. The
capture cross section also influences the rate with which electrons are emitted.
For more in-depth information on DLTS, see, for instance, Pellegrino 2001 [24],
Mikelsen 2007 [25], Alfieri 2005 [26] or Blood and Orton 1992 [27].
Alternative applications of DLTS set-ups
A DLTS set-up can also be used for other investigations than ordinary DLTS measurements. Keeping the temperature constant and varying the duration of the of the filling
pulse allows for the real capture cross section of a charge carrier trap to be found. Then
the DLTS signal will become stronger when the pulse is sufficiently long for the traps to
capture charge carriers.
Keeping the temperature and the steady state reverse bias constant while varying
the pulse voltage amplitude allows for the defect concentration at different depths to be
measured. This can be used to get at depth profile of a specific defect level. It is my
personal opinion that the importance of this possibility can not be overestimated! For
instance, profiling was essential for understanding the defect dynamics in the studies
presented in paper V and paper VI.
14
2. Basic concepts
T3
T2
T1
T2
T4>T3>T2>T1
1
Time window
DLTS signal
Weighting function
Capacitance
T4
T3
0
T1
T4
−1
Time
Temperature
Figure 2.11: The rate with which traps emit their captured electrons depends on the temperature.
The DLTS extraction will give the maximum result when the capacitance transient resonates with
the chosen weighting function.
Chapter
3
Experimental details
3.1
Sample structures
The results published in this project are all obtained using SINTEF-processed detectorgrade material. Float-zone (FZ) grown samples, diffusion-oxygenated FZ (DOFZ) samples and magnetic-Czochralski (MCz) grown samples have all been used for various
investigations. The physical measures and the structure, which are the same for all
these types of samples, are shown in figure 3.1. The thin ring of p-doped material
around the p-type layer is known as the guard ring; with this attached to the ground
potential, it will prevent unwanted currents from flowing along the edge surfaces of the
detector and it will cause the geometry of the active volume to be defined more accurately. The guard rings have, however, not been used during these experiments since
only minor improvements of the DLTS measurements are expected, given that the front
contact and back contact are good.
All samples used in this work have been of high purity and have had a phosphorous
concentration as low as ∼5 × 1012 cm−3 . Mainly, the studied defects have been generated by irradiation by 6-MeV electrons and they have always been characterised by
DLTS; the irradiation dose has, therefore, also been low: ∼5 × 1012 cm−2 . The electron
irradiation was performed at the Alfvén laboratory at KTH in Stockholm. Table 3.1 shows
the oxygen concentration and the carbon concentration of the three various materials
used.
Table 3.1: Details of the various samples investigated in the present work.
Material
FZ
DOFZ
MCz
Oxygen conc.
<5 × 1015 cm−3
2–3 × 1017 cm−3
0.5–1 × 1018 cm−3
15
Carbon conc.
2–4 × 1016 cm−3
2–4 × 1016 cm−3
≤1 × 1016 cm−3
16
3. Experimental details
SiO2
0.3 mm
Al
p+
n−
5 × 1012 P/cm3
n+
7 mm
Figure 3.1: Illustration of the appearance and structure of the investigated detectors. The p+
layers have a doping concentration of ∼1019 cm−3 after ion implantation of boron and annealing.
The illustration on the right is not to scale.
3.2
Hydrogenation
The first samples investigated (paper I) were hydrogenated at IMEC in Belgium where
the samples were exposed to a remote deuterium plasma for up to 4 h. The motivation
for using deuterium will be explained in chapter 4.
Wet chemical etching is a known technique for introducing hydrogen (see, for instance, Yoneta et al. 1991 [28] and Tokuda 1998 [29]). In an attempt to find a simple,
in-house alternative to the plasma hydrogenation, we tried submerging samples in hydrofluoric (HF) acid diluted to 10%. This proved to be an effective method for hydrogenation.
The exact method that was used to introduce hydrogen with HF goes as follows:
Dilute the 40% HF in water solution to a 10% solution in a plastic (of course)
beaker. The recipe is 40% solution to water in the ratio 1:3 (gives 40 parts pure
HF in the final solution containing 40 + 60 + 300 = 400 parts).
Heat a shallow water bath to ∼60 °C on a hot plate. Monitor the temperature of
this bath at all times.
Let the HF beaker float around in the water bath. If it is unstable, there is too
much water in the outer bath.
Let the temperature stabilise for 10 min; by then the HF solution should be at 50
to 52 °C (once I checked this with water also in the inner beaker).
Place the samples in the HF solution.
3.3. Connecting electrically to the samples
17
The samples will often float around on the surface because of the surface tension or lie close to the beaker walls, so use a tool to move the samples around
every now and then. Long protective gloves should be worn as there is surely
considerable amounts of HF vapour in the air.
Half an hour of sample stirring is, apparently, sufficient to get an amount of hydrogen that has considerable impact on the defect dynamics in the surface region.
Very little of the surrounding parameter space in this procedure has been explored.
However, it does appear that submerging a sample in 10% HF at room temperature
for 3 min introduces enough hydrogen to have a measurable effect on the annealing
of V2 : After annealing at 275 °C there is a reduction in the V2 concentration of ∼33%
compared to the non-hydrogenated reference samples. Also, in the single experiment
where it was tried, 10% HF at 50 °C for 5 min seemed to introduce no more hydrogen
than 3 min at room temperature. However, no conclusions can be drawn from this
without more experiments.
A major disadvantage of both plasma hydrogenation and HF dipping is that no usable contacts remain after the treatment, and new contacts must be created.
3.3
Connecting electrically to the samples
Achieving good electrical contacts after removing them with HF caused many months
of hard work with much frustration and slow progress. Eventually, after one and a half
years, I ended up with a method that was satisfactorily satisfactory. My procedure is
currently as follows:
With plastic tweezers (to avoid breaking off pieces at the edges), place the sample
at a clean tissue paper.
If the sample is unclean, soak the sample with acetone1 and move it around on
the tissue paper until it is reasonably clean on both sides.
Clean the front side and back side of the sample with a cotton bud2 soaked in
acetone.
Use cotton buds with acetone to clean the edges of the sample when resting it
vertically on the table in the grip of the tweezers.
If necessary, repeat the previous two steps.
Whether the sample has a metallic back contact or not, make a silver-glue pad:
1
Concerns have been expressed about using acetone, so some caution may be wise.
Concerns have been raised also about this procedure as cotton buds tend to cause residue. Cleaning
with a spray of acetone may be a cleaner method.
2
18
3. Experimental details
Apply a droplet of silver glue and smear it out. A cotton bud is a good tool for
this also – just roll the stem of the cotton bud back and forth over the sample
and let it smear out the silver glue.
When the glue is rather flat and almost dry, place the sample (with the pad
in the making down) on a hard, flat surface, like a table, and rub the contact
entirely flat. Don’t apply too much force as the contact may become too thin.
The sample should, ideally, have an evaporated aluminium contact.3 If not, an
emergency contact can be made with silver glue:
Make a dry, flat contact on the front side in the same way as for the back
side.
With a cotton bud with a tiny amount of acetone, stroke the edges to take
away the silver glue that is extending outside the guard ring. This step will
surely leave behind visible or invisible paths of silver particles, so continue
the stroking with new cotton buds for as long as necessary.
Again, use cotton buds with a little acetone to clean the edges of the sample when
resting it vertically on the table in the grip of the tweezers.
Similar care should be given when preparing the sample holder (in my case, usually
the sample holder shown in figure 3.2):
Clean the sample holder thoroughly with cotton buds and acetone. Do not use
too much acetone as it will cause conductive particles to float around and be
deposited in inaccessible places where there should not be electrical contact.
To obtain a flat layer of silver glue on the sample holder, apply a droplet of silver
glue and smear this out by rotating a metal rod with a flat end in the droplet until
the silver glue becomes almost dry.
The contact properties will continue to change as the silver glue becomes more
and more dry. This process can be accelerated by heating the sample holder.
If there is a silver-glue layer with appropriate thickness and topography on both the
sample holder and the back side of the sample, there should immediately be good
contact when the sample is installed. In practice this is not always the case, so my
procedure goes as follows:
Insert the sample and lower the needle.
Push a corner of the sample to rotate it slightly to search for a high-friction area.
3
Aluminium seems to be the best for silicon – the Schottky barrier is low and the adhesion of the pads
seems rather good. I tried one deposition of gold, but the adhesion was very poor. It is usually not worthwhile
trying to maximise the contact area within the guard ring as there is always a risk of getting too close, and the
contact should be sufficiently good even if it is just a moderately big spot in the middle.
3.3. Connecting electrically to the samples
19
Figure 3.2: The sample holder of the Asterix set-up. Here, a thin pad of silver glue has been
prepared (Photo: Klaus Magnus Johansen).
Sequentially, put pressure on all the corners of the sample.
Here, the needle may be lifted for a moment to release its tension.
The capacitance should now, at room temperature, be (260 ± 20) pF for the
300-µm detectors I have been using. If it is not, even after a forward voltage of
5 V has been applied,4 check if the silver glue pads are sufficiently thick and flat.
Run a CV and GV (conductance versus voltage) measurement, and pay close
attention to the conductance – the smaller the value, the better the contacts. A
perfect sample of this type can go down to 2 × 10−6 S at a bias of −10 V, while
a sample with silver-glue contacts may reach 1.2 × 10−5 S. Any conductance
smaller than ∼4 × 10−5 S at −10 V may give a good DLTS measurement.
An alternative route for reliable contact formation would be to clean the sample
thoroughly and do a high-quality deposition of aluminium at both the front and back of
the samples. The deposition should be done directly after the hydrogen introduction,
while the native oxide is still thin. This route has, however, not been explored in my
work.
A survey of the less successful contact methods investigated is given in table 3.2.
4
The HP capacitance meter will anyway not give more than 1 mA.
20
3. Experimental details
Table 3.2: Methods to avoid (listed in chronological order). The results are ranged on a scale
from A to F, where A is the currently best method, described in section 3.3.
Front-side contact
The needle on a small, dry dot of
silver glue
Needle directly onto the sample
Needle directly onto the sample
with much additional pressure
Front contact with a piece of flat
copper between a silver-glue pad
and the needle
Silver-glue pad
A piece of indium
A droplet of InGa with a piece of
aluminium on top to protect the
needle
Silver-glue pad
Back-side contact
InGa (AKA GaIn)
Result
Ca
InGa
InGa
E
Ca
InGa
Ba
A droplet of InGa
InGa
InGa
Da
Da
Da
A droplet of InGa distributed and
scratched into the back surface
C
a
I am not entirely sure about the uselessness of this method as limited attention was paid to the coverage
of the back contact.
3.4
Experimental set-ups
The first annealing series were measured with the set-up labelled Tiffy (figure 3.3). This
uses a Boonton 7200 capacitance meter and is cooled with a closed helium system.
The helium system is sometimes controlled by a computer; the switch that allows this
is described in section B.2. Some more details about the set-up are given by Mikelsen
2007 [25].
The Asterix set-up (figure 3.2) was used for most of the measurements. This is
equipped with at HP 4280A capacitance meter. The samples are cooled by simply
submerging the sample holder in liquid nitrogen. See Mikelsen 2007 [25] for a few
more details. Section A.1 gives details on some of the programs on the Asterix set-up.
Section B.1 gives some information about the temperature-controlling nitrogen lift.
3.4. Experimental set-ups
Figure 3.3: The sample holder of the Tiffy set-up (Photo: Klaus Magnus Johansen).
21
22
3. Experimental details
Chapter
4
Hydrogen-concentration
measurements
Several of the samples in the present work have been exposed to deuterium rather than
protium (ordinary hydrogen); this facilitates measurements of hydrogen–versus–depth
profiles after the hydrogenation, because secondary-ion mass spectrometry (SIMS) is a
factor of &100 more sensitive to deuterium than to protium. The conditions used for the
deuterium measurements were, most commonly, sputtering with 15-keV caesium-ions
using a primary-beam current of ∼50 nA and a raster size of 150 µm and detection of
negatively charged deuterium ions. The concentrations were calibrated with the use of
a deuterium-implanted reference sample.
Figure 4.1 shows the SIMS profiles of the deuterium concentration measured from
the front side (upper graph) and from the back side (lower graph) of four samples. These
samples are plasma-deuterated DOFZ Si of the same kind as described in paper I.
The samples were dipped in HF to remove the aluminium contact before they were
deuterated under a pressure of 700 mTorr by remote plasma from the back side with
the use of an OXFORD Plasmalab microwave system.
The deuterium profiles of sample 4-69 and sample 4-74, which are both deuterated
for 4 h, display different behaviour: Before any annealing there is a substantial amount
(∼1017 cm−3 ) of deuterium at the back side of both samples – somewhat more in 4-69
than in 4-74. After a 1-h anneal at 450 °C the deuterium concentration at the back side
is slightly above the resolution limit in sample 4-74, but it is very low in all samples. At
the front side, 4-74 has a deuterium concentration up to 1017 cm−3 before the anneal,
while after the anneal, this has been reduced by about a factor of ten. Just a very thin
layer of deuterium is measured at the front side of 4-69 before the anneal, and an even
smaller amount after the anneal. This difference in the deuterium concentration at the
front sides of 4-69 and 4-74 may be due to the mounting of the samples during the
plasma deuteration; the results suggest non-homogeneous and unintentional exposure
of the front surface of sample 4-74.
Sample 4-66 was exposed to the deuterium plasma for only half an hour. Similarly
23
24
4. Hydrogen-concentration measurements
to 4-74, there is a considerable amount of deuterium at the back side of 4-66 which is
undetectable after the 1-h anneal. The deuterium concentration at the back side of 4-66
is slightly less than that in 4-74, but the difference is smaller than that of 4-74 compared
to 4-69, which are deuterated with the same duration. Similarly with 4-69, the deuterium
concentration at the front side of 4-66 is very small and decreasing during the anneal.
The last of the four samples in figure 4.1, sample 4-67, was deuterated for 1 h and
not annealed. The front-side measurement shows that also this sample has received a
substantial amount of deuterium from the front, but the profile is smoother compared to
that of 4-74.
Figure 4.2 shows the deuterium profiles of two FZ samples submerged for half an
hour in a 10% HF/DF solution (HF:DF:H2 O in the ratio 5:5:90, where DF is hydrofluoric
acid with deuterium rather than protium) at 50 °C. Also, an aluminium contact was
deposited onto the front side of the samples before the samples were annealed for 1 h
in a nitrogen ambient – sample 7-28 at 450 °C and 7-39 at 250 °C. Both samples were
then irradiated with 6-MeV electrons to a dose of 2 × 1012 cm−2 . Sample 7-39 was
used for DLTS measurements and was exposed to 15-min anneals up to 150 °C before
the SIMS measurements were undertaken.
Sample 7-28 is seen to contain a considerable amount (∼1017 cm−3 ) of deuterium
directly below the aluminium contact down to a depth of ∼0.2 µm where the concentration reduces sharply. This is in sharp contrast to the profile measured at the oxide
layer outside the guard ring where just a thin layer of deuterium is detected. A negligible amount of deuterium is measured at the back side of sample 7-28. The single
measurement of sample 7-39 shows, like for 7-28, a presence of deuterium under the
deposited aluminium contact, but with a concentration up to a factor of ten larger than
in 7-28. This can readily be explained by the pre-irradiation annealing being performed
at a lower temperature such that less hydrogen has diffused into the bulk or out of the
sample. We have not performed SIMS measurements of non-annealed samples hydrogenated with this method.
We have, from these SIMS data, not been able to estimate the deuterium concentration in the bulk of any of the samples. No estimation can be made by extrapolating the
surface concentration, either, since we do not have a model describing how the hydrogen diffuses from the boron layer into the bulk. The only thing we can say with certainty
is that the bulk concentration is not above ∼1015 cm−3 in any of the measured samples.
However, it is possible that more thorough investigations of non-annealed samples and
samples annealed at temperatures below 450 °C could give deuterium profiles measurable also beyond the boron layer at the front side and the highly doped phosphorus
layer at the back side.
25
20
10
4-74 − 4 h D, non-ann.
4-74 − 4 h D, 1 h @ 450 °C
4-69 − 4 h D, non-ann.
4-69 − 4 h D, 1h @ 450 °C
4-66 − 0.5 h D, non-ann.
4-66 − 0.5 h D, 1 h @ 450 °C
4-67 − 1 h D, non-ann.
Boron profile
19
Concentration, cm
−3
10
18
10
17
10
16
10
15
10
0
0.2
0.4
0.6
Depth, µm
0.8
1
20
10
19
Concentration, cm
−3
10
18
10
4-74 − 4 h D, non-ann.
4-74 − 4 h D, 1 h @ 450 °C
4-69 − 4 h D, non-ann.
4-69 − 4 h D, 1 h @ 450 °C
4-66 − 0.5 h D, non-ann.
4-66 − 0.5 h D, 1 h @ 450 °C
Phosphorus profile
17
10
16
10
15
10
−1.4
−1.2
−1
−0.8
−0.6
Depth, µm
−0.4
−0.2
0
Figure 4.1: SIMS measurements of the deuterium concentration in samples exposed to deuterium plasma for 0.5, 1 and 4 h, respectively. For most of the samples, the deuterium profiles
have been measured before (solid lines) and after (dashed lines) a 1-h anneal at 450 °C. The
upper graph shows the deuterium concentration at the front side of the samples, while the lower
graph depicts the concentration at the back side (the surface is at zero depth); the scale of the
two is identical. The boron concentration and phosphorus concentration are also shown.
26
4. Hydrogen-concentration measurements
20
10
19
Concentration, cm
−3
10
7-28 − D meas’ed at Al pad
7-28 − D meas’ed at oxide layer
7-39 − D meas’ed at Al pad
7-28 − Boron meas’ed at Al pad
18
10
17
10
16
10
15
10
−0.2
0
0.2
0.4
0.6
Depth, µm
0.8
1
1.2
20
10
19
Concentration, cm
−3
10
18
10
7-28 − Deuterium
17
10
16
10
15
10
−0.6
−0.4
−0.2
Depth, µm
0
Figure 4.2: SIMS measurements of the deuterium concentration in samples submerged in a
HF/DF solution for half an hour at 50 °C. Sample 7-28 was annealed for 1 h at 450 °C, while 7-39
for 1 h at 250 °C. The upper graph shows the deuterium concentration at the front side of the
samples, while the lower graph displays the concentration at the back side (the surface is at zero
depth). The front-side measurements conducted through the deposited 0.25-µm-thick aluminium
contact have been shifted by 0.25 µm such that the silicon surface is at about zero depth. The
boron concentration at the front side is also shown.
Chapter
5
Fitting and modelling
5.1
Fitting algorithms (general aspects)
The general algorithm used for fitting of the experimental data has remained rather
unchanged throughout all of this work, using a method called ”simulated annealing”.
This is an algorithm that searches for the global optimum by first making a parameter
guess, then calculating a value describing the degree of success and accepting the new
parameters with a probability depending on the error and a ”temperature” parameter
(URL [30]). If the error is smaller than before, the new parameters will be accepted; if
the error is larger, the new parameters will be accepted with a probability of exp dE
T ,
where dE is the difference in error and T is the algorithm ”temperature”. The algorithm
is started at a high ”temperature”, at which the input-parameter guesses are volatile, i.e.
the guesses are made relatively far from the input-parameter values giving the currently
most optimal fit. The ”temperature” is reduced with a certain rate down to a certain
value, and if the ”temperature” is lowered sufficiently slowly, the global optimum will be
reached; if not, the algorithm will end up in a local optimum.
The algorithm used is a slightly simplified version of the ”simulated annealing”, as I
have let the volatility of the input-parameter guessing depend on the ”temperature”, but
there is a zero probability of keeping the new parameters if they produce a result with a
larger deviation than the currently best parameters.
5.2
Fitting of DLTS spectra
Two main approaches for extracting the activation enthalpy and apparent capture cross
section of the various energy levels have been used. The first method is based on the
assumption that the measured DLTS spectra follow the theoretical ones perfectly and
that the capture cross section is temperature independent. The developed algorithm
fits, simultaneously, a given number of DLTS peaks (calculated from three parameters:
amplitude, activation enthalpy and apparent capture cross section) to the spectra of all
27
28
5. Fitting and modelling
the time windows of a set of measurements performed after different heat treatments –
only the amplitudes are fitted independently for each spectrum.
The advantage of this method is that the algorithm has limited freedom to move the
DLTS peaks around when trying to fit overlapping peaks. This may result in a realistic
fit even of DLTS peaks that overlap strongly. An example of this is shown in figure 3
in paper I where the contribution of the di-vacancy–oxygen (V2 O) centre is separated
from that of the di-vacancy (V2 ) centre. The disadvantage of this routine is that it is
so restricted by the massive amount of data that the the best fit normally does not
reproduce each individual peak optimally. This may be caused by noise in the first
windows, temperature-dependent capture cross sections, stray capacitance and series
resistance in the apparatus, and limited accuracy of the temperature measurements.
As I was particularly interested in the accurate amplitude of the DLTS peaks, this first
method did not give satisfactory results. Therefore, a routine that fits each peak, or sum
of peaks, in a particular spectrum, independently of any other spectra was developed.
This effort evolved into the program described in section A.2. The main limitation with
this program, is, apart from its user interface, that one must take great care when fitting
overlapping DLTS peaks.
5.3
Modelling of reaction equations
Paper VI presents a defect-reaction model accounting for the variation in defect concentration with depth which reproduces fairly well the measured annealing behaviour
in hydrogenated samples for temperatures below ∼200 °C. Initially, an attempt was
made to describe the annealing kinetics by a model only involving the different defect
concentrations without taking into account the depth distribution; the corresponding program is described in section A.3. This was successful for the measurements obtained
at the annealing temperatures 150 and 180 °C, but it was not possible to fit both data
sets simultaneously with a consistent set of values for the reaction parameters. Moreover, the evolution of the DLTS amplitudes measured during the 195-°C annealing was
difficult to simulate even by itself. Thus, realising experimentally that the defect concentrations exhibited a substantial variation as a function of depth and the unsuccessful
modelling when assuming uniform defect distributions provided strong motivation for the
introduction of a model addressing the measured depth profiles rather than the DLTS
amplitudes. This proved successful in that it was possible to reproduced the annealing dynamics closely – from the point of view of comparison of the DLTS amplitudes
calculated from the measured and simulated depth profiles. This comparison of DLTS
amplitudes calculated from depth profiles was performed as a first test to see if the
result looked better than when modelling depth-independent defect reservoirs. Since
the result looked satisfactory, it was considered meaningful to rather optimise the fit
of the simulated depth profiles to the measured depth profiles. In the simulations, the
Matlab function pdepe is used for solving the differential equations numerically – more
technical details can be found in section A.4.
Several different defect-reaction models, including two hydrogen sources, various
5.3. Modelling of reaction equations
29
shapes of the initial concentrations both of the hydrogen and of the hydrogen traps, were
evaluated. It seemed not possible, however, to reproduce the experimental data without
introducing a small effective hydrogen-capture radii for both the VO centre and the V2
centre, indicating the presence of reaction barriers as further discussed in paper VI.
30
5. Fitting and modelling
Chapter
6
Summary of results
6.1
Paper I
This paper presents the results from an isochronal annealing study with deuterated
DOFZ samples. The reaction where VO captures a hydrogen atom and forms vacancy–
oxygen–hydrogen (VOH; or VOD in this case) is prominent – especially for the sample
exposed to the deuterium plasma for the longest time. This sample also shows a substantial concentration of two presumably hydrogen-related levels at Ec − 0.17 eV (labelled E2) and Ec − 0.58 eV (labelled E3), respectively. In the sample deuterated for
only half as long, the E1 level, at Ec − 0.37 eV, reaches a higher concentration than
that of the VOH centre. Also one of the non-hydrogenated reference samples shows an
annealing behaviour indicating the presence of some residual hydrogen.
A curiosity worth mentioning is that the H1 level (see paper V), at Ev + 0.23 eV, is
clearly visible in the results obtained with the Boonton set-up (figure 1); we just did not
realise at that time that this was the signal from a real charge-carrier trap.
6.2
Paper II
This study shows that the V2 O centre (which was in most cases formed by a 15-min
anneal at 300 °C) anneals out via dissociation which results in a VO centre. The binding
energy between V and VO in the V2 O complex is estimated to be ∼1.7 eV. The VO
centre anneals through migration and capturing by an oxygen atom. In oxygen-lean
material, the VO is captured at such a low rate that there is an initial increase in the
VO concentration when the V2 O centre dissociates; this increase is not seen in oxygenrich DOFZ material. The evolution of the measured defect concentrations is closely
reproduced by the proposed model. Hydrogen is included in the model such that it
reproduces also the observed concentration of the VOH centre. The results suggest that
VOH is formed when monatomic hydrogen reacts with VO, and also that this complex
dissociates in the opposite reaction.
31
32
6.3
6. Summary of results
Paper III
What is considered to be one defect with two energy levels in the upper half of the band
gap – E4 at Ec − 0.37 eV and E5 at Ec − 0.45 eV, which exhibit a close one-to-one
proportionality with each other – is found to anneal out with first-order kinetics during a
few weeks at room temperature. It is argued that the defect is fundamental, intrinsic and
extended in space. It is speculated that a {110}-planar tetravacancy chain (V4 ) might be
a defect with these properties. V4 is also known to have limited thermal stability.
6.4
Paper IV
An isothermal annealing study performed with DLTS shows that the annealing kinetics
of the E4/E5 centre is very similar to the annealing kinetics of the 936-cm−1 band measured by Fourier-transform infra-red spectroscopy (FTIR) even though the samples were
irradiated with different particles to very different doses, resulting in very different defect
concentrations. Since the 936-cm−1 band is previously reported to be a di-interstitial–
oxygen (I2 O) complex, it is suggested that the E4/E5 centre and the I2 O centre are
identical. The combined results from DLTS and FTIR give an activation barrier for the
annealing of 1.1 eV with a pre-factor of 9 × 1012 s−1 , and it is argued that the defect is
not annealing by migration, but rather by dissociation or changing atomic configuration.
E5 is previously shown to have a strong correlation with a change in the leakage current
of silicon detectors, and it is, therefore, argued that one should reduce the concentration
of oxygen and carbon to reduce the leakage current in silicon devices.
6.5
Paper V
Strong evidence is given that monatomic, positively charged hydrogen diffuses in from
the surface layer at temperatures below 200 °C – probably involving dissociation of the
boron–hydrogen (BH) centre – and reacts with the VO centre to form a meta-stable
VOH∗ centre. This centre has an energy level at Ec − 0.37 eV and dissociates at longer
annealing times. The V2 centre also reacts with the in-diffusing hydrogen; this reaction
probably causes the V2 H centre to be generated. The growth of the hole trap H1 at
Ev + 0.23 eV displays a close one-to-one proportionality with the loss of the V2 trap,
and it was therefore suggested that H1 is an energy level arising from the V2 H centre.
6.6
Paper VI
This paper presents a model which reproduces closely the depth profiles from paper V
measured during annealing at 195 °C where monatomic hydrogen diffuses in from the
surface and causes the transformation of VO into VOH∗ and the annealing of V2 , before
VOH∗ dissociates and VO is restored. Profiles measured during annealing at 225 °C
6.6. Paper VI
33
for up to 11 days reveal that continued annealing after the VOH∗ centre has annealed
causes the VO centre to start annealing again; here, VO is not replaced by VOH∗ , but
rather by VOH. However, the concentration of the VOH centre is too small to account
for the loss in VO; this is explained by VOH being transformed into a vacancy–oxygen–
di-hydrogen (VOH2 ) centre. This is further supported by the depth profile of the VOH
centre having a reduced concentration both towards the bulk and towards the surface
of the sample – a clear indication that VOH is passivated by something diffusing in from
the surface.
34
6. Summary of results
Chapter
7
Concluding remarks
A main achievement of this work has been to identify the energy level at Ec − 0.37 eV
as a vacancy–oxygen–hydrogen complex, labelled VOH∗ in this work, which is different from the VOH centre that has energy levels at Ec − 0.32 eV and Ev + 0.28 eV
(paper V). The observation that the H1 level, which we argue can be identified as V2 H,
has a one-to-one correlation with the energy levels of V2 , may also prove valuable for
future studies of hydrogen in silicon (paper V). Further evidence has been given that
VOH anneals out by capturing a hydrogen atom to form VOH2 (paper VI). There are
also indications that this breaks up and restores the VO centre at ∼325 °C.
Several other hydrogen-related levels have been observed; speculations on their
identity have been put forward for some of them, but a satisfying identification of all
the levels is still lacking. Further investigations are clearly needed to reach a complete understanding of how hydrogen affects the defect dynamics in silicon. It would be
interesting to perform more annealing studies of hydrogenated samples with different
oxygen concentrations to check if some of the speculations in paper VI can be verified
or disproven. For instance, whether the E2 level and E3 level are affected by the oxygen
concentration and whether they always appear with the same concentration.
There was a hope that the present work would clarify under which conditions the
hydrogen diffuses and reacts as monatomic and under which conditions it is molecular
or maybe a more loosely bound dimer; it seems, however, that all the results that were
obtained can be explained by monatomic hydrogen alone, and little knowledge has been
gained regarding when molecular hydrogen is present. However, there may be a possibility of checking if molecular hydrogen is passivating V2 if the assumption that the level
labelled H1 is indeed the result of the reaction
V2 + H → V2 H.
(7.1)
Then, if VO and V2 are passivated by molecular hydrogen, the H1 level should not
appear.
Increased understanding of how hydrogen affects the defect dynamics has been
the main aim in this work. A potential application is fabrication of more radiation-hard
35
36
7. Concluding remarks
detectors with the use of hydrogen. The V2 (−/0) level can, in the presence of positively
charged hydrogen, be passivated by annealing at temperatures below 200 °C (paper V),
but even if this level is as deep as Ec − 0.43 eV, it is not considered particularly harmful
to the detector operation. However, the hydrogen-related E3 level at about Ec − 0.58 eV
(see paper VI) is, due to its position, likely to be an effective generation centre which
increases the leakage current. Identification of this level might, thus, be particularly
useful.
I put much effort into the investigation of the E4/E5 defect (see paper III and paper IV).
This centre may be particularly important as it has been shown by Moll et al. 2002 [31]
that the annealing of E4/E5 may be strongly correlated to a reduction in the leakage
current of irradiated diode structures. After I had completed an isothermal annealing
study of the E4/E5 annealing with the use of DLTS, it was discovered that the annealing
behaviour of what is from FTIR expected to be a I2 O centre in samples with entirely different properties is strikingly similar to the annealing behaviour of E4/E5. This resulted
in paper IV, where we argue that the E4/E5 centre may be identified as a I2 O complex.
Regarding the E4/E5 defects, it should certainly be made an attempt to reproduce
the generation of what seems to be these levels by applying a large forward-current
density, as performed by Fleming et al. 2007 [32]. If this is successful, it should be
very easy to determine with FTIR whether the E4/E5 defect is identical to the I2 O centre measured by FTIR, as was suggested in paper IV. However, a current density of
12.5 A/cm2 will surely heat our samples substantially and possibly also damage them.
DLTS spectra are never ideal; various deforming of the DLTS peaks is introduced
due to effects from the apparatus and from emission parameters which may be temperature dependent. Therefore, another possible investigation would be to find if it is
possible to include a temperature-dependent apparent capture cross section in the fitting routine as this changes the shape of a DLTS peak. One should always take care
when increasing the freedom of a fitting algorithm, but the first fitting algorithm described
in section 5.2 has so little freedom that one could possibly introduce both temperaturedependent capture cross sections and parameters for set-up artefacts (e.g. temperature
offset and baseline offset) and still get trustworthy results.
Appendix
A
User guides on software
A.1
Asterix how-to
A.1.1 CV measurements
As was mentioned in section 3.3, it is a large advantage to pay attention to the conductance of the sample. I therefore included in the CV program a graph showing the
conductance versus the voltage. I also included output terminals for the values of the
starting and ending conductance and the ending capacitance, such that I can save these
parameters as a characterisation of the contact. I also made a graph showing 12 (V)
C
and the deviation of this from a straight line.
Figure A.1 shows a screenshot of CVmeas with G.vi.
It should also be mentioned that the HP 4280A capacitance meter performs CV
measurements at a probe frequency of 1 MHz.
A.1.2
DLTS measurements
DLTS measurements have been performed extensively, with the natural consequence
that the DLTS program (figure A.2) has undergone several modifications. The first and
most important change was, for obvious reasons, to make the program save the data
continuously rather than after the Stop button has been pushed.
The most noticeable (and by far the most time consuming) change to the program
was implementation of the automatic temperature control. The automatic control is activated by Autolift(TM). The Heat/Cool switch is of utmost importance to achieve
the desired result. The heating/cooling rate is set in #scans setpoint. This is
a rather rough estimate of how many transient recordings the capacitance meter will
manage during a 1-K interval if the longest time window is (640 ms)−1 (if # Windows
is 6). If longer time windows are used, the temperature rate will still be similar, but
#scans setpoint and Estimated number of scans will no longer refer to
the actual number of transient recordings during a 1-K interval. The most common use
37
38
A. User guides on software
of the temperature control is to just Disable the lift when the temperature is outside the given range; this is to avoid damage to the stepper motor (see section B.1 for
more). The temperature will usually go down to liquid-nitrogen temperature (currently
∼78.1 K)1 when the lower disabling limit is set to the default 80.1 K. The higher disabling limit should not be set above 0 °C unless the temperature rate is very low or the
heater power is more than ∼30%, as melting of the ice dramatically slows down the
temperature rate. Faster lift is just an option that causes the Lift to be triggered
twice rather than once if the temperature rate is far too low.
A more exotic feature is the one that will Turn the lift (or rather the sign of
the temperature rate). This function will, when the lower temperature limit is reached,
flip Cool to Heat and continue measuring with increasing temperature. Make sure to
disable Turning disabled if using this feature during more than one measurement.
Possibly even more exotic, yet, is the possibility to make the program calculate the
temperature rate as a given function of the current temperature. This was implemented
in a period when the Asterix set-up was very popular and it seemed like a good idea to
scan quickly at the temperatures where there are no DLTS peaks. The default example,
r=s+s*0.7*exp(-(t-80)^2/(2*10^2))+→
→s*0.7*exp(-(t-114)^2/(2*20^2))+→
→s*0.7*exp(-(t-196)^2/(2*20^2))-→
→(1+sign(t-210))*0.5*(t-210)/15,
where s is the value in #scans setpoint and t is the current temperature, describes a uniform number of scans per temperature interval (given by the first s) with the
addition of Gaussian peaks, with the height of 70% of #scan setpoint, at the positions of VO, V2 (=/−) and V2 (−/0). This will cause the temperature rate to slow down in
these areas. If the temperature is above 210 K ((1+sign(t-210))*0.5 = 1) and
increasing, the heating rate will be set higher and higher (r lower and lower). A negative
r does not cause errors, but is not different from r being zero.
Save each transient is a feature I always enable; it causes the generation of
an additional .trans file which contains each single transient recorded, preceded by
the temperature at that point. I have a special liking for large amounts of data, so many
users can live happily without this feature.
Autostop is very useful when performing overnight measurements with all the
transients being stored – the difference is tens of Mb. The feature also reduces the
possibility of the stepper motor being stuck for eternity with a task it can not perform
(such as lowering the lift through the table).
I have added a boolean variable Update graphs which, when disabled, allows
the user to zoom in on the spectra without being disturbed by the auto-scaling. It has
also become possible to show the DLTS spectra extracted by a range of time windows by changing the variables Window – being the first window to display – and
Display # windows.
1
According to the Asterix set-up.
A.1. Asterix how-to
39
A peculiarity worth noting is that when High Resolution is enabled (this is a
feature of the HP 4280A capacitance meter), the C-range setting has no effect – it is
automatically the most sensitive setting (10 pF).
The currently newest program is DLTS_Asterix_current_version.vi.
This is a copy of DLTS_Asterix_20070215r.vi. A change log can be found
in DLTS_Asterix_current_version.txt.
A.1.3
Depth-profile measurements
The first changes I made to the profiling program was to include a routine that would control the Lift and such keep the temperature constant.
This has some drawbacks, because when the profiling is finished, the temperature will no longer be kept constant.
This was solved by keeping
the temperature-control routine in a separate program that always runs in
the background: stand-alone_PID_control_current_version.vi (section A.1.4).
Thus, the only change I have made to the current program
(Profiling_semitrap_with_dS_vs_dV_with_stopnow.vi) is to include a
graph showing dS
dV ; this gives a rough picture of the profile and is helpful when determining whether the number of averages is large enough to get a smooth profile. There is
also a button Stop now which finishes the profiling and quits even if the temperature is
not within range. The last voltage sweep is then not included in the average. Figure A.3
shows a screenshot of the program.
The depth-profiling program would benefit from the possibility of changing the voltage in a quadratic manner such that the concentration is plotted with equidistant depth
intervals. This requires, however, a substantial reprogramming, because instead of instructing the capacitance meter which voltage to use for each transient, it is instructed
to change the voltage stepwise in an interval.
A.1.4
PID control that keeps the temperature constant
This program (stand-alone_PID_control_current_version.vi) moves
the Lift (section B.1) up and down in order to keep the temperature constant. In the
beginning I made this program an integrated part of the depth-profiling program (see
section A.1.3), but I later realised that several programs can be run simultaneously, so I
took it out as a separate program to be run together with the depth-profiling program or
the capture-cross-section program.
The program is rather tedious and complicated to use, so I will just leave it to evolution to decide if the program is worthy of the operating instructions being transferred
from one generation of Ph.D. students to the next. I have made an attempt to write a
user guide in the program itself.
The biggest disadvantages of the program are, apart from the non-intuitive user
interface, that it usually takes 10 to 30 min, or more, before the program is able to keep
the temperature constant, and the program takes up non-negligible run time (hence, the
40
A. User guides on software
measurements are performed slower). On the positive side, the program can, on a very
good day, keep the temperature constant with a deviation of no more than 0.05 K until
the nitrogen boils away.
A.1.5
Temperature logger
I find it very useful to have the temperature history whenever I try to stabilise the temperature. temperature_logger.vi is a simple program that provides this.
A.2
DLTS-transient analyser
This program (screenshot in figure A.4) has evolved through many generations; one
later generation was even started again from scratch, but this has not prevented several
quick and dirty implementations of solutions and features. On the positive side, the
program does have some useful features. The program is made for running through a
data set of any size and I believe, therefore, that given a sufficiently large number of
DLTS measurements, it is worth the trouble of setting all the parameters to make the
program run.
A.2.1
Feature overview
Load standard DLTS files (data files containing transients averaged within a fixed
temperature interval, and the reverse capacitance)
Load transient files (these are optionally generated by the Asterix set-up and contain each single transient recorded and the temperature at which it was measured)
Generate DLTS spectra with any user-defined weighting function, although currently only stepwise constant functions (lock in, GS4 and such)
Average the temperature and amplitude of points in the DLTS spectra closer to
each other than a given temperature interval
Save generated DLTS spectra as a standard DLTS file (similar to the output files
from the Asterix set-up)
Fit any part of the DLTS spectrum by any assumed number of overlapping peaks
to extract the amplitude, activation enthalpy and apparent capture cross section
Average the Arrhenius plots of several weighting functions, windows and files to
enlarge the amount of data before calculating the average activation enthalpy and
apparent capture cross section
Make a graph showing the evolution, for instance, from annealing step to annealing step, of the amplitude of a set of DLTS peaks
A.2. DLTS-transient analyser
41
In case of a DLTS peak with changing amplitude being overlapped by one having
constant amplitude, subtract each transient of one data file from the closest (in
temperature) available transient in another data file before generating the DLTS
spectra and performing the analysis
Make a graph showing, for each weighting function, activation enthalpy versus
apparent capture cross section to see how the results make a line
Save .png files of all the generated spectra and each best fit of the chosen DLTS
peaks to be able to check what has happened during an overnight analysis
FFT smoothing of the spectra (not working)
A.2.2
Description of each of the features
The present section will discuss some of the most important settings in the input file
(which, at present, should bear the name inputdata_temp.m). Appendix C shows
an example of an input file for this transient-analysis program.
Load standard DLTS files
Loading the transients correctly from a DLTS file is maybe what is the most difficult with
this program and usually the reason for all the mysterious error messages.
All the file names of the DLTS files (containing temperature interval, reverse capacitance, spectra and transients) should be listed in the variable name, where
name=char(’file_1.dat’,’file_2.dat’,[. . . ],’file_n.dat’).
The path of the files goes into path. The program must be told which format the files in
name have. This goes into the variable format_of_files. This is a 2-by-n matrix,
where n is the number of data files. The first row has value 0 if the file is a transient file
(containing only the temperature and transient), 1 if it is a last-generation standard DLTS
file from the Asterix set-up (contains temperature, number of scans at that temperature,
reverse capacitance, pulse capacitance, lock-in spectrum, GS4 spectrum and transient),
2 if it is an older standard DLTS file from Asterix (like 1, but without the GS4 columns).
The second column should contain the number of windows stored in the data file (six
with default settings).
If one of the two numbers in format_of_files does not describe correctly the
corresponding input file, there will be problems. The program may go on without error
messages, but the spectra will usually look special; they may, for instance, increase
almost monotonically with temperature.
As said, the strength of this program is that it can handle large sets of data. Microsoft
Windows may be time consuming – certainly not less so when it comes to performing
repetitive tasks on a large number of files. To load 1000 DLTS files, it is necessary to
write 1000 file names in the variable name. On a POSIX system this can easily be
achieved by, for instance,
42
A. User guides on software
ls *.dat|tr ’\n’ ’,’|sed ’s/,/’\’’,’\’’/g’|→
→sed ’s/\(.*\),’\’’$/name=char(’\’’\1);/g’<enter>
which produces the required
char(’1000_files_of_transients_on_the_disk_to_load.dat’,→
→’999_files_of_transients_on_the_disk_to_load.dat’,[. . . ]);
which can just be pasted into the input file. Information from Crname is not used,
since the reverse capacitance is contained in the standard DLTS files, and information from outname is not necessary unless the resulting spectra are to be written
to disk (described below); despite this, both variables must be declared (just do a
variable=[];).
Variables in the input file relevant for this feature:
path
name
format_of_files
Load transient files
What I refer to as transient files are additional data files from the DLTS program (the
option is presently only available at the Asterix set-up) which contain each single transient recorded, preceded by the present temperature. My motivation for implementing
this was my liking for large amounts of data and avoiding the negative consequences
of averaging: with a varying temperature rate it is not correct to use the temperature in
the centre of the interval, with averaging it is difficult to discover incorrect transients and
un-averaging is difficult.
As with standard DLTS files, the variable name lists the file names, but now
.trans files instead of .dat files. The .trans files do not contain the reverse
capacitance; each of the transient files must, therefore, be coupled with the standard data file containing these values. The .dat files corresponding to the .trans
files are listed in Crname, but not necessarily in an ordered one-to-one pattern as
belongs_to_name_index maps the .dat files to the .trans files.2 Like for the
.trans files, format_of_Cr_files contains the format and number of windows
of the .dat files. The format should not be 0, since a transient file does not contain
reverse capacitance (see previous section on loading standard files).
As I tend to use long file names, analyse many measurements and, besides, do
anything to avoid repetitive tasks, I have written a bash script for generating the three
input variables name, Crname and outname from a set of files. This is called
choosefiles. My system is to have a folder with all measurements, e.g. Sample_A.
In this folder I have a subfolder Best with a symbolic link to the standard DLTS files of
all the best measurements in the parent folder. Then, with Best as the working directory, I run choosefiles .. *.dat. This will give three Matlab lines loading all the
2
Right now this does not seem to make much sense to me, whereas the opposite could have a mission.
A.2. DLTS-transient analyser
43
.dat files (if *.dat is used) into Crname and the corresponding .trans files into
name. Also, a corresponding list of names for output files will be placed in outname.
I have mostly used the transient-analysis program with transients from the transient
files rather than the standard averaged data files – I therefore expect the former method
to have less bugs than the latter.
Variables in the input file relevant for this feature:
path
name
format_of_files
Crname
format_of_Cr_files
belongs_to_name_index
Generate DLTS spectra with any user-defined weighting function
DLTS spectra will be calculated with the weighting functions in the cell structure
weights and only those. For instance, weights may contain six time windows of
a lock-in type weighting function. Then
weights{1}{1}=[-1 1]
weights{1}{2}=[-1 -1 1 1]
weights{1}{3}=[-1 -1 -1 -1 1 1 1 1]
.
.
.
all the way to weights{1}{6} which contains 64 elements. The six first time windows
of the lock-in function can be loaded into the first cell of weights by simply giving the
command
weights{1}=binary_pattern2dlts_weight([-1 1],64).
The term binary is somewhat misleading as the first five time windows of the GS4 function can be loaded by, for instance,
weights{2}=binary_pattern2dlts_weight([1 -25 48 -24],64).
I did not have sufficient need of using anything else than stepwise constant weighting
functions and have not programmed anything more sophisticated than this; if sine functions and such are desired, the routine binary_pattern2dlts_weight would
have to be replaced by something loading weights with sine values in arrays of different lengths. I do not foresee any reason why this should not be trivial.3
transientlength is automatically taken as the number of data points in the
transients of the measurement with the fewest windows. Sometimes it is desirable to
3
Then again, I rarely foresee any obstacles before being halfway into the programming task.
44
A. User guides on software
override this if only the spectrum in one window is fitted; for instance, VO is not so easily
fitted in the (2.56 s)−1 window (window 8 for lock in), so transientlength=2^6
may be a good idea in order to discard windows 7 and 8 (lock in).
Variables in the input file relevant for this feature:
weights
plot_spectra=1
divide_by_Cr=1
transientlength
Average points in the DLTS spectra closer than a given temperature
All DLTS points are sorted, and this algorithm starts with the data point with the lowest
temperature, makes an average of all the points closer than average_interval (K),
and then repeats this process for the first point with a temperature outside this interval
(only points with higher temperatures are included in the average). If no averaging is
wanted, use average_interval=0.
Variables in the input file relevant for this feature:
average_interval
Save generated DLTS spectra as a standard DLTS file
If this option is enabled, the generated spectra will be saved in a data file that is filled
up with numbers (the values for the pulse capacitance and conductivity are currently ignored and just set to zero) to resemble a last-generation data file from the Asterix set-up.
The program will give a warning unless divide_by_Cr=1, because in the standard
DLTS files, the spectrum is not divided by the reverse capacitance. I suspect that the
current algorithm will fail if weights contains more than one weighting function, i.e. if
length(weights)>1.
Variables in the input file relevant for this feature:
write_outfiles=1
outname
divide_by_Cr=0
Fit any part of the DLTS spectrum
Here lies the core function of this program. With the fitting procedure enabled
(do_arrhenius=1), the program will fit the calculated spectra with an ideally-looking
synthetic DLTS peak or a combination of several of these. When an optimal fit is found,
the temperature position of the peak and its amplitude is kept. If the weighting function
(in weights) has more than one window, an Arrhenius plot is made, from which the
enthalpy and apparent capture cross section are extracted.
A.2. DLTS-transient analyser
The
algorithm
45
will
search for peaks defined in the cell structure
Each cell will cause a best-fit search in one particular
area in the spectra of all windows of all weighting functions. For instance,
dlts_peak_guesses.
dlts_peak_guesses{1}=[5.1e-14 0.1817],
where the first value is the apparent capture cross section and the second the activation
enthalpy, will result in an attempt to fit one synthetic DLTS peak somewhere close to
the VO peak (these values are chosen empirically and for the (640 ms)−1 window
in this case). If there are overlapping peaks in the spectra, it may be required to fit
simultaneously with two or more synthetic DLTS peaks.
dlts_peak_guesses{2}=[1.1418e-14 0.37252;3.1e-15 0.429]
will lead to a simultaneous fitting of the peaks of VOH∗ and V2 (−/0). Fitting two overlapping peaks is difficult – fitting three and more is hazardous as it opens for a lot of
different interpretations.
The variable range_to_include_beside_outermost_peaks states how
large part of the spectrum to include when fitting the set of peaks given in a single cell
of dlts_peak_guesses. The variable name is meant to mean how many Kelvin of
the spectra to include on either side of the temperature positions calculated from the
values in dlts_peak_guesses. If one of these cells tells to fit two peaks at 165 and
196 K, respectively, range_to_include_beside_outermost_peaks=10 will
cause all the data in the range 155 to 206 K to be included when calculating the error of
the two synthetic peaks. It is difficult to give advice here, because including a large temperature range gives more data and more accuracy, but the exact maximum of the peak
will often be in the wrong position with a wrong amplitude, while fitting a narrow range
of data gives the correct peak amplitude, but more noise and uncertainty (especially
for low concentrations). range_to_include_beside_outermost_peaks sets
the range for all the fitting sets in dlts_peak_guesses while T_range_offset
can be used to alter this individually. Each cell of T_range_offset corresponds to
a cell of dlts_peak_guesses. If T_range_offset{1}=[-3 5], the range of
data will be increased by 3 K on the low-temperature side of the first fitting set and increased by 5 K on the high-temperature side. The range of measurement data included
for each of the fitting sets is marked, in the graphs showing the spectra, by vertical lines
connected by a horizontal line.4
When it is defined in which temperature range to search for which energy levels, it
remains to define how to search. For each synthetic DLTS peak, there are three parameters: amplitude, apparent capture cross section and activation enthalpy. I realised that
it is more effective to optimise the peak position and peak width rather than the capture
cross section and enthalpy. Therefore, in the fitting routine, the parameters that are
being optimised are the peak amplitude, the peak width and the peak position. Despite
4
Or, to be more specific: A horizontal line at the average of the amplitudes of the DLTS points lying closest
to the peak positions calculated from the defect properties in dlts_peak_guesses.
46
A. User guides on software
of this, the old variable names remain, and the variables amplitude_volatility,
sigma_volatility and energy_volatility state how much to change the
amplitude, width and position, respectively, in each fitting attempt. These values are
standard deviations of the distribution functions used to pick random values for the fitting attempt. Which distribution function to use for each of the three parameters is given
in guessmethod_init. Gaussian distribution (0), gamma distribution (1) and uniform distribution (2) are currently supported. I have been using the gamma distribution
for the amplitude and peak width and the Gaussian distribution for the peak position. Not
all parameters will be changed in each fitting attempt; the probability of any parameter
being changed is chanceofchange (currently 60%).
The three volatility parameters are multiplied by a fitting temperature. This temperature starts high and is reduced as the fitting proceeds. In this manner, the synthetic
DLTS peaks move violently around at first, while smaller and smaller changes are tested
towards the end of the fitting of that particular set of peaks. The initial fitting temperature is given in T_init and the fitting temperature at which to stop is given by T_end.
After iterations_in_fitting_function attempts to find better values for the
three (unless there are overlapping peaks) fitting parameters have been made, the fitting temperature is multiplied by T_change (which is less than 1). These four variables
together define how many fitting attempts to make for each point of interest in each window.
It is nothing short of terribly difficult to find good values for the volatility and fitting
temperature – i.e. to find an effective (in terms of CPU time) way to reach the optimal
fit. Increasing the value of plot_frequency (e.g. to 4) may simplify the task as the
fitting window will then be updated more frequently. It is then possible to see how far
away the guesses are from the currently best fit, and if any of the three fitting parameters
are varied too little compared to the others.
When a fitting starts, only the amplitude of the peak(s) will be optimised
such that the fit will be roughly correct (if the values in dlts_peak_guesses
are good) before all the parameters are let loose.
The internal parameters
number_of_cool_steps_in_amplitude_optimisation
and
iterations_in_amplitude_optimisation determine how much time to
spend for this initial process.
Sometimes the fitting algorithm will print a lot of asterisks (*) – this is a warning that
one of the fitting parameters (usually the peak width) has been chosen very close to
the illegal limit in the gamma distribution (usually zero) and that the guess value will be
forced away from this limit. This frequently happens if the fitting routine tries to move
the base line up (or down if allow_negative_amplitude=1) by having one very
broad peak. If a peak is chosen sufficiently broad, it will cause a division by zero.
It is also possible to fit minority-carrier traps;
this requires
allow_negative_amplitude=1.
Variables in the input file relevant for this feature:
do_arrhenius=1
dlts_peak_guesses
A.2. DLTS-transient analyser
47
T_init
T_end
range_to_include_beside_outermost_peaks
T_range_offset
weights
window_offset
iterations_in_fitting_function
errorlimit
T_change
plot_frequency
amplitude_volatility
sigma_volatility
energy_volatility
guessmethod_init
allow_negative_amplitude
Average the Arrhenius plots of several weighting functions windows and files
This is done automatically in the fitting routine if there are several weighting functions
windows and/or several measurement files. There must be more than one window for
the weighting function(s), and preferably as many as possible to maximise the number
of points in the Arrhenius plot.
Sometimes peaks are misfitted; if the activation enthalpy extracted from the Arrhenius plot of a single weighting function is more than a factor errorlimit away from
the activation enthalpy given in dlts_peak_guesses, the result will not be included
when averaging the apparent capture cross section and activation enthalpy for all the
different weighting functions. If the result is ignored, the linear fit in the Arrhenius plot is
drawn in black.
Tp,LI,W6 in the Arrhenius plot, is the temperature position in lock-in window 6 of the
DLTS peak arising from a defect with the given properties.
Variables in the input file relevant for this feature:
do_arrhenius=1
errorlimit
weights
dlts_peak_guesses
allow_negative_amplitude
T_init
T_end
range_to_include_beside_outermost_peaks
T_range_offset
iterations_in_fitting_function
48
A. User guides on software
Figure A.1: Screenshot of the CV program CVmeas with G.vi.
A.2. DLTS-transient analyser
Figure
A.2:
Screenshot
49
of
DLTS_Asterix_current_version.vi.
the
DLTS
program
on
Asterix:
50
Figure
A. User guides on software
A.3:
Screenshot
of
the
depth-profiling
Profiling_semitrap_with_dS_vs_dV_with_stopnow.vi.
program
A.2. DLTS-transient analyser
51
Figure A.4: Screenshot after the DLTS-transient analyser is done fitting the VOH peak and the
E1 peak in the spectra recorded after three different annealing times. Lock in and GS4 are used
as weighting functions.
52
A. User guides on software
Generate a peak-amplitude evolution plot
As I have investigated defect dynamics throughout the whole of this project, it has been
important to extract all the peak amplitudes from the spectra after each annealing step.
This program usually does a good job in this respect if do_peakplot=1.
When extracting peak amplitudes, I tend to use a rather small value for
range_to_include_beside_outermost_peaks (e.g. 4, or even 2), although
this is always a difficult decision. The advantage of a small range is a much faster fitting
and the peak value is usually visually correct; the disadvantage is that this peak value
may be wrong due to the peak being misshaped or overlapped by other peaks.
When I extract peak amplitudes, I usually do that and nothing else; hence, I need
only one window of one weighting function. Usually I want to have the amplitude of
the VO peak, and therefore I use the (640 ms)−1 window (window 6 for lock in), unless the signal-to-noise ratio is low – in which case I also use the (2.56 s)−1 window
(window 8). peakplotwindow and peakplotweight gives which window to use
from which weighting function, respectively, for extracting the peak amplitudes of the
peaks sought after (those listed in dlts_peak_guesses). The most effective way to
extract the peak amplitudes from the spectrum calculated with the sixth lock-in window,
is to load weights{1}{1} with the 64-element long lock-in pattern and give explicitly
that transientlength=2^6. The window index enters, however, the calculation
of the DLTS signal and it is therefore necessary to set window_offset=5. A more
general syntax can be found in the input file:
weights{length(weights)+1}=binary_pattern2dlts_weight→
→([repmat(-1,1,transientlength/2) →
→repmat(1,1,transientlength/2)],transientlength);
window_offset=-1;
elements_in_first_window=2;
If window_offset=-1 it will automatically be set to one less than the longest
window possible with the given transient length and the given number of elements
in the first window of the weighting function. In other words, with these lines only
transientlength needs attention.
A useful function in this business is complete_peak_plot. I call it like this:
[all_peakamplitudes,amplitudetable]=→
→complete_peak_plot(all_best_fits,e_n,weights,→
→abscissa,peaks_to_ignore,window_offset),
where all_best_fits is the structure resulting from a DLTS-peak fitting run, e_n is
the emission rates at the peak maxima (these are calculated by generate_e_n_max
and should already be in the memory after the fitting), abscissa is either the annealing times or the annealing temperatures of each annealing step, and peak numbers
listed in peaks_to_ignore will not be included in the resulting amplitudetable.
A figure with the peak-amplitude evolution should have emerged by now, and
amplitudetable{1}{1} will give the same data organised in a table.
A.2. DLTS-transient analyser
53
Variables in the input file relevant for this feature:
do_peakplot=1
peakplotweight
peakplotwindow
do_arrhenius=1
dlts_peak_guesses
T_init
T_end
range_to_include_beside_outermost_peaks
T_range_offset
weights
window_offset
iterations_in_fitting_function
T_change
allow_negative_amplitude
Subtract each transient of one data file from those in another
This feature is used to follow the evolution of small DLTS peaks overlapped by
other constant peaks.
subtractname, format_of_subtract_files,
Crname_subtract,
format_of_Cr_files_subtract
and
Cr_belongs_to_subtract_name_index should contain file names, file
formats, .dat file names corresponding to each of the transient files (unless standard
DLTS files are used), the format of these, and the array mapping the .dat files to
the .trans files, everything analogous to the variables for loading files for normal
calculation of DLTS spectra (see above).
In addition to these variables is subtract_belongs_to_name_index which
maps the files listed in subtractname to the files in name. With do_subtract=1,
each transient of each file in name will be subtracted by the closest (in temperature)
transient from the corresponding file in subtractname before the program continues
exactly as usually.
Variables in the input file relevant for this feature:
do_subtract=1
subtractname
format_of_subtract_files
Crname_subtract
format_of_Cr_files_subtract
Cr_belongs_to_subtract_name_index
subtract_belongs_to_name_index
54
A. User guides on software
Make a graph showing activation enthalpy versus apparent capture cross section
When an Arrhenius plot is being made, a graph will be plotted to show how the activation
enthalpy and apparent capture cross section (calculated for each file with all weighting
functions) relate. The point is that they will spread out on a diagonal line, because the
temperature position of a DLTS peak is rather well defined and the temperature position calculated from a set of activation enthalpies and apparent capture cross sections
is rather well defined, but there is significant uncertainty in the extracted activation enthalpy and apparent capture cross section. Therefore I like to take the average of the
activation enthalpies I calculate and look at this graph to find the apparent capture cross
section that will give the DLTS peaks in the correct positions.
Save .png files
Most of the graphs that are being plotted can be saved automatically to a
.png file.5
If plot_spectra=1 and save_spectra=1, files such as
Spectrum_wg03_f01.png will contain all the windows of the calculated spectra for each weighting function and each file. If do_arrhenius=1, files such as
Totalarrheniusplot_pk02.png will contain all the Arrhenius plots calculated
for one particular peak and Defectplot_pk02.png will contain the corresponding
plot of the activation enthalpies versus the apparent capture cross sections.
If save_fitting_plots=1 and plot_frequency is larger than zero, the
fitting window will be saved to files like Fitting_pk02_win07_wg03_f04.png
when the best fit is reached. The three (or multiples of three if fitting overlapping peaks)
fitting parameters are also displayed in the graph.
Variables in the input file relevant for this feature:
save_spectra=1
save_fitting_plots=1
plot_spectra=1
do_arrhenius=1
plot_frequency
FFT smoothing of the spectra
FFT smoothing was supposed to be a sophisticated method for reducing the noise in
DLTS spectra, but was never fully implemented. I wanted to do FFT, make a frequency
cut-off to remove fast fluctuations and then do an inverse FFT. Later I learnt that polynomial fitting (polyfit in Matlab) is the way to go about these matters,6 but this is also
not implemented.
5
If a bitmap format for line drawings is needed, then .png is the one to use; it does not require a patent
license like .gif, it supports palettes of 24-bit RGB colours (compared to the 8-bit palette of .gif), it is
lossless (unlike .jpg which causes horrendous compression artefacts in single-coloured surfaces such as
those found in graphs) and with simple graphs, .png files are smaller than normal .jpg files.
6
Lasse Vines, private communication.
A.3. Defect-reaction modeller
55
Variables in the input file relevant for this feature:
do_fft=1
Functions not implemented
Some functions never got developed further than the introduction of an unused, distractive variable in the code. In the input file, some of these variables are:
successlimit: Some annealing-fitting algorithms lower the temperature
after a given number of successes; for this purpose such a variable would
be necessary
plot_raw_also: When the graph shows a smoothened spectrum, it
would be nice to compare with the raw one (lying as a shade in the background)
Other comments
The spectra calculated with all the different weighting functions are located in
spectrum. The averaged spectra are in spectrum_avg. The corresponding temperatures are in T and T_avg, respectively. The final fitting parameters are stored in
the cell structure all_best_fits. fitted_peak_positions contains all the
peak positions found during the fitting. The data points of the resulting Arrhenius plots
are stored in the cell structure arrhenius_points. e_n contains the emission
rates at the peak maxima – one value for each window of each weighting function.
generate_e_n_max generates these values with a rather generic algorithm.
A.3
Defect-reaction modeller
Already at an early stage I was sufficiently aware of my own limitations when it comes to
correctly punching long differential equations to see the necessity of making a program
that would do this task automatically. This program solves just this problem – from
just simple reaction equations as input, it will construct the whole set of differential
equations necessary to describe the model. Further, the differential equations will be
solved numerically by the Matlab function ode15s. Some versions of the program will
also run an infinite number of simulations, simultaneously for any number of annealing
temperatures, while changing the desired parameters to search for a model that fits
better the measured defect concentrations.
Appendix D shows an example of an input file for the defect-reaction modeller. This
file, named props_and_reactions.m, contains most variables that requires attention. In this program the various defects are not referred to by name, but rather
by an index. The index of a defect is given by its position in the cell structure
defect_properties; its labelling should be put in corresponding cell in the cell
56
A. User guides on software
structure legendstr. The various properties of the defect essential to the model
should also be placed in defect_properties. The properties, organised in a fiveelement vector, are initial defect concentration (−1 will be replaced by the initial concentration from the measurement files), pre-factor and activation energy for dissociation
of this defect, pre-factor and activation energy for migration of this defect. Values not
essential to the model are ignored and can be set to NaN.
Once the various defects are given an index, the reaction equations can be entered.
These reside in the two cell structures dissociation and bonding. For instance,
if the defects have the following indices: VO: 1, Oi : 2, VO2 : 3, H: 4, VOH: 5, the reaction
VOH → VO + H
(A.1)
can be set as the first dissociative reaction by giving the command
dissociation{1}=[5 1 4].
In other words: Defect 5 dissociates into the defects 1 and 4. The order of
the two latter has no importance. The dissociation rate will be calculated from
defect_properties{5}(2) (pre-factor) and defect_properties{5}(3)
(dissociation energy of defect 5). The reaction
VO + Oi → VO2
(A.2)
can be set as the second migration reaction by giving the command
bonding{2}=[1 2 3].
In other words: Defect 1 migrates to defect 2 – these react and form defect 3. Here the
order is important, as the migration rate will be calculated from the properties of the first
defect.
The effective capture radius of the bonding reactions is given by R_bonding. The
syntax of this changed under way as I opened for the possibility of having an energy
barrier for a bonding reaction. In the latest versions, each cell of R_bonding should
correspond to the cell in bonding with the same index. The cells of R_bonding
should have a three-element vector with the capture radius for the corresponding bonding reaction, the pre-factor of the barrier for this reaction to happen and the energy barrier for this reaction, respectively. A bonding reaction without a reaction barrier would
typically require
R_bonding{2}=[5e-8 1 0] % cm 1 eV,
where the capture radius is 0.5 nm.
This model-input structure is not entirely general; for instance, some reprogramming
is necessary to give the possibility for a defect to dissociate in two different reactions.
Also, the bonding reactions assumes that one of the species is stationary.
A.3. Defect-reaction modeller
57
To automatically optimise the parameters to model as close as possible measured
concentrations, it is necessary to load the measurement data. The variables for this
is in the beginning of props_and_reactions.m. filenames and path point
to the files to load. These files should have the annealing time in the first column followed by columns with the concentration of various defects. The two dimensional matrix
columns_to_import tells which columns to read – the columns of one file for each
row with the corresponding defects arranged in columns. The vector data_map tells
the program which defects are being loaded by stating the defect index of each of the
defects in columns_to_import. The width of the two variables should, thus, be
equal. annealing_temperatures_of_files_C (C for Celsius) gives the annealing temperature of each of the measured annealing series and will also give the
temperatures at which to run the simulation. The measurement data from each file will
be multiplied by the corresponding value in the vector conversion_factors (this
allows for a mixture of files containing both DLTS amplitudes and concentrations to be
loaded) and subtracted by the concentration in background (which can be either a
single number or a vector with elements corresponding to each data file).
What remains now is to tell which parameters to optimise.
These variables have, unfortunately, become somewhat spread around in the program.
Some are found in model_optimiser_multi_temperature.m.
do_pin_start_concentration
should
be
zero
or
one
and
states whether or not to optimise the initial defect concentrations.
If
unpin_measured_start_concentration=1,
even
the
measured
initial concentrations (which are loaded by setting the initial concentration in defect_properties equal to −1) will be optimised.
do_keep_concentrations_equal_for_different_samples
states
whether or not to guess the initial defect concentrations independently for
each sample/annealing temperature (if the processing of the samples is not
identical, it is probably correct to set this to zero).
This file also contains
plotfrequency which can be increased from 1 to 3 to print information
about the parameter guessing to simplify trouble shooting. Taking these various
choices into account, initialise_guess_rules.m will generate the matrix
guess_and_guessmethod_init with the following columns: measurement set
(the sample for which this parameter is used; 0 if the parameter is common to all
samples/annealing temperatures), defect identifier (defect index), defect property
(1 for initial concentration, 2 and 3 for dissociation properties, 4 and 5 for diffusion
properties), initial guess value, probability distribution (0 for Gaussian, 1 for gamma,
2 for linear), volatility with which to guess, optional parameter for the distribution. The
parameters from R_bonding are included similarly, but the second column refers to
the cell index of R_bonding and the third to the column index of the property plus
100.7 The capture radius is not optimised by default (i.e. not automatically included in
guess_and_guessmethod_init) if it is 0.5 nm (in R_bonding). The reaction
7
The
addition
of
100
(R_bonding_propertycounter_offset
in
model_optimiser_multi_temperature.m) is a non-optimal trick to make it possible to distin-
guish the bonding-reaction parameters from the normal defect properties.
58
A. User guides on software
barrier will not be optimised by default if the pre-factor is 1 and the energy barrier is 0.
If
the
algorithm
in
initialise_guess_rules.m
does
not
prepare for the optimisation of the desired parameters,
and only
those,
guess_and_guessmethod_init
can
be
customised
in
customise_guess_rules.m.
The solver of ordinary differential equations, ode15s, requires a function that contains the set of differential equations. display_diff_eqns.m generates a file
dN_function.m which contains all this. Thus, after the command
display_diff_eqns(defect_properties,dissociation,→
→bonding,R_bonding,’generate_file’),
the simulation can be run for each annealing temperature by simply issuing the command
[time,concentrations]=→
→ode15s(@(t,N)dN_function(t,N,new_defect_properties,→
→new_R_bonding,model_temperature,k_B),→
→measurement_times,new_initial_concentrations),
where new means that the current guessing values replace the initial values. In the first
generations of this program, I tried solving the differential equations my own way, but
things became a lot faster and reliable after I was told about the ode functions.8
Over time, the program for automatic parameter optimisation has become more
developed than the program doing one single simulation run, but this can still be
used by calling the outermost function manual_run.m. The program that searches
for the parameters giving the best fit to the measured data is started by running loop_multi_temperature.m. As for the transient-analysis program (section A.2) this program has a fitting temperature which determines how volatile to
choose the guessing parameters. The initial fitting temperature is loaded from the
file T_init.dat. This kind of input from files allows the values to be changed
during run time – even remotely. After simulating as many times as given in
iterations_in_fitting_function.dat, the fitting temperature is multiplied
by 0.9 (T_change).9 When the value in T_end.dat is reached, the currently best
simulation is stored as a .png picture and a .mat file such as, for instance,
model_optimiser_result_→
→042_06-Dec-1976 16:52:32_1.626e-02.mat,
where the latter number is the minimum error returned by calc_deviation.m. This
function gives a certain contribution from linear deviation and another for the logarithmic
deviation. This because if only the linear deviation mattered, only the evolution of the
large concentrations would be fitted, while minimisation of the logarithmic error would
8
9
Lars Løvlie, private communication.
In model_optimiser_multi_temperature.m.
A.4. Depth-dependent defect-reaction modeller
59
take into account concentrations too small to be measured. The current algorithm is the
result of some trial and error and is unlikely to be optimal.
Figure A.5 shows the optimal result of running the optimisation program for a few
days. Here, measurements from annealing at only one temperature, namely 150 °C,
was fitted.
A.4
Depth-dependent defect-reaction modeller
Unlike the defect-reaction modeller (section A.3), which attempts to reproduce DLTS
amplitudes (or indeed any kind of concentration measurements), the depth-dependent
defect-reaction modeller searches for parameters that make the model reproduce depth
profiles of the various defect concentrations.
As the ode functions of Matlab can not handle both time and space simultaneously,
this program uses the Matlab function pdepe to perform the defect simulation. I expect
it to be possible to write a general algorithm that takes reaction equations as input
and generates a function that can simulate the described model – like the algorithm
described in section A.3 – but I have not done this for the depth-dependent program.
The program is, therefore, rather rigid and some programming is required whenever the
reaction equations of the model is changed.
pdepe, which runs the whole simulation, is called in simulate_diffusion.m.
simulate_diffusion.m also contains the structure of the model.
The
parameters with which to simulate are fed to simulate_diffusion.m
by
guess_parameters2simulation_parameters.m,
which
collects
and bundles the current model parameters in a pattern understandable to
simulate_diffusion.m.
auto_fit_hdiffusion_single_run.m searches for model parameters that
reproduces better (in terms of the error calculated, from a mixture of the linear and logarithmic deviation, by calc_profile_deviation.m) the measured depth profiles.
The depth resolution, initial values of the parameters to optimise and the volatility with
which to make guesses for these are loaded from start_values.m. Similarly to the
defect-reaction modeller described in section A.3, the initial value of the fitting temperature, T_fit, is loaded from T_init.dat and is used to calculate a fitting volatility
which hdiffusion_annealfit.m will use to make parameter guesses. This function takes the currently best parameters, perturb them according to the volatility, and
runs the simulation by calling simulate_diffusion. The deviation from the measured data is calculated; if the deviation is smaller, the new parameters are kept for
the next run. This is repeated iterations_in_fitting_function.dat times,
after which T_fit is reduced one step. When T_end.dat is reached, the best parameters are returned.
The outermost function to run is loop.m. This will cause an infinite calling of parameter optimisations and saving the result of each run to a .png and .mat file. The
latest generation of loop.m also stores the currently best set of parameters in a file
60
A. User guides on software
so that it is transferred to the next run. This allows for several computers to use the
currently best result to try, in parallel, to further improve the parameters.
In summary, the model is defined in simulate_diffusion.m which must have
a compatible guess_parameters2simulation_parameters.m. The initial
parameter values to be optimised are set in start_values.m. The most automated
optimisation routine is run by loop.m. Figure A.6 shows the final result of such a
process.
A.5
DLTS-movie maker
Comparing hundreds of DLTS spectra can be challenging at times. Therefore, I
made a program that interpolates the DLTS spectra between the annealing temperatures. The name of the files,10 their format, their path and various labelling information is defined in fileinfo.m. The remaining settings are in the main program:
dlts_visualisation.m. The code (and commenting) is not particularly mature,
but it is also not a very complicated program. The interpolation is done by
interpolated_spectra_of_single_sample=→
→interp1([1:number_of_annealing_steps)],→
→spectra_of_single_sample,→
→[1:1/annealing_resolution:number_of_annealing_steps],→
→’pchip’).
Figure A.7 shows a snapshot from a movie created from some 100 DLTS spectra
that shows, rather effectively, how the seven samples behave differently throughout the
annealing series. The small graphs that can be seen on the left of the even pages
throughout this thesis are also created by this program.
10
This is, again, a time-consuming task made easy by Linux. An example script can be found in the program.
A.5. DLTS-movie maker
61
Figure A.5: Example of a parameter optimisation that causes the simulation (circles and dashed
lines) to reproduce rather well the measured DLTS amplitudes (stars and solid lines). This sample
was annealed isothermally at 150 °C. This particular model has one source of hydrogen and the
hydrogen can be captured by VO, V2 and a hydrogen trap. Also, VOH∗ dissociates. The x-axis
shows the annealing time in minutes; the y -axis shows trap concentration. Both graphs show the
same data, but with different axes.
62
A. User guides on software
Figure A.6: The result of a continuous run of the depth-dependent defect-reaction modeller. The
measured profiles are shown as stars and the simulation is shown as solid lines. This sample
was annealed isothermally at 195 °C; this is actually the complete result of which a few annealing
times is shown in paper VI.
A.5. DLTS-movie maker
63
Figure A.7: Snapshot from a movie showing, simultaneously, how the DLTS spectra of seven
samples changes throughout an isochronal annealing series. The annealing temperature is indicated by the red column on the right. The annealing was performed in steps of 25 °C – the nine
frames in-between are interpolated. The thin, coloured line shows where the DLTS spectrum was
five frames ago – the thick, grey line shows the difference of this to the current spectrum (scaled
up).
64
A. User guides on software
Appendix
B
User guides on hardware
B.1
Lift for automatically controlling the nitrogen level
on the Asterix set-up
The purpose of the Lift is to have a way of controlling the temperature of the sample by
the computer programs. Viewed as a black box, the Lift takes two input signals and a
power supply of ∼16 V. A pulse going from 0 to 5 V on one of the two input signals will
cause 100 clockwise or counter-clockwise steps on the stepper motor. The voltage for
driving the system is not critical, but 16 V seems to give a good balance between lifting
force and noise level (the motor runs less smoothly at higher voltages).
At present, the input signals of the Lift is connected to two pins in the parallel port of
the computer and the letters ”A” and ”B” will cause the bit pattern 01 and 10, respectively,
causing the Lift to lift or lower (or vice versa, depending on how the triggers from the
parallel port is connected to the microcontroller) the level of nitrogen.
The stepper motor is very robust, but the users of the DLTS program are, nevertheless encouraged to make sure the lift is started sufficiently high such that it will not
reach the lower limit before the stop-lift temperature (Disable lift when T>) is
reached. Make sure the stop-lift temperature is set at a temperature matching the temperature rate and heater power and also that automatic Lift stopping is enabled. After
the measurement is started, please wait half a minute to check that the Lift is able to lift
and that it lifts in the correct direction.
Trivia: In the first version of the Lift, the stepper motor was controlled by simply
closing four relays in the HP 34970A Data Acquisition Switch Unit in sequential order.
The system worked satisfactory, but was noisy, slow and not sufficiently aesthetic to
remain as it was.
65
66
B. User guides on hardware
Figure B.1: The Lift.
B.1.1
Trouble shooting
Sometimes it may be necessary to reconnect lose wires according to figures B.2 and
B.3. Sometimes the stepper motor will make noise, but not actually be able to apply any
force. In this case there is usually a bad contact on one of the six wires (four red and
two white wires) connected to the stepper-motor contact. Take out and reinsert all of
them one at a time. The same symptoms will occur if the red wires are not connected
in the correct sequence. For a stepper motor to run, it depends on getting pulses on
its terminals in the correct order. Thus, if there is a signal to each of the terminals at
different times, but the motor head does not rotate even if it is free to, the four input
signals must be rearranged (or there may be a problem inside the stepper motor).
B.1. Lift for automatically controlling the nitrogen level on the Asterix set-up
LPT
GND A B
67
+−
470 Ohm
5V
−+
INT0
ADC0
Yellow Brown
Black Orange
ADC1
INT1
ADC2
16 V
1 kOhm
ADC3
10 Ohm
Figure B.2: A diagram of the electrical circuit of the stepper driver. The big rectangle is the
microcontroller (ATmega8-16PI), into which (on INT0 and INT1 on pin 4 and pin 5, respectively)
the trigger signals from the parallel port goes. The computer is separated from the microcontroller
by sending the two trigger signals through an optocoupler (HCPL-2531). On the out signals
(ADC0 to ADC3 on pin 23 to pin 26) there are 10-Ω resistors in front of the MOSFETs (BUZ11A).
1-kΩ resistors are connected in front of the coils of the stepper motor. Behind the motor, there
are zener diodes (BZT03C24) and high-current diodes (HER604) to shield the driver circuit from
voltage spikes. The voltage for the microcontroller and optocoupler (5 V) is supplied by a voltage
regulator (MC7805).
B.1.2
Relevant LabView programs
c:\measurements_A\dlts\DLTS_library_based_on_Obelix.llb:
Lift control with PID cluster own PID c.vi1 (for keeping the
heating rate constant)
c:\measurements_A\Misc\stand-alone_PID_control.vi
(for
keeping the temperature constant)
c:\measurements_A\Misc\fastforward_lift_lpt.vi2 (for continuously lowering or lifting)
1
The file name states that the input and output parameters are transferred through cluster-type variables,
that the standard PID algorithm of LabView has been replaced and that this is version c.
2
It is very slow, as a matter of fact.
68
B. User guides on hardware
Figure B.3: An example of how the driver circuit may look when it is working. Ironically, this
picture shows that a wire from one of the diodes has become disconnected at some point in time,
but the Lift was working nevertheless. If there is no sound from the Lift when it is triggered by the
computer, check for loose wires and symmetry breaks.
B.1.3
Spare parts
The stepper motor and gear system is taken from a Star LC-10. It is ever more
difficult to find these, but any stepper motor should work.
Microcontroller: ATmega8-16PI
Optocoupler: HCPL-2531
Resistors: 10 Ω and 1 kΩ
MOSFET: BUZ11A
Zener diode: BZT03C24
B.2. Controllable mains switch on Tiffy
−+
12 V
69
DAC1 OUT
Figure B.4: Diagram of the electrical circuit of the computer-controllable mains switch. A coaxial
cable connected to the BNC-2110 interface (on the DAC1 OUT) should be connected between
the gate and the negative pole of the voltage source. The voltage on the gate should be 5 V to
connect the relay and 0 V to disconnect. The voltage source for the relay should match the relay;
this is currently 12 V.
High-current diode: HER604
Voltage regulator: MC7805
B.2
Controllable mains switch on Tiffy
This device was constructed to be able to use the computer to switch on and off the
cooling pump on the closed helium system, but it can be used for switching on and off
the voltage to any appliance that runs on the mains. After having failed a couple of
times, the device is now in its third generation and has a design more pragmatic than
ever. The input voltage is 12 V (for the coil in the relay) and a signal of 5 V is what is
needed on the input signal to make the MOSFET switch the relay. For trouble shooting,
compare the circuit with figures B.4 and B.5.
B.2.1
Relevant LabView programs
c:\measurements_tiffy\TSC\relaycontrol.vi
B.2.2
Spare parts
Any MOSFET that can run the relay without drawing much current from the input
signal – for instance BUZ11A.
Any 12-V relay that can withstand the desired current and can be driven by the
MOSFET. An Omron G2R-1-SN(S) is currently installed, but it seems this may not
be commercially available any longer.
70
B. User guides on hardware
Figure B.5: The mains switch in operation.
B.3
Power amplifier for the heating elements on the
Obelix set-up
This circuit is a solution to the problem that Obelix is equipped with two 50-W heating
elements connected in series, while the current temperature controller, a Neocera LTC11, can supply no more than 50 W. The circuit uses the analogue output signal of the
temperature controller as input. This signal varies from 0 to 12 V as the internal PID
controller in the Neocera gives an output of 0 to 100%, accordingly. The concern with
this circuit is the temperature of the bipolar transistor. The BUT12A is expected to work
if the junction temperature is below 150 °C, but this is easily exceeded if one is not
cautious. The generation of heat in the transistor is
Ptrans = (Vext − Rheater I)I ,
(B.1)
where Vext is the voltage applied with the power supply, Rheater the total resistance of
the heaters and I the current through the circuit (heaters). This is at maximum when I
is 50% of the maximum current. This is the current when the PID on the the Neocera
B.3. Power amplifier for the heating elements on the Obelix set-up
71
Figure B.6: A napkin diagram of the power amplifier for the heaters on the Obelix set-up. The coil
is actually the two 50-W heating elements connected in series. The uppermost voltage source
is the high-voltage power source (up to ∼90 V). The bipolar transistor is a BUT12A. In front of
the transistor base there is a resistor which should be ∼340 Ω. The lowermost power source is
the analogue output from the Neocera. The higher potential from the Neocera (see figure B.7)
is connected to ground (marked here by a WARNING!); for this reason the high-voltage power
source should be isolated from the ground. To me, at least, it seems not optimal to have two
ground connections at different potentials in the circuit. The heating elements have, in total, a
resistance of 100 Ω; the maximum current – when the Neocera wants 100% heating and gives
11.7 V on the analogue output – is, as the formula says, 1 A.
gives 50%.
The set-up has been operated with an voltage supply of 90 V to reach a sample temperature of 750 K, but then extreme caution must be taken with the transistor
temperature. If the temperature of the junction becomes sufficiently large, it will start
conducting regardless of what the base current is. Hence, if this situation arises, the
set-up will heat 100% until the mains run dry. To avoid this, make sure the air cooling
is switched on, monitor the temperature of the transistor, make sure the transistor has
good thermal contact with the radiator fins and be very concerned if the power stays at
∼50% for several seconds.
If the transistor overheats and becomes uncontrollable, just switch off the voltage
supply and let it cool off. The transistor will normally recover again after being cooled.
With this design there is a large voltage drop across the transistor, and if reliability
and sensible use of energy is in focus, the circuit should be designed differently. A
system with a duty cycle (such that the heaters are either on or off periodically) would
satisfy these requirements. Then, if the output is 20% the heaters will be switched on
for one second each five seconds. This is surely much more elegant, but I am slightly
concerned about whether the constant changing of the current in the heater coils might
cause noise in sensitive measurements – either via the magnetic field or the mains.
Also, it would cost more time and money to construct such a circuit. I was planning to
72
B. User guides on hardware
+
−
Figure B.7: The analogue output socket. The lowest potential (marked with a − here) is connected to the ground of the power source in figure B.6, and the highest potential (marked with a
+ here) is connected to the base resistor in figure B.6. The wire that is to be connected to + is
marked with ”up” and the one for the − with ”left”.
improve the reliability of the circuit by replacing the bipolar transistor by two, or more,
field-effect transistors in parallel to share the generation of heat between them, but this
remains as a task for future generations of Ph.D. students.
B.3.1
Software
There are no LabView programs for this amplifier circuit – all that is needed is to make
the Neocera give analogue output. This is achieved by choosing, on the Analog line in
the Output configuration menu, SENSOR: #1, MODE: PID, MAX PWR: Ramp.
It is also worth mentioning that Ioana Pintilie and I have, with great effort, arrived at a
set of PID parameters that are currently being used for the Obelix set-up. They are not
perfect (optimal parameters anyway depend on the maximum heating power, i.e. the
voltage source), but may get the job done:
P
I
D
=
=
=
10
(B.2)
100
(B.3)
50
(B.4)
These parameters should be put on the Analog line. Also, the value of P0 is zero.
B.3.2
Spare parts
As pointed out previously, the circuit should be redesigned rather than fixed, but if someone insists on still using it:
The transistor handling the most power and the highest junction temperature –
my choice was BUT12A
B.3. Power amplifier for the heating elements on the Obelix set-up
Figure B.8: The power amplifier. The cooling fan runs on 240 V AC.
73
74
B. User guides on hardware
Appendix
C
Example input file for the
DLTS-transient analyser
inputdata_temp.m
% 2006 by Jan H. Bleka
1
2
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5
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>>
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>>
>>
>>
>>
>>
>>
>>
function[name,format_of_files,Crname,belongs_to_name_index
,format_of_Cr_files,path,dlts_peak_guesses,T_range_offset,
allow_negative_amplitude,guessmethod_init,T_init,T_end,T_c
hange,iterations_at_T,iterations_in_fitting_function,succe
sslimit,range_to_include_beside_outermost_peaks,errorlimit
,divide_by_Cr,do_arrhenius,do_peakplot,peakplotweight,peak
plotwindow,do_fft,average_interval,plot_frequency,save_fit
ting_plots,plot_spectra,save_spectra,plot_raw_also,write_o
utfiles,verbose,transientlength,weights,window_offset,do_s
ubtract,subtractname,subtract_belongs_to_name_index,format
_of_subtract_files,Crname_subtract,Cr_belongs_to_subtract_
name_index,format_of_Cr_files_subtract,outname]=inputdata(
)
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
16
17
18
% Should contain every input variable ever necessary to ch >>
>> ange
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25
26
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% Run e.g. choosefiles .. *MCz-32*.dat in /j/eksperimenter
>> /raw/A/MCz-32/best/
% /j/eksperimenter/Transient\\ converter/choosefiles .. *M
>> Cz-32*_3V_*6W*.dat
% To extract the list of annealing times from the file nam
>> es:
% ls *MCz-32*_3V_*6W*.dat|sed ’s/non-ann/0m/g;s/.*_\\([0-9
>> o]\\+\\)m_.*/\\1/g’|tr ’\\n’ ’ ’|tr ’o’ ’.’
% Returns: 0 8 18.1 38 78 158 318 760 1740
30
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>>
76
C. Example input file for the DLTS-transient analyser
32
>>
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>>
>>
name=char(’A070304a_MCz-32_non-ann_f_ev_Al_b_dry_Ag_paste
_fwdnrev_-10V_3V_6W_cool_.dat.trans’,’A070404c_MCz-32_8m_1
95C_f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool_.dat.tr
ans’,’A070406a_MCz-32_18o1m_195C_f_ev_Al_b_old_Ag_paste_fw
dnrev_-10V_3V_6W_cool_.dat.trans’,’A070407a_MCz-32_38m_195
C_f_ev_Al_b_Ag_paste_hot-air_dried_10s_fwdnrev_-10V_3V_6W_
cool_.dat.trans’,’A070408a_MCz-32_78m_195C_f_ev_Al_b_old_A
g_paste_fwdnrev_-10V_3V_6W_cool_.dat.trans’,’A070408g_MCz32_158m_195C_f_ev_Al_b_Ag_paste_hot-air_dried_5s_fwdnrev_10V_3V_6W_cool_.dat.trans’,’A070409f_MCz-32_318m_195C_f_ev
_Al_b_Ag_paste_hot-air_dried_15s_fwdnrev_-10V_3V_6W_cool_.
dat.trans’,’A070410f_MCz-32_760m_195C_f_ev_Al_b_dry_Ag_pas
te_fwdnrev_-10V_3V_6W_cool_.dat.trans’,’A070411c_MCz-32_17
40m_195C_f_ev_Al_b_added_dry_Ag_paste_hot-air_dried_10s_fw
dnrev_-10V_3V_6W_cool_.dat.trans’);
Crname=char(’A070304a_MCz-32_non-ann_f_ev_Al_b_dry_Ag_past
e_fwdnrev_-10V_3V_6W_cool_4.dat’,’A070404c_MCz-32_8m_195C_
f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool_4.dat’,’A07
0406a_MCz-32_18o1m_195C_f_ev_Al_b_old_Ag_paste_fwdnrev_-10
V_3V_6W_cool_4.dat’,’A070407a_MCz-32_38m_195C_f_ev_Al_b_Ag
_paste_hot-air_dried_10s_fwdnrev_-10V_3V_6W_cool_4.dat’,’A
070408a_MCz-32_78m_195C_f_ev_Al_b_old_Ag_paste_fwdnrev_-10
V_3V_6W_cool_4.dat’,’A070408g_MCz-32_158m_195C_f_ev_Al_b_A
g_paste_hot-air_dried_5s_fwdnrev_-10V_3V_6W_cool_4.dat’,’A
070409f_MCz-32_318m_195C_f_ev_Al_b_Ag_paste_hot-air_dried_
15s_fwdnrev_-10V_3V_6W_cool_4.dat’,’A070410f_MCz-32_760m_1
95C_f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool_4.dat’,
’A070411c_MCz-32_1740m_195C_f_ev_Al_b_added_dry_Ag_paste_h
ot-air_dried_10s_fwdnrev_-10V_3V_6W_cool_3.dat’);
outname=char(’A070304a_MCz-32_non-ann_f_ev_Al_b_dry_Ag_pas
te_fwdnrev_-10V_3V_6W_cool_4_alltrans.dat’,’A070404c_MCz-3
2_8m_195C_f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool_4
_alltrans.dat’,’A070406a_MCz-32_18o1m_195C_f_ev_Al_b_old_A
g_paste_fwdnrev_-10V_3V_6W_cool_4_alltrans.dat’,’A070407a_
MCz-32_38m_195C_f_ev_Al_b_Ag_paste_hot-air_dried_10s_fwdnr
ev_-10V_3V_6W_cool_4_alltrans.dat’,’A070408a_MCz-32_78m_19
5C_f_ev_Al_b_old_Ag_paste_fwdnrev_-10V_3V_6W_cool_4_alltra
ns.dat’,’A070408g_MCz-32_158m_195C_f_ev_Al_b_Ag_paste_hotair_dried_5s_fwdnrev_-10V_3V_6W_cool_4_alltrans.dat’,’A070
409f_MCz-32_318m_195C_f_ev_Al_b_Ag_paste_hot-air_dried_15s
_fwdnrev_-10V_3V_6W_cool_4_alltrans.dat’,’A070410f_MCz-32_
760m_195C_f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool_4
_alltrans.dat’,’A070411c_MCz-32_1740m_195C_f_ev_Al_b_added
_dry_Ag_paste_hot-air_dried_10s_fwdnrev_-10V_3V_6W_cool_3_
alltrans.dat’);
>>
>>
>>
>>
>>
name_oldformat=char(’A070304a_MCz-32_non-ann_f_ev_Al_b_dry
_Ag_paste_fwdnrev_-10V_3V_6W_cool_4.dat’,’A070404c_MCz-32_
8m_195C_f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool_4.d
at’,’A070406a_MCz-32_18o1m_195C_f_ev_Al_b_old_Ag_paste_fwd
nrev_-10V_3V_6W_cool_4.dat’,’A070407a_MCz-32_38m_195C_f_ev
_Al_b_Ag_paste_hot-air_dried_10s_fwdnrev_-10V_3V_6W_cool_4
33
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>>
.dat’,’A070408a_MCz-32_78m_195C_f_ev_Al_b_old_Ag_paste_fwd
nrev_-10V_3V_6W_cool_4.dat’,’A070408g_MCz-32_158m_195C_f_e
v_Al_b_Ag_paste_hot-air_dried_5s_fwdnrev_-10V_3V_6W_cool_4
.dat’,’A070409f_MCz-32_318m_195C_f_ev_Al_b_Ag_paste_hot-ai
r_dried_15s_fwdnrev_-10V_3V_6W_cool_4.dat’,’A070410f_MCz-3
2_760m_195C_f_ev_Al_b_dry_Ag_paste_fwdnrev_-10V_3V_6W_cool
_4.dat’,’A070411c_MCz-32_1740m_195C_f_ev_Al_b_added_dry_Ag
_paste_hot-air_dried_10s_fwdnrev_-10V_3V_6W_cool_3.dat’);
>>
>>
>>
>>
>>
>>
>>
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101
format_of_files=[repmat(0,1,size(name,1))]; % 1, or more, >>
>> are old fashion DLTS files with averaged transients and C_ >>
>> r. 0 are files with each single transient and requires a c >>
>> orresponding traditional file to get C_r.
102
103
104
105
106
%Add information on number of windows:
format_of_files=[format_of_files;repmat(6,1,length(format_ >>
>> of_files))];
%format_of_files(2,x)=8;
107
108
109
110
111
belongs_to_name_index=[1:size(name,1)]; % Files of format
>> 0 must have a corresponding C_r file.
format_of_Cr_files=[repmat(1,1,size(Crname,1))]; % Format
>> can not be 0.
>>
>>
112
113
114
115
116
117
% Now a function that subtracts the transients of one file >>
>> from another. If the format is 0, the transients of the f >>
>> iles in name are subtracted by the transient closest in te >>
>> mperature from the corresponding file from subtractname
118
119
120
121
subtractname=[]; % Spectra to subtract from spectra in nam >>
>> e
122
123
124
125
126
127
subtract_belongs_to_name_index=[1:size(subtractname,1)]; % >>
Which file in name do we subtract this from?
format_of_subtract_files=[repmat(0,1,size(subtractname,1)) >>
>> ];
>>
128
129
130
131
132
% Window information:
format_of_subtract_files=[format_of_subtract_files;repmat( >>
>> 8,1,length(format_of_files))];
%format_of_subtract_files(2,x)=8;
133
134
135
Crname_subtract=[];
136
137
Cr_belongs_to_subtract_name_index=[1:size(Crname_subtract) >>
78
138
139
140
C. Example input file for the DLTS-transient analyser
>> ]; % Files of format 0 must have a corresponding C_r file.
format_of_Cr_files_subtract=[repmat(1,1,size(Crname_subtra >>
>> ct,1))];
141
142
143
path=char(’~/j/eksperimenter/raw/A/MCz-32/’);
144
145
146
147
148
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end of file-related
>> variables
>>
149
150
151
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153
154
>>
155
156
157
158
159
160
>>
161
162
163
164
>>
165
166
167
>>
168
169
>>
% Fitting parameters:
VO_properties=[5.1e-14 0.1817];
p89K_properties=[1e-15 0.174]; % Just a rough approximatio
n assuming 1e-15.
V2double_properties=[1.2e-14 0.252];
VOH_properties=[4e-15 0.32];
VOH_properties=[1.1963e-17 0.24561]; % For GS4 W7 25012007
%p165K_properties=[1e-18 0.24];%[8e-15 0.37];
p165K_properties=[1.1418e-14 0.37252]; % For GS4 W7 250120
07
p165K_unstable_properties=[1.3e-15 0.341];
%V2single_properties=[3.1e-15 0.429];
V2single_properties=[3.5326e-16 0.39244]; % For GS4 W7 250
12007
V2single_overlap_properties=[1.5e-14 0.474];
p214K_properties=[5.5633e-17 0.38994]; % For GS4 W7 250120
07
H1_properties=[2.7388e-17 0.16214] % Doing some fitting in
GS4W5 01052007
>>
>>
>>
>>
>>
170
171
172
173
>>
174
175
>>
176
177
>>
178
179
>>
180
181
>>
182
183
>>
184
185
>>
186
187
>>
188
189
190
>>
dlts_peak_guesses={};
dlts_peak_guesses{length(dlts_peak_guesses)+1}=[H1_propert
ies];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[VO_proper
ties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[V2double_
properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[VOH_prope
rties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[p165K_pro
perties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[p165K_pro
perties;V2single_properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[V2single_
properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[p214K_pro
perties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[p165K_uns
table_properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[p165K_uns
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
79
191
192
193
194
195
196
197
>> table_properties;V2single_properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[p165K_uns >>
>> table_properties;V2single_overlap_properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[V2single_ >>
>> properties];
%dlts_peak_guesses{length(dlts_peak_guesses)+1}=[V2single_ >>
>> overlap_properties];
198
199
200
201
202
203
204
205
206
207
208
209
T_range_offset={}; % NaN for automatic. The range of data
>> to use when fitting a certain set of peaks
%T_range_offset{length(T_range_offset)+1}=[-5 0];
T_range_offset{length(T_range_offset)+1}=[NaN];
T_range_offset{length(T_range_offset)+1}=[NaN];
T_range_offset{length(T_range_offset)+1}=[NaN];
T_range_offset{length(T_range_offset)+1}=[NaN];
T_range_offset{length(T_range_offset)+1}=[NaN];
%T_range_offset{length(T_range_offset)+1}=[-5 0];
%T_range_offset{length(T_range_offset)+1}=[-10 30];
%T_range_offset{length(T_range_offset)+1}=[NaN];
>>
210
211
212
213
214
215
216
217
218
>>
>>
>>
219
220
221
222
223
>>
>>
>>
>>
224
225
226
227
228
229
230
>>
>>
231
232
233
>>
>>
234
235
>>
236
237
238
>>
>>
amplitude_volatility=1e-2;
sigma_volatility=5e-2;
energy_volatility=1e-3;
allow_negative_amplitude=1; % Needed to fit contribution f
rom minority carriers. If 1, guessmethod should probably b
e Gaussian, not gamma (I.e. guessmethod(1,1)=0 instead of
1
guessmethod_init=[1 amplitude_volatility 0;1 sigma_volatil
ity 0;0 energy_volatility 123]; % distribution (Gaussian=0
,gamma=1,linear=2), volatility/distribution width (for Gau
ssian/gamma) / lower limit (for linear), NaN (for Gaussian
) / min/max limit (for gamma) / max limit (for linear)
T_init=30 ;
T_end=3;
T_change=0.9; % 0.9 gives a reduction of 10%
iterations_at_T=1; % 1. Not implemented
iterations_in_fitting_function=200; % 300. Number of itera
tions in annealfit. So the number of guesses at each T is
actually iterations_at_T * iterations_in_fitting_function
successlimit=iterations_at_T/20; % Not implemented. Reduce
temperature after successlimit successes even if iteratio
ns_at_T is not reached
range_to_include_beside_outermost_peaks=2; % Kelvin. 7. Ho
w much of the adjecent data to fit
errorlimit=60/100; % Ignore result if it is more than erro
rlimit*100% outside the original guess in dlts_peak_guesse
s
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
239
240
241
242
243
do_subtract=0; % Do subtract the transients of files in na >>
>> me by those in subractname
divide_by_Cr=1; % Wether to divide the DLTS signal by the >>
>> reverse capacitance
80
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
C. Example input file for the DLTS-transient analyser
do_arrhenius=1; % Fit data to find peaks and create Arrhen
>> ius plot
do_peakplot=1; % Plot amplitudes vs time/annealing temper
>> ature
peakplotweight=1; % Weight to use when making a peak-amp
>> litude plot
peakplotwindow=1; % Window to use when making a peak-amp
>> litude plot
do_fft=0; % Not functioning. Whether or not to do FFT afte
>> r the averaging
average_interval=0.1; % Kelvin. If several points are with
>> in this interval they will be joined in an average. Use 0
>> if averaging is not desired.
plot_frequency=1; % 1. 0-6. How much to plot during fittin
>> g. Above 1 is slower.
save_fitting_plots=1; % Creates png files
plot_spectra=1; % Show the generated spectra
save_spectra=1; % Makes png files
plot_raw_also=0; % Not implemented. Include raw data for
>> comparison
write_outfiles=0; % Save generated spectra in given outfil
>> es
verbose=1; % Tell which files are being opened
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
267
268
269
270
271
272
273
274
275
276
277
% Calculate the maximum common transient length:
if size(format_of_files,1)>1
% We only construct weights to cover the file with the lea >>
>> st data points in the transients:
transientlength=2^min(format_of_files(2,:));
else
% If # of windows is not defined for the files, assume 6 w >>
>> indows = 64 data points:
transientlength=2^6;
end
278
% VO is not in window 8, so six windows may be wanted:
%transientlength=2^6;
279
280
281
weights={};
282
283
284
285
286
287
288
289
>>
>>
>>
>>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
window_offset=0; % is used for the 2^window and must be ch
anged to 5 if only the weight of window 6 is used (Don’t c
hange here. See further down.). Set window_offset=-1 to ge
t the longest window. Keep window_offset=0 if there is mor
e than one weight.
>>
>>
>>
>>
290
291
292
293
% R1, Lock in:
%weights{length(weights)+1}=binary_pattern2dlts_weight(-[1 >>
>> -1],transientlength);
294
295
296
% Lock in: Only longest window
%weights{length(weights)+1}=binary_pattern2dlts_weight(-[r >>
81
297
298
299
>> epmat(1,1,transientlength/2) repmat(-1,1,transientlength/2 >>
>> )],transientlength);window_offset=-1;elements_in_first_win >>
>> dow=2;
300
301
302
303
% R2:
%weights{length(weights)+1}=binary_pattern2dlts_weight(-[0 >>
>> 1 0 -1],transientlength);
304
305
306
307
% R3:
%weights{length(weights)+1}=binary_pattern2dlts_weight(-[1 >>
>> 0 0 -1],transientlength);
308
309
310
311
% R4:
%weights{length(weights)+1}=binary_pattern2dlts_weight(-[1 >>
>> -1 -1 1],transientlength);
312
313
314
315
% Double rectangular:
%weights{length(weights)+1}=binary_pattern2dlts_weight([0
>> -1 -1 1 1 1 1 0 0 -1 -1 -1 -1 1 1 0],transientlength);
>>
316
317
318
319
320
321
322
323
>>
>>
>>
>>
>>
% Double rectangular: Only longest window:
%weights{length(weights)+1}=binary_pattern2dlts_weight([re
pmat(0,1,transientlength/16) repmat(-1,1,transientlength*2
/16) repmat(1,1,transientlength*4/16) repmat(0,1,transient
length*2/16) repmat(-1,1,transientlength*4/16) repmat(1,1,
transientlength*2/16) repmat(0,1,transientlength/16)],tran
sientlength);window_offset=-1;elements_in_first_window=16;
>>
>>
>>
>>
>>
324
325
326
327
% GS4:
%weights{length(weights)+1}=binary_pattern2dlts_weight(-[- >>
>> 1 25 -48 24],transientlength);
328
329
330
331
332
333
334
>>
>>
>>
>>
% GS4: Only longest window:
weights{length(weights)+1}=binary_pattern2dlts_weight(-[re
pmat(-1,1,transientlength/4) repmat(25,1,transientlength/4
) repmat(-48,1,transientlength/4) repmat(24,1,transientlen
gth/4)],transientlength);window_offset=-1;elements_in_firs
t_window=4;
>>
>>
>>
>>
335
336
%%%%%%%%%%%%%%%%%%%%%
337
338
339
340
341
if window_offset==-1
window_offset=log(transientlength/elements_in_first_windo >>
>> w)/log(2);
end
82
C. Example input file for the DLTS-transient analyser
Appendix
D
Example input file for the
defect-reaction modeller
props_and_reactions.m
% 2006 by Jan H. Bleka
1
2
3
4
5
6
7
>>
>>
>>
>>
function[defect_properties,legendstr,dissociation,bonding,
R_bonding,k_B,elements_not_to_plot,filenames,path,annealin
g_temperatures_of_files,columns_to_import,data_map,convers
ion_factors,background,data_correction_factors]=props_and_
reactions()
>>
>>
>>
>>
8
9
10
% Don’t plot these elements:
elements_not_to_plot=[5 8 10 19]; % B Y Z X
11
12
13
14
15
16
17
18
19
20
21
22
23
filenames=char(’A061024a_MCz-29_VO_V2mm_165K_0-10640m.peak
>> ’,’A070412d_MCz-32_A070412a_and_b_peaks_fixed_with_A070412
>> c_GS4_W5_and_W7_conc.peak’);
path=char(’~/j/eksperimenter/raw/A/Selected_peak_files/’);
annealing_temperatures_of_files_C=[150 195]; % Celsius
annealing_temperatures_of_files=annealing_temperatures_of_
>> files_C+273.15; % K
columns_to_import=[2 3 4;2 3 4]; % Sensitive to order. 1 (
>> time) is ignored as it is always imported.
data_map=[1 2 14]; % A map of which element each of the da
>> ta columns corresponds to. Column 1 is the first non-one n
>> umber in columns_to_import.
>>
>>
>>
>>
>>
>>
24
25
26
27
28
29
conversion_factors=[5.0072e13 1]; % The factors to get fro >>
>> m concentration from the .peak files. 5.0072e13 for LI W6 >>
>> at a sample with N_d=5e12 cm^-3.
background=1e10; % 24042007. This is usually the value i f >>
>> ind.
30
31
files_to_exclude=[2]; % []. A simple way of not including
83
>>
84
32
33
34
35
36
37
38
39
D. Example input file for the defect-reaction modeller
>> certain temperatures
filenames=remove_rows(filenames,files_to_exclude);
annealing_temperatures_of_files=remove_elements(annealing_ >>
>> temperatures_of_files,files_to_exclude);
columns_to_import=remove_rows(columns_to_import,files_to_e >>
>> xclude);
conversion_factors=remove_elements(conversion_factors,file >>
>> s_to_exclude);
40
41
42
43
data_correction_factors=repmat(1,1,size(filenames,1)); % C >>
>> hange from 1 if individual data set should be scaled. For >>
>> instance to account for different irradiation doses.
44
45
46
% Physical constant:
k_B=8.617386e-5; % eV/K
47
48
49
50
51
52
53
%%%%%%%%%%%%%%%%%%%%%%%
% DEFECT PROPERTIES
defect_properties={}; % E.g. [VO_init(cm^-3) Dissociation: >>
>> C_0_VO(1/s) C_E_VO(eV) Diffusion:D_0_VO(cm^2/s) D_E_VO(eV) >>
>> ]
legendstr={};
54
55
56
57
58
% 1: VO
legendstr{length(legendstr)+1}=’VO’;
defect_properties{length(defect_properties)+1}=[-1 NaN NaN >>
>> NaN NaN];
59
60
61
62
63
% 2: V2
legendstr{length(legendstr)+1}=’V2’;
defect_properties{length(defect_properties)+1}=[-1 NaN NaN >>
>> NaN NaN];
64
65
66
67
68
% 3: O_i
legendstr{length(legendstr)+1}=’O_i’;
defect_properties{length(defect_properties)+1}=[2.5e17 NaN >>
>> NaN NaN NaN];
69
70
71
72
73
% 4: BH
legendstr{length(legendstr)+1}=’BH’;
defect_properties{length(defect_properties)+1}=[6.727e+16
>> 1.3364e+11 2.6802e-07 NaN NaN]; % fit
>>
74
75
76
77
78
% 5: B
legendstr{length(legendstr)+1}=’B’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
79
80
81
82
83
84
% 6: H
legendstr{length(legendstr)+1}=’H’;
defect_properties{length(defect_properties)+1}=[1.8396e+07 >>
>> NaN NaN 0.00056472 0.63003]; % fit
85
85
86
87
88
% 7: YH
legendstr{length(legendstr)+1}=’YH’;
defect_properties{length(defect_properties)+1}=[5e13 NaN N >>
>> aN NaN NaN];
89
90
91
92
93
% 8: Y
legendstr{length(legendstr)+1}=’Y’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
94
95
96
97
98
% 9: ZH2
legendstr{length(legendstr)+1}=’ZH2’;
defect_properties{length(defect_properties)+1}=[5e11 NaN N >>
>> aN NaN NaN];
99
100
101
102
103
% 10: Z
legendstr{length(legendstr)+1}=’Z’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
104
105
106
107
108
% 11: H2
legendstr{length(legendstr)+1}=’H2’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> 2.6e-4 0.78]; % From Markevich 1998
>>
109
110
111
112
113
% 12: VOH2
legendstr{length(legendstr)+1}=’VOH2’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
114
115
116
117
118
% 13: VOH
legendstr{length(legendstr)+1}=’VOH’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
119
120
121
122
123
% 14: VOH*
legendstr{length(legendstr)+1}=’VOH*’;
defect_properties{length(defect_properties)+1}=[-1 2.6252e >>
>> +12 1.4028 NaN NaN]; % fit
124
125
126
127
128
% 15: V2H2
legendstr{length(legendstr)+1}=’V2H2’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
129
130
131
132
133
% 16: V2H
legendstr{length(legendstr)+1}=’V2H’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
134
135
136
137
% 17: VO2
legendstr{length(legendstr)+1}=’VO2’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>>
86
138
D. Example input file for the defect-reaction modeller
>> NaN NaN];
139
140
141
142
143
% 18: XH
legendstr{length(legendstr)+1}=’XH’;
defect_properties{length(defect_properties)+1}=[0 NaN NaN
>> NaN NaN];
>>
144
145
146
147
148
% 19: X
legendstr{length(legendstr)+1}=’X’;
defect_properties{length(defect_properties)+1}=[6.7033e+16 >>
>> NaN NaN NaN NaN]; % fit
149
150
151
152
153
154
>>
>>
155
156
>>
157
158
>>
% REACTIONS
dissociation={}; % [initial_element final_element1 final_e
lement2 final_element3...]. The order of the final element
s have no importance.
% E.g.: V2O -> VO + V (V2O:defect_properties{1}, VO:2, V:3
): [1 2 3]
% E.g.: V2 -> 2V (V2:1, V:2): [1 2 2] But this function is
not tested!
>>
>>
>>
>>
159
160
161
162
163
dissociation{length(dissociation)+1}=[4 5 6]; % H source 1
dissociation{length(dissociation)+1}=[14 1 6]; % VOH* -> V >>
>> O + H
164
165
166
167
168
169
170
171
172
% dissociation{length(dissociation)+1}=[7 8 6]; % H source
2
% dissociation{length(dissociation)+1}=[9 10 11]; % H2 sou
>> rce
% dissociation{length(dissociation)+1}=[12 1 11]; % VOH2 >> > VO + H2
% dissociation{length(dissociation)+1}=[13 1 6]; % VOH ->
>> VO + H
>>
bonding={}; % [initial_element1 initial_element2 initial_e
>> lement3... final_element]. The first element is assumed to
>> be the migrating one.
% E.g.: VO + V -> V2O (VO:defect_properties{1}, V:2, V2O:3
>> ): [1 2 3]
% E.g.: 2V -> V2 (V:1, V2:2): [1 1 2] But this function is
>> not tested!
>>
>>
>>
>>
>>
>>
173
174
175
176
177
178
179
180
181
>>
>>
182
183
184
185
bonding{length(bonding)+1}=[6 1 14]; % H + VO -> VOH*
bonding{length(bonding)+1}=[6 2 16]; % H + V2 -> V2H
bonding{length(bonding)+1}=[6 19 18]; % H + X -> HX
186
187
188
189
190
R_bonding={}; % Bonding radii and formation barriers. [rad >>
>> ius(cm) Formation barrier:C_0(1) E_b(eV)]. Pre-factor has >>
>> no unit. 1 0 means no barrier.
R_default=5e-8; % cm
87
191
192
193
194
195
196
197
R_bonding{length(R_bonding)+1}=[R_default 0.017446 0.04300 >>
>> 3]; % fit
R_bonding{length(R_bonding)+1}=[1.8093*R_default 0.023659 >>
>> 0.040163]; % fit
R_bonding{length(R_bonding)+1}=[R_default 0.82918 0.079831 >>
>> ]; % fit
88
D. Example input file for the defect-reaction modeller
Bibliography
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[20] G. Lindström, M. Ahmed, S. Albergo, P. Allport, D. Anderson, L. Andricek, M. M.
Angarano, V. Augelli, N. Bacchetta, P. Bartalini, et al., Nucl. Instrum. Methods Phys.
Res. A 465, 60 (2001)
[21] URL http://rd48.web.cern.ch
[22] URL http://rd50.web.cern.ch
[23] G. Kramberger, D. Contarato, E. Fretwurst, F. Hönniger, G. Lindström, I. Pintille,
R. Röder, A. Schramm, and J. Stahl, Nucl. Instrum. Methods Phys. Res. A 515,
665 (2003)
[24] P. Pellegrino, Ph.D. thesis, KTH, Stockholm (2001)
[25] M. Mikelsen, Ph.D. thesis, University of Oslo (2007)
[26] G. Alfieri, Ph.D. thesis, University of Oslo (2005)
[27] P. Blood and J. W. Orton, The Electrical Characterization of Semiconductors: Majority Carriers and Electron States (Academic Press, London, 1992)
[28] M. Yoneta, Y. Kamiura, and F. Hashimoto, J. Appl. Phys. 70, 1295 (1991)
[29] Y. Tokuda, Jpn. J. Appl. Phys. 37, 1815 (1998)
[30] URL http://en.wikipedia.org/wiki/Simulated_annealing
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Res. B 186, 100 (2002)
[32] R. M. Fleming, C. H. Seager, D. V. Lang, E. Bielejec, and J. M. Campbell, Appl.
Phys. Lett. 90, 172105 (2007)
I
Solid State Phenomena
Online available at: http://www.scientific.net
Copyright Trans Tech Publications, Switzerland
Defect behaviour in deuterated
and non-deuterated n-type Si
J. H. Bleka1,a , E. V. Monakhov1,b , A. Ulyashin1,c , F. D. Auret2,d ,
A. Yu. Kuznetsov1,e , B. S. Avset3,f and B. G. Svensson1,g
1 Department
of Physics, Physical Electronics, University of Oslo,
P.O. Box 1048 Blindern, 0316 Oslo, Norway
2 Department of Physics, University of Pretoria, Pretoria 0002, Republic of South Africa
3 SINTEF ICT, Microsystems, P.O. Box 124 Blindern, 0314 Oslo, Norway
a j.h.bleka@fys.uio.no, b edouard.monakhov@fys.uio.no, c alexander.ulyashin@fys.uio.no,
d fauret@postino.up.ac.za, e andrej.kuznetsov@fys.uio.no, f berit.s.avset@sintef.no, g b.g.svensson@fys.uio.no
Keywords: Si, DLTS, hydrogen, deuterium, defects
Abstract Deep level transient spectroscopy (DLTS) has been performed on deuterated and
non-deuterated p+ -n− -n+ Si-diode detectors made from oxygenated, low-doped, high-purity
FZ-Si wafers. The deuterated samples were exposed to deuterium plasma at 150 ◦ C for 2
and 4 h, respectively. All the samples were then irradiated with 6-MeV electrons to a dose
of 2 × 1012 cm−2 . In the as-irradiated state the concentration of electrically active defects is
the same in all groups of samples. The samples were subsequently annealed isochronally for
15 minutes at temperatures from 100 to 400 ◦ C. No difference in the DLTS spectra is seen
for the samples after annealing up to 200 ◦ C. After annealing at 200 ◦ C and above, however,
pronounced differences in the annealing behaviour of the defects are observed. In the nondeuterated samples, the peaks of the two known divacancy levels (V2 ) shift slightly during the
annealing steps up to 300 ◦ C. This shift is, from previous reports, ascribed to the interaction
of V2 with interstitial oxygen which results in the divacancy-oxygen centres (V2 O). In the
deuterated samples the two V2 centres are fully annealed at 250 ◦ C, without the transition to
V2 O. In the sample deuterated for 4 h the disappearance of the VO peak, starting during the
annealing at 200 ◦ C, coincides with the appearance of two peaks with positions at 0.17 and
0.58 eV below the conduction band, respectively.
Introduction
In recent years the energy levels in Si has been explored by different techniques. Some energy
levels are identified with large certainty, such as the vacancy-oxygen centres (VO) [1, 2, 3],
the doubly negatively charged divacancy (V2 (=/–)) [4, 5, 6] and the singly negatively charged
divacancy (V2 (–/0)) [1, 5, 6].
Recently, it has been reported that hydrogen can significantly affect the annealing of V2 [7].
It is suggested that V2 can interact with molecular hydrogen (H2 ) directly to form the V2 H2
complex. However, no peak identified as V2 H2 has been observed in DLTS spectra. At the same
time, theoretical studies have suggested that V2 H2 can have a level at ∼ 0.2 eV below the
conduction band [8]. The lacking observation of V2 H2 suggests that it has a shallower position
in the band gap than predicted or that it is electrically inactive, altogether.
2
Sample
Doping
Oxidation
Oxygenation
A
B
C
D
12
5 × 10
P · cm−3
21 h dry at
1200 ◦ C
80 h in N2 at
1150 ◦ C
Deuteration
Pre-annealing
—
—
2 h in D plasma
at 200 ◦ C
1 h in N2
at 450 ◦ C
—
—
4 h in D plasma
at 200 ◦ C
—
Table 1: Survey of the investigated samples.
Despite the pronounced effect of hydrogen on the annealing of V2 , quantitative studies could
not be performed due to the lack of information on the exact hydrogen concentration in the
samples. Low solubility makes it challenging to determine the hydrogen content in hydrogenated
Si samples. If protium is replaced by deuterium, secondary ion mass spectrometry (SIMS) can
be used to detect concentrations down to about 1015 cm−3 , or even lower.
In this work we have performed DLTS studies of V2 annealing in deuterated Si. The DLTS
signal has been measured in a temperature range of 30 to 290 K. Thus shallow electrical levels
can also be investigated.
Experiment
The p+ -n− -n+ Si diodes were produced from low-doped, high-purity FZ wafers. The wafers were
oxidised in a dry oxygen atmosphere at 1200 ◦ C for 21 h, followed by an oxygenation in N2
atmosphere at 1150 ◦ C for 80 h, during which oxygen from the silicon-dioxide layer was diffused
into the sample. An ordinary silicon diode process with boron and phosphorus implantation
and post-annealing was then performed. The oxygen and carbon concentrations in the region of
DLTS measurements, as determined by SIMS, are (2 − 3) × 1017 and ≤ 1016 cm−3 , respectively.
Aluminium was used as contact metal.
Two samples, labelled B and D, were submerged in an HF solution to remove the aluminium
layers before their n+ sides were exposed to a deuterium plasma with a pressure of 700 mTorr
and a temperature of 150 ◦ C for 2 or 4 h, respectively, with an OXFORD Plasmalab microwave
system. Hydrogenation under these conditions normally results in the formation of a hydrogenrich layer with a thickness of 0.5 µm and a hydrogen content of ∼ 1020 cm−3 near the exposed
surface. However, the concentration of deuterium near the front p+ side of the diodes (∼
200 − 300 µm from the exposed surface), where the DLTS measurements take place, is expected
to be substantially lower and not to exceed 1016 cm−3 . All the samples were irradiated at room
temperature with 6.2-MeV electrons and a dose of 2 × 1012 cm−2 . Sample B was annealed at
450 ◦ C in an N2 atmosphere for 1 h prior to the electron irradiation. The preparation steps for
the different samples are listed in Table 1.
DLTS measurements were performed using two setups. One is based on a Boonton 7200
capacitance meter, and the other on an HP 4280A capacitance meter (described by Svensson
et al. 1989 [9]). The temperature was scanned between 30 and 290 K with the Boonton setup
and between 77 and 290 K with the HP setup, and the measured capacitance transients were
averaged in intervals with a width of 1 K. The duration of the filling pulse was 50 ms. The
DLTS signal was extracted by using a lock-in-type weighting function, and different spectra were
3
obtained with rate windows in the range (20 ms)−1 to (640 ms)−1 from a single temperature
scan. The concentration, energy level and apparent capture cross section of the traps were then
evaluated from the spectra.
The annealing was done isochronally for 15 minutes in an N2 atmosphere at temperatures
from 100 to 400 ◦ C.
Results and discussion
Fig. 1 shows the DLTS measurements performed using the Boonton setup for the non-deuterated
sample A and the deuterated sample B. One can see that the as-irradiated spectra are practically
identical and contain the three peaks VO, V2 (–/0) and V2 (=/–), similarly to that seen by
Monakhov et al. [7]. In addition, a minor peak can be seen at ∼ 50 K. Only small changes occur
after annealing at ≤ 200 ◦ C, and this holds also at 250 ◦ C for the non-deuterated sample where
the transition from V2 to V2 O has started. For the deuterated sample, however, considerable
changes have occurred. The amplitude of the VO peak is decreased significantly and both V2
peaks are completely annealed out. These changes are accompanied by the appearance of a
peak assigned to the VOD defect [7] and also a faster growing peak, labelled E1.
After annealing at 300 ◦ C the transition from V2 to V2 O in sample A has finished, while the
VO peak retains its as-irradiated amplitude. For sample B the amplitude of E1 has decreased
while that of VOD has continued to increase.
The DLTS signal obtained by the Boonton capacitance meter is negative for some temperatures. This is due to an unintentional injection of minority carriers which becomes very
significant due to the low doping of the samples. The effect is stronger for the deuterated sample, indicating a higher resistance which might be caused by modification of the n+ layer during
the deuteration. Since no level directly correlated with the annealing of V2 is observed in the
deuterated sample at temperatures below 77 K, we performed the subsequent measurements,
an annealing series with the non-deuterated sample C and the deuterated sample D, using the
HP setup. The results are shown in Fig. 2. A fitting was performed, with the method of least
mean squares, to find which 9 synthetic DLTS peaks would best fit the DLTS data from all the
rate windows at each annealing step for samples C and D. Fig. 3 shows the fitted amplitudes
of some of these peaks after different annealing steps. Table 2 gives an overview of different
levels observed with an estimate of their respective energy position and apparent capture cross
section as obtained from Arrhenius plots.
Trap
E2
VOD
E1
E3
Ec −Ea
[eV]
0.17
0.32
0.37
0.58
App. capt. cross
section [cm2 ]
4 × 10−16
2 × 10−15
8 × 10−15
4 × 10−16
Table 2: Arrhenius-plot results for the energy levels and apparent capture cross sections of
different electron traps, which are believed to be hydrogen related.
The non-deuterated sample C displays similar behaviour to that of A throughout the annealing series. However, when the transition from V2 to V2 O has finished, after the annealing
at 300 ◦ C, the amplitude of the V2 O peaks for sample C has decreased compared to the V2
4
Sample A
DLTS signal·1000/Cr
5
As irr.
200 °C
250 °C
300 °C
VO
4
3
V2(=/−)
V2O(=/−)
2
V2(−/0)
V2O(−/0)
1
0
Sample B
DLTS signal·1000/Cr
5
As irr.
200 °C
250 °C
300 °C
VO
4
3
2
V2(=/−)
1
VOD
E1
V2(−/0)
0
-1
50
100
200
150
Temperature/K
250
Figure 1: DLTS spectra for the non-deuterated sample A and the deuterated (2 h) sample
B after the different isochronal annealing steps. The curves are obtained with rate window
(640 ms)−1 using a Boonton setup.
peaks, whereas for sample A the defect concentration remains the same. This may indicate a
higher residual concentration of hydrogen in C.
After the annealing at 250 ◦ C the amplitude of the VO peak has dropped substantially for
sample D. This is accompanied by the appearance of two new peaks, E2 and E3, and the growth
of VOD and E1. This is not seen for sample B where there is no drop in the concentration of
VO and no visible presence of E2 or E3 after the annealing at 250 ◦ C.
No peak was found in the shallow end of the band gap that shows the behaviour expected
theoretically for V2 D2 . It can be suggested, however, that the hydrogen related E1 can be a
result of V2 reacting with D2 , because the rise of E1 corresponds very well to the annealing of
V2 .
It may be speculated that the difference between samples B and D arises not only from a
lower deuterium concentration in the former one (2 h vs. 4 h deuteration), but also from the
5
Sample C
DLTS signal·1000/Cr
5
4
As irr.
200 °C
250 °C
300 °C
VO
3
2
V2(=/−)
V2(−/0)
V2O(=/−)
V2O(−/0)
1
0
Sample D
DLTS signal·1000/Cr
5
4
As irr.
200 °C
250 °C
300 °C
VO
3
2
1
0
VOD
V2(−/0)
V2(=/−)
E2
E1
E3
100
200
150
Temperature/K
250
300
Figure 2: DLTS spectra for the non-deuterated sample C and the deuterated (4 h) sample D.
The HP setup is used with the (640 ms)−1 rate window.
thermal pre-treatment of sample B. The pre-treatment may for instance have effected the state
of hydrogen by changing the concentration of molecular hydrogen relative to that of atomic.
The non-deuterated samples A and C show similar behaviour to that of the non-hydrogenated
sample in Ref. [10, 11]. For all of these samples the VO peak remains unchanged up to the annealing at 300 ◦ C, while the two V2 peaks gradually transform to V2 O.
In sample C there is also a weak trace of the mid-band gap level E3. This, together with
the lack of a one-to-one correlation of the amplitudes of the V2 and V2 O peaks, indicates that
there may be a non-negligible presence of H also in non-hydrogenated samples. This presence
is probably due to cleaning processes in the sample fabrication.
E1 is not observed in the hydrogenated samples used in Ref. [7], while the trap ascribed
to VOH/VOD is present in both Ref. [7] and the present experiment. The fact that E1 is not
seen may indicate either a difference in the defect dynamics for samples containing protium
and deuterium, respectively, or that the samples compared contain hydrogen of different forms
(atomic vs. molecular).
6
Sample C
DLTS signal·1000/Cr
5
VO
V2O(=/−)
V2(=/−)
V2(−/0)
V2O(−/0)
4
3
2
1
0
Sample D
DLTS signal·1000/Cr
5
VO
E2
V2(=/−)
VOD
E1
V2(−/0)
4
3
2
1
0
50
100
200
300
150
250
Annealing temperature/°C
350
400
Figure 3: The amplitude to some of the peaks from sample C and D after each of the annealing
steps.
Conclusion
Comparative studies of deuterated and non-deuterated samples show distinct differences in
the annealing behaviour. For non-deuterated samples a transition from V2 to V2 O is seen,
in accordance with previous reports. For deuterated samples the two V2 peaks are annealed
out already at 250 ◦ C with no corresponding growth of V2 O. Enhanced annealing of VO due
to deuterium is also seen with an associated increase of VOD. A trap with an energy level
0.37 eV below the conduction band is revealed for these samples after V2 anneals and a possible
assignment is V2 D2 . Results for the sample with the highest deuterium concentration also shows
two peaks at 0.17 and 0.58 eV below the conduction band, respectively, and they are presumably
due to hydrogen-related defects.
7
References
[1] S. D. Brotherton and P. Bradley: J. Appl. Phys. 53, 5720 (1982)
[2] L. W. Song, X. D. Zhan, B. W. Benson and G. D. Watkins: Phys. Rev. B 42, 5765 (1990)
[3] N. Keskitalo, A. Hallén, J. Lalita and B. G. Svensson: Defects and Diffusion in Silicon Processing,
edited by T. Diaz de la Rubia, S. Coffa, P. A. Stolk and C. S. Rafferty, Mater. Res. Soc. Symp.
Proc. No. 469 (Materials Research Society, Pittsburg, 1997), p. 233
[4] A. O. Evwaraye and E. Sun: J. Appl. Phys. 47, 3776 (1976)
[5] L. C. Kimerling: Radiation Effects in Semiconductors 1976, edited by N. B. Urli and J. W.
Corbett (Inst. Phys., Bristol, 1977), p. 221
[6] B. G. Svensson and M. Willander: J. Appl. Phys. 62, 2758 (1987)
[7] E. V. Monakhov, A. Ulyashin, G. Alfieri, A. Yu. Kuznetsov, B. S. Avset and B. G. Svensson:
Phys. Rev. B 69, 153202 (2004)
[8] J. Coutinho, V. J. B. Torres, R. Jones, S. Öberg and P. R. Briddon: J. Phys.: Condens. Matter
15, S2809 (2003)
[9] B. G. Svensson, K.-H. Rydén and B. M. S. Lewerentz: J. Appl. Phys. 66, 1699 (1989)
[10] E. V. Monakhov, B. S. Avset, A. Hallén and B. G. Svensson: Phys. Rev. B 65, 233207 (2002)
[11] G. Alfieri, E. V. Monakhov, B. S. Avset and B. G. Svensson: Phys. Rev. B 68, 233202 (2003)
This article was processed using the LATEX macro package with TTP style
II
PHYSICAL REVIEW B 75, 155202 共2007兲
Annealing of the divacancy-oxygen and vacancy-oxygen complexes in silicon
M. Mikelsen, J. H. Bleka, J. S. Christensen, E. V. Monakhov, and B. G. Svensson
Department of Physics, Physical Electronics, University of Oslo, P.O. Box 1048, Blindern, N-0316 Oslo, Norway
J. Härkönen
Helsinki Institute of Physics, P.O. Box 64, FIN-00014, University of Helsinki, Finland
B. S. Avset*
SINTEF ICT, P.O. Box 124, Blindern, N-0314 Oslo, Norway
共Received 18 December 2006; revised manuscript received 1 February 2007; published 9 April 2007兲
After low dose electron irradiation, annealing kinetics of divacancy-oxygen 共V2O兲 and vacancy-oxygen
共VO兲 complexes in carbon-lean n-type magnetic Czochralski 共MCZ兲 and diffusion-oxygenated float-zone
共DOFZ兲 Si samples has been studied in detail. The samples were of n type with a phosphorus doping concentration in the 1012 cm−3 range, and the analysis was conducted by means of deep-level transient spectroscopy
共DLTS兲. An exponential decrease in the V2O concentration with time during isothermal annealing at temperatures in the range 275– 355 ° C has been observed. The activation energy for the V2O annealing is found to be
2.02± 0.12 eV, with a preexponential factor in the 1013 s−1 range, which strongly suggests that dissociation of
V2O is the dominating mechanism. The binding energy of the vacancy to the V2O complex has been estimated
as ⬃1.7 eV. An increase in the VO concentration is observed in the initial phase of the V2O annealing, which
is supportive of V2O dissociation through the reaction V2O → VO + V. After the initial increase, a close to first
order decrease in the VO concentration is observed, consistent with that VO mainly anneals by migration and
trapping at oxygen interstitial sites, similarly to what has been reported in previous high-dose studies using
infrared spectroscopy. The vacancy-oxygen-hydrogen complex 共VOH兲 is formed after long time annealing. The
formation of VOH is followed by a decrease at the same rate as VO, and it is suggested that VOH dissociates
共VOH → VO + H兲. The experimental data have been compared with kinetic simulations and show good agreement with a model where the main processes are dissociation of VO and V2O, migration and subsequent
trapping of VO ultimately giving rise to the electrically inactive vacancy-dioxygen pair 共VO2兲 and interactions
involving atomic hydrogen.
DOI: 10.1103/PhysRevB.75.155202
PACS number共s兲: 71.55.⫺i, 61.80.Fe
I. INTRODUCTION
Oxygen is one of the most common and important impurities in silicon, and is mainly present in the form of an
electrically inactive interstitial configuration 共Oi兲. It is, therefore, important to understand the behavior of oxygen-related
complexes, and one of the most fundamental of these is the
divacancy-oxygen complex 共V2O兲. Irradiation at room temperature of silicon with a sufficient oxygen concentration is
known to produce O related defects since Oi is an effective
trap for mobile vacancies. Initially, at low radiation doses,
vacancy-oxygen 共VO兲 complexes are formed.1,2 As the dose
increases, VO can capture another vacancy forming V2O.3
V2O can also be formed when Oi traps migrating divacancies
at elevated temperatures.4–7 Despite the fundamental nature
of V2O, the positions of its electrical levels in the band gap
have not been established until recently.5–8
The experimental identification of V2O was made in an
electron paramagnetic resonance 共EPR兲 study by Lee and
Corbett.3 The defect was found to be present with an intensity similar to that of the divacancy 共V2兲 in high-dose
electron-irradiated 共5 ⫻ 1018 cm−2兲 Czochralski 共CZ兲 Si. It
was found that V2O disappeared after annealing at 350 ° C,
and it was speculated that V2O either acts as a sink for migrating vacancies giving rise to V3O or is lost via interaction
with Oi, forming V2O2. In a positron annihilation spectros1098-0121/2007/75共15兲/155202共8兲
copy study on Cz-Si irradiated by electrons with a lower
dose of 1 ⫻ 1018 cm−2, no considerable concentration of V2O
was observed in as-irradiated samples.4 It was found, however, that V2O could be formed when V2 annealed. It was
proposed that V2O was formed as a result of divacancy migration and subsequent trapping at an Oi site 共V2 + Oi
→ V2O兲. A similar conclusion has also been reached in low
dose studies of high resistivity silicon using deep-level transient spectroscopy 共DLTS兲.5,7 In Ref. 4, the positron trap
assigned to V2O was found to decrease in concentration at
⬃400 ° C, simultaneously as two other traps emerged. The
activation energy for the annealing of the trap attributed to
V2O was estimated to 2.1 eV and mechanisms such as dissociation, trapping during migration 共V2O + Oi → V2O2兲 and
capturing of released vacancies 共V2O + V → V3O兲 were discussed. For further progress, detailed studies of the annealing
kinetics of V2O and associated multivacancy-oxygen complexes are required using electrical and optical techniques.
Such studies are, however, scarce in the literature and this is
in part due to the fact that V2O has a Si-O-Si bonding structure that is very similar to that of VO. Techniques such as
infrared 共IR兲 spectroscopy, which can be used to determine
the local vibrational modes and electronic transitions of defects, cannot easily distinguish the V2O absorption band
from the dominating VO band: calculations based on density
functional theory have predicted that the absorption band of
155202-1
©2007 The American Physical Society
PHYSICAL REVIEW B 75, 155202 共2007兲
MIKELSEN et al.
these two defects are very close in position.9 In a lowtemperature IR absorption study on irradiated silicon an absorption band at 833 cm−1 was ascribed to V2O.10 This band
did, however, appear only as a shoulder at the low energy tail
of the much more intense VO absorption band located at
836 cm−1.
Furthermore, despite the early EPR observations, the electrical activity of V2O was established only recently. In a
series of DLTS studies it was shown that V2O can be formed
in irradiated diffusion-oxygenated float-zone 共DOFZ兲 Si via
annealing of V2.5,7 The electrical properties of V2O are similar to those of V2, with a 共0/⫹兲 donor level at ⬃Ev
+ 0.24 eV,11 a 共⫺/0兲 acceptor level at ⬃Ec − 0.47 eV and a
共⫽/⫺兲 acceptor level at ⬃Ec − 0.23 eV,5 where Ev and Ec are
the energies of the edges of the valence- and conductionband, respectively. It has also been shown that the transition
from V2 to V2O can occur in Cz-Si with mechanically polished surfaces, minimizing the exposure to hydrogen during
the sample preparation.8
Other DLTS studies on Cz-Si and FZ-Si did not reveal
any levels related V2O, neither directly after irradiation nor
after V2 annealing.12 However, DLTS is applicable to very
low concentrations of defects, contrary to EPR, IR, and
positron-annihilation spectroscopy. The mechanism for V2
annealing in DLTS studies may therefore be sensitive to the
presence of impurities with a relatively low concentration. It
has been shown that H affects considerably the annealing of
V2, effectively preventing formation of V2O.13 Hence, one
can speculate that the annealing of V2 in Ref. 12 may be
caused by interaction with residual hydrogen.
In this work, we have performed a detailed DLTS study
on the annealing of V2O and VO, using two different kinds
of electron-irradiated Si materials; high purity DOFZ-Si and
carbon-lean magnetic Czochralski 共MCZ兲 Si. Isothermal annealing has been carried out at different temperatures in the
range 275– 355 ° C. The annealing of V2O follows first-order
kinetics and suggests that dissociation is the dominant annealing mechanism with minor 共if any兲 formation of higher
order multivacancy-oxygen complexes. The loss of VO displays a more complex behavior than V2O, and invokes several mechanisms such as migration, trapping by Oi, dissociation, and interaction with residual hydrogen impurities. The
annealing of VO and V2O is modeled, applying the theory of
diffusion limited reactions.14 The results of the simulation
agree well with those of the experiments.
II. EXPERIMENT
Two sets of samples were studied: the first set was prepared from n− MCZ-Si and the second set was prepared from
n− DOFZ-Si, see Table I for doping concentrations. The
preparation of the second material includes a step where high
purity FZ-Si is oxygen enriched: the FZ-wafers are dry oxidized for 21 h at 1200 ° C, and a subsequent anneal is then
performed at 1200 ° C in a N2 atmosphere where O atoms
from the preformed SiO2 surface layer diffuse into the bulk
Si. For all samples boron and phosphorus implantations with
post-implant annealing were performed in order to form
p+-n−-n+ diodes. As a final step aluminum contacts were de-
TABLE I. Survey of the samples used in the study.
Sample
Doping
concentration
共cm−3兲
Carbon
concentration
共cm−3兲
Oxygen
concentration
共cm−3兲
MCZ-Si
DOFZ-Si
5.5⫻ 1012
5.0⫻ 1012
艋1016
共2 – 4兲 ⫻ 1016
共5 – 10兲 ⫻ 1017
共2 – 3兲 ⫻ 1017
posited. Secondary-ion mass spectrometry 共SIMS兲 has been
used to determine the oxygen and carbon concentrations. A
survey of the samples is found in Table I. All of the samples
were irradiated with 6 MeV electrons at room temperature to
doses in the range 2 – 4 ⫻ 1012 cm−2.
The DLTS measurements were performed using two setups. One is based on a Booton 7200 capacitance meter, and
the other on a HP 4280A capacitance meter described
elsewhere.15 The temperature of the sample was scanned between 77 K and 300 K, and in some cases between 12 K and
300 K. The measured capacitance transients were averaged
in intervals of 1 K. The DLTS signal was extracted by using
a lock-in type weighting function, and different spectra were
obtained corresponding to six rate windows ranging from
共20 ms兲−1 to 共640 ms兲−1.
After irradiation the samples were preannealed in two
steps. The first step involved annealing for 15 min at
225 ° C, in order to remove minor, unstable defects that overlap with V2 in the DLTS spectrum. The second step consisted
of extended annealing at 255 or 300 ° C in order to ensure a
transition from V2 to V2O.7 One sample was also annealed
for 70 h at 205 ° C before this annealing step. An overview
of the annealing history for each sample can be found in
Table II.
Isothermal annealing treatment was then performed at
temperatures in the range 275– 355 ° C. This annealing temperature always exceeded the temperatures used in the pretreatment. DLTS measurements were conducted before and
after each annealing step.
III. RESULTS
Three dominant DLTS peaks at ⬃Ec − 0.18, Ec − 0.23, and
Ec − 0.43 eV are present after irradiation. These are identified
as the vacancy-oxygen pair, VO, the doubly negative divacancy, V2共= / −兲, and the singly negative divacancy,
V2共− / 0兲, respectively. After annealing for 15 min at 225 ° C,
some minor defects overlapping with V2共− / 0兲 are annealed
out, resulting in relatively pure V2 peaks with a close oneto-one relation between the amplitudes of the Ec − 0.23 and
Ec − 0.43 eV levels. In the second step of the preannealing
the expected transition from V2 to V2O takes place in both
the DOFZ- and MCZ-Si samples 关Fig. 1共a兲兴 and the corresponding levels appear at Ec − 0.23 and Ec − 0.47 eV.
A minor peak forms at ⬃157 K in the 共640 ms兲−1 spectrum during the V2 to V2O transition 关Fig. 1共a兲兴. This peak is
present in all the samples. The formation kinetics and identity of this level is discussed elsewhere.16 The 157 K peak is
slightly broader in the MCZ-Si than in the DOFZ-Si samples
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ANNEALING OF THE DIVACANCY-OXYGEN AND…
PHYSICAL REVIEW B 75, 155202 共2007兲
TABLE II. Annealing history of the samples used in the
study.
TABLE II. 共Continued.兲
Preannealing
treatment
Annealing
temperature
共isothermal兲
Sample number
Type
A
MCZ
15 min at
225 ° C
15 min at
300 ° C
355 ° C
B
MCZ
15 min at
225 ° C
15 min at
300 ° C
335 ° C
C
MCZ
15 min at
225 ° C
15 min at
300 ° C
325 ° C
D
MCZ
15 min at
225 ° C
15 min at
300 ° C
315 ° C
E
MCZ
15 min at
225 ° C
15 min at
300 ° C
305 ° C
F
MCZ
15 min at
225 ° C
360 min at
255 ° C
290 ° C
G
MCZ
15 min at
225 ° C
360 min at
255 ° C
275 ° C
H
DOFZ
15 min at
225 ° C
15 min at
300 ° C
355 ° C
I
DOFZ
15 min at
225 ° C
15 min at
300 ° C
350 ° C
J
DOFZ
15 min at
225 ° C
15 min at
300 ° C
335 ° C
K
DOFZ
15 min at
225 ° C
70 h at
205 ° C
15 min at
300 ° C
325 ° C
L
DOFZ
15 min at
225 ° C
360 min at
255 ° C
290 ° C
Sample number
Type
M
DOFZ
Preannealing
treatment
15 min at
225 ° C
360 min at
255 ° C
Annealing
temperature
共isothermal兲
275 ° C
关Fig. 1共b兲兴, and improving the energy resolution of the DLTS
spectra using a weighting function described in Ref. 17, it is
observed that the broadening in MCZ-Si samples is caused
by an additional minor peak at ⬃150 K.
During isothermal annealing in the temperature range
275 to 355 ° C, the intensity of the two V2O peaks decrease
关Figs. 1共a兲 and 1共b兲兴. After prolonged annealing, 关250 min at
325 ° C, Fig. 1共b兲兴, the amplitude of the doubly negative
peak, V2O共= / −兲, reaches the background level. However, a
peak still remains at the position of V2O共− / 0兲. This observation supports a suggestion made previously, that a minor
FIG. 1. DLTS spectra of irradiated DOFZ-Si 共a兲 and MCZ-Si 共b兲
samples after annealing.
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MIKELSEN et al.
FIG. 3. Arrhenius plot for the annealing rates of V2共= / −兲 in
MCZ- and DOFZ-Si. The dotted line is an exponential fit to all the
data from both the DOFZ- and MCZ-Si samples. The error bars
indicate an experimental error of 15%.
FIG. 2. Normalized intensities of V2O共− / 0兲, V2O共= / −兲 and VO
with respect to those at t = 0 versus annealing time during isothermal annealing at 325 ° C for MCZ-Si 共a兲 and DOFZ-Si 共b兲 samples.
The dotted line represents an exponential decay fit 关Eq. 共1兲兴 to
V2O共= / −兲.
peak forms at this position during the V2 to V2O transition,7
and it appears to grow somewhat further during the loss of
V2O in the DOFZ samples.
In the temperature interval between the two V2O peaks
several minor overlapping levels occur, and the DLTS spectra in this region can be fit with a sum of single peaks. The
fitting is done by a computer program that explores an array
of different possible combinations of single peaks, applied to
all six rate windows, and returns the best fit.18 It is possible
to estimate the activation enthalpy and apparent capture
cross sections, although, the accuracy of these values are
limited. The fitting reveals the presence of three peaks in this
region. One of these is the ⬃157 K level discussed previously, which decreases gradually in intensity after annealing.
There is also a level at ⬃170 K, with an estimated activation
enthalpy of ⬃0.31 eV and an apparent capture cross section
of 4 ⫻ 10−17 cm2. This level has a larger intensity in the
DOFZ-Si samples than in the MCZ-Si samples. This also
holds for a third level at ⬃148 K, which has an estimated
activation enthalpy of ⬃0.27 eV and an apparent capture
cross section of 5 ⫻ 10−17 cm2. The appearance of this third
level depends on how the pretreatment was performed: in a
DOFZ-Si sample that was pretreated for 70 h at 205 ° C, this
level does not form after subsequent annealing at 325 ° C.
In the MCZ-samples a level is also observed at ⬃280 K,
Fig. 1共b兲. This level has been reported previously,18 and is
located close to the middle of the band gap, with an activation enthalpy of 0.58 eV below Ec and an apparent capture
cross section of 4 ⫻ 10−16 cm2. Finally, a minor level at
⬃50 K, 0.10 eV below Ec, is revealed in DOFZ-Si 共not
shown兲, and it remains stable during the V2O annealing.
In the following we will mainly focus on the VO and V2O
peaks, which dominate the spectra. The concentration of
V2O共= / −兲 exhibits a exponential decrease with time:
关V2O兴共t兲 = 关V2O兴共t = 0兲exp关− c共T兲t兴,
共1兲
where 关V2O兴 denotes the concentration of V2O and c共T兲 is a
temperature dependent rate constant. This relation holds for
all annealing temperatures in both DOFZ- and MCZ-Si. As
an example, the normalized concentration is plotted versus
annealing time at 325 ° C for MCZ- and DOFZ-Si in Figs.
2共a兲 and 2共b兲, respectively. The amplitude of V2O共− / 0兲 is
consistently higher than for V2O共= / −兲, which is caused by
the minor level overlapping with V2O共− / 0兲.
In Fig. 3, the rate constant, c共T兲, for V2O共= / −兲 is depicted
versus the inverse absolute temperature. For a singly activated process, an Arrhenius behavior is expected;
c共T兲 = c0 exp共− Ea/kT兲,
共2兲
where Ea is the activation energy and c0 is the prefactor. For
both MCZ- and DOFZ-Si c共T兲 obeys an Arrhenius behavior
with some scatter. By fitting all the data for both types of
samples with a straight line, an activation energy of
2.02± 0.12 eV is obtained. The prefactor is determined to 2
⫻ 1013 s−1, with about one order of magnitude in uncertainty.
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ANNEALING OF THE DIVACANCY-OXYGEN AND…
IV. DISCUSSION
FIG. 4. DLTS spectra of DOFZ-Si after annealing for prolonged
duration at 350 ° C.
In parallel to the annealing of V2O a slight increase in the
VO concentration is observed in the DOFZ-Si samples,
while the opposite holds for the MCZ-Si samples. In order to
study the annealing behavior of VO more closely, a DOFZ-Si
sample was subjected to heat treatment at 350 ° C for extended periods of time. The initial increase in the VO concentration is followed by a decrease after longer annealing
times 共Fig. 4兲. Ultimately, this decrease approaches an exponential decay, as illustrated in Fig. 5 where the concentrations of VO and V2O are depicted versus annealing time at
350 ° C. Figure 4 also reveals the appearance of VOH共− / 0兲,
which is located 0.32 eV below Ec,12,19–22 after sufficiently
long times. Initially, the concentration of VOH increases, but
is later followed by a decrease which also approaches an
exponential decay, with a rate similar to that of VO, Fig. 5.
FIG. 5. Comparison between simulated and experimental concentrations of VO, VOH, and V2O in a DOFZ-Si sample versus
time during isothermal annealing at 350 ° C. The dotted lines are the
simulation results.
For a dissociative process first order annealing kinetics
and a prefactor in the range of 1012 – 1013 s−1 is expected.23
Both these features characterize the annealing V2O, suggesting strongly that the complex dissociates. V2O migration and
subsequent trapping at oxygen interstitial sites, similar to the
annealing process for V2, is not likely to be a main annealing
mechanism. In addition to the magnitude of the prefactor,
two other arguments against migration and trapping can be
put forward. The first one is that the Oi concentration is
higher in MCZ-Si than in DOFZ-Si, which would result in a
substantially faster annealing of V2O in MCZ-Si than in
DOFZ-Si, but this does not agree with the experimental data.
The second reason is that migration and trapping would result in the formation of V2O2, which is believed to be electrically active with two acceptor centers similar to V2 and
V2O.24 No such levels have been observed. For dissociation
of V2O, two possible dissociation reactions can be considered: V2O → VO + V and V2O → V2 + Oi. However, calculations employing density functional theory have predicted a
dissociation barrier of 1.5– 1.6 eV for the first reaction while
the other reaction has a barrier of 2.6 eV.24 The first reaction
is, therefore, likely to dominate, and this reaction will contribute to an increase in the VO concentration consistent with
the results for the DOFZ-Si samples. However, VO is not
very stable at temperatures above 300 ° C, and infrared spectroscopy studies have identified at least two different annealing mechanisms.25,26 It was found that VO is mobile above
300 ° C, and can anneal by migration and trapping at
oxygen-interstitial sites, forming the electrically inactive
VO2 complex 共VO + Oi → VO2兲. The rate of this process increases linearly with the Oi concentration and is presumably
a major reason for the lack of increase in VO concentration
in the MCZ-Si samples when V2O starts to break up. Furthermore, dissociation of VO is also known to occur 共VO
→ V + Oi兲. However, in a material where oxygen is the dominant impurity, most of the monovacancies will be retrapped
at an Oi site, yielding a substantial reforming of VO.
In order to reach a more quantitative understanding of the
role of the various defect reactions, a kinetic model for the
annealing process has been developed. In the model, dissociation of VO and V2O and migration and trapping of VO
are assumed. Further, the appearance of VOH in the DLTS
spectra 共Fig. 4兲 reveals the presence of hydrogen. VOH occurs after quite long annealing times, and at relatively low
concentrations, suggesting a rather limited supply of hydrogen. Since hydrogen is expected to be highly mobile in the
studied temperature range, the formation of VOH is presumably controlled by the release of trapped hydrogen. In the
model, a complex XH is introduced where X denotes a trapping site for H; at elevated temperatures XH breaks up
共XH → X + H兲 and provides migrating hydrogen atoms. Several studies have reported that complexes can release H in
such a way, and activation energies for trap-limited release
are reported to be in the range 1.1– 1.5 eV.27–29 The released
hydrogen atoms will migrate and bond to VO, forming VOH.
VOH can subsequently capture a second H atom forming the
electrically inactive VOH2.12 After an initial increase in the
155202-5
PHYSICAL REVIEW B 75, 155202 共2007兲
MIKELSEN et al.
TABLE III. Rate equations derived from Eqs. 共3兲–共13兲. Numerical values for the constants are given in Table IV.
Defect
species
Rate equation
d关V2O兴
V 2O
dt
VO
d关VO兴
dt
Diss
关V2O兴 + 4␲RDV关V兴关VO兴 − 4␲RDH关H兴关V2O兴
= −CV20
Diss
Diss
关V2O兴 + 4␲RDV关V兴关Oi兴 − 4␲RDVO关VO兴关Oi兴−CVO
关VO兴 − 4␲RDV关V兴关VO兴 − 4␲RDH关H兴关VO兴
= CV2O
d关VO2兴
VO2
dt
d关Oi兴
Oi
dt
d关V兴
V
dt
2
dt
H
d关H兴
dt
Diss
关VO兴 − 4␲RDVO关VO兴关Oi兴 − 4␲RDV关V兴关Oi兴
= CVO
Diss
Diss
= CV
O关V2O兴 − 4␲RDV关V兴关Oi兴 + CVO 关VO兴 − 4␲RDV关V兴关VO兴
d关VOH兴
VOH
= 4␲RDVO关VO兴关Oi兴
Diss
关VOH兴
= 4␲RDH关H兴关VO兴 − 4␲RDH关H兴关VOH兴 − CVOH
Diss
关HX兴 − 4␲RDH关H兴关X兴 − 4␲RDH关H兴关VO兴−4␲RDH关H兴关VOH兴 − 4␲RDH关H兴关V2O兴
= CHX
d关VOH2兴
VOH2
dt
d关HX兴
HX
dt
d关X兴
X
dt
VOH concentration, a decrease with annealing time is observed 共Fig. 4兲. The rate of this decrease is, however, too
high to be explained by reactions with hydrogen only. In fact,
the annealing rates of VOH and VO approach almost exactly
the same value after sufficiently long times. This can be explained by dissociation of VOH through the reaction VOH
→ VO + H. A substantial amount of VOH will reform as released H atoms again are trapped at VO complexes during
migration, and the rate of this process is proportional to the
concentration of VO. Since the VO concentration decreases
with time, so does the rate of VOH reformation, and the
annealing rate for VOH becomes essentially the same as for
VO. Trapping of hydrogen by V2O, resulting in V2OH, is
also taken into account in the model. It has, however, only a
minor effect since the reaction rate between V2O and H is
expected to be of the same magnitude as that for VO and H,
assuming similar capture radii, which is much lower than the
dissociation rate for V2O.
On the basis of the considerations discussed above, the
following reactions have been included in the simulation
V2O → VO + V,
共3兲
V + VO → V2O,
共4兲
= 4␲RDH关H兴关VOH兴
Diss
关HX兴 + 4␲RDH关H兴关X兴
= −CHX
Diss
关HX兴 − 4␲RDH关H兴关X兴
= CHX
VO → V + Oi ,
共5兲
V + Oi → VO,
共6兲
VO + Oi → VO2 ,
共7兲
XH → X + H,
共8兲
X + H → XH,
共9兲
VOH → VO + H,
共10兲
VO + H → VOH,
共11兲
VOH + H → VOH2 ,
共12兲
V2O + H → V2OH.
共13兲
The corresponding coupled differential equations can be derived by applying the theory for diffusion limited reactions
developed by Waite14 and they are given in Table III. The
rate equations are solved numerically, and a survey of the
values used for the various constants and boundary conditions is given in Table IV.
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ANNEALING OF THE DIVACANCY-OXYGEN AND…
TABLE IV. Numerical values for the constants used in the simulation.
Constant
Explanation
Value
R
Diss
CV
O
Capture radius
Dissociation rate for
V2O.
Diss
CVO
Dissociation rate for
VO.
Diss
CHX
Dissociation rate for
HX.
Diss
CVOH
Dissociation rate for
VOH.
Diss
Diss
CHX
= 0.6⫻ CVO
DVO.
Diffusivity of VO.
DV , DH
Diffusivities of V and
H.
Initial concentration
of HX.
5.0⫻ 10−16 cm2 s−1
at 350 ° C,
with Ea = 2.06 eV
DV = DH = 104 ⫻ DVO
2
关HX兴t=0
关V2O兴t=0
关VO兴t=0
关VOH兴t=0
关V兴t=0
关H兴t=0
关X兴t=0
Initial concentrations
of V2O and VO.
Initial concentrations
of VOH, V, H, and
X.
5Å
c共T兲 for V2O, see Eq.
共2兲.
Ea = 2.02 eV
c0 = 2 ⫻ 1013 s−1
5.5⫻ 10−4 s−1 at 350
°C, with Ea = 2.51
eV
Diss
CHX
= c0 exp共−Ea / kT兲
where Ea = 2.11 eV
and c0 = 1 ⫻ 1013 s−1
1 ⫻ 1013 cm−3
Comment
The annealing rate of V2O,
c共T兲, found in this study.
共Fig. 3兲
Values taken from Ref. 25
Free parameter, determined
by fitting of the VOH
annealing curve with c0
typical for dissociation. The
accuracy is within 50%.
Free parameter, determined
by fitting of the VOH
annealing curve. The
accuracy is within 50%.
Values taken from Ref. 25,
but increased by 25%.
Assumed to be very high.
Free parameter determined
by fitting of the VOH
annealing curve. The
accuracy is 1–2 orders of
magnitude with ⬃1013 cm−3
as a lower limit.
Measured
Put equal to 0.
Figure 5 displays the result of the simulations together
with the data from DOFZ-Si after annealing at 350 ° C.
Three parameters were free when fitting the curves to the
data in Fig. 5; the initial HX concentration, 关HX兴t=0, the HX
Diss
Diss
dissociation rate, CHX
, and the VOH dissociation rate, CVOH
.
The result of the fit is not very sensitive to 关HX兴t=0, and an
increase from the value given in Table IV by one order of
magnitude results in no significant change of the fitting
curves. Estimates of the errors in the free parameters are
given in Table IV. The diffusivity prefactor for VO is increased by 25% compared to the value given in Ref. 25.
Otherwise, the parameter values used are identical with those
in Ref. 25 and those deduced from the current experiment.
As can be seen from Fig. 5, the model is in good quantitative
agreement with the experimental data for V2O, VO as well
as VOH annealing, and provides additional support for the
conclusion that V2O annealing is dominated by dissociation.
Furthermore, as shown in Fig. 5, the model also accounts for
the increase in VO concentration observed during V2O annealing in DOFZ-Si. Moreover, in MCZ-Si, where the O
content is higher and annealing of VO via migration to Oi is
strongly promoted, no increase in the VO concentration during annealing of V2O is predicted by the model, fully consistent with the experimental observations.
In this context, it is interesting to note that a dissociation
energy of ⬃2.0 eV for reaction 共3兲 implies a binding energy
of ⬃1.7 eV. This assumes a migration energy of ⬃0.3 eV
for V,30 which is expected to be in the neutral charge state
during annealing, and no extra reaction barrier, i.e., the dissociation energy equals the sum of the binding and migration
energy for V. The value of ⬃1.7 eV is somewhat higher than
1.3 eV, which has been predicted by theory,24 but of the
same magnitude.
Finally, it should be pointed out that several studies, using
IR absorption, DLTS and Hall-effect techniques, have reported a metastable configuration of VO2 labeled VO2*,31–33
which is considered to be electrically active with a shallow
acceptor state at Ec − 0.06 eV.32,33 VO2* has a total energy
that is only 0.25 eV higher than VO2, and the equilibrium
fraction of VO2* increases with temperature.31 During sub-
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PHYSICAL REVIEW B 75, 155202 共2007兲
MIKELSEN et al.
sequent rapid cooling to room temperature, centers in the 共 *兲
configuration are frozen and do not revert back to the ground
state. Indeed, after annealing for 9 h at 350 ° C and then
quenching to room temperature we observe a level at ⬃Ec
− 0.06 eV in the DOFZ-Si sample. The concentration of this
level is ⬃5% of the initial VO concentration, in close agreement with that expected for VO2* according to the IR-data in
Ref. 31 where the remaining fraction of annealed VO centers
occurs as VO2. Hence, these data provide additional evidence for reaction 共7兲 being the dominant one for the annealing of VO in our samples.
kinetic model is developed invoking dissociation of VO and
V2O, migration of VO and subsequent trapping at Oi sites,
release of trapped hydrogen atoms and interaction of hydrogen with vacancy-type defects. Taking diffusivity and dissociation values from literature and from the current study, the
model displays excellent agreement with experimental data.
In particular, the simulation results represent further solid
support for dissociation as the dominant annealing mechanism for V2O. Finally, based on the experimental results, the
binding energy of V to the V2O complex is estimated as
⬃1.7 eV, in reasonable agreement with theoretical predictions.
V. SUMMARY
ACKNOWLEDGMENTS
The annealing of V2O is shown to exhibit first order kinetics in both MCZ and DOFZ-Si. The activation energy of
the process is determined to 2.02± 0.12 eV, and the prefactor
is ⬃2 ⫻ 1013 s−1. The value of the prefactor strongly suggests
dissociation as the main annealing mechanism for V2O. A
Financial support by the Norwegian Research Council
共“Forskerprosjekt” and Strategic University Program on Advanced Sensors for Microtechnology兲 is gratefully acknowledged. Enlightening discussions with Leonid Murin are also
highly appreciated.
*Present address: Statens Strålevern, Grini næringspark 13, P.O.
Kuznetsov, B. S. Avset, and B. G. Svensson, Solid State Phenom. 108, 553 共2005兲.
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B. G. Svensson, K.-H. Rydén, and B. M. S. Lewerentz, J. Appl.
Phys. 66, 1699 共1989兲.
16 M. Mikelsen, E. V. Monakhov, B. S. Avset, and B. G. Svensson,
Phys. Scr., T 126, 81 共2006兲.
17 P. Pellegrino, Ph.D. Thesis, Royal Institute of Technology, Stockholm 共2001兲.
18
J. H. Bleka, E. V. Monakhov, A. Ulyashin, F. D. Auret, A. Yu.
155202-8
III
PHYSICAL REVIEW B 76, 233204 共2007兲
Room-temperature annealing of vacancy-type defect in high-purity n-type Si
J. H. Bleka,* E. V. Monakhov, and B. G. Svensson
Department of Physics, Physical Electronics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
B. S. Avset
SINTEF ICT, Microsystems and Nanotechnology, P.O. Box 124 Blindern, N-0314 Oslo, Norway
共Received 21 May 2007; revised manuscript received 9 August 2007; published 28 December 2007兲
Electron-irradiated p+-n−-n+ diodes produced from low-doped high-purity Si wafers were found, by deeplevel transient spectroscopy 共DLTS兲, to have a prominent defect, labeled E4, with an energy level 0.37 eV
1
below the conduction-band edge and a concentration of ⬃ 4 relative to the divacancy. The samples were kept
at room temperature, and the E4 concentration was seen to reduce to half during five weeks. Annealing data
revealed a similar peak E5 overlapping that of the single-negatively charged divacancy and showing a oneto-one proportionality with E4. E4 and E5 arise most likely from a vacancy-type defect and a tentative
assignment to a planar tetravacancy is put forward.
DOI: 10.1103/PhysRevB.76.233204
PACS number共s兲: 61.72.Ji, 61.80.Fe, 71.55.Cn
1098-0121/2007/76共23兲/233204共3兲
meter, is a refined version of one described elsewhere.7 Both
a lock-in-type weighting function and a GS4 weighting
function8 were used to extract the DLTS signal. Subsequently, the concentration, energy level position and apparent capture cross section of the electron traps were derived.
Figure 1 shows the DLTS spectra measured for MCz and
STFZ samples 175 and 28 h after the electron irradiation,
respectively. Alongside the peaks of the vacancy-oxygen
共VO兲, V2共= / −兲 and V2共− / 0兲 levels is also the peak E4 which
has a similar amplitude in the two materials. The STFZ spectrum is multiplied by a factor of 1.05 to remove a 5% difference in the peak amplitudes relative to the MCz sample, well
within the irradiation dose accuracy. After 2036 h at RT, the
E4 peak disappears and a decrease in the amplitude of
V2共− / 0兲 is observed. It will later be shown more clearly that
3
Lock in, (640 ms)
×1
11
−3
cm )
4
2 · Nd · ∆C / Cr (10
Irradiation of Si with high-energy particles causes formation of intrinsic defects, which constitute charge carrier traps
that reduce the concentration of free charge carriers. In most
applications today a change in the charge-carrier concentration is undesired. One such application is the use of Si detectors in the Large Hadron Collider 共LHC兲 and the planned
Super LHC at CERN. With total doses up to 1015–1016 cm−2,
the generation of defects trapping charge carriers is of major
concern, as this trapping is regarded to set the ultimate limit
for operation at very high radiation fluences.1 The radiation
tolerance of Si is, therefore, of great interest, and considerable effort has been put into a series of investigations 共e.g.,
report of the CERN RD50 collaboration2 and references
therein兲.
At the same time, p-n structures fabricated from highpurity detector-grade Si represent an almost ideal model system for studies of fundamental defects. For example, using
such structures, divacancy 共V2兲 migration and interaction
with impurities has been studied in detail,3,4 and electronic
properties of the divacancy-oxygen 共V2O兲 complex have
been investigated.5,6 In this contribution, we have observed
two defect states, presumably of acceptor type, which display a limited stability at room temperature 共RT兲 and can be
a fundamental vacancy-type complex.
Two types of p+-n−-n+ high-purity Si diodes have been
investigated. One type is produced from magneticCzochralski 共MCz兲 wafers with a phosphorus doping of
5 ⫻ 1012 cm−3, while the other is produced from standardfloat-zone 共STFZ兲 wafers with a doping of 4 ⫻ 1012 cm−3.
For the MCz samples the oxygen and carbon concentrations
are found, by secondary-ion mass spectrometry 共SIMS兲,
to be 0.5− 1 ⫻ 1018 cm−3 and ⱕ1016 cm−3, respectively.
For the STFZ samples, the bulk concentration of oxygen
is ⬍5 ⫻ 1015 cm−3; the carbon concentration is
2 − 4 ⫻ 1016 cm−3. Aluminum was used as contact metal. The
samples were kept at RT 共⬃23° C兲 after they had all been
irradiated at RT with 6-MeV electrons to a dose of
5 ⫻ 1012 cm−2.
The setup used for the deep-level transient spectroscopy
共DLTS兲 measurements, based on a HP 4280A capacitance
VO
2
V2(=/−)
−1
MCz 175 h after irradiation
MCz 2036 h after irradiation
STFZ 28 h after irradiation × 1.05
E4
V2(−/0)
1
0
100
150
Temperature (K)
200
FIG. 1. DLTS spectra of MCz and STFZ samples obtained 175
and 28 h after the electron irradiation, respectively, compared with
the spectrum of the MCz sample annealed 2036 h at RT. The
共640 ms兲−1 rate window of the lock-in weighting function is used
and the low-temperature end of the spectrum is reduced by a factor
of 4.
233204-1
©2007 The American Physical Society
PHYSICAL REVIEW B 76, 233204 共2007兲
BRIEF REPORTS
12
VO
V2(=/−)
V2(−/0)
y=x
y = −x
4
Change in concentration (10
10
−3
Trap concentration (cm )
−3
cm )
10
VO (Lock in)
V2(=/−) (Lock in)
V2(−/0) (Lock in)
11
10
E4 (GS4)
10
4.1 × 10
cm
−3
−7
·e
−2.3 × 10
−1
s
·t
10
10
2000
−4
there is also a corresponding increase in the amplitude of
VO.
The trap concentration Nt is deduced from the DLTS spectra using the expression Nt = 2Nd⌬C / Cr at the peak maxima
in the spectra.9 This expression neglects a ⬃10% reduction
due to the depletion depth at zero bias and the so-called
lambda correction.
In Fig. 2, the evolution of the amplitudes of the defect
peaks in the MCz sample is shown. The time dependence of
the E4 concentration is fitted, by the method of least mean
squares, by an exponential curve. The data points have a
slight upwards curvature compared to the exponential fit.
This curvature can be explained by a nonzero baseline in the
spectra causing an offset of ⬃1 ⫻ 1010 cm−3.
Given
the
deduced
annealing
rate
of
E4 of 2.3⫻ 10−7 s−1, one can estimate that the activation
energy is in the range 0.9− 1.2 eV, depending on the prefactor 共typically 109 − 1013 s−1兲.
Figure 3 shows the change in amplitude of the VO,
V2共= / −兲 and V2共− / 0兲 peaks as a function of the loss in amplitude of the E4 peak. It can be seen that the amplitude of
the V2共− / 0兲 peak is reduced by about the same amount as
that of the E4 peak throughout the investigation. Although
the large amplitude of the VO peak causes some scatter, the
VO concentration can be seen to increase with an amount
similar to the loss of E4. No significant change occurs for
V2共= / −兲.
Figure 4 shows the temperature interval 100− 280 K of
the DLTS spectra measured 78, 499, and 1111 h after the
irradiation subtracted by the spectrum measured after
2036 h. The data suggest that the reason for the one-to-one
proportionality between E4 and V2共− / 0兲, shown in Fig. 3, is
a peak overlapping with V2共− / 0兲. This peak, labeled E5, has
an amplitude identical, within the experimental accuracy, to
that of E4 and anneals at the same rate as E4. This observation suggests that the E4 and E5 peaks are due to two different charge states of the same defect.
The signatures of E4 and E5 have been deduced from
1
2
10
−3
Loss in E4 concentration (10 cm )
3
FIG. 3. The data from Fig. 2 rearranged to show defectconcentration changes as a function of the loss in the concentration
of E4. The change of E4 is shown as the line y = −x. The lost
concentration of E4 is shown as y = x.
spectrum differences such as the ones in Fig. 4; an average of
these gives for E4 an energy position at 0.37 eV below the
conduction-band edge and an apparent capture cross section
of 1 ⫻ 10−14 cm2, and the corresponding values for E5 are
0.45 eV and 3 ⫻ 10−15 cm2. The values for the apparent capture cross section are of the same order of magnitude, suggesting significant influence by entropy factors and/or
temperature-dependent cross sections, similar to that found
for the different charge states of V2.10
The presence and annealing of E4 at RT is seen with the
same concentration and rate also in STFZ samples, diffusionoxygenated FZ 共DOFZ兲 samples and hydrogenated samples.
Given the different oxygen and carbon concentrations in
MCz and STFZ material, this indicates a fundamental intrinsic nature of E4.
E4 may be assumed to originate from the previously
observed substitutional-phosphorus–interstitial-carbon 共PsCi兲
4
−1
Lock in, (640 ms)
Nt, 78 h − Nt, 2036 h
MCz Si
−3
FIG. 2. The concentration of the four defect configurations from
Fig. 1 after different annealing times at RT. The concentration of E4
is deduced using the GS4 weighting function and fitted by an exponential curve 共t is the annealing time兲. The other lines are guides
to the eye.
0
cm )
1000
1500
Annealing time (h)
−2
10
500
0
Difference of 2 · Nd · ∆C / Cr (10
0
2
Nt, 499 h − Nt, 2036 h
3
Nt, 1111 h − Nt, 2036 h
E5
2
V2(=/−)
1
0
100
E4
150
V2(−/0)
200
Temperature (K)
250
FIG. 4. The three DLTS spectra calculated from the capacitance
transients measured after 78, 499, and 1111 h subtracted by the
transients measured after 2036 h, respectively. The positions of the
V2共= / −兲, E4, and V2共− / 0兲 peaks are marked for comparison with
Fig. 1.
233204-2
PHYSICAL REVIEW B 76, 233204 共2007兲
BRIEF REPORTS
center which has a similar DLTS signature and is unstable at
RT.11 The samples investigated in the present work, however,
have too low phosphorus concentration relative to the oxygen concentration to form a measurable concentration of
PsCi. In Ref. 11, for instance, no PsCi is detected when the
oxygen-to-phosphorus ratio is 2 ⫻ 103, as most of the Ci is
then captured by oxygen. For the STFZ material in the
present work this ratio is ⱗ1 . 共3兲 ⫻ 103, while for the MCz
material it is ⬃105. The concentration of E4 in the MCz and
STFZ materials is, nevertheless, similar. Hence, an assignment of E4 to PsCi is excluded. Indeed, it seems E4 is not
related to carbon at all, as the carbon-capturing defect needs
to have a high concentration to compete with the formation
of interstitial-carbon–interstitial-oxygen 共CiOi兲 pairs. However, the E4 generation rates are similar in the MCz and
STFZ materials despite the very different carbon-to-oxygen
ratios.
In 7-MeV proton-irradiated DOFZ samples the generation
of E4 is enhanced relative to that of VO and V2 in comparison with the present results for 6-MeV electron irradiation.12
In Ref. 12 E4 共and most likely E5兲 disappears rapidly and is
below the detection limit after 15 min at 50° C. As proton
irradiation causes a higher density of intrinsic defects compared to electron irradiation, the enhanced generation of the
E4 and E5 levels in proton-irradiated samples indicates that
these levels arise from a higher-order center larger than, for
instance, a divacancy. This speculation is further supported
by the small difference in the energy-level positions of the,
presumably, two different charge states. Indeed, as the distance between the dangling bonds is increased in a larger
center, the Coulomb repulsion and thus the difference in
binding energy between the two trapped electrons decreases.
It should be mentioned that peaks similar to E4 and E5
have been observed also in neutron-irradiated Si.13–15 However, these reported peaks do not exhibit a one-to-one ratio in
the amplitudes,13 in contrast to what is shown in Fig. 4. The
absence of a one-to-one ratio between E4 and E5 in neutron-
irradiated Si does not contradict the identification of the levels as two charge states of the same defect, but indirectly
supports it. This difference in peak amplitudes can readily be
explained by incomplete occupation of the shallower state,
similarly to the effect observed for V2共= / −兲 in neutronirradiated Si.14
The correlation between the growth of VO and the loss of
E4 and E5 indicates that E4 and E5 are due to a vacancyrelated defect. This, together with the indication that E4 and
E5 arise from a higher-order defect center, may suggest an
assignment to the 兵110其-planar tetravacancy chain 共V4兲 observed by Lee and Corbett in neutron-irradiated Si.16 This is
also consistent with the speculations of Watts et al.17 In this
context, it should be pointed out that the maximum energy
transfer of a 6-MeV electron to a Si atom is of the order of a
few keV and despite being rather rare events, defect clusters
such as V4 共or even higher order兲 can be formed by recoiling
Si atoms having sufficient energy. The planar V4 exhibits a
rather limited temperature stability which may be consistent
with that of E4 and E5, but further studies must be pursued
for a more definite assignment.
In summary, a defect with a level 0.37 eV below the
conduction-band edge is found to arise when high-purity
n-type Si is electron irradiated. The defect anneals exponentially at RT and has a half-life of about five weeks. Another
defect level, with the same concentration and temperature
stability as the one at 0.37 eV, is found 0.45 eV below the
conduction-band edge. These two levels are presumably due
to two different charge states of the same defect. As the two
defect levels anneal out, an equal increase in the VO concentration occurs. A tentative identification of E4 and E5 as two
charge states of the 兵110其-planar tetravacancy chain is put
forward.
*janhb@fys.uio.no
10
1
C. Da Via and S. J. Watts, Nucl. Instrum. Methods Phys. Res. A
501, 138 共2003兲.
2 URL http://rd50.web.cern.ch
3 M. Mikelsen, E. V. Monakhov, G. Alfieri, B. S. Avset, and B. G.
Svensson, Phys. Rev. B 72, 195207 共2005兲.
4 E. V. Monakhov, A. Ulyashin, G. Alfieri, A. Yu. Kuznetsov, B. S.
Avset, and B. G. Svensson, Phys. Rev. B 69, 153202 共2004兲.
5 G. Alfieri, E. V. Monakhov, B. S. Avset, and B. G. Svensson,
Phys. Rev. B 68, 233202 共2003兲.
6
V. P. Markevich, A. R. Peaker, S. B. Lastovskii, L. I. Murin, and
J. L. Lindström, J. Phys.: Condens. Matter 15, S2779 共2003兲.
7
B. G. Svensson, K.-H. Rydén, and B. M. S. Lewerentz, J. Appl.
Phys. 66, 1699 共1989兲.
8
A. A. Istratov, J. Appl. Phys. 82, 2965 共1997兲.
9 D. V. Lang, J. Appl. Phys. 45, 3023 共1974兲.
Fruitful discussions with Ioana Pintilie, Michael Moll,
Eckhart Fretwurst, and Gunnar Lindström, and financial
support by the Norwegian Research Council are greatly
appreciated.
A. Hallén, N. Keskitalo, F. Masszi, and V. Nágl, J. Appl. Phys.
79, 3906 共1996兲.
11 M. T. Asom, J. L. Benton, R. Sauer, and L. C. Kimerling, Appl.
Phys. Lett. 51, 256 共1987兲.
12 E. V. Monakhov, B. S. Avset, A. Hallén, and B. G. Svensson,
Phys. Rev. B 65, 233207 共2002兲.
13 M. Moll, Ph.D. thesis, University of Hamburg, Hamburg 1999.
14 M. Moll, E. Fretwurst, M. Kuhnke, and G. Lindström, Nucl. Instrum. Methods Phys. Res. B 186, 100 共2002兲.
15 R. M. Fleming, C. H. Seager, D. V. Lang, E. Bielejec, and J. M.
Campbell, Appl. Phys. Lett. 90, 172105 共2007兲.
16 Y.-H. Lee and J. W. Corbett, Phys. Rev. B 9, 4351 共1974兲.
17 S. J. Watts, J. Matheson, I. H. Hopkins-Bond, A. Holmes-Siedle,
A. Mohammadzadeh, and R. Pace, IEEE Trans. Nucl. Sci. 43,
2587 共1996兲.
233204-3
IV
APPLIED PHYSICS LETTERS 92, 132102 共2008兲
On the identity of a crucial defect contributing to leakage current
in silicon particle detectors
J. H. Bleka,1,a兲 L. Murin,2 E. V. Monakhov,1 B. S. Avset,3 and B. G. Svensson1
1
Department of Physics, Physical Electronics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo,
Norway
2
Joint Institute of Solid State and Semiconductor Physics, National Academy of Sciences of Belarus,
220072 Minsk, Belarus
3
Microsystems and Nanotechnology, SINTEF ICT, P.O. Box 124 Blindern, N-0314 Oslo, Norway
共Received 7 February 2008; accepted 21 February 2008; published online 31 March 2008兲
The annealing kinetics of the so-called E4/E5 center or E4a/E4b center in electron-irradiated Si
particle detectors has been studied at four different temperatures from 23 to 65 ° C using deep-level
transient spectroscopy 共DLTS兲. The center gives rise to two energy levels at 0.37 and 0.45 eV below
the conduction-band edge, and the annealing process is found to be of dissociative nature with an
energy barrier of 1.1– 1.2 eV. A striking similarity of the annealing rates 共and kinetics兲 is revealed
with that obtained for the 936- cm−1 infrared absorption band, studied by Fourier-transform infrared
spectroscopy using identical type of Si material as in the DLTS study but irradiated with neutrons.
The result strongly suggest that the E4/E5 levels and the 936- cm−1 band originate from the same
defect, and the latter has been attributed to a di-interstitial-oxygen 共I2O兲 complex. The E4/E5 center
plays a crucial role for the detrimental leakage current in irradiated Si particle detectors, and an
assignment of E4/E5 to I2O implies that oxygen-lean Si material 共⬍1014 cm−3兲 should be
advantageous to enhance detector performance. © 2008 American Institute of Physics.
关DOI: 10.1063/1.2896313兴
Si detectors are widely used to provide particle detection
and localization in a variety of applications, ranging from
high-energy physics experiments to medical studies. Because
of a high signal-to-noise ratio, high spatial resolution, and
fast direct charge readout, these detectors are ideal for such
use. The detectors suffer, however, from considerable degradation of their performance in intense radiation environment
with fluences up to 1014 – 1015 cm−2 as, for instance, in the
Large Hadron Collider1 共LHC兲 and as high as 1016 cm−2 in
the future Super LHC at CERN. The radiation tolerance of Si
detectors is, therefore, of great concern, and considerable
efforts have been devoted in a series of investigations 共see
Ref. 2 and references therein兲.
Also, other semiconductor devices, such as bipolar transistors, are affected by ionizing radiation. For instance,
Fleming et al.3 have addressed the observation of slow improvements of the gain in Si bipolar transistors at room temperature 共RT兲 after an initial degradation due to neutron irradiation. This improvement was correlated with the annealing
of an unidentified, electrically active center.
p-n structures fabricated from high-purity detector-grade
Si represent an excellent model system for studies of fundamental point defects. For example, using such structures, divacancy 共V2兲 migration and interaction with impurities have
been studied in detail,4,5 and electronic properties of the
divacancy-oxygen 共V2O兲 complex have been revealed.6,7
Furthermore, it has recently been shown that in electronirradiated samples an intrinsic defect exists with two energy
levels at 0.37 eV below the conduction-band edge 共Ec兲, labeled E4, and at Ec − 0.45 eV, labeled E5.8 These levels were
tentatively assigned to different charge states of a vacancy
cluster, and it was speculated that a possible candidate for
a兲
Electronic mail: janhb@fys.uio.no.
such a cluster is a 兵110其-planar tetravacancy chain 共V4兲. Two
similar energy levels were previously reported in neutronand proton-irradiated Si,9,10 and the annealing of the E5 level
has been seen to have a strong correlation with the initial
stage of a reduction of the leakage current in Si detectors.11 It
has also been shown that the concentration of what appears
to be the E4/E5 center increases when a large forward current density 共12.5 A / cm2兲 flows through the device at RT.3
In the present contribution, we investigate the thermal
stability and annealing kinetics of the E4/E5 center, measured by deep-level transient spectroscopy 共DLTS兲, and compare to that of the di-interstitial-oxygen 共I2O兲 complex, measured by Fourier-transform infrared 共FTIR兲 spectroscopy.
We also discuss how the annealing of these defects can be
related to the reduction of the leakage current in Si particle
detectors.
p+-n−-n+ detector structures 共diodes兲 produced from
high-purity magnetic-Czochralski 共MCz兲 Si wafers with a
phosphorus doping of 5 ⫻ 1012 cm−3 were used for the DLTS
investigations. The oxygen concentration and carbon concentration have been found, by secondary-ion mass spectrometry, to be 共0.5– 1兲 ⫻ 1018 cm−3 and 艋1016 cm−3, respectively. Aluminum was used as the contact metal. The diodes
were irradiated at RT with 6 - MeV electrons to a dose of
5 ⫻ 1012 cm−2, and then stored at −19 ° C after a period of
28 h at RT for sample transport.
For the FTIR investigations, samples were cut from a
similar MCz material as used for the DLTS investigations
and then irradiated at RT with 1 - MeV neutrons to doses of
1 ⫻ 1016 and 3 ⫻ 1016 cm−2.
The setup used for the DLTS measurements is a refined
version of one described elsewhere.12 The IR-absorption
measurements were carried out at ⬃20 and ⬃300 K using a
0003-6951/2008/92共13兲/132102/3/$23.00
92, 132102-1
© 2008 American Institute of Physics
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
132102-2
Appl. Phys. Lett. 92, 132102 共2008兲
Bleka et al.
FIG. 1. DLTS spectra measured after different annealing times at 65 ° C.
The VO peak is reduced by a factor of 4. The background signal 共the dotted
line at ⬃1 ⫻ 1010 cm−3兲, used for correcting the E4 concentration, is obtained by fitting the outannealing of the E4 level.
Bruker 113v FTIR spectrometer. The spectral resolution was
0.5 or 1.0 cm−1.
Four electron-irradiated diodes were annealed isothermally at ⬃23, 40.5, 55, and 65 ° C, respectively. Figure 1
shows the DLTS spectra, extracted using the GS4 weighting
function13 to get well-resolved peaks, for the sample annealed at 65 ° C for three different durations. The nonannealed spectrum reveals the vacancy-oxygen 共VO兲
center,14–16 the level of the doubly negatively charged divacancy 关V2共= / −兲兴,17–19 the E4 level,3,8,9,11 and the singly negatively charged divacancy 关V2共− / 0兲兴 共Refs. 14, 18, and 19兲
with the overlapping E5 level.3,8,9,11 The concentration of E4
共关E4兴兲 is identical to that of E5, and both peaks are reduced
simultaneously during annealing, supporting previous conclusions that the two levels originate from the same
defect.8–10 All the four diode samples studied show similar
annealing behavior: The V2共= / −兲 and V2共− / 0兲 peaks remain
unchanged, and the E4 and E5 peaks disappear with similar
rates.
The concentration deduced from the E4 peak versus the
annealing time can be fitted by the expression 关E4兴0e−ct
+ N⬁, where t is the annealing time, and the three fitting
parameters are 关E4兴0 共关E4兴 at t = 0兲, c 共the annealing rate兲,
and N⬁ 共the background signal in the DLTS spectra兲. Table I
shows the result of this fitting procedure performed for all
the four different annealing temperatures. The similarity of
the values obtained for N⬁ indicates that it is indeed reasonable to include a free parameter for the background signal in
the fitting routine.
To compare the annealing behavior at the four different
temperatures, the concentrations deduced from the E4 peak
are subtracted by N⬁, then normalized by 关E4兴0 and plotted
FIG. 2. Annealing kinetics of the E4 level at four different temperatures.
The amplitudes of the E4 peak are subtracted by the background signal, N⬁,
and normalized by 关E4兴0. The time is scaled by the respective annealing
rates for different temperatures 共Table I兲. The dotted line represents firstorder kinetics.
as a function of ct. The result is shown in Fig. 2, where all
the data are demonstrated to follow closely first-order kinetics, represented by the dotted line.
Figure 3 shows an Arrhenius plot of the data given in
Table I. A least-squares fit 共dashed line兲 to the DLTS results
gives an activation barrier of 1.27 eV and a pre-exponential
factor of 2 ⫻ 1015 s−1. The first-order kinetics and the large
value for the prefactor indicate that the E4/E5 defect anneals
out by a dissociative process or by a transformation of the
atomic configuration, as these processes normally have prefactors similar to the Debye frequency.20 The four data points
for the E4 annealing 共black squares兲 exhibit some scatter
relative to the exponential fit. The maximum uncertainty in
Tann is for the RT-annealed sample with a value of ⬃2 K, but
because the annealing rates range over three orders of magnitude, the Arrhenius plot is not particularly sensitive to the
uncertainty in Tann. The determination of the background signal in the DLTS spectra is probably the largest source of
error.
TABLE I. Optimal parameters for fitting the outannealing of the E4 peak by
the expression 关E4兴0e−ct + N⬁ 共see text兲. Tann is the annealing temperature.
Tann 共°C兲
关E4兴0 共1010 cm−3兲
c 共s−1兲
N⬁ 共1010 cm−3兲
⬃23
40.5
55
65
3.1
2.3
2.6
3.8
4.39⫻ 10−7
1.46⫻ 10−5
8.47⫻ 10−5
2.03⫻ 10−4
0.93
0.98
1.12
1.01
FIG. 3. Arrhenius plot of the annealing rates 共c兲 obtained by DLTS 共squares;
values from Table I兲 and FTIR 共crosses兲 vs the reciprocal annealing temperature 共Tann兲. The dashed line is a least-squares fit by an exponential curve
to the four data points measured by DLTS. The solid line is the corresponding fit to all the points of both techniques. kB is Boltzmann’s constant.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
132102-3
Appl. Phys. Lett. 92, 132102 共2008兲
Bleka et al.
Included in Fig. 3 are also the annealing rates measured
by FTIR for the 936- cm−1 band 共crosses兲. Three of these
data points are obtained by isothermal annealing at 45, 60,
and 80 ° C, respectively, of samples neutron irradiated to a
dose of 1 ⫻ 1016 cm−2, and the annealing process shows firstorder kinetics. At 80 ° C, a sample irradiated to a dose of
3 ⫻ 1016 cm−2 was also studied, resulting in a point very
close to that obtained from the low-dose sample.
The solid line in Fig. 3 shows the best fit to all data
points obtained by both DLTS and FTIR. The resulting activation energy is 1.1共2兲 eV with a prefactor of 9 ⫻ 1012 s−1.
Considering that these are results from two different techniques, from samples irradiated with different particles and
doses causing entirely different concentrations of defects
共⬃1013 cm−3 in DLTS versus ⬃1016 cm−3 in FTIR兲, the data
in the Arrhenius plot follow the exponential fit remarkably
well, and it appears justified to suggest that the defect giving
rise to the energy levels E4 and E5 and that giving rise to the
936- cm−1 band are of the same origin. Here, it should be
emphasized that the first-order kinetics observed by both
DLTS and FTIR is of crucial importance since otherwise a
direct comparison between the annealing rates is not valid.
Hermansson et al.21 concluded that the 936- cm−1 band
is most likely due to a I2O complex.21,22 The identification of
the E4/E5 defect as a I2O complex is consistent with many of
the observed properties: E4/E5 is a fundamental defect, as it
occurs with the same concentration 共generation rate兲 regardless of whether the samples are MCz 共high oxygen concentration and low carbon concentration兲, standard float zone
共FZ兲 共low oxygen and low carbon兲, or diffusion-oxygenated
FZ 共high oxygen and low carbon兲, and irrespective of
whether or not the samples have been hydrogenated.8 The
lack of dependence on the oxygen concentration can readily
be explained by the availability of I2 being the limiting factor
for the formation of I2O in the concentration regime studied
共艋1013 cm−3兲. Also, the defect is expected to be of higher
order as it seems to have a projectile-mass dependence, and
the relatively small difference in energy position between the
E4 and E5 levels can be accounted for if the defect is of
higher order.8 However, by assigning the E4/E5 defect to
I2O, it is not obvious to explain the one-to-one correlation
between the loss of 关E4/E5兴 and the increase of 关VO兴 reported in Ref. 8, unless the dissociation/transformation process of I2O gives rise to VO centers. Further work is being
pursued to resolve this issue.23
In a study by Moll et al.,11 the annealing of the E5 level
was shown to strongly correlate with a reduction in the detector leakage current, and it seems very plausible that the
exponential contribution to the reduction in the leakage
current is due to the dissociation or reconfiguration of the
E4/E5 center. In particular, the E5 level is located close to
the middle of the band gap and constitutes an effective
recombination/generation center. Moll9 has also shown that
the leakage current is similar using several different types of
Si material. This, together with the observed material independence of the E4/E5 defect, further strengthens the argument that the E5 level is directly associated with the leakage
current.
In conclusion, annealing studies of the E4/E5 center,
monitored by DLTS, and the I2O center, monitored by FTIR,
strongly suggest that the E4/E5 center may be identified as
I2O. The combined results from DLTS and FTIR yield an
energy barrier of 1.1 eV for an annealing process of dissociative nature. The leakage current in irradiated Si particle
detectors hinges closely on the concentration of E4/E5
centers; the results from the present work strongly imply
that the concentration of oxygen should be minimized
共艋1014 cm−3兲 to suppress the formation of I2O centers and
hence reduce the detrimental leakage current.
Fruitful discussions with Ioana Pintilie, Eckhart
Fretwurst, and Gunnar Lindström, and financial support by
the Norwegian Research Council are greatly appreciated.
This work was partly performed within the frame of the
RD50 CERN collaboration.
S. Stapnes, Nature 共London兲 448, 290 共2007兲.
URL http://rd50.web.cern.ch.
3
R. M. Fleming, C. H. Seager, D. V. Lang, E. Bielejec, and J. M. Campbell,
Appl. Phys. Lett. 90, 172105 共2007兲.
4
M. Mikelsen, E. V. Monakhov, G. Alfieri, B. S. Avset, and B. G. Svensson, Phys. Rev. B 72, 195207 共2005兲.
5
E. V. Monakhov, A. Ulyashin, G. Alfieri, A. Yu. Kuznetsov, B. S. Avset,
and B. G. Svensson, Phys. Rev. B 69, 153202 共2004兲.
6
G. Alfieri, E. V. Monakhov, B. S. Avset, and B. G. Svensson, Phys. Rev.
B 68, 233202 共2003兲.
7
V. P. Markevich, A. R. Peaker, S. B. Lastovskii, L. I. Murin, and J. L.
Lindström, J. Phys.: Condens. Matter 15, S2779 共2003兲.
8
J. H. Bleka, E. V. Monakhov, B. G. Svensson, and B. S. Avset, Phys. Rev.
B 76, 233204 共2007兲.
9
M. Moll, Ph.D. thesis, University of Hamburg, 1999.
10
M. Ahmed, S. J. Watts, J. Matheson, and A. Holmes-Siedle, Nucl. Instrum. Methods Phys. Res. A 457, 588 共2001兲.
11
M. Moll, E. Fretwurst, M. Kuhnke, and G. Lindström, Nucl. Instrum.
Methods Phys. Res. B 186, 100 共2002兲.
12
B. G. Svensson, K.-H. Rydén, and B. M. S. Lewerentz, J. Appl. Phys. 66,
1699 共1989兲.
13
A. A. Istratov, J. Appl. Phys. 82, 2965 共1997兲.
14
S. D. Brotherton and P. Bradley, J. Appl. Phys. 53, 5720 共1982兲.
15
L. W. Song, X. D. Zhan, B. W. Benson, and G. D. Watkins, Phys. Rev. B
42, 5765 共1990兲.
16
N. Keskitalo, A. Hallén, J. Lalita, and B. G. Svensson, Mater. Res. Soc.
Symp. Proc. 469, 233 共1997兲.
17
A. O. Evwaraye and E. Sun, J. Appl. Phys. 47, 3776 共1976兲.
18
L. C. Kimerling, Radiation Effects in Semiconductors 1976 共IOP, Bristol,
1977兲, p. 221.
19
B. G. Svensson and M. Willander, J. Appl. Phys. 62, 2758 共1987兲.
20
J. W. Corbett, Electron Radiation Damage in Semiconductors and Metals
共Academic, New York, 1966兲, p. 39.
21
J. Hermansson, L. I. Murin, T. Hallberg, V. P. Markevich, J. L. Lindström,
M. Kleverman, and B. G. Svensson, Physica B 302, 188 共2001兲.
22
G. Davies, S. Hayama, L. Murin, R. Krause-Rehberg, V. Bondarenko, A.
Sengupta, C. Da Via, and A. Karpenko, Phys. Rev. B 73, 165202 共2006兲.
23
L. Vines 共unpublished兲.
1
2
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
V
PHYSICAL REVIEW B 77, 073206 共2008兲
Rapid annealing of the vacancy-oxygen center and the divacancy center by diffusing hydrogen
in silicon
J. H. Bleka,1,* I. Pintilie,2 E. V. Monakhov,1 B. S. Avset,3 and B. G. Svensson1
1Department
of Physics, Physical Electronics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
Institute for Experimental Physics, Hamburg University, D-22761 Hamburg, Germany
and National Institute of Materials Physics, Bucharest-Magurele 077125, Romania
3Microsystems and Nanotechnology, SINTEF ICT, P.O. Box 124 Blindern, N-0314 Oslo, Norway
共Received 5 September 2007; revised manuscript received 2 November 2007; published 26 February 2008兲
2
In hydrogenated high-purity Si, the vacancy-oxygen 共VO兲 center is shown to anneal already at temperatures
below 200 ° C and is replaced by a center, identified as a vacancy-oxygen-hydrogen complex, with an energy
level 0.37 eV below the conduction-band edge and a rather low thermal stability. At long annealing times, the
process is reversed and the concentration of the latter defect is reduced, while the VO center partly recovers.
The divacancy 共V2兲 center anneals in parallel with the initial annealing of the VO center, and the loss in V2
exhibits a one-to-one proportionality with the appearance of a hole trap 0.23 eV above the valence-band edge
attributed to a divacancy-hydrogen 共V2H兲 center.
DOI: 10.1103/PhysRevB.77.073206
PACS number共s兲: 71.55.Cn, 66.30.J⫺, 61.80.Fe
1098-0121/2008/77共7兲/073206共4兲
hydrogenated sample measured prior to and after three different annealing times at 195 ° C. The DLTS spectrum recorded after the electron irradiation shows three major peaks
related to the VO center and the V2 center. A peak labeled
E1, which is not detectable in nonhydrogenated control
samples, is seen as a small shoulder on the V2共− / 0兲 peak.
Here, it is important to emphasize that E1 should not be
confused with the level referred to as E4 and recently discussed in detail in Ref. 16. Despite having almost identical
DLTS signatures, E1 and E4 originate from different defects;
E4 is unstable already at RT and occurs with the same concentration irrespective of the hydrogen content, in direct contrast to that of E1 which does not appear in nonhydrogenated
control samples. In fact, E4 was found to disappear in the
studied hydrogenated samples long time 共up to nine months
storage at RT兲 before the annealing at elevated temperatures
was undertaken. Moreover, the E4 level is never observed
without a corresponding energy level at Ec − 0.45 eV; this
11
−3
cm )
8
2 Nd ∆C / Cr (10
Hydrogen in Si readily reacts with vacancy-type defects
by passivating the dangling bonds. It is known, for instance,
that the vacancy-oxygen 共VO兲 center and the divacancy 共V2兲
center disappear at low temperatures in the presence of
hydrogen.1 The VO center is believed to be transformed into
a VOH center,2–10 while the annealing mechanism for the V2
center is less documented. Evidence for the existence of a
V2H center has been obtained by electron-paramagneticresonance measurements,2 and based mainly on comparison
of the threshold temperatures during isochronal annealing of
V2 and V2H, a level at about Ec − 0.43 eV 共Ec being the energy of an electron at the conduction-band edge兲 has been
tentatively assigned to V2H.9
Further, in contrast to the diffusion of molecular hydrogen, where the activation energy was firmly established ten
years ago,11 the diffusivity of monatomic hydrogen has been
more difficult to determine. Reported values for the migration energy of monatomic hydrogen range from 0.48 eV
共Ref. 12兲 to 1.2 eV 共Ref. 13兲 and, presumably, depend on the
charge state of the hydrogen. Recently, it has been shown
that the lower value of these activation energies is close to
that of the diffusivity of protons.14
In the present work, hydrogen-assisted annealing of
vacancy-type defects in irradiated high-purity Si is studied,
by deep-level transient spectroscopy 共DLTS兲, to reveal which
mechanisms are present and to clarify which form of hydrogen is involved during different annealing stages.
The samples investigated were p+-n−-n+ Si diodes produced from high-purity detector-grade magnetic-Czochralski
wafers with a phosphorous concentration of 5 ⫻ 1012 cm−3.
Hydrogen was introduced by submerging the samples in 10%
hydrofluoric acid at 50 ° C for 21 h. Aluminum contacts were
deposited before irradiation at room temperature 共RT兲 with
6-MeV electrons to a dose of 5 ⫻ 1012 cm−2. The concentrations of oxygen and carbon were found, by secondary-ion
mass spectrometry, to be 共0.5– 1兲 ⫻ 1018 cm−3 and
艋1016 cm−3, respectively. The setup used for the DLTS measurements is a refined version of one described elsewhere.15
Figure 1 shows the results of DLTS measurements for a
6
−1
Nonannealed
8 min at 195 °C
158 min at 195 °C
1740 min at 195 °C
Lock in, (640 ms)
VO
E1
4
2
V2(=/−)
V2(−/0)
Vbias = −10 V
Vpulse = 0 V
0
−2
−4
H1
100
CiOi
×
1
3
150
200
Temperature (K)
Vbias = −10 V
Vpulse = 3 V
250
FIG. 1. DLTS spectra at four different annealing stages of a
hydrogenated sample measured with 共Vpulse = 3 V兲 and without
共Vpulse = 0 V兲 forward injection. An estimate for the trap concentration, which does not account for the so-called lambda effect, can be
read out at each of the peaks 共Ref. 17兲.
073206-1
©2008 The American Physical Society
PHYSICAL REVIEW B 77, 073206 共2008兲
BRIEF REPORTS
Trap concentration (10
11
−3
cm )
12
10
8
VO
V2(=/−)
E1
VO + E1
6
4
Tann = 150 °C
2
0
0
5
10
15
3
Annealing time (10 min)
20
cm )
10
VO
V2(=/−)
E1
H1
VO + E1
V2(=/−) + H1
Trap concentration (10
11
−3
8
6
Tann = 195 °C
4
2
0
0
100
200
300
Annealing time (min)
400
FIG. 2. Time dependence of the defect concentrations in two
samples annealed isothermally at 150 and 195 ° C 共the sample from
Fig. 1兲, respectively. 关H1兴 is measured only for the latter.
function of the loss in 关VO兴 and 关V2兴, respectively. The data
points of 关E1兴 versus 关VO兴 appear close to the line y = x for
both temperatures as 关E1兴 first increases and later decreases.
The figure also shows that the appearance of the H1 center
E1 vs VO (150 °C)
E1 vs VO (195 °C)
H1 vs V2(=/−) (195 °C)
y=x
−3
cm )
5
4
11
Change in [E1] and [H1] (10
level appears with the same concentration as E4, indicating
that the complex causing E4, unlike the E1 center, has two
charge states in the upper half of the band gap.16 All four
DLTS spectra in Fig. 1 measured with forward injection
show the presence of a major hole trap identified as the
interstitial-carbon–interstitial-oxygen 共CiOi兲 center. After the
initial 8-min anneal, the concentration of the VO center
共关VO兴兲 has decreased by 35% and the E1 peak has grown
with an amplitude similar to the reduction of the VO peak.
The concentration of the V2 center 共关V2兴兲 has dropped by
55%, concurrent with the appearance of the hole trap labeled
H1. It should be pointed out that nonhydrogenated control
samples show no annealing of the VO center and V2 center
during the anneals up to 200 ° C.
The E1 level is found at Ec − 0.37 eV and has an apparent
electron capture cross section of 8 ⫻ 10−15 cm2. The energy
level measured for the H1 center is found to be at Ev
+ 0.23 eV 共Ev being the energy of an electron at the top of
the valence band兲 with an apparent hole capture cross section
of 1 ⫻ 10−13 cm2.
By employing a concept outlined by Hallén et al.18 involving minority-carrier injection and a double-pulse sequence for majority carriers, the H1 center was found to
exhibit an effective hole capture cross section several orders
of magnitude larger than that for electrons 共10−14 cm2 versus
10−19 cm2 at 100 K兲. These values suggest a complete occupation of the H1 center during DLTS measurements with
forward injection, resulting in a direct correspondence of the
amplitude of the H1 peak with the concentration of H1 centers.
The trends continue as the hydrogenated sample is annealed for 158 min: The loss in 关VO兴 is similar to the gain in
关E1兴, and the loss in 关V2兴 is similar to the further increase in
关H1兴. After the sample has been annealed for 1740 min,
关VO兴 has recovered by ⬃50% from the 158-min anneal and
a similar loss is seen for 关E1兴. The apparent transformation
of V2 to H1 is completed after the 158-min anneal, and
within the experimental accuracy, no further changes are observed after the 1740-min anneal.
Figure 2 shows the concentration of the various defects as
a function of time in two hydrogenated samples annealed
isothermally at 150 and 195 ° C, respectively. Similar annealing behavior is seen at both temperatures: 关VO兴 is reduced at
a high rate initially, but is partly recovered after longer annealing times, and 关V2兴 is reduced at an even higher relative
rate compared to 关VO兴 in the early stage, and continues to
decrease at a lower rate in the stages where 关VO兴 has ceased
to decrease. The sum of 关VO兴 and 关E1兴 is constant, within
the experimental accuracy. For the sample annealed at
195 ° C, 关H1兴 was also measured and the sum of 关V2兴 and
关H1兴 remains constant, within the experimental accuracy.
关H1兴 is taken as the value at the H1 peak subtracted by the
background signal in this temperature range. The appearance
of the H1 center has also been detected during isochronal
annealing studies at temperatures below 195 ° C and a similar correlation to 关V2兴 is observed.19
The close one-to-one proportionality between the variations in 关VO兴 and 关E1兴, and 关V2兴 and 关H1兴, is also illustrated
in Fig. 3, where the gain in 关E1兴 and 关H1兴 is shown as a
3
E1 vs VO (195 °C)
10 µm
35 µm
60 µm
2
5
1
0
0
0
0
5
1
4
2
3
11
−3
Loss of [VO] and [V2(=/−)] (10 cm )
5
FIG. 3. Correlation of the change in 关E1兴 and 关H1兴 to the loss in
关VO兴 and 关V2兴, respectively. The concentrations are from Fig. 2.
The inset has axes units identical to those of the main graph and
shows the correlation of the change in 关E1兴 to the loss in 关VO兴
deduced from depth profiles 共see Fig. 5兲 at three different depths.
073206-2
PHYSICAL REVIEW B 77, 073206 共2008兲
−3
V2(=/−) (195 °C)
10
VO + E1
VO
E1
V2(=/−)
11
Conc. (10
1
H1 (195 °C)
y = −0.30x
y = 0.30x
5
0 min
8 min
0
10
11
−3
cm )
0
Conc. (10
Change in [H1] and [V2(=/−)] (10
cm )
V2(=/−) (150 °C)
2
11
−3
cm )
BRIEF REPORTS
−1
5
1740 min
158 min
0
−2
0
0
1
2
3
11
−3
Loss of [VO] (10 cm )
4
FIG. 4. Correlation of the change in 关H1兴 and 关V2兴 to the loss in
关VO兴 共concentrations from Fig. 2兲. The solid line is fitted to the V2
points. The broken line is a reflection of the solid one.
has a correlation to the disappearance of the V2 center, which
is nearly one to one. The concentrations in this plot are extracted from the DLTS signal and are, thus, weighted averages of the defect concentrations between the depletion
depths with Vbias = 0 V and Vbias = −10 V, respectively. The
correlation between 关E1兴 and 关VO兴 shown in the inset is
derived from concentrations measured at specific depths, and
it shows a similar picture as that obtained from the weighted
average of the defect concentrations.
Figure 4 shows the change in 关H1兴 and 关V2兴 versus the
loss in 关VO兴 during the initial stage of the annealing. The
losses in 关V2兴 and 关VO兴 are correlated, and the data can be
closely fitted by the line y = −0.30x. The data points of 关H1兴
versus 关VO兴 lie close to the line y = 0.30x. The small deviation from this line is within the experimental uncertainty, but
is practically constant and may be due to an uncertainty in
the DLTS background.
The initial value of 关VO兴 is a factor of 5.2 larger than that
of 关V2兴. If the VO center and the V2 center anneal with the
same relative rate, the data for the change in 关V2兴 versus that
in 关VO兴 should follow a line with the slope 共5.2兲−1 = 0.19 共cf.
0.30 in Fig. 4兲. Isochronal annealing of samples similar to
those used in this study shows that the V2 center anneals out
together with the VO center, but at a slightly higher relative
rate, for all temperatures in the range from 100 to 225 ° C.19
It is, therefore, reasonable to assume that the VO center and
the V2 center interact with the same migrating species, but
with different probabilities. Since this difference in probability is, as revealed in Fig. 4, independent of the annealing
temperature, it is most likely caused by a difference in capture radius rather than in reaction barrier. The observations
can be explained by the V2 center having a capture radius
0.30/ 0.19⬇ 1.6 times that of the VO center, which seems
plausible considering the geometrical size of the two defects.
Figure 5 displays the depth profiles, corrected for the
lambda effect, of 关VO兴, 关E1兴, and 关V2兴 at each of the four
annealing steps shown in Fig. 1. In the nonannealed state
after the electron irradiation, 关E1兴 is too low for a depth
20
40
Depth (µm)
60
20
40
Depth (µm)
60
FIG. 5. Depth profiles of the four major electron traps at each of
the annealing steps 共195 ° C兲 shown in Fig. 1.
profile to be measured. The absence of hydrogen-related
peaks 共such as, e.g., E1 and VOH兲 does, however, show that
the hydrogen is mainly located shallower than the zero-bias
depletion width 共⬃5 ␮m兲. After the 8-min anneal, 关VO兴 and
关V2兴 are reduced in the near-surface region, while 关E1兴 increases toward the surface. The sum of the profiles of 关VO兴
and 关E1兴 after the 8-min annealing step is similar to the
profile of 关VO兴 before the annealing; this suggests strongly
that a certain configuration of hydrogen, Hx, is released at the
surface of the sample and diffuses into the bulk, causing the
reactions VO + Hx → VOHx and V2 + Hx → V2Hx, where E1 is
identified as VOHx. The signal from the V2 center is rather
weak already after the 8-min anneal, but it is evident that the
profile of 关V2兴 also decreases toward the surface, possibly
with a slightly higher relative rate than that of the VO center
共which is expected to be the case if the V2 center has a larger
capture radius for Hx兲.
The depth profiles measured after annealing for 158 min
show that more hydrogen has entered the sample from the
front-surface side and more VO centers are transformed into
E1 centers. 关V2兴 is hardly measurable at this stage.
Annealing for 1740 min causes VOHx to break up in the
reaction VOHx → VO + Hx. 关E1兴 is reduced at all depths,
while the sum of 关VO兴 and 关E1兴 is still similar to the initial
关VO兴. Thus, VOHx is rather unstable and appears to have a
high concentration only as long as there is a large supply of
Hx. The latter consideration is further supported by the annealing behavior of the V2 center as the dissociation of VOHx
constitutes a source of Hx. As a result, annealing of the V2
center continues after the Hx surface source is exhausted and
the annealing of the VO center has ceased 共see Fig. 2兲.
The diffusion coefficient of molecular hydrogen 共H2兲 is
reported to have an activation energy of 共0.78⫾ 0.05兲 eV
with a preexponential factor of 共2.6⫾ 1.5兲 ⫻ 10−4 cm2 / s.11
Assuming a one-dimensional diffusion of H2 from the
surface at 195 ° C shows that an unphysical amount
共Ⰷ10300 cm−2兲 of H2 is required in the surface region to obtain a concentration of 1012 cm−3 at a depth of 30 ␮m. In
addition, VOH2 is, from theoretical work, expected to be
electrically inactive.10 Hence, an identification of Hx as H2
does not appear to be likely.
073206-3
PHYSICAL REVIEW B 77, 073206 共2008兲
BRIEF REPORTS
On the other hand, the one-dimensional diffusion model
shows that if the diffusivity of protons is assumed, monatomic hydrogen is sufficiently mobile to provide the amount
of hydrogen required to account for the profiles in Fig. 5.
Atomic hydrogen is known to interact with the VO center
and form the well-established VOH center.2–10 VOH exhibits
a rather high stability 共⬃350 ° C兲 and gives rise to one acceptorlike level at ⬃0.32 eV below Ec and one donorlike
level at ⬃0.28 eV above Ev. Levels with such positions and
thermal properties are not found in this study and, hence, E1
cannot be ascribed to the previously established VOH center.
The most consistent interpretation seems to be that Hx is
positively charged monatomic hydrogen, which combines
with the VO center to form a complex with an atomic configuration different from that of the established VOH center.
Thus, the E1 center is assigned to a VOH* center, being a
more unstable configuration than VOH. This assignment implies that the established reaction causing hydrogen and VO
to combine into the VOH center must have a formation barrier larger than that of the VOH* center. This is consistent
with the fact that the formation of the VOH center normally
occurs at higher temperatures than the ones used in the
present study. The assignment of Hx to atomic hydrogen is
further supported by the fact that the boron-hydrogen center
in the p+ layer is anticipated to release monatomic hydrogen
at ⬃100 ° C.20
Our results provide clear evidence that the VO center and
the V2 center anneal through interaction with the same species, and if Hx is monatomic hydrogen, the hydrogen-driven
annealing of the V2 center is expected to result in the V2H
center through the reaction V2 + H → V2H. It has been speculated that the V2H center has a level at ⬃0.43 eV below
Ec,2,9 but this level is not observed in the present study. In
fact, the close one-to-one proportionality between the loss in
关V2兴 and the increase in 关H1兴 strongly favors an assignment
of H1 to V2H. This implies that V2H has only a donor level
in the band gap, which is in direct contrast to V2 having two
acceptor levels and one donor level in the band gap:
V2共= / −兲 at Ec − 0.23 eV, V2共− / 0兲 at Ec − 0.43 eV, and
V2共0 / + 兲 at Ev + 0.19 eV. V2共0 / + 兲 cannot be observed by
performing DLTS with hole injection, because the capture
cross section for electrons is considerably larger than that for
holes, resulting in a very low hole occupancy of this charge
state.18 When a hydrogen atom is captured by the V2 center,
it is believed to partially passivate the center, causing the
disappearance of the 共= / −兲 transition, while the 共− / 0兲 transition remains. Thus, V2H may be expected to have two levels: V2H共− / 0兲 and V2H共0 / + 兲, with activation energies similar to the corresponding ones of V2. The interpretation of the
present results is partially in disagreement with this picture:
The V2H共0 / + 兲 level, at Ev + 0.23 eV, is similar to V2共0 / + 兲,
but a V2H共− / 0兲 level is not observed. It should also be
pointed out that the H1 level, unlike V2共0 / + 兲, can be saturated with forward-injection DLTS; this supports a modified
atomic configuration of V2H compared to that of V2.
In summary, a hydrogen-mediated annealing mechanism,
acting at low temperature, for the VO center and the V2 center has been revealed. A one-to-one proportionality is found
between the changes in 关VO兴 and 关E1兴. The E1 center gives
rise to a level at Ec − 0.37 eV, and is identified as a vacancyoxygen center with a loosely bound hydrogen atom 共VOH*兲.
As the hydrogen supply is exhausted, this center breaks up
and 关VO兴 partly recovers. We have also found a one-to-one
proportionality between the loss in 关V2兴 and the growth of a
hole trap at Ev + 0.23 eV 共labeled H1兲. It is suggested that the
H1 level originates from a V2H center, although the electrical
properties of the latter are in disagreement with assignments
made in previous reports.
*janhb@fys.uio.no
A. R. Peaker, R. Jones, S. Öberg, and P. R. Briddon, Phys. Rev.
B 68, 184106 共2003兲.
11
V. P. Markevich and M. Suezawa, J. Appl. Phys. 83, 2988 共1998兲;
C. Herring and N. M. Johnson, ibid. 87, 4635 共2000兲; V. P.
Markevich and M. Suezawa, ibid. 87, 4637 共2000兲.
12 A. Van Wieringen and N. Warmoltz, Physica 共Amsterdam兲 22,
849 共1956兲.
13 R. C. Newman, J. H. Tucker, A. R. Brown, and S. A. McQuaid, J.
Appl. Phys. 70, 3061 共1991兲.
14 J. Weber, S. Knack, O. V. Feklisova, N. A. Yarykin, and E. B.
Yakimov, Microelectron. Eng. 66, 320 共2003兲.
15 B. G. Svensson, K.-H. Rydén, and B. M. S. Lewerentz, J. Appl.
Phys. 66, 1699 共1989兲.
16
J. H. Bleka, E. V. Monakhov, B. G. Svensson, and B. S. Avset,
Phys. Rev. B 76, 233204 共2007兲.
17
D. V. Lang, J. Appl. Phys. 45, 3023 共1974兲.
18 A. Hallén, N. Keskitalo, F. Masszi, and V. Nágl, J. Appl. Phys.
79, 3906 共1996兲.
19 J. H. Bleka 共unpublished兲.
20
T. Zundel and J. Weber, Phys. Rev. B 39, 13549 共1989兲.
1 E.
V. Monakhov, A. Ulyashin, G. Alfieri, A. Yu. Kuznetsov, B. S.
Avset, and B. G. Svensson, Phys. Rev. B 69, 153202 共2004兲.
2
K. Bonde Nielsen, L. Dobaczewski, K. Goscinski, R. Bendesen,
Ole Andersen, and B. Bech Nielsen, Physica B 273–274, 167
共1999兲.
3
B. G. Svensson, A. Hallén, and B. U. R. Sundqvist, Mater. Sci.
Eng., B 4, 285 共1989兲.
4 K. Irmscher, H. Klose, and K. Maass, J. Phys. C 17, 6317 共1984兲.
5 A. R. Peaker, J. H. Evans-Freeman, P. Y. Y. Kan, L. Rubaldo, I.
D. Hawkins, K. D. Vernon-Parry, and L. Dobaczewski, Physica
B 273–274, 243 共1999兲.
6 Y. Tokuda and T. Seki, Semicond. Sci. Technol. 15, 126 共2000兲.
7
P. Lévêque, P. Pellegrino, A. Hallén, B. G. Svensson, and V.
Privitera, Nucl. Instrum. Methods Phys. Res. B 174, 297 共2001兲.
8
P. Pellegrino, P. Lévêque, J. Lalita, A. Hallén, C. Jagadish, and B.
G. Svensson, Phys. Rev. B 64, 195211 共2001兲.
9
P. Lévêque, A. Hallén, B. G. Svensson, J. Wong-Leung, C. Jagadish, and V. Privitera, Eur. Phys. J.: Appl. Phys. 23, 5 共2003兲.
10
J. Coutinho, O. Andersen, L. Dobaczewski, K. Bonde Nielsen,
Financial support by the Norwegian Research Council is
greatly appreciated. One of the authors 共I.P.兲 thanks the
Alexander von Humboldt Foundation for enabling her participation in this work.
073206-4
VI
Dynamics of irradiation-induced defects in
high-purity silicon in the presence of hydrogen
J. H. Bleka,∗ E. V. Monakhov, and B. G. Svensson
Department of Physics, Physical Electronics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
B. S. Avset
SINTEF ICT, Microsystems and Nanotechnology, P.O. Box 124 Blindern, N-0314 Oslo, Norway
(Dated: 17th March 2008)
A simulation reproducing the hydrogen-mediated transformation of the vacancy–oxygen (V O)
centre into a vacancy–oxygen–hydrogen centre with an energy level at 0.37 eV below the conductionband edge (Ec ) (V OH∗ ) and the passivation of the di-vacancy centre is presented. V OH∗ dissociates
at a rate of 2 × 10−5 s−1 at 195 ◦ C, causing V O to recover. The diffusivity of the monatomic
hydrogen used in the model is found to be similar to established values for protons. After V O has
partly recovered, further annealing causes the V O centre to transform into the vacancy–oxygen–
hydrogen centre with an energy level at Ec − 0.32 eV (V OH). V OH is subsequently transformed
into V OH2 at a high rate due to hydrogen diffusing in from the sample surface.
PACS numbers: 66.30.Jt,71.55.Cn,61.80.Fe
I.
INTRODUCTION
Hydrogen in Si readily reacts with vacancy-type defects by passivating the dangling bonds. It is known,
for instance, that the vacancy–oxygen (V O) centre and
the di-vacancy (V2 ) centre disappear at temperatures below 300 ◦ C in the presence of hydrogen.1 The V O centre
transforms into a V OH centre,2–10 while the annealing
mechanism for the V2 centre is less documented, although
there have been several suggestions that the hydrogenmediated annealing may cause a di-vacancy–hydrogen
(V2 H) centre.2,9,11
Reported values for the migration energy of monatomic
hydrogen in Si range from 0.48 eV (ref. 12) to
1.2 eV (ref. 13) and, presumably, depend on the charge
state of the hydrogen. This complicates the investigation
of hydrogen-related defect reactions and calls for more
isothermal annealing data in order to quantify the kinetics.
In ref. 11 it was shown that during annealing at
low temperatures (below 200 ◦ C) of hydrogenated highpurity silicon, monatomic hydrogen reacts with the
vacancy–oxygen (V O) centre to form what is expected to be an unstable vacancy–oxygen–hydrogen complex (V OH∗ ); this complex has an energy level at
Ec − 0.37 eV (Ec being the energy of an electron at the
conduction-band edge), in the following labelled as E1.
At longer annealing times, V OH∗ was seen to dissociate
back to V O and monatomic hydrogen; probably due to a
depletion of hydrogen in the material. The V2 centre was
also observed to disappear due to monatomic hydrogen,
at a slightly higher rate than the V O centre. It was suggested that this results in a V2 H centre. Thus, at these
low annealing temperatures, the defect behaviour can,
in a first approximation, be described by the following
reactions:
V O + H → V OH∗ ,
V OH∗ → V O + H,
V2 + H → V2 H.
(1)
(2)
(3)
In the present contribution we show the result of a
numeric simulation that reproduces the experimental results in ref. 11, but the main focus will be on the defect
dynamics in hydrogenated samples treated at higher temperatures and/or with longer durations than those used
in ref. 11.
II.
TECHNICAL DETAILS
The samples investigated were p+ –n− –n+ Si diodes
produced from high-purity detector-grade magneticCzochralski (MCz) and diffusion-oxygenated float zone
(DOFZ) wafers with a phosphorous concentration of
5 × 1012 cm−3 . Hydrogen was introduced by submerging the samples in 10% hydrofluoric acid (HF) at 50 ◦ C
for 21 h.
Aluminium contacts were deposited on the MCz samples before irradiation at room temperature (RT) with
6-MeV electrons to a dose of 5 × 1012 cm−2 .
The DOFZ samples were annealed for 1 h at 450 ◦ C in
nitrogen ambient prior to irradiation at RT with 15-MeV
electrons to a dose of 2 × 1012 cm−2 . The contact material used for the DOFZ samples was silver glue.
The concentrations of oxygen and carbon in the different types of materials were measured by secondary-ion
mass spectrometry and are listed in table I.
The set-up used for the deep-level transient spectroscopy (DLTS) measurements and depth-profiling measurements is based on a HP 4280A capacitance meter and
is a refined version of one described elsewhere.14 Both
a lock-in–type weighting function and a GS4 weighting
2
20
Non-annealed
20 min at 225 °C
2560 min at 225 °C
16320 min at 225 °C
VO
−3
cm )
2 Nd ∆C / Cr (10
III.
−1
Lock in, (640 ms)
15
11
function15 were used to extract the DLTS signal. Subsequently, the concentration, energy-level position and
apparent capture cross section of the electron traps were
derived.
VOH(−/0)
10
E1
V2(−/0)
V2(=/−)
5
0
ISOTHERMAL ANNEALING UP TO 225 ◦ C
−5
A.
DLTS measurements
A hydrogenated MCz sample (sample A in table I) was
isothermally annealed at 225 ◦ C for 272 h; figure 1 shows
the DLTS spectra of this sample for the non-annealed
state and after three different annealing times. The nonannealed DLTS spectra show the well-known V O centre, V2 centre and interstitial-carbon–interstitial-oxygen
(Ci Oi ) centre. After 20 min, the reactions 1 and 3 have
caused a large concentration of V OH∗ centres ([V OH∗ ])
and the disappearance of most of the V2 centres, in accordance with that observed in ref. 11. The energy level
at about Ev + 0.23 eV, labelled H1, has also appeared
with an amplitude similar to that of the loss of the V2
peaks. As discussed in ref. 11, this level may be due to
the V2 H centre resulting from reaction 3, although the
V2 H centre is, from ab initio calculations, expected also
to have an energy level at about Ec − 0.4 eV, but no such
level is detected here.16 After 2560 min, the hydrogen has
diffused deeper into the sample, and most of the V OH∗
centres have dissociated through reaction 2. However,
the V O peak is not fully recovered and is lower than the
initial value. The V2 centre has annealed out completely,
while [H1] has been reduced only slightly. The vacancy–
oxygen–hydrogen (V OH) centre2–10 has started to appear at this stage. After an annealing time of 16320 min,
V OH∗ is no longer visible, [V O], [H1] and [Ci Oi ] are
all reduced by roughly a factor of two, and [V OH] has
increased.
Figure 2 displays the amplitude of a selection of the
peaks observed in figure 1. Figure 2a shows in greater
detail how [V O] initially drops and is replaced by a similar amount of the V OH∗ centre before it reappears at the
expense of the V OH∗ centre. The one-to-one relation between [V O] and [V OH∗ ] results in a rather constant sum
of the two (depicted as stars). After 2000 min at 225 ◦ C,
[V O] is again reduced, but not replaced by the V OH∗
centre. This is, however, the stage when V OH starts
appearing; although, in a concentration smaller than the
loss of [V O]. In figure 2b, the sum of [V2 ] and [H1] is seen
to be rather constant initially, as discussed in great detail
in ref. 11. The uncertainty in [H1] is substantial, but it
seems this defect decreases gradually at long annealing
times.
VOH(0/+)
H1
100
CiOi
×
1
3
150
200
Temperature (K)
Vbias = −10 V
Vpulse = 0 V
Vbias = −10 V
Vpulse = 3 V
250
Figure 1: DLTS spectra of sample A measured with (Vpulse =
3 V) and without (Vpulse = 0 V) forward injection after different annealing times at 225 ◦ C. An estimate for the trap concentration, which does not account for the so-called lambda
effect, can be read out at each of the peaks.17 The nonannealed spectrum was not measured with forward injection
and is therefore taken from sample B, which was prepared
in parallel with sample A. The amplitude of this single spectrum is increased by 20% to account for a difference in the
irradiation dose.
B.
1.
Depth distribution
Hydrogen-diffusion model at 195 ◦C
Figure 3 reveals how the depth profiles of [V O],
[V OH∗ ] and [V2 ] evolve during annealing at 195 ◦ C for a
hydrogenated MCz sample (sample B). The sum of [V O]
and [V OH∗ ] remains rather constant as monatomic hydrogen diffuses in from the surface and temporarily transforms many of the V O centres into V OH∗ centres.11
The defect behaviour in figure 3 can be modelled rather
well merely by the reactions 1, 2 and 3 together with indiffusion of monatomic hydrogen from the surface. The
solid lines in figure 3 are the result of this model which
is described by the differential equations in table II and
the input parameters listed in table III. The sample is
treated as a medium stretching from x = −50 µm to
x = 200 µm, and the surface is regarded as a reference
plane at x = 0. The boundary condition of the model is
constant concentrations, but the extension of the medium
is so large that the result is not affected if the boundary
condition is zero concentration (for instance, by decreasing the initial concentrations linearly to zero from 20 µm
within the boundary). The simulation was run with the
r
, and the input
use of the function pdepe in MATLAB
parameters were optimised by an algorithm which perturbs the parameters and calculates the deviation from
the measured depth profiles, keeping for the next iteration only those parameter sets which give a deviation
smaller than the currently best.
3
Table I: Survey of the three samples investigated. Sample C was annealed between the hydrogenation and the irradiation.
Sample Material
Oxygen conc.
Carbon conc. Hydrogenation Pre-irr. ann. Annealing In figure
1, 2, 4
HF
None
225 ◦ C
A
MCz 0.5–1 × 1018 cm−3 ≤1 × 1016 cm−3
−3
16
−3
18
3
HF
None
195 ◦ C
≤1 × 10 cm
B
MCz 0.5–1 × 10 cm
5
HF
1 h at 450 ◦ C 15 min
C
DOFZ 2–3 × 1017 cm−3 2–4 × 1016 cm−3
Table II: Differential equations describing a model where only monatomic hydrogen diffuses and the V O centre captures hydrogen to form the unstable V OH∗ centre. An unspecified centre X which traps hydrogen is also included. All the concentrations
are functions of the annealing time t and the depth x. The result of the simulation is shown in figure 3.
Defect species
H
VO
V OH∗
V2
BH
X
Rate equation
d[H]
dt
d[V O]
dt∗
d[V OH ]
dt
d[V2 ]
dt
d[BH]
dt
d[X]
dt
=
=
=
=
=
=
2
d[V O]
2]
DH ddx[H]
− d[BH]
+ d[V
+ d[X]
2 +
dt
dt
dt
dt
d[V OH∗ ]
− dt
∗
4πRV O DH [H][V O] − CVdiss
OH∗ [V OH ]
−4πRV2 DH [H][V2 ]
diss
[BH]
−CBH
−4πRX DH [H][X]
A uniform concentration of hydrogen sinks ([X]) is also
included in the model, but the result of the parameter
optimisation is that the closest fit to the measured depth
profiles is obtained when the trap is not present (low
concentration and small hydrogen-capture radius RX ).
The modelling parameters listed in table III are not
the only ones producing a simulation fitting the observed data as closely as the one displayed in figure 3.
For instance, the 1-µm-deep surface concentration of the
boron–hydrogen (BH) centre, which is assumed to be
the source of monatomic hydrogen, is known to have
a dissociation barrier of 1.28 eV and a pre-factor of
2.8 × 1014 s−1 ,18 and is, therefore, mainly consumed already after the initial 8-min anneal. Thus, the model is
not particularly sensitive to the distribution of the initial concentration of hydrogen and the BH centre. Furthermore, the hydrogen-capture radius of the V O centre,
RV O , and that of V2 , RV2 can be reduced by several orders of magnitude if [BH] is increased by a similar factor.
However, the value of 5 × 10−11 m used for RV O in the
simulation seems to constitute an upper limit as larger
capture radii cause steeper profiles and less correlation
with the measured data. This value is still somewhat below the 0.5 nm that is normally used due to geometrical
considerations. This suggests that reaction 1 may have
an energy barrier, or possibly that the hydrogen diffusion
is altered for instance by the presence of oxygen causing
temporary trapping. Although the value of RV O can be
varied by many orders of magnitude, RV2 must always be
a factor of 1.5–2 larger to make the simulation reproduce
[V2 ].
The dissociation rate of the V OH∗ centre, CVdiss
OH∗ ,
can not be changed significantly without also changing
the result of the simulation. Dissociative processes normally have pre-exponential factors similar to the De-
bye frequency.19 Typical values are in the range 1011 –
1013 s−1 which, with the value for CVdiss
OH∗ resulting from
the model optimisation, gives an activation energy for
dissociation in the range 1.5–1.6 eV.
One encouraging result of the simulations is that the
optimal value (according to the method of least squares)
for the hydrogen diffusivity, DH , is only about a factor
of four less than that calculated from the pre-exponential
factor and migration barrier found by Van Wieringen and
Warmoltz12 for temperatures larger than 1000 ◦ C. Weber et al.20 later found that the values found by Wieringen and Warmoltz agree well with the diffusion properties
of positively charged hydrogen at RT.
2.
Extended annealing at 225 ◦C
Figure 4 shows the depth profiles measured for a sample treated at 225 ◦ C (sample A). When the sample has
been annealed for 2560 min, the V OH∗ centre has, as
demonstrated in figures 1 and 2, appeared and almost
disappeared again. [V OH] is not yet large enough to
allow for a depth profile to be measured. [V O] has, at
this stage, first decreased significantly at the surface side,
then almost recovered to the initial concentration, and,
subsequently, started to decrease again at the surface –
similar to that seen in figure 3. After the 5500-min anneal, [V O] has decreased mainly in the shallow region
of the probing volume and [V OH] is large enough to be
profiled. Here, it should be noted that [V OH] has a bellshaped profile. After 9770 min, [V O] is reduced a little
more, and [V OH] has increased slightly. The maximum
value of [V OH] has shifted to a slightly larger depth.
After 16320 min, [V O] is, again, reduced slightly, as is
[V OH] with the peak position gradually shifting to larger
4
Table III: Constants used for the equations in table II. The diffusion coefficient, dissociation rates and effective hydrogen-capture
radii are specific to the modelling temperature of 195 ◦ C.
Constant
DH
CVdiss
OH∗
diss
CBH
RV O
RV2
RX
[H]t=0
[V O]t=0
[V OH∗ ]t=0
[V2 ]t=0
[BH]t=0
[X]t=0
Explanation
Diffusion coefficient
Dissociation rate of V OH∗
Dissociation rate of BH
Eff. H-capture radius of V O
Eff. H-capture radius of V2
Eff. H-capture radius of X
Value
2
1.7 × 10−8 cms
−5 −1
2.3 × 10 s
4.7 s−1
5.0 × 10−11 m
9.0 × 10−11 m
8.1 × 10−12 m
0 cm−3
0 cm−3
Uniform conc. down to 1 µm
Uniform concentration
1.1 × 1014 cm−3
6.5 × 1010 cm−3
depths.
The V OH centre is expected to be generated by the
reaction
V O + H → V OH
(4)
as monatomic hydrogen diffuses in from the surface,2–10
and V OH has a higher formation barrier than V OH∗ .11
The hydrogen source for this reaction causes a smaller
flow of hydrogen, due to a more stable complex and/or
lower hydrogen diffusivity, than that for reaction 1, which
acts at lower temperatures. The shape of the V OH profile
can not be explained by reaction 4 alone if the hydrogen
diffuses in from the surface. However, it can readily be
accounted for by a sequence where reaction 4 is followed
by an additional process where the V OH centre is passivated by another (or the same) defect diffusing in from
the surface:
V OH + Z → V OHZ.
(5)
According to Pellegrino et al.,8 Z in this equation is
monatomic hydrogen and the result is the electrically inactive V OH2 centre:10,21
V OH + H → V OH2 .
(6)
The V O centre has been shown to anneal out in the
reaction
V O + Oi → V O2 ,
(7)
where the diffusion coefficient of the V O centre has an2activation barrier of 2.06 eV and a pre-factor of 22.9 cms .22
At 225 ◦ C, this gives a decrease in [V O] of less than
Comment
Found by optimisation
Found by optimisation
Zundel and Weber:18 1.28 eV, 2.8 × 1014 s−1
Found to be the upper limit (see text)
Found by optimisation
Found by optimisation
Assumed zero
Conc. fitted by a polynomial func.
Assumed zero
Conc. fitted by a polynomial func.
Found by optimisation
Found by optimisation (Note: [X]t=0 [V O]t=0 )
1010 cm−3 in 104 s and will not contribute significantly
to the observed loss. It appears, therefore, reasonable to assume that reaction 4 together with reaction 6
is the main route for the V O centre to disappear in
this temperature regime. Within this scenario, the initial [V O] ([V O](x, t = 0)) subtracted by [V O](x, t) and
[V OH](x, t) yields [V OH2 ](x, t), assuming no further reactions of V OH2 . The result deduced is shown as the
solid lines in figure 4, and indeed, the profiles obtained
look plausible for a defect caused by in-diffusion of a reactant from the surface.
IV.
ISOCHRONAL ANNEALING UP TO 400 ◦ C
Figure 5 shows DLTS spectra of a hydrogenated DOFZ
sample (sample C) that was annealed isochronally for
15 min from 175 to 400 ◦ C in steps of 25 ◦ C. This sample was annealed for 1 h at 450 ◦ C after the HF treatment and before the electron irradiation; in samples preannealed in this way, the generation of V OH∗ still exists,
but is strongly suppressed. This is attributed to the fact
that the pre-annealing causes the hydrogen to spread out
and the locally high hydrogen concentration promoting
reaction 1 diminishes. The amplitude of the E1 peak
reaches its maximum value after the 250-◦ C anneal, and
significant changes occur during this treatment: [V O]
and [V2 ] decrease substantially, the V OH level emerges,
and the E2 level and the E3 level appear, with energy positions of Ec − 0.17 eV and about Ec − 0.58 eV, respectively. These two levels seem to always appear simultaneously and also with the same concentration; hence, it
is speculated that they are two different charge states of
one defect. We have only observed these levels in samples containing hydrogen and they occur in a higher concentration in oxygen-rich samples; hydrogen and oxygen
may, thus, be part of this complex. V2 OH, formed by the
5
11
Conc. (10
8
Trap concentration (10
10
VO + E1
VO
E1
V2(=/−)
11
−3
−3
Tann = 225 °C
a)
cm )
cm )
10
6
5
8 min
0 min
0
−3
10
11
Conc. (10
4
cm )
VO
VOH(−/0)
E1
VO + E1
2
5
1740 min
158 min
0
0
1
10
2
0
4
3
10
10
10
Annealing time (min)
20
40
Depth (µm)
60
20
40
Depth (µm)
60
2.5
−3
cm )
Figure 3: Evolution of the depth profiles during annealing at
195 ◦ C. The measurements are from ref. 11, and the solid
lines are the result of the simulation described by tables II
and III. The profiles are corrected for the lambda effect.
Tann = 225 °C
b)
1.5
Conc. (10
0.5
1
2
3
10
10
Annealing time (min)
5
VO(t = 0)
VO
VOH
0
VO(t = 0) − VO − VOH
4
10
2560 min
5500 min
10
Figure 2: Concentration deduced from the DLTS peaks arising from defects related to the V O centre (a) and the V2
centre (b) (see figure 1). An offset of 5 min was given to all
the annealing times to allow for the initial amplitudes to be
included. [H1] was not measured after the 10-min anneal.
reaction
V2 H + Oi → V2 OH,
(8)
with V2 H as the mobile species is one possible assignment,
although another level has previously been tentatively
ascribed to V2 OH.23
There is not a large change as the sample is annealed
sequentially for 15 min at 275 and 300 ◦ C; mainly that
[V O] and [V OH∗ ] decrease (figure 5b). Even though
V OH∗ anneals out during annealing for a few hundred
minutes at 195 ◦ C (see figure 2a), it is possible that it
remains after a 15-min anneal at 300 ◦ C; typical values
for CVdiss
OH∗ (discussed in section III B 1) can give up to a
factor of ∼100 in difference between the annealing rates
at 195 and 300 ◦ C.
As the the sample is annealed at 325 ◦ C, the V O peak
grows strongly. The E1 peak shifts to a higher temperature (peak labelled E6), so it seems possible that V OH∗
Conc. (10
11
10
−3
0
10
11
−3
cm )
V2(=/−)
H1
V2(=/−) + H1
1
cm )
Trap concentration (10
11
2
5
9770 min
16320 min
0
0
20
40
Depth (µm)
60
20
40
Depth (µm)
60
Figure 4: Depth profiles of sample A (see figures 1 and 2)
measured after long annealing times at 225 ◦ C. The profiles
are corrected for the lambda effect. The depth profiles were
not measured in the non-annealed state; V O(t = 0) is, therefore, taken from the similar sample B and increased by 20%
to account for the difference in the amplitude of the DLTS
peaks of the V O level.
breaks up and causes an increase in [V O], but it is not
enough to account for the large change observed. Since a
large fraction of the initial V O centres is expected to be
”stored” as V OH2 at this stage, it may be suggested that
V OH2 breaks up and restores the V O centre through the
reactions
V OH2 → V OH + H and
V OH + H → V O + 2H.
(9)
(10)
The existing data are, however, not sufficient to determine whether V OH2 breaks up directly (V OH2 →
6
4
3
−1
During the anneals at 375 and 400 ◦ C, the peaks
V O, V OH and E6 disappear gradually, while [E3] remains constant up to 375 ◦ C before increasing during
the 400-◦ C anneal. Most noteworthy in this regime is
the strong growth of the E7 peak, which is probably different from the E2 peak, as the position of the latter is
2 K lower. The identity of the E7 level is not known,
although it is, just like E2 and E3, only observed in hydrogenated samples with a large oxygen concentration.
Non-annealed
15 min at 225 °C
15 min at 250 °C
GS4, (640 ms)
VO
2 Nd ∆C / Cr (10
11
−3
cm )
a)
2
1
V2(=/−)
E1
V2(−/0)
E3
VOH
E2
V.
0
100
150
200
Temperature (K)
4
3
−1
300
Non-annealed
15 min at 300 °C
15 min at 325 °C
15 min at 350 °C
15 min at 400 °C
Lock in, (640 ms)
VO
2 Nd ∆C / Cr (10
11
−3
cm )
b)
250
2
E7
E6
1
V2(=/−)
E1
V2(−/0)
VOH
E3
0
100
150
200
Temperature (K)
250
300
Figure 5: DLTS spectra measured after isochronal annealing
of the hydrogenated DOFZ sample (sample C). The spectra in
a) are deduced using the 640-ms window of the GS4 weighting
function15 to better separate the E2 peak from the V O peak.
V O + 2H) or through the intermediate stage involving
V OH, as indicated by reactions 9 and 10. Here, it should
be emphasised that the signatures of the growing peak
(energy position and capture cross section) are identical
with those of V O and we have no indications that the
peak arises from a different defect than V O.
In the subsequent annealing at 350 ◦ C, [V O] decreases
slightly and [V OH] increases by the same amount – possibly again due to reaction 4, but with a more stable
source of monatomic hydrogen.
∗
1
2
3
CONCLUSION
Electronic address: janhb@fys.uio.no
E. V. Monakhov, A. Ulyashin, G. Alfieri, A. Yu.
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K. Bonde Nielsen, L. Dobaczewski, K. Goscinski, R. Bendesen, Ole Andersen, and B. Bech Nielsen, Physica B 273–
274, 167 (1999).
B. G. Svensson, A. Hallén, and B. U. R. Sundqvist, Mater.
A simple model where monatomic hydrogen diffuses in
from the sample surface and temporarily binds with the
V O centre to form V OH∗ was shown to reproduce well
the observed concentration-versus-depth profiles of V O,
V OH and V2 during annealing at 195 ◦ C. In particular,
the V O centre is first transformed into V OH∗ which later
breaks up and V O reappears.
It was shown that during annealing at 225 ◦ C for several days, monatomic hydrogen diffuses in from the sample surface and reacts with the V O centre, resulting in
the V OH centre which is more stable than the V OH∗
centre. The higher temperature required for the formation of V OH compared to that of V OH∗ is taken as clear
evidence that the formation of V OH has a reaction barrier. Further, the V OH centre was seen to anneal due to
yet another release of monatomic hydrogen from the surface which causes the electrically inactive V OH2 centre
to form.
It was also speculated on the identity of other
hydrogen-related DLTS peaks, but further investigations
are required to achieve a clear identification of these energy levels which occur at temperatures above 250 ◦ C.
Especially, a firm identification of the H1 level is highly
desirable as it may prove to be a significant step forward
in the matter of understanding the effect of hydrogen on
multi-vacancy–type defects.
ACKNOWLEDGMENTS
Financial support by the Norwegian Research Council
is greatly appreciated.
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