INVESTIGATION OF MINORITY CARRIER TRAPPING IN SILICON BY MWPCD MEASUREMENTS
Kevin Lauer1,2*, Michael Blech1, Abdelazize Laades1, Alexander Lawerenz1
1
CiS Forschungsinstitut für Mikrosensorik und Photovoltaik GmbH, SolarZentrum Erfurt, Konrad-Zuse-Str. 14, 99099
Erfurt, Germany
2
Institut für Physik, TU Ilmenau, Weimarer Str. 32, 98693 Ilmenau, Germany
*
corresponding author: klauer@cismst.de, Phone: +49 - 361 - 663 12 11, Fax: +49 - 361 - 663 14 13
ABSTRACT: Minority carrier trapping, which is often observed in silicon used for photovoltaics, influences the
determination of the excess carrier density from photoconductance measurements. In this contribution the HornbeckHaynes-model is used to simulate the apparent excess carrier density, which can be determined by MWPCD
measurements. The three trap parameters: trap density, emission and trapping time constant are varied and their
impact on the apparent excess carrier density is discussed. A kink in the apparent excess carrier density is found to
correlate with the trap density. This result is used to determine the trap density from MWPCD measurements. The
impact of a constant bias light on the apparent excess carrier density is investigated by simulation and experiment.
The influence of trapping on the MWPCD signal can be eliminated by the bias light.
Keywords: Silicon, Photoconductivity, Defects
1
INTRODUCTION
2
THEORY
The excess carrier decay ∆n(t) in silicon after turning
off a light source, as measured by MWPCD, can be
explained by recombination and trapping of charge
carriers.
2.1 Recombination
Recombination describes the annihilation of an electronhole-pair and can be quantified by the recombination rate
U. The carrier lifetime τ is defined by
n
10
n
n .
U
(1)
4
τrad
τA
10
lifetime τ [µs]
Microwave-detected
photoconductance
decay
(MWPCD) measurements, which are based on the
measurement of the conductivity after laser excitation by
reflected microwaves [1], are a powerful tool to
characterize the quality of silicon. Recently, we
introduced a method, which analyses the MWPCD signal
in detail to obtain the lifetime as a function of the excess
carrier density [2]. This method is well suited to
characterize low quality silicon, which is used to
fabricate industrial solar cells.
In this contribution we are advancing the possibilities
of the MWPCD method by analyzing the MWPCD signal
at low excess carrier densities. MWPCD measurements
on silicon nitride passivated multicrystalline or
Czochralski silicon wafers yield a strong increase in this
range pretending an abnormal high lifetime. This effect
can in principle be due to trapping of minority carriers by
states in the band gap of the silicon caused by defects [3]
or due to trapping-like measurement artifacts caused by a
depletion layer at the surface (DRM effect) [4]. The latter
effect can be neglected for low quality silicon [5]. To
simulate the impact of minority carrier trapping on the
photoconductance decay the Hornbeck-Haynes-model [6]
is applied. The trap parameters are varied systematically
and a way to determine the trap density from MWPCD
measurements is developed. The impact of a constant
bias light on the measured excess carrier density is
investigated.
The physical origin of the traps in silicon for solar
cells has not yet been conclusively clarified. As the most
likely cause crystallographic defects, such as dislocations,
are identified [3, 5, 7]. The boron-oxygen complex may
be a cause of the traps [8]. Recent studies show that
crystal defects, which are decorated with oxygen
precipitates, cause these types of traps [9]. Finally, it was
also an oxygen complex with an unknown, fast-diffusing
impurity, which is not iron, found to be the cause of the
traps [10]. In any case, the measured trap density is
always associated with crystal defects or impurities in the
silicon, so that it can be used as a quality characteristic of
the silicon.
3
τSRH, Fe
10
2
τSRH, Cr
τb
16
10
1
p0 = 1x10 cm
-3
0
10 11
10
10
13
10
15
10
17
-3
excess carrier density ∆n [cm ]
Fig. 1: Impact of different recombination processes
on the total lifetime τb. The SRH lifetimes are
calculated for interstitial iron (τSRH, Fe) [14] and
interstitial chromium (τSRH, Cr) [15] with a density of
[Fei] = 1012 cm-3 and [Cri] = 1011 cm-3, respectively.
In general there are three different recombination
processes. The lifetime for each recombination process
Beside the annihilation of electron-hole-pairs a defect
state in the band gap can cause a temporary storing of
carriers, called trapping. If the defect state lies near the
conduction band an electron can be trapped and
subsequently released into the conduction band again.
While the electron is trapped, charge neutrality requires a
hole in the valence band. This implies a mismatch
between excess electrons and excess holes (∆n ≠ ∆p).
This effect of a defect state can be described by the
Hornbeck-Haynes (HH)-trapping-model [6]. Within this
model the spatial averaged excess carrier density ∆n(t)
and the density of carriers within the trap nt(t) are given
by a differential equation system
d
n
dt
n 1 nt N t
n
Gn
b
n
n ,t
nt
n,e
(2)
p
n
nt
n
p
.
(4)
The mobilities of electrons and holes are denoted by µn
and µp, respectively.
To investigate the apparent excess carrier density,
which can be determined by conductance measurements,
Eq. (2) and (3) are solved numerically using Mathematica
[17]. In the following the apparent excess carrier density
is simulated for different parameters of the trap. The trap
density Nt, the emission time constant τn, e and the
trapping time constant τn, t are varied systematically. In
our case the excess carrier density is generated by light.
Our calculation starts with an initial excess carrier
density ∆n0. Generation is neglected during the
recombination and trapping process, which is simulated.
It is assumed that initially all traps are filled (nt = Nt).
The recombination lifetime τb(∆n) is taken from the
model displayed in Fig. 1.
2.2.1. Trap density Nt
The first simulation demonstrates the impact of the
trap density on the decay of the apparent excess carrier
density (see Fig. 2). The emission and trapping time
constants are set to constant values of 100 µs and 10 µs,
respectively. The trap density is increased from
Nt = 1012 cm-3 to 1016 cm-3. If the trap density is less than
the initial excess carrier density, which was chosen to be
∆n0 = 3·1015 cm-3, then a kink in the apparent excess
carrier density occurs. In this case the decay of the
-3
2.2. Minority carrier trapping
na
apparent excess carrier density ∆na [cm ]
can be calculated. In Fig. 1 the lifetime is exemplarily
simulated for two impurities and parameters, which are
often observed in low quality silicon for photovoltaics.
Radiative recombination (τrad) [11] does not affect the
total lifetime (τb) at all. Auger recombination (τA) [12]
has an impact on the total lifetime only for excess carrier
densities above ~1016 cm-3. For lower excess carrier
densities, the dominating recombination process is the
Shockley-Read-Hall (SRH)-recombination (τSRH) [13] via
defect-induced states in the band gap. In Fig. 1 two SRHrecombination centers are assumed. One is interstitial
iron (lifetime: τSRH, Fe) [14] and one interstitial chromium
(lifetime: τSRH, Cr) [15] with a density of [Fei] = 1012 cm-3
and [Cri] = 1011 cm-3, respectively. Because the total
lifetime at an excess carrier density less than
∆n ~ 1016 cm-3 is dominated by SRH-recombination,
lifetime measurements below this point can be used to
characterize the electronic quality of silicon.
The SRH-statistic in its simple form has two
constraints. First, the density of SRH-recombination
centers has to be below a critical value [16] and, second,
the excess electron density has to equal the excess hole
density [13]. If both conditions are not fulfilled, other
models to describe the excess carrier decay ∆n(t) have to
be used.
10
16
10
15
10
14
10
13
10
12
10
11
16
Nt = 10 cm
15
10 cm
τn, e = 100 µs
τn, t = 10 µs
14
10 cm
13
10 cm
12
10 cm
0
100
200
300
-3
-3
-3
-3
-3
400
500
time t [µs]
dnt
dt
n 1 nt N t
n,t
nt
n ,e
.
(3)
Here, Gn and τb(∆n) are the generation rate and the
lifetime due to recombination, respectively. The trap
specific parameters are the trap density Nt, the mean time
an electron spends in the trap τn, e , and the mean time an
electron spends in the conduction band if all traps are
empty τn, t.
Measurements of the excess conductance reveal an
apparent excess carrier density ∆na, which takes into
account the actual excess carrier density and a carrier
density term caused by the trapped carriers [6]
Fig. 2: Simulation of the apparent excess carrier
density as a function of time for different trap
densities.
apparent excess carrier density can be divided into two
regions I and II before and after the kink, respectively. In
region I all traps are filled nt = Nt and the excess carrier
density is larger than the carrier density within the traps
∆n à nt. Hence the apparent excess carrier density in
Eq. (4) equals the excess carrier density ∆na = ∆n. This
changes in region II. There the excess carrier density
becomes less than the carrier density within the traps
∆n á nt caused by specific parameters of the traps. The
small trap escape ratio τn, t/τn, e of 0.1 in combination with
a small recombination lifetime τb causes the carriers to
2.2.2. Emission time constant τn, e
-3
apparent excess carrier density ∆na [cm ]
In Fig. 3 the emission time constant τn, e is varied
while the other parameters of the trap are kept constant at
Nt = 1014 cm-3 and τn, t = 10 µs. In this case the
recombination lifetime at the kink of the apparent excess
carrier density is assumed to be much lower than the trap
time constant. Hence, the released carriers from the trap
recombine immediately and the inverse slope of the
apparent excess carrier decay represents the emission
time constant. In the case of a low emission time constant
the carriers stay in the trap only for a short time period
and thus the apparent excess carrier decay is not affected
by trapping.
10
14
Nt = 10 cm
15
10
14
10
13
10
12
-3
10
16
10
15
10
14
10
13
10
12
14
Nt = 10 cm
-3
τn, e = 100 µs
τn, t = 0.1 µs
1 µs
10 µs
100 µs
1 ms
10
10 ms
11
0
100
200
300
400
500
time t [µs]
Fig. 4: Simulation of the apparent excess carrier
density as a function of time for different trapping
time constants.
Fig. 4). For high trapping time constants the trap density
cannot be determined by the position of the kink.
2.2.4. Impact of bias light
16
10
carriers are trapped and released several times before
recombination takes place. The second effect occurs for
high trapping time constants. Now trapping of carriers is
very unlikely and the slope of the apparent excess carrier
density is determined by the emission time constant. Due
to the low trapping probability, the traps are not
completely filled in region I. Hence, the position of the
kink in the apparent excess carrier density changes (see
apparent excess carrier density ∆na [cm ]
recombine immediately after they are released from the
trap into the conduction band. Hence, region II of the
measured excess carrier density is dominated by the
carrier density within the traps and Eq. (4) becomes
∆na = µp/(µp+µn)nt. Thus the apparent excess carrier
density at the kink represents the trap density Nt. This
holds for arbitrary values of the emission and trapping
time constants (unless the trapping time constant is large,
see Sec. 2.2.3) and can therefore be used to determine the
trap density from MWPCD measurements as shown
below.
If the trap density becomes larger than the initial
excess carrier density, the kink disappears and the
apparent excess carrier density is completely dominated
by the carrier density in the traps.
-3
In addition to the variation of the trap parameters the
impact of a bias light is demonstrated. By applying a bias
light the generation term in Eq. (2) cannot be neglected
as done before. Thus the apparent excess carrier density
can be split into a steady state ∆na, ss and a dynamic part
∆na, d
τn, t = 10 µs
τn, e = 1 ms
100 µs
1 µs
na
10 µs
na , ss
na, d .
(5)
0.1 µs
10
11
0
100
200
300
400
500
time t [µs]
Fig. 3: Simulation of the apparent excess carrier
density as a function of time for different emission
time constants.
2.2.3. Trapping time constant τn, t
As the last parameter of the trap, the trapping time
constant τn, t is changed. In Fig. 4 the trapping time
constant is varied from 0.1 µs to 10 ms. The trap density
and the emission time constant are not changed. Two
effects on the apparent excess carrier density can be
observed. First, if the trapping time constant becomes
lower than the recombination lifetime, the slope of the
apparent excess carrier density increases. In this case the
In Fig. 5 only the dynamic part of the apparent excess
carrier density ∆na, d is displayed as a function of time,
because this quantity can be determined by MWPCD
measurements. For simplicity, the recombination lifetime
is set to τb = 5 µs in this simulation. The results for
different generation rates Gn are shown in Fig. 5. Clearly
visible is the changing trapping kinetic with increasing
generation rate. Due to the constant generation rate the
traps are partly filled and the position of the kink in the
decay of the dynamic excess carrier density decreases.
Thus the impact of trapping on the apparent excess
carrier density can be eliminated using a constant bias
light. But in the case of a large generation rate in relation
to the initial excess carrier density, measurements of the
photoconductance decay reveal just a differential
recombination lifetime [18].
10
16
15
Nt = 10 cm
10
15
10
14
10
13
10
12
-1
-3
Gn = 0 s cm
18
τn, e = 100 µs
-3
∆na, d [cm ]
τb = 5 µs
100
200
-3
-3
10 s cm
18.5 -1
-3
10 s cm
19 -1
-3
10 s cm
19.5 -1
-3
10 s cm
20 -1
-3
10 s cm
20.5 -1
-3
10 s cm
τn, t = 10 µs
0
-1
300
400
wafer yields nearly no change in the photoconductance
decay. Hence, the recombination lifetime is low and not
limited by recombination at the surface. As can be seen in
Fig. 6 only a small part -drop at the beginning- of the
photoconductance decay measured on umg-silicon is
dominated by recombination of carriers. Thus it is hard to
determine the recombination lifetime from MWPCD
measurements for this material.
Applying an additional constant bias light during the
MWPCD measurement yields the expected effect (see
Sec. 2.2.4). The impact of trapping is reduced. But the
intensity of the applied bias light is not sufficient to
eliminate the trapping artifacts completely.
500
time t [µs]
3.2. Determination of the minority carrier trap density
3
EXPERIMENT
The theoretical results are compared to experimental
data. Measurements of the photoconductance decay after
turning off a light source are done using the commercial
device WT-2000® from Semilab. This measurement
system generates excess carriers by a laser pulse
(λ = 904 nm) with a maximum intensity of 16.4 Wcm-2
and a spot size of about 1 mm2. The change in
conductance of the silicon due to excitation of carriers by
the laser is measured using reflected microwaves [1].
100
Ib = 282 mSun
10
Ib = 1678 mSun
Ib = 2537 mSun
1
-3
MWPCD signal ∆U [mV]
without bias
Ib = 73 mSun
As discussed in Sec. 2.2.1 the minority carrier trap
density can be determined by the kink in the
photoconductance decay (see Sec. 2.2.1). This procedure
is tested in the following by comparison of the measured
MWPCD signal with the theoretical simulation. The
MWPCD measurement, which is displayed in Fig. 7, is
performed on a siliconnitride passivated multicrystalline
silicon wafer. The differential equation system Eqs. (2)
and (3) is solved numerically (see Sec. 2.2) using the
bulk lifetime from the model displayed in Fig. 1. The
SRH term due to chromium is substituted by a constant
lifetime of 200 µs. The second SRH term is calculated
from the interstitial iron content of this sample
([Fei] = 1.4·1012 cm-3).
Four parameters, which are the initial excess carrier
density ∆n0, the trap density Nt, and the trapping and
emission time constants τn, t and τn, e, are adjusted to
achieve the best approximation of the measurement. The
results of the simulation are displayed in Fig. 7. A very
good agreement between measurement and simulation is
found, which reveals the lifetime model and the
Hornbeck–Haynes trapping model to be suitable for
describing the measured apparent excess carrier decay.
The trap density of this sample is determined to
Nt = 5·1013 cm-3.
apparent excess carrier density ∆na [cm ]
Fig. 5: Simulation of the dynamic part of the apparent
excess carrier density as a function of time for
different constant generation rates.
0.1
0
500
1000
1500
2000
time t [µs]
Fig. 6: MWPCD signal measured on an umg-silicon
wafer without surface passivation. The impact of
trapping is reduced by applying a constant bias light.
3.1. Impact of strong trapping
As an example for the impact of strong trapping on
the photoconductance decay an upgraded metallurgicalgrade (umg)-silicon wafer is investigated. In
compensated p-type silicon phosphorous-induced states
in the band gap presumably cause trapping of electrons.
Fig. 6 shows the MWPCD signal measured on umgsilicon wafers without surface passiviation. A surface
passivation using iodine ethanol solution [19] on this
10
16
Region I
10
Region II
16
p0 = 1.6x10 cm
15
12
-3
[Fei] = 1.4x10 cm
13
10
14
10
13
10
12
Nt = 5x10 cm
measurement
simulation
-3
-3
τn, t = 4 µs
τn, e = 40 µs
Nt = (µn+µp)/µp ∆na
0
50
100
150
200
time t [µs]
Fig. 7: Comparison of the MWPCD signal, which is
measured
on
a
siliconnitride
passivated
multicrystalline silicon wafer, with a simulation of
the apparent excess carrier density.
4
CONCLUSION
Minority carrier trapping is often observed in silicon
for photovoltaics. It disturbs the determination of the
excess minority carrier density by conductance
measurements. In this contribution the impact of minority
carrier trapping on photoconductance measurements after
turning off a light pulse is investigated in detail. The
Hornbeck-Haynes-model is applied and the apparent
excess carrier density is simulated for different trap
parameters. For special parameter sets (low trap-escaperatio, trap density smaller than initial excess carrier
density, emission time constant larger than recombination
lifetime) a kink in the apparent excess carrier density
appears, which is correlated to the trap density.
Evaluating this kink, the trap density can be determined
from microwave-detected photoconductance decay
(MWPCD) measurements. The impact of a constant bias
light on the apparent excess carrier density is simulated
and compared with MWPCD measurements. The bias
light eliminates the trapping artifacts, but in this case the
measured recombination lifetime is just a differential one.
5
ACKNOWLEGDEMENT
This work is supported by the German Federal
Ministry of Economics and Technology in the framework
of the project xµ-Material (contract no. 03SF0336A).
6
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