Defect control in silicon crystal growth and wafer
processing
Robert Falster
MEMC Electronic Materials SpA
Novara, Italy
Abstract
Accurate control of the defectivity of silicon crystals and wafers is a subject of immense
importance to both the silicon and IC industries. Exploding costs of wafer development
and production as well as the processing of 300mm wafers means that predictive defect
engineering is now, more than ever a requirement for both industries. There is little
scope any more for iterative approaches to these problems. It is simply too expensive.
Where ever possible generic – as opposed to application specific or tailored - wafer
products suitable for a wide variety of demanding applications must be developed in
order meet cost targets. This paper reviews recent developments in the understanding
several aspects of defect control in silicon crystal growth and wafer processing which are
of particular relevance to 300mm silicon products and processes. Among the subjects
covered are the problems of intrinsic point defect concentration and reaction control in
the growth crystals including effects of impurities and the uses of vacancy concentration
profiles installed into silicon wafer in order to achieve ideal oxygen precipitation
performance. The importance of accurate modeling of defect dynamics is stressed.
Finally, the requirement of dealing with significantly higher levels of mechanical stress in
300 mm processing has led to a new appreciation of the role played by oxygen in the
locking of dislocations and the dynamics of wafer hardening during processing. These
developments are reviewed briefly.
Introduction
Many aspects of the silicon industry have changed over the past few years. Quite a few
of the changes have been a result of two simple facts. There has been a huge increase in
both the costs of developing new (and in particular 300mm) silicon products and the costs
of testing new silicon products by users. Control of defectivity has always been and
remains a critical aspect of silicon product design. In the past much of this was done on a
more or less empirical basis with a close coupling of product development to individual
application. This is changing as more positive control and specification and more
universal defect solutions are sought. The major issues remain the control of the intrinsic
point defects in crystal growth and the behavior of oxygen in silicon wafers during wafer
processing.
There are two central general problems associated with defectivity in conventional
silicon wafers which have plagued the silicon industry in many ways over many years.
One relates to difficulties in specification and the other to the generally complex
interaction between material and process. Both are of these problems are equally
important and each has outward-rippling implications of their own.
Defectivity specification has been a highly problematic aspect of the silicon industry for
many years. For example, specifying the oxygen concentration for a given conventional
silicon wafer order obviously does not accurately describe or predict the oxygen behavior
of any specified lot of wafers in any specific application. Likewise, specifying such
things as “flow pattern defect” or “COP” density does not accurately describe the state of
agglomerated point defects – the other main defectivity issue in silicon technology.
Simple specifications, and their accompanying roadmap goals for conventional silicon,
do not guarantee that – in general, let alone for the specific wafer group in question - this
will be sufficient to meet the needs of this, that or the other technology node. It has
created huge problems for product road map development.
Metrology and sampling issues are only part of the problem. The second major problem
of defectivity lies in the fact that there is a strong coupling between the various defect
formation mechanisms the ultimate performance of the material in specific applications.
The reason why oxygen concentration alone doesn’t accurately portray the oxygen
performance of a silicon order is that oxygen concentration (the one thing which is
relatively easily determined) is but a small part of the complex phenomena which control
the state (the actual important feature) of oxygen in a silicon wafer. Similar statements
can be made of the state of agglomerated intrinsic point defects where such things as size
distribution are important.
An upshot of this state of affairs is that this produces a dilemma in product design. It is
unclear what the target is. Recent solutions such as micro-defect free PerfectSiliconTM
and Magic Denuded Zone® (MDZ®) materials offer a pathway out of this dilemma.
Important to their development has been an improved understanding of the behavior of
intrinsic point defects and their interactions with impurities. Some of this is briefly
reviewed here. This understanding has greatly improved our ability to design and specify
material and to develop cost effective processes to manufacture them. An important
aspect of this has been a significant improvement in our ability to model the complex
thermal fields and point defect dynamics of silicon crystal growth.
Intrinsic point defects in silicon crystal growth
Figure 1 shows schematic illustrations of the space of the various important features of
vacancies and their reactions in CZ silicon [1]. Illustrated are solubility concentration
versus the conditions under which voids (COPs) are formed their binding to oxygen and
subsequent sharp reduction in mobility and the space where vacancies and oxygen join
forces to dramatically alter oxygen clustering (and subsequent oxygen precipitation)
behavior. With such diagrams many of the processes important to defect control can be
visualized.
Mapped onto the space are two simple illustrations of vacancy defect reaction paths.
Figure 1 illustrates the close coupling between the problem of simultaneously controlling
void number density and size and oxygen precipitation behaviour. The initial vacancy
concentration is controlled by conditions near the growth interface [2], the void density
by conditions near the nucleation temperature (itself a function of melt interface
conditions) [3] and the void size, which depends on the cooling conditions just below the
void nucleation temperature (and also depends on void density and initial vacancy
concentration) [4]. Oxygen behavior is then furthermore complicated by details of
cooling at lower temperatures and the oxygen concentration itself. Process changes at
any of these stages in the crystal growth process can have a large impact on the
subsequent behaviour of oxygen.
CV [cm-3]
CV*
O2V Binding
1015
Void Nucleation
Enhanced Oxygen
Clustering
1014
1015
Start
Enhanced Oxygen
Clustering
CV*
1014
1013
1013
1012
1012
Vacancy Path:
Standard V-type Crystal Growth
1011
1011
1010
1010
700
800
900
1000 1100 1200 1300 1400
T [°C]
700
800
900
1000 1100 1200 1300 1400
CI [cm-3]
CI [cm-3]
(a)
Figure 1.
Void Nucleation
O2V Binding
CV [cm-3]
(b)
Schematic illustrations of vacancy reactions and concentration paths
during the cooling of crystal during growth. Illustrated are cases of crystal
vacancy type crystals grown with sufficiently large vacancy concentrations
nucleate voids. In (a) the cooling rates near the void nucleation
temperature are slow enough to result in the consumption of free, grownin, vacancies to low enough levels so as not to cause oxygen precipitation
enhancement. (b) illustrates the case of more rapid cooling in this phase
with the result of strong vacancy-enhanced oxygen precipitation.
Techniques for the production of micro-defect free silicon have been developed over the
past several years [1,5,6]. They involve processes which control and manage the intrinsic
point defect concentrations throughout the crystal growth process such that critical supersaturations of either vacancies or silicon self-interstitials are never reached in temperature
ranges where micro-defect formation (voids and dislocation loops, respectively) is a risk.
Much has been learned through the intense engineering efforts of these past years
T [°C]
resulting in great strides in the efficiency and cost effectiveness of such processes.
Processes for 300mm PerfectSilicon have been developed.
A truly micro-defect free wafer (as opposed to a merely controlled defect) product
effectively side-steps the question of what degree of defectivity is acceptable in a given
application. It is also very simple to specify. As long as the “Perfect” criterion is met,
there is no question of hard-to-determine-effectively micro-defect density or size
distributions. There is no question of the suitability of such material (from the microdefect point of view) in advanced applications.
Importantly, the simplicity and completeness of the specification (“perfect”) implies that
it is the material and not the process which is specified. This is an important fact and one
which is central to a maturing product such as silicon. Perfect Silicon is not a process; it
is a result. It is a result which can, in principle, be reached by a variety of paths with a
variety of hardware solutions. It is an orthogonal solution to the application in the sense
that, independent of the exact details of the approach used to achieve it, the well-defined
defect-free result insures that there is no impact of the micro-defectivity of the wafer – or
indeed process variation (so long as the result “perfect” is maintained) - on the resultant
yield or performance of the IC produced by it. No other crystal approach can achieve this
clarity in specification and ultimate simplicity of use - for now and in the long term.
The engineering of vacancy concentration profiles in silicon wafers and
the control of oxygen precipitation
The problem of oxygen precipitation control in silicon has been an important area
research in silicon technology for over 20 years. Since it was first recognized that
oxygen precipitates could act a gettering sites for fast diffusing and harmful transition
metal contamination [7], the use of oxygen precipitates has played an important role in a
contamaination management schemes throughout the IC industry. Such systems are
called Internal Gettering (IG) systems. It has, however, turned out to be quite a difficult
problem from a practical perpective. The gettering part is largely easy [8]; the difficult
part lies in the precise control of oxygen precipitation behavior to insure effective
gettering without harmful side effects - in every wafer. In particular, a firm grasp of the
nucleation processes has proved illusive [9]. The result of this has been often less than
ideal and reliable control of oxygen precipitation performance in practice.
In general, the distribution of oxygen precipitation achieved in an ensemble of silicon
wafers depends strongly on a close coupling of the oxygen content, the details of the
crystal growth processes and the details of the application to which the wafers are
submitted [10,11]. Many, often complicated and expensive, approaches have been
developed over the years to manage these coupled complications and achieve the desired
gettering effect without side effects. These include such wafer pre-treatments as the socalled “Hi-Low-High” treatments in which oxygen is first out-diffused at high
temperatures (to create a low oxygen content surface layer) followed by a generally long,
low temperature treatment to (re-) nucleate oxygen clusters followed by another high
temperature treatment to grow them into precipitates. Other approaches have included
attempts to very narrowly specify oxygen concentration and crystal growth process or
even the segments of the crystal from which wafers should be taken for specific
application.
The MDZ® wafer is a serious departure from previous attempts at solving the
problem of oxygen precipitation control. The RTP family of processes which produce
MDZ® wafers result in a radical change of the wafer’s material properties. At its core is
the enormous effect that vacancies have on the control of the nucleation processes of
oxygen in silicon [12]. The process which produces the MDZ® wafer installs a useful
vacancy concentration profile (or template) into a silicon wafer which subsequently takes
over the control the wafer’s oxygen precipitation behavior from all of the difficult factors
important in conventional silicon: crystal growth, IC application, and even oxygen
concentration itself. An MDZ® wafer is a wafer which is programmed through the RTP
treatment to behave in a well defined, ideal manner in any application, sweeping aside an
entire raft of technological difficulties.
An illustration of the huge affect that vacancies have on oxygen precipitation
behavior is shown in Fig. 2 in which the dependence of the resulting oxygen precipitate
density on vacancy concentration is shown. The core concept of the MDZ® wafer is to
utilize this very strong dependence and engineer a profile of vacancies into a silicon
wafer. The very steep, switch-like dependence of precipitate density on vacancy
concentration means that a profile of vacancy concentration rising from the surface and
going through the threshold value produces a rather sharply layered structure with a
highly precipitating bulk underneath a non-precipitating surface layer. The threshold for
this layered design lies at a vacancy concentration of about 1012 cm-3.
Figure 3
schematically illustrates the design of such a wafer and compares it to a conventional
oxygen – out diffusion approach to the problem of forming a denuded zone.
Vacancies may be introduced into silicon wafers at high temperatures by a number of
different mechanisms. Two examples are nitridation [15,16] or through simple high
temperature Frenkel pair generation [17]. Generating large concentrations of vacancies
in wafers at high temperatures is not a difficult task at all. The problem lies in fighting
the tendency of the wafer return to equilibrium during the cooling of the wafer and
keeping them in the wafer in sufficiently large concentrations to be useful. This is where
RTP comes in.
The simplest procedure for installing a useful profile of vacancies in a silicon wafer relies
solely on Frenkel pair generation and the close proximity (relative to vacancy diffusion
lengths) of the two wafer surfaces. Heating a thin wafer to a high temperature T results
in the rapid equilibration of vacancy-interstitial system. First, Frenkel pairs – vacancies
and self-interstitials in equal amounts - are produced. This - very fast – reaction leads to a
recombination-generation equilibrium. The product CiCv of the two concentrations
acquires the equilibrium value Ci*Cv*, with the concentration of both equal to
(Ci*Cv*)1/2. Were the sample to be cooled at this point under the condition of equal
concentration, the vacancies and interstitials would merely mutually annihilate each other
10
11
10
10
Measurement
8
10
-3
Fit using Data between 10 and 10 cm
10 3.838
[OPD] ≈ ([Pt] / 2.19 10 )
-3
Oxygen Precipitation Density (cm )
completely in the reverse process of their generation resulting in no vacancy
concentration enhancement by the time the samples reach room temperature.
9
10
8
10
7
10
6
10
12
10
10
13
-3
Vacancy Concentration (cm )
Figure 2.
Oxygen precipitate densities produced following test heat-treatments
(800°C 4 hours + 1000°C 16 hours) as a function of wafer vacancy
concentration. Vacancy concentration was determined by platinum
diffusion experiments [13,14].
This is averted by the next stage of the process: equilibration. Both Ci and Cv will
approach their equilibrium values, Ci*and Cv*, due to exchange with the wafer surface
(considered as ideal sink/source of point defects). This coupled process is controlled
mainly by diffusion of self-interstitials which are the faster diffusers – the two
concentrations being comparable. The total time to achieve the complete equilibrium in a
standard wafer (ca. 700 :m thick) was found to be extremely short, less than several
seconds at 1250oC. The speed of the equilibration is, in fact, a measure of interstitial
diffusivity and implies that the interstitial diffusivity is high, on the order of 2.5x104
cm2/s.
After equilibration, the vacancies become the dominant species since Cv*>Ci*. On
subsequent cooling the point defects quickly recombine, only now, some of the vacancies
survive. If the equilibration effect had not occurred, and vacancies and interstitials
remained in equal concentrations, they would recombine equally with each other leaving
no excess concentration of either species. When equilibration is reached, and positions
remote from the wafer surfaces the majority vacancies consume the minority interstitials
until there are no more to consume leaving behind an excess concentration of surviving
vacancies which is equal to the initial concentration difference at the anneal temperature,
∆C= Cv*-Ci*.
Conventional DZ
Vacancy controlled DZ
Cv or COi (cm-3)
1018
COi
COi
1016
1014
1012
CV
CV
1010
0
50 100
0
50 100
Depth from wafer surface (m)
Figure 3.
A schematic illustration of the difference between conventional methods
of installing denuded zones (DZ) in silicon wafers via oxygen outdiffusion and renucleation and a new method based on the installation of
tailored vacancy concentration profiles.
The proximity of the wafer surfaces during cooling adds another component to the
process. In addition to recombination, vacancies will out-diffuse to the wafer surfaces
where the local (equilibrium) vacancy concentration is rapidly decreasing. However, if
the cooling rate is fast enough – in the range of about 40 to 100K/s (readily accessible
through using RTP) - the middle of the wafer will be not affected by vacancy outdiffusion, and the vacancy species will be present there in the concentration ∆C. The
regions near the surfaces will be strongly affected however. At lower temperatures the
profile is effectively frozen-in by the binding of vacancies to oxygen which becomes
complete by about 900 oC [18]. At this point the vacancies convert from their relatively
mobile state (free mono-vacancies) to their relatively immobile state, VO2. The profiling
of the vacancy concentration through out-diffusion achieved in a given RTP heat
treatment is largely the result of the cooling conditions of the wafer above this
temperature.
In the present discussion, the most important thing is that the near-surface regions of a
quenched wafer are depleted of vacancies, by vacancy out-diffusion during the cooling
stage of RTP. In the near-surface zones the vacancy concentration is below Cv*, and
oxygen precipitation is suppressed in a practical sense as a result of prohibitively long
incubation times (the tabula rasa effect). The rapid increase in temperature during the
ramp-up to the process temperature serves to dissolve all pre-existing oxygen clusters. In
the middle of a wafer the precipitation is strong, due to the presence of vacancies in
concentration over Cv*. Such a precipitation profile is precisely what is required for ideal
IG. The width of DZ (precipitation-denuded zone) is easily controlled by the cooling rate.
Faster cooling rates mean a shorter vacancy diffusion length, and thus a narrower DZ. If
the cooling rate is too slow, such as occurs in conventional furnace annealing, the high
temperature vacancy concentration profile will be allowed to fully relax throughout the
sample thickness to its equilibrium value near the binding temperature, which is well
below the threshold for precipitation enhancement. At this point the entire wafer
thickness becomes of the tabula rasa type.
Installing a vacancy concentration profile which rises from the wafer surface into the
bulk of the wafer crossing the critical concentration Cv* at some desired depth is the core
of the concept behind the MDZ® wafer. The installed vacancies have full control of the
oxygen precipitation behavior of the wafer. An example of a depth distribution of oxygen
precipitates produced by vacancy concentration control is shown in Fig 4.
11
10
13
Platinum Concentration (cm-3 )
10
10
9
10
8
10
PlatinumDiffusion 730 °C, 300 min
PlatinumDiffusion 800 °C, 300 min
Simulation of Vacancy Concentration
Oxygen Precipitate Density, 1250 °C, 30s
12
10
0
100
200
300
400
500
600
7
10
6
10
Oxygen Precipitate Density (cm-3)
10
700
Depth (µm)
(a)
Figure 4
(b)
(a) Depth profiles of platinum diffusion profiles (~ vacancy concentration)
measured at 730 and 800°C, calculated vacancy concentrations, and
measured oxygen precipitate densities in an RTP treated sample processed
at 1250°C. The oxygen precipitate density axis is scaled to correspond to
the vacancy-precipitate density calibration and (b) an etched cross section
of a silicon wafer containing such a profile following a precipitation heat
treatment (800°C 4 hours + 1000°C 16 hours) showing the depth profile of
oxygen precipitates resulting from an RTP-installed vacancy concentration
profile. The bulk density of precipitates in this example is 1 x 1010 cm-3.
Largely because of the speed of the vacancy-interstitial recombination reaction and the
rapid diffusivities of both vacancies and interstitials (with that of the vacancies being
conveniently lower than that of the interstitials) the process which produces an MDZ®
wafer is very rapid indeed. It is accomplished in several seconds compared to the
typically many hours required of the conventional oxygen-based approach. The denuded
zones produced are also in general larger than conventional DZ. Larger denuded zones
insure no risk of precipitation induced side effects and complete gettering even in the
reduced “thermal budget” processes. Since gettering proceeds by precipitation driven
undercooling, it happens during cooling. The length of process time is essentially
irrelevant. Important technologically is the fact that the structure developed is
independent of oxygen concentration, crystal growth process and to a large extent the
details of the subsequent thermal processing. This last result is due to the consumption of
the vacancies during the very rapid initial nucleation processes. Any subsequent
nucleation is then again subject to the “normal” prohibitively long incubation
requirements which exist in essentially all practical situations.
In the simplest case, the shape of the profile which produces the MDZ® wafer is
controlled by two parameters. The first is the soak temperature, Tp, with controls the
quenched-in vacancy concentration at the center of the wafer (= {Cv*(Tp) – Ci*(Tp)}) and
hence the bulk oxygen precipitate density. The second is the cooling rate controlling the
depth of the DZ and, at slower rates, eventually the vacancy concentration (and with it,
resulting precipitate density) at the center of the wafer. Fig 5 illustrates the cooling rate
effect.
Vacancy controlled DZ
Cv or COi (cm-3)
10 18
C Oi
10 16
Decreasing cooling rate
10 14
10 12
DZ thr eshold
CV
10 10
0
50 100
Depth from wafer surface (m)
Figure 5.
Schematic illustration of cooling rate effect.
The minimum Tp for an effective straightforward RTP treatment corresponds to Cv*(Tp) –
Ci*(Tp) /1012 cm-3, the threshold value. This happens around 1150°C. The quenched-in
vacancy concentration (and with it bulk precipitate density) rises with increasing Tp. The
bulk precipitate density reaches about 1010 cm-3 by about 1250°C.
In RTP treatments, the concentrations of intrinsic point defects in silicon wafers can be
dynamically and very rapidly altered means other than temperature and cooling rate.
Ambient is also very important in these technologies. Examples include interstitial
injection from the wafer surfaces during oxidation, and vacancy enhancements due to
nitridation effects. One example is the complete elimination of the effect when oxygen
ambient concentrations exceed about 2000 ppma [19].
Figure 6.
Oxygen precipitation behavior (BMD) sampling for MDZ® wafers (filled
circles) and normal (open circles) precipitation distributions. BMD stands
for Bulk Microdefect Density, in this case equal to the oxygen precipitate
density.
There are many advantages to using a RTP-vacancy based system to control oxygen
precipitation behavior in silicon wafers: simplicity, copy-exactability, ease-of-use and
reliability of results. Figure 6 shows just one example of the degree of control such a
process results in. In this plot, random examples of precipitation behavior (4 hours
800°C + 16 hours 1000°C) for various sampled crystals over a long period of time is
shown. The performance of MDZ® wafers is compared to conventional uncontrolled
material as a function of oxygen concentration. The width of the signal of the MDZ®
wafers is roughly equal to the counting error. The data of conventional wafers span 5
orders of magnitude, essentially the entire range of possible values.
Oxygen of the locking of dislocations
The requirement of dealing with significantly higher levels of mechanical stress in 300
mm processing has led to a new appreciation of the role played by oxygen in the locking
of dislocations and the dynamics of wafer hardening during processing. Recently a large
amount of detail relating to the dynamics of oxygen locking of dislocations has been
worked out [20,21]. The increased hardness due to the attachment of oxygen to
dislocations is a highly dynamic effect with the size of the oxygen induced unlocking
stress a strong function of oxygen concentration, time, temperature and path taken
through a high temperature treatment. Examples of the time dependence of the increase
of locking stress during an isothermal anneal at 650C with applied stress at 550C for
three different oxygen concentrations is shown in Fig 7.
Successful models for the transport and binding of oxygen to dislocations have been
developed [22]. These have led to models which can simulate the instantaneous
resistance to applied stresses of a wafer during arbitrary process cycles. It is expected
that such new capability will lead to improvements in slip resistant wafer/process design.
175
(b) 650 oC
L-CO
M-CO
H-CO
unlocking stress (MPa)
150
125
100
75
50
25
0
0
Figure 7:
5
10
time (h)
15
20
Unlocking stress as a function of annealing time for different oxygen
concentrations (DIN: 2.6x1017cm-3, L-CO; 6.3x1017cm-3, M-CO; 10.4 x
1017 cm-3, H-CO) and annealing temperatures 650oC.
Acknowledgements
Acknowledgements are due many people for their contributions over the years Some of
these include Vladimir Voronkov, Joe Holzer, Daniela Gambaro, Max Olmo of MEMC
Electronic Materials; Peter Pichler of the Fraunhofer Instititut, Erlangen; Semih
Senkader, Armando Giannattasio and Peter Wilshaw of Oxford University; Harold Korb
and Paolo Mutti.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
R. Falster, V. Voronkov and F. Quast, phys. stat. sol. (b) 222 (2000), pp. 219ff.
V.V.Voronkov, J. Crystal Growth 59 (1982), pp.625ff.
V.V.Voronkov and R. Falster, J Crystal Growth, 194 (1998), pp. 76ff.
V.V.Voronkov and R.Falster, J.Crystal Growth 204 (1999), pp. 462ff.
R Falster, JC Holzer, S Markgraf, P Mutti, S McQuaid and B Johnson, United
States Patent 5,919,302, Jul. 6, 1999.
R Falster and VV Voronkov, Materials Science and Engineering B73 (2000) pp.
87ff.
TY Tan, EE Gardner and WK Rice, Appl. Phys. Lett. 30, 175 (1977).
R Falster, Semiconductor Fabtech, 13th Edition, p. 187-193, 2001.
F Kelton, R Falster, D Gambaro, M Olmo, M Cornara and PF Wei, J Appl Phys,
85, 8097 (1999).
Y Shinamuki, H Furuya, I Suzuki and K Maurai, Jpn. J. Appl. Phys., 24, 1595
(1985).
G Fraundorf, P Fraundorf, RA Craven, RA Moody and RW Shaw, J.
Electrochem. Soc., 132, 1701 (1985).
VV Voronkov and R Falster, J Appl Phys 91, 5802 (2002).
H. Zimmermann and H.Ryssel, Appl. Phys. Lett. 59, 1209 (1991).
M. Jacob, P. Pichler, H. Ryssel and R. Falster, J. Appl. Phys., 82, 182 (1997).
R. Falster, M Pagani, D Gambaro, M. Cornara, M. Olmo, G. Ferrero, P. Pichler
and M. Jacob, Solid State Phenomena, Vols, 57-58, 129 (1997).
M. Jacob, P Pichler, H. Ryssel, R. Falster, M. Cornara, D. Gambaro, M. Olmo and
M. Pagani, Solid State Phenomena, Vols, 57-58, 349 (1997).
R. Falster, D Gambaro, M Olmo, M Cornara, and H Korb, Mat. Res. Soc. Syp.
Proc. Vol. 510 (1998), pp.37ff .
VV Voronkov and R Falster, J Crystal Growth, 204 (4), pp 462-474 (1999)
R Falster, M Cornara, D Gambaro and M Olmo, United States Patent 5,994,761,
Nov 30, 1999.
S. Senkader, K. Jurkschat, D. Gambaro, R. J. Falster, and P. R. Wilshaw: Philos.
Mag. A Vol. 81 (2001), p. 759.
S. Senkader, P. R. Wilshaw, and R. J. Falster: J. Appl. Phys. Vol. 89 (2001), p.
4803.
A Giannattasio, S Senkader, S Azam, RJ Falster and PR Wilshaw, submitted to
Microelectronic Engineering 2003.