Rise-time and fall-time profile of erbium luminescence in silicon
M. Q. HUDA, S. I. ALI, S. A. SIDDIQUI
Dept. of Electrical and Electronic Engineering
Bangladesh University of Engineering and Technology
Dhaka 1000
BANGLADESH
Abstract: - Shockley-Read-Hall recombination kinetics has been applied to explain the luminescence
mechanism of erbium luminescence in silicon. Erbium atoms in silicon have been considered as recombination
centers with specific values of capture and emission coefficients. Electron-hole recombination through these
levels has been considered to be the origin of erbium excitation. Equating the capture and emission processes of
photo generated excess carriers in the erbium related level, luminescence profiles during rise-time and fall-time
has been calculated. The extended rise of erbium luminescence after termination of short excitation pulses of
micro second durations has been explained by the model.
Key-words: - Silicon, Luminescence, Erbium, excitation, Recombination.
1. Introduction
The rare earth atom erbium has the interesting
property of light emission in silicon environment.
This luminescence phenomenon of erbium in
silicon has attracted considerable interest in recent
years for its prospective use in silicon based
optoelectronics. Since the first demonstration of
atomically sharp luminescence at 1.54 µm by
Ennen et al, numerous work has been done on this
field.[1-4] Si:Er LED working at room temperature
has already been reported few years ago[2,3].
Practical use of erbium luminescence however is
yet to be achieved due to strong quenching of the
luminescence at room temperature. Apart from that
the longer lifetime of erbium decay might also be
another issue in achieving high speed modulation.
Complete understanding of the mechanism of
erbium luminescence is thus necessary before
achieving the ultimate goal of silicon based light
emitters.
The luminescence from erbium actually involves
three steps- i) generation of excess carriers by
optical or electrical excitation, ii) transmission of
electron-hole recombination energy into erbium
atoms, and iii) radiative transition of erbium atoms
from their excited state to the ground state. In case
of glass or wide band gap semiconductors, the 4I13/24
I15/2 transition of erbium atoms is largely radiative
with a lifetime of the order of milliseconds.[5]
However in case of silicon, the property of an
excited erbium is somewhat influenced by the
surrounding host. Apart from radiative transition,
an erbium atom can also dissipate its energy
through back transfer or impurity Auger processes.
In the back transfer process, energy released from
an erbium atom promotes an electron from the
valence band to the erbium related level in the
silicon band gap. In impurity Auger processes, the
erbium energy is transferred either to a bound or a
free carrier. Both these effects on erbium
luminescence, especially on the temperature
quenching mechanism has been reported.[6,7]
There is however reasonable confusion over the
actual mechanism that excites the erbium atom to
its higher energy state. It has been suggested that
the mechanism involves electron-hole complexes
through sequential capture of electrons and holes at
an erbium related level.[7,8] The involvement of
bound excitons in the process of erbium excitation
was suggested by Palm et al.[6] This idea has
recently been supported by Thao et al.[9]
An interesting phenomenon regarding the erbium
luminescence however needs some careful study.
Time resolved measurements with laser excitation
pulses of the order of milliseconds show typical
luminescence profiles that correspond to the
lifetime of erbium decay.[10] In case of laser
excitation pulses of 30 µs or shorter, the erbium
luminescence continues to increase, in some cases
substantially, for a certain duration of time after the
laser excitation has been terminated. [8,11] The
phenomenon has been described by Taguchi et al.
to be resulting from a slower system response.[12]
Nevertheless, this effect of extended increase of
erbium luminescence has been considered to be an
indirect proof for erbium excitation involving
bound excitons or electron-hole complexes.
Appearance of the extended luminescence only in
cases of short excitation pulses, as opposed to that
in conventional measurements lacks an explanation
to date.
We propose that the erbium excitation process is
not through bound-excitons or e-h complexes, but
through electron-hole recombination in erbium
sites. We have analyzed capture and emission
processes of electrons and holes in erbium related
levels
by
Shockley-Read-Hall
(SRH)
recombination kinetics. Our model explains the
effect of extended enhancement of erbium
luminescence under short excitation pulses.
2. Luminescence mechanism
Erbium atoms have been considered as impurity
centers (Shockley-Read-Hall) in silicon. The
corresponding defect level in the band gap, referred
as erbium level from now on, has been assigned
with values of thermal emission and capture
coefficients for charge carriers. In accordance with
published experimental results, we have taken this
erbium level to be situated in the upper half of the
band-gap. The electron trapped in the erbium level
can either jump back to the conduction band, or it
can capture a hole in the valence band. The later
process corresponds an electron-hole recombination
in the erbium site.
Let NEr be the total number of active erbium sites
per unit volume and nEr of them are filled by
electrons at a steady state of optical excitation. The
process of capturing an electron or emitting a hole
from the erbium level depends on the number of
empty sites. Similarly, the process of electron
emission or hole capture in the erbium level
depends on the number of erbium sites being
occupied. The balance between capture and
emission of carriers in the erbium level is then
given as:
en nEr + c p pnEr = e p (NEr − nEr ) + cn n(N Er − nEr ), (1)
where en, ep are the electron and hole emission rates
respectively with units of s-1; and cn, cp are the
corresponding capture coefficients with units of
cm3s-1. n and p represents the electron and hole
densities respectively. The first term on the left
hand side represents the rate of electron emission
from the erbium level, whereas the second term
represents the rate of hole capture. The two terms
on the right hand side represents the rate of hole
emission and electron capture respectively. The
fraction of erbium levels being occupied by
electrons at steady state is given as:
c n+ e
(2)
f t = NnEr = e + c np + c pn + e .
Er
n
p
n
p
If an electron occupied level manages to capture a
hole before the electron is being emitted back to the
conduction band, the recombination energy
becomes available to the corresponding erbium
atom for possible excitation through an impurity
Auger process. However, even with a 100%
quantum efficiency of coupling between the erbium
level and the 4f shell electrons, not every
recombination will be useful for exciting erbium
atoms. Energy released by electron-hole
recombination at sites where erbium atom is still in
the excited state, would naturally be a wastage in
terms of erbium luminescence. For simplicity, it is
assumed that electronic properties (i.e., emission
and capture rate of carriers, energy position in the
band diagram, etc.) of an erbium level remains
independent of the energy state of the
corresponding atom.
If NEr* is the number of excited erbium ions in
steady state, number of atoms available for
excitation is given by (NEr - NEr*). The rate of useful
recombination of electron-hole pairs through
erbium sites is then given by ft(NEr-NEr*)cpp. Taking
τEr as the decay lifetime of the 4I13/2 state to the
ground state, the rate of excitation and decay of
erbium atoms can be equated as,
N*
(3)
f t (N Er − N *Er )cp p = Er .
τ Er
Here, τEr constitutes the radiative and non-radiative
processes of erbium relaxation. The non-radiative
relaxation mechanism involves the back transfer
and impurity Auger processes, and thus depends on
doping technique, material quality, measuring
temperature, etc. Luminescence from erbium
corresponds only to the radiative transition, and is
given by:
cp p
N*
f t N Er
(4)
,
I ∝ Er =
1
τ rad
τ
rad
f t cp p +
τ Er
where, τrad is the radiative lifetime of relaxation for
erbium atoms.
When a laser pulse is applied to an erbium doped
silicon sample, excess electron-hole pairs are
generated almost instantly. However, rate of
capture and emission of carriers through erbium
sites is controlled by the corresponding emission
3XPS 'HFD\ FP V
3/ ,QWHQVLW\ DX
(
3XPSLQJ
6WHDG\ VWDWH
(
'HFD\
(
7LPH PLFUR VHF
Fig. 1. Calculated luminescence profile from
erbium under constant photo-excitation. Several
tens of microseconds are needed for the
luminescence to reach the steady state.
and capture coefficients. As a result, a finite
amount of time is needed for the erbium
luminescence to reach the steady state. Equating the
capture and emission rate of carriers from the
erbium level as a function of time, we obtain,
d
nEr (t) = (ep + cn n)(NEr − nEr (t)) − (en + c p p)nEr (t). (5)
dt
Solution of equation (5) gives the density of
electron occupied erbium sites as:
b
(6)
nEr (t) = NEr (1− e − at ),
a
where,
a = (en + c p p + cn n + ep ), b = cn n + ep .
Time variation of nEr represents variations in
capture and emission rates of carriers in the erbium
level. Rate of excitation through erbium level, i.e.
the pumping rate of erbium atoms to the higher
energy state is then given as:
*
(7)
P(t) = f t (t)[NEr − NEr
(t)]c p p.
Rate of decay of erbium atoms on the other hand is
proportional to N*Er(t), and thus the time variation
of the density of excited atoms is given as:
d *
N* (t)
*
N Er (t) = f t (t)[NEr − NEr (t)]c p p − Er . (8)
dt
τ Er
The erbium luminescence, as a time function is
given by:
N * (t)
(9)
I(t) ∝ Er .
τ rad
Initial rise of erbium luminescence under constant
photo-excitation is given in Fig. 1. Pumping rate of
atoms to the higher energy state and the
corresponding decaying rate is also given. It is
apparent that the pumping action is more than an
order of magnitude stronger for several tens of µs
since the beginning of the laser illumination. This is
due to the fact that the density of erbium atoms in
excited state (N*Er(t)) initially remains a small
fraction of the total density. As a result, larger
fraction of electron-hole recombination energies are
utilized by erbium atoms during this period.
Gradual increase of N*Er(t) corresponds to increase
of luminescence intensity and also the rate of
decay. The pumping rate obviously remains
stronger than the decaying rate until reaching the
point of steady luminescence. When the laser
illumination is terminated, the excess carrier
density starts decaying exponentially in accordance
with the carrier lifetime. Electron occupancy of
erbium levels and the luminescence follows
equations (5-9) with proper boundary conditions.
The solution gives typical decay patterns of erbium
luminescence, as shown in Fig. 2.
3. Short excitation pulses
If a laser excitation pulse can be made short
enough, luminescence from erbium fails to reach
the steady level at the time of termination of the
pulse. The pumping rate of erbium atoms, as a
result, remains stronger than that of their decay.
(
7 .
3/ ,QWHQVLW\ DX
3/
(
(
7LPH PV
Fig. 2 Calculated decay profile
luminescence for typical set of values.
of
erbium
Termination of laser illumination, on the other
hand, results in exponential decay of photogenerated excess carrier density. As a consequence,
the pumping rate gradually retards down to zero.
But it takes a certain duration of time for the
/DVHU 3XOVH
3XPS 'HFD\ DX
3/ ,QWHQVLW\ DX
3/
Shin et. al. [8]
'HFD\
7LPH PLFUR VHF
Fig. 3. Calculated photoluminescence intensity
from an erbium doped sample under a short
excitation pulse of 30 µs. Symbols indicate the
experimental results from Shin et al. [8]
decaying rate of erbium atoms to become stronger
than that of the pumping. As a result, enhancement
of luminescence is observed for a certain duration
even after the laser pulse has been terminated.
Using our model, we have been able to simulate
experimental results reported on short excitation
pulses.[11] As seen in Fig. 3, excellent matching
with the experimental result has been achieved. We
put a wide variation of values regarding emission
and capture coefficients, lifetimes, laser power, etc.,
and found similar effect of extended peak in erbium
luminescence profile when the excitation pulse
duration becomes shorter than the time needed for
the luminescence to settle.
4. Conclusion
In conclusion, we have developed a new model for
erbium luminescence in silicon. We propose that
erbium atoms are excited through electron-hole
recombination in erbium related levels in the silicon
band
gap.
Shockley-Read-Hall
(SRH)
recombination kinetics has been used for
mathematical analysis of the luminescence process.
Our model explains the phenomenon of extended
rise of erbium luminescence under short excitation
pulses. Good agreement with the published
experimental results has been achieved.
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