Comparison between transient and frequency modulated excitation: Application to silicon nitride and aluminum oxide coatings of silicon D. Klein, W. Ohm, S. Fengler, and M. Kunst Citation: Review of Scientific Instruments 85, 065105 (2014); doi: 10.1063/1.4880201 View online: http://dx.doi.org/10.1063/1.4880201 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Surface passivation of nano-textured silicon solar cells by atomic layer deposited Al2O3 films J. Appl. Phys. 114, 174301 (2013); 10.1063/1.4828732 High-quality surface passivation of silicon using native oxide and silicon nitride layers Appl. Phys. Lett. 101, 021601 (2012); 10.1063/1.4733336 Modulation of atomic-layer-deposited Al2O3 film passivation of silicon surface by rapid thermal processing Appl. Phys. Lett. 99, 052103 (2011); 10.1063/1.3616145 Detailed study of the composition of hydrogenated SiN x layers for high-quality silicon surface passivation J. Appl. Phys. 92, 2602 (2002); 10.1063/1.1495529 Hydrogenation of defects in edge-defined film-fed grown aluminum-enhanced plasma enhanced chemical vapor deposited silicon nitride multicrystalline silicon J. Appl. Phys. 87, 7551 (2000); 10.1063/1.373427
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 065105 (2014)
Comparison between transient and frequency modulated excitation: Application to silicon nitride and aluminum oxide coatings of silicon D. Klein,1 W. Ohm,2 S. Fengler,2 and M. Kunst1 1 Helmholtz-Zentrum Berlin für Materialien und Energie, Institute Solar Fuels (E-IF), Hahn-Meitner-Platz 1, D-14109 Berlin, Germany 2 Helmholtz-Zentrum Berlin für Materialien und Energie, Institut für Heterogene Materialsysteme (E-IH), Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
(Received 20 March 2014; accepted 15 May 2014; published online 6 June 2014) Contactless measurements of the lifetime of charge carriers are presented with varying ways of photo excitation: with and without bias light and pulsed and frequency modulated. These methods are applied to the study of the surface passivation of single crystalline silicon by a-SiNx :H and Al2 O3 coatings. The properties of these coatings are investigated under consideration of the merits of the different methods. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4880201] I. INTRODUCTION
B. Photo-conductance measurement equipment
The determination of the lifetime of excess charge carriers in semiconductor is of essential importance for electronic and opto-electronic devices. For example, the efficiency of volume and surface treatments, crucial for photovoltaic and photo-catalytic devices, can be detected by lifetime measurements. Measurement of photo-conductance decay is a well-known technique to determine the lifetime of excess charge-carrier.1, 2 In this work, a comparison between three varieties of photo-conductance measurements will be presented. They are all based on measurements of the change of the microwave energy absorbed in the sample induced by optical excitation. The difference lies in the generation of the excess charge carriers: pulsed, harmonically modulated, and under bias illumination. A description of the measurements will be first given and in the last part, a practical use of the measurements will be shown by the investigation of two different coatings, i.e., silicon nitride (a-SiNx :H) and aluminum oxide (Al2 O3 ) deposited on crystalline silicon. The experimental results will be presented and the merits of the different methods discussed.
The effect of electrical passivation coating on the lifetime of excess charge-carrier in mono-crystalline silicon was measured by contactless photo-conductance measurements in the microwave frequency range.4 In these measurements (Fig. 1) the sample is placed in a waveguide, on one side it is irradiated by 10 GHz microwave generated by a Gunn diode, on the other side it is positioned a variable short circuit which will reflect the microwave. A good adjustment of the short circuit will optimize the absorption of the microwaves in the sample and enhance the sensitivity of the detection. During the measurement, a light source depending on the measurement method will generate charge carriers in the sample. Reflected microwaves will pass through a circulator and will be measured by a microwave detector diode. Three different varieties of light excitation will be used:5–7 –Excitation by a laser pulse (10 ns FWHM) at 1064 nm. This transient method will be named the Time Resolved Microwave Conductivity (TRMC) measurement. –Frequency modulated excitation by a periodic modulation at different frequencies of the intensity of a cw laser. The modulation is performed by an acousto-optic modulator (AOM) where the zeroth order of the AOM yields the stationary bias illumination. The modulation depth is about 5% and the intensities given for this method represent the laser intensity without modulation, the bias illumination. This method is named Frequency Resolved Microwave Conductivity (FRMC). –The third method, TRMC with bias light (b-TRMC), is a combination of both methods described above and uses illumination of the sample with a stationary bias light and performs a small perturbation with a light pulse at the same wavelength. This will be done with the AOM. The pulse has a square shape and its length can be varied. The faster pulse is set to 10 μs in order to have enough sensitivity to perform a measurement.
II. EXPERIMENT A. Sample preparation
The samples used are mono-crystalline silicon substrates (n c-Si 21 cm, 500 μm single side polished or p c-Si 130 cm, 350 μm double side polished) covered on both sides with silicon nitride (a-SiNx :H) or aluminum oxide (Al2 O3 ). The substrates are first cleaned and prior to the deposition, the oxide surface layer is etched in 1% HF. The a-SiNx :H layer was deposited by plasma enhanced chemical vapor deposition (PECVD) which allowed an easy modification of the parameters of deposition and so the properties of the coating itself. The conditions for deposition of the silicon nitride were 32 sccm Silane (SiH4 ), 200 sccm Ammonia (NH3 ), and 54 sccm Nitrogen (N2 ) at 350 ◦ C. The layer is 70 nm thick. The Al2 O3 layer was deposited by the ILGAR technique.3 0034-6748/2014/85(6)/065105/9/$30.00
The intensity of the laser light can be modified by optical filters with different optical densities. The TRMC, FRMC,
85, 065105-1
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065105-2
Klein et al.
Rev. Sci. Instrum. 85, 065105 (2014)
FIG. 1. Equipment of the photoconductivity measurement device in the case of (1) pulse excitation and (2) modulated excitation.
and b-TRMC methods are contactless measurements of the free charge-carrier absorption performed in the gigahertz (GHz) frequency range. The lateral dimensions of the sample are considered much larger than the thickness d and consequently the system can be considered as one-dimensional where excitation light and microwaves are directed on the same spot and perpendicular to the sample. C. The experimental signal and charge carrier kinetics
The techniques are based on the measurement of the reflected microwave power in the small perturbation range. The techniques measure the relative change of the reflected microwave power (MP) upon pulsed optical excitation (for TRMC) and upon optical modulation (for FRMC and bTRMC) which is proportional to the photo-conductance P induced by these excitations:8 MP = B · P . (1) MP With B, a constant coefficient and where MP refers to the unperturbed sample for TRMC measurements and to the sample under the non-modulated bias perturbation for b-TRMC and FRMC measurements. The photo-conductance is defined as follows: d P =
σ (x)dx,
(2)
0
with
Equations (2)–(4) imply that the contribution of the excess charge carriers to the signal does not depend of their position in the sample. The dependence of the number of excess charge-carriers and consequently P on time t since the start of the excitation is monitored for pulsed excitation (TRMC method) or on the modulation frequency (FRMC method). The mechanism of charge carrier decay in silicon can be described by three processes:9–11 –Auger recombination. –Bimolecular radiative recombination. –Recombination and trapping via defects. At low injection level, which is the case here, the third case represents the main recombination process in silicon. This case reflects the interaction between mobile chargecarriers and defects in the lattice and it is described by the Shockley-Read-Hall theory.11, 12 As said previously, the only difference between the methods studied in this paper is the way used to generate the excess charge-carriers: –For the transient excitation mode (TRMC), the number of excess charge-carriers increases from zero to the maximum value during the excitation and decays afterwards. The decay of the TRMC signal reflects the decay of the number of excess charge carrier (Eqs. (1)–(4)). The most general definition of the TRMC decay time and so the effective lifetime of the excess charge carriers is given by 1
σ = qnμn + qpμp ,
(3)
where σ is the excess conductivity at time t, q the elementary charge, n(x) (p(x)) the concentration of excess electron (hole) at a distance x in the sample, and μn (μp ) the electron (hole) mobility. If we assume that an equal number of electrons and holes are generated, then, d n(x)(μn + μp )dx.
P = q 0
(4)
tr τeff
=−
1 ∂P (t) , P (t) t
(5)
with t, the time passed since the start of the excitation. –For the modulation mode (FRMC), the sample is continuously illuminated by a bias light and the modulation represents a small perturbation (generation of excess charge-carriers). The FRMC signal P(ω) is measured as a function of the modulation frequency ω. The lifetime determined by this kind of excitation represents the differential lifetime for the bias induced (i.e., stationary) excess charge carrier concentration.
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065105-3
Klein et al.
Rev. Sci. Instrum. 85, 065105 (2014)
In the modulation mode the signal, P(ω), is given by13 P (ω = 0) P (ω) = mo 2 . 1 + ωτeff
(6)
TABLE I. b-TRMC differential lifetimes obtained for different pulse length for p-type silicon covered with silicon nitride. Pulse length (μs) Differential lifetime (μs)
1100 735
220 770
110 790
22 790
11 790
D. The generation of excess charge carriers
A. b-TRMC
The generation function G(x,t) can be expressed as the product of a time-dependent function representing the temporal profile of the excitation f(t) and a spatial-dependent function g(x) representing the spatial extension of the excitation given by the Beers law,
The TRMC measurements with bias light (b-TRMC) are very interesting because they allow a direct comparison with lifetimes found by FRMC measurements due to the stationary part of the excitation. In general, the bias light tends to saturate defects and the b-TRMC signal is rather sensitive to recombination. Comparison with TRMC signals can provide useful information. Unlike TRMC, the pulse in b-TRMC measurements is longer. As long as we measure with a small modulation of the intensity of the bias light (5% in this case) the length of the pulse should not play a role: even with a long pulse the maximum of the perturbation will be small and remain in the small perturbation condition. This happens if the power intensity of the bias is not too high and the effective lifetime is smaller than the pulse repetition frequency. In order to confirm this, experiments with different pulse lengths have been performed. Table I shows the (exponential) decay time of the signal for different length of the excitation pulse. An exponential fit of the signal decay after the pulse shows no significant modification of the differential lifetime (760 μs ± 4%) as shown in Table I. The measurements show that the lifetimes determined do not depend on the pulse length in this range. All measurements presented in this work have been performed with 1.1 ms pulses. It must be noted that the amplitude of the b-TRMC signal (i.e., the signal height after the end of the pulse) reflects the convolution of the generation function of excess charge carriers with an average of the relevant decay processes during the pulse characterized by the effective differential lifetime.
G(x, t) = f(t) · g(x).
(7)
For the experiments presented here the shape of the excitation function f(t) for the pulsed excitation (TRMC) can be considered as a delta function because all decay processes are much slower than the duration of the excitation pulse. In the case of modulated excitation, the generation function Gmod (x,t) is composed of two parts, a dc-part representing the bias illumination and an ac-part coming from the modulation. Gmod (x, t) = gdc (x) + gac (x) · ei τ ,
(8)
where is the frequency of the modulation. The evolution of the b-TRMC signal is also composed of a dc and an ac-part. Here, the pulse is not a delta function anymore. Already during the excitation, excess charge carrier decay occurs. Evolution of the number of excess charge carriers (n(t)) as a function of the time is given by n(t) = n0 e−t/τ ,
(9)
where τ is in this case a differential effective lifetime τ diff .14 The differential character of b-TRMC at low bias level implies that the signal decay is exponential as given by Eq. (9), if the differential lifetime is smaller than the inverse of the pulse repetition frequency. Only excitation by photons with energy larger than the band gap will be considered. So an equal concentration of electrons (n0 (t)) and holes (p0 (t)) is generated. The spatial distribution of the electron hole pairs (g(x)) generated is given by Beers law assuming that for semiconductors the quantum efficiency is unity. So the density of electron-hole pairs generated by a monochromatic light of wavelength λ in a sample with absorption coefficient α λ with a photon density Iλ is given by n0 (x, t) = p0 (x, t) = (1 − R) · f (t) · Iλ · αλ · e−αx , (10) where the factor (1 − R) takes the reflection of the incident light into account and multiple reflections are neglected. III. EVALUATION OF THE EXPERIMENTS
TRMC, FRMC, and b-TRMC measurements were performed to compare the effect induced by two different kinds of coatings (a-SiNx :H or Al2 O3 ) on silicon substrates. Previously to the interpretation of the measurements some words must be said about the methods for a better understanding.
B. FRMC
The differential FRMC lifetime τ diff is obtained by fitting the FRMC signal with Eq. (6). Another way to obtain the differential lifetime is by the use of the phase shift between the reflected microwave power and the light excitation as a function of the modulation frequency,13 tan ϕ(ω) = ωτdiff .
(11)
With ϕ the phase shift at frequency ω. This method will not be used in the present work. Due to the bias light, FRMC measurements give the differential lifetime for a specific intensity of illumination, i.e., stationary concentration of excess charge carriers. A third way to analyze the data is to use the amplitude (A) of the FRMC signal, i.e., the FRMC signal height as the frequency tends to zero. A is proportional to the stationary concentration of excess charge carriers induced by the modulation: A = Cn = CGτdiff .
(12)
With G the generation of excess charge carriers, τ diff the differential lifetime of excess charge carriers, and C is a constant.
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065105-4
Klein et al.
Rev. Sci. Instrum. 85, 065105 (2014)
FIG. 2. b-TRMC signal induced by 1064 nm light of p-Si covered with Al2 O3 (full markers) and a-SiNx :H (hollow markers) coating deposited on p Si (130 cm, 350 μm) for different bias intensities as indicated on the graph. Lines are the exponential fits of the curves.
This equation can be used as a simple verification in order to avoid errors due to the measurement device. To determine the lifetime, a fit with Eq. (6) must be preferred. C. TRMC
For TRMC measurements induced by 1064 nm light pulses as presented here the theory developed for the principal mode in Refs. 4 and 7 is used. It must be noted that the TRMC amplitude, i.e., the (maximum) signal height after the excitation, is proportional to the number of photons of the excitation light absorbed if decay processes during the excitation of about 10 ns can be neglected. For a more sound interpretation of the TRMC results complementary SPV measurements were performed as described previously.15 The SPV measurements are induced by 532 nm (10 ns FWHM) pulses. The usual sign convention for the SPV signal is used where positive signals refer to a positive charge at the surface.15 The theory of excess charge carrier kinetics for TRMC measurements is given in Refs. 4 and 7.
pSi/Al2 O3 system whereas for higher bias power the lifetime of the pSi/a-SiNx :H system is larger. It must be noted that b-TRMC (and also FRMC) measurements of pSi/Al2 O3 at 17 mW cm–2 have not been performed because they were felt to be of less importance due to the only minor change of the behavior in this range. More important is the observation that at higher bias level (68 and 135 mW cm−2 ) the b-TRMC signal of the pSi/a-SiNx :H system is no longer characterized by an exponential decay. This is explained by the high excess charge carrier concentration corresponding to the modulation depth of 5% at these power densities of the excitation density. Consequently, the approximation of small perturbation and so Eq. (1) is no longer valid and/or the lifetime is too long compared to the pulse repetition frequency. For the pSi/Al2 O3 system the concentration of excess charge carriers is much larger and the lifetime much smaller at the same power densities. So for this system the bTRMC signal is exponential. TABLE II. Differential lifetimes obtained by FRMC and b-TRMC measurements for an Al2 O3 and a-SiNx :H coating on a p Si substrate(130 cm, 350 μm) under different bias intensities. Al2 O3 coating
IV. RESULTS AND DISCUSSION A. p-type silicon substrate
b-TRMC measurements of pSi/Al2 O3 (full markers) and pSi/a-SiNx :H (empty markers) performed at 1064 nm bias excitation are shown in Fig. 2. The corresponding differential lifetimes are listed in Table II. For both systems the differential lifetimes increase strongly with increasing bias power, i.e., stationary excess charge carrier concentration. At low bias intensity (
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 065105 (2014)
Comparison between transient and frequency modulated excitation: Application to silicon nitride and aluminum oxide coatings of silicon D. Klein,1 W. Ohm,2 S. Fengler,2 and M. Kunst1 1 Helmholtz-Zentrum Berlin für Materialien und Energie, Institute Solar Fuels (E-IF), Hahn-Meitner-Platz 1, D-14109 Berlin, Germany 2 Helmholtz-Zentrum Berlin für Materialien und Energie, Institut für Heterogene Materialsysteme (E-IH), Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
(Received 20 March 2014; accepted 15 May 2014; published online 6 June 2014) Contactless measurements of the lifetime of charge carriers are presented with varying ways of photo excitation: with and without bias light and pulsed and frequency modulated. These methods are applied to the study of the surface passivation of single crystalline silicon by a-SiNx :H and Al2 O3 coatings. The properties of these coatings are investigated under consideration of the merits of the different methods. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4880201] I. INTRODUCTION
B. Photo-conductance measurement equipment
The determination of the lifetime of excess charge carriers in semiconductor is of essential importance for electronic and opto-electronic devices. For example, the efficiency of volume and surface treatments, crucial for photovoltaic and photo-catalytic devices, can be detected by lifetime measurements. Measurement of photo-conductance decay is a well-known technique to determine the lifetime of excess charge-carrier.1, 2 In this work, a comparison between three varieties of photo-conductance measurements will be presented. They are all based on measurements of the change of the microwave energy absorbed in the sample induced by optical excitation. The difference lies in the generation of the excess charge carriers: pulsed, harmonically modulated, and under bias illumination. A description of the measurements will be first given and in the last part, a practical use of the measurements will be shown by the investigation of two different coatings, i.e., silicon nitride (a-SiNx :H) and aluminum oxide (Al2 O3 ) deposited on crystalline silicon. The experimental results will be presented and the merits of the different methods discussed.
The effect of electrical passivation coating on the lifetime of excess charge-carrier in mono-crystalline silicon was measured by contactless photo-conductance measurements in the microwave frequency range.4 In these measurements (Fig. 1) the sample is placed in a waveguide, on one side it is irradiated by 10 GHz microwave generated by a Gunn diode, on the other side it is positioned a variable short circuit which will reflect the microwave. A good adjustment of the short circuit will optimize the absorption of the microwaves in the sample and enhance the sensitivity of the detection. During the measurement, a light source depending on the measurement method will generate charge carriers in the sample. Reflected microwaves will pass through a circulator and will be measured by a microwave detector diode. Three different varieties of light excitation will be used:5–7 –Excitation by a laser pulse (10 ns FWHM) at 1064 nm. This transient method will be named the Time Resolved Microwave Conductivity (TRMC) measurement. –Frequency modulated excitation by a periodic modulation at different frequencies of the intensity of a cw laser. The modulation is performed by an acousto-optic modulator (AOM) where the zeroth order of the AOM yields the stationary bias illumination. The modulation depth is about 5% and the intensities given for this method represent the laser intensity without modulation, the bias illumination. This method is named Frequency Resolved Microwave Conductivity (FRMC). –The third method, TRMC with bias light (b-TRMC), is a combination of both methods described above and uses illumination of the sample with a stationary bias light and performs a small perturbation with a light pulse at the same wavelength. This will be done with the AOM. The pulse has a square shape and its length can be varied. The faster pulse is set to 10 μs in order to have enough sensitivity to perform a measurement.
II. EXPERIMENT A. Sample preparation
The samples used are mono-crystalline silicon substrates (n c-Si 21 cm, 500 μm single side polished or p c-Si 130 cm, 350 μm double side polished) covered on both sides with silicon nitride (a-SiNx :H) or aluminum oxide (Al2 O3 ). The substrates are first cleaned and prior to the deposition, the oxide surface layer is etched in 1% HF. The a-SiNx :H layer was deposited by plasma enhanced chemical vapor deposition (PECVD) which allowed an easy modification of the parameters of deposition and so the properties of the coating itself. The conditions for deposition of the silicon nitride were 32 sccm Silane (SiH4 ), 200 sccm Ammonia (NH3 ), and 54 sccm Nitrogen (N2 ) at 350 ◦ C. The layer is 70 nm thick. The Al2 O3 layer was deposited by the ILGAR technique.3 0034-6748/2014/85(6)/065105/9/$30.00
The intensity of the laser light can be modified by optical filters with different optical densities. The TRMC, FRMC,
85, 065105-1
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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 130.70.241.163 On: Sat, 20 Dec 2014 18:56:21
065105-2
Klein et al.
Rev. Sci. Instrum. 85, 065105 (2014)
FIG. 1. Equipment of the photoconductivity measurement device in the case of (1) pulse excitation and (2) modulated excitation.
and b-TRMC methods are contactless measurements of the free charge-carrier absorption performed in the gigahertz (GHz) frequency range. The lateral dimensions of the sample are considered much larger than the thickness d and consequently the system can be considered as one-dimensional where excitation light and microwaves are directed on the same spot and perpendicular to the sample. C. The experimental signal and charge carrier kinetics
The techniques are based on the measurement of the reflected microwave power in the small perturbation range. The techniques measure the relative change of the reflected microwave power (MP) upon pulsed optical excitation (for TRMC) and upon optical modulation (for FRMC and bTRMC) which is proportional to the photo-conductance P induced by these excitations:8 MP = B · P . (1) MP With B, a constant coefficient and where MP refers to the unperturbed sample for TRMC measurements and to the sample under the non-modulated bias perturbation for b-TRMC and FRMC measurements. The photo-conductance is defined as follows: d P =
σ (x)dx,
(2)
0
with
Equations (2)–(4) imply that the contribution of the excess charge carriers to the signal does not depend of their position in the sample. The dependence of the number of excess charge-carriers and consequently P on time t since the start of the excitation is monitored for pulsed excitation (TRMC method) or on the modulation frequency (FRMC method). The mechanism of charge carrier decay in silicon can be described by three processes:9–11 –Auger recombination. –Bimolecular radiative recombination. –Recombination and trapping via defects. At low injection level, which is the case here, the third case represents the main recombination process in silicon. This case reflects the interaction between mobile chargecarriers and defects in the lattice and it is described by the Shockley-Read-Hall theory.11, 12 As said previously, the only difference between the methods studied in this paper is the way used to generate the excess charge-carriers: –For the transient excitation mode (TRMC), the number of excess charge-carriers increases from zero to the maximum value during the excitation and decays afterwards. The decay of the TRMC signal reflects the decay of the number of excess charge carrier (Eqs. (1)–(4)). The most general definition of the TRMC decay time and so the effective lifetime of the excess charge carriers is given by 1
σ = qnμn + qpμp ,
(3)
where σ is the excess conductivity at time t, q the elementary charge, n(x) (p(x)) the concentration of excess electron (hole) at a distance x in the sample, and μn (μp ) the electron (hole) mobility. If we assume that an equal number of electrons and holes are generated, then, d n(x)(μn + μp )dx.
P = q 0
(4)
tr τeff
=−
1 ∂P (t) , P (t) t
(5)
with t, the time passed since the start of the excitation. –For the modulation mode (FRMC), the sample is continuously illuminated by a bias light and the modulation represents a small perturbation (generation of excess charge-carriers). The FRMC signal P(ω) is measured as a function of the modulation frequency ω. The lifetime determined by this kind of excitation represents the differential lifetime for the bias induced (i.e., stationary) excess charge carrier concentration.
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065105-3
Klein et al.
Rev. Sci. Instrum. 85, 065105 (2014)
In the modulation mode the signal, P(ω), is given by13 P (ω = 0) P (ω) = mo 2 . 1 + ωτeff
(6)
TABLE I. b-TRMC differential lifetimes obtained for different pulse length for p-type silicon covered with silicon nitride. Pulse length (μs) Differential lifetime (μs)
1100 735
220 770
110 790
22 790
11 790
D. The generation of excess charge carriers
A. b-TRMC
The generation function G(x,t) can be expressed as the product of a time-dependent function representing the temporal profile of the excitation f(t) and a spatial-dependent function g(x) representing the spatial extension of the excitation given by the Beers law,
The TRMC measurements with bias light (b-TRMC) are very interesting because they allow a direct comparison with lifetimes found by FRMC measurements due to the stationary part of the excitation. In general, the bias light tends to saturate defects and the b-TRMC signal is rather sensitive to recombination. Comparison with TRMC signals can provide useful information. Unlike TRMC, the pulse in b-TRMC measurements is longer. As long as we measure with a small modulation of the intensity of the bias light (5% in this case) the length of the pulse should not play a role: even with a long pulse the maximum of the perturbation will be small and remain in the small perturbation condition. This happens if the power intensity of the bias is not too high and the effective lifetime is smaller than the pulse repetition frequency. In order to confirm this, experiments with different pulse lengths have been performed. Table I shows the (exponential) decay time of the signal for different length of the excitation pulse. An exponential fit of the signal decay after the pulse shows no significant modification of the differential lifetime (760 μs ± 4%) as shown in Table I. The measurements show that the lifetimes determined do not depend on the pulse length in this range. All measurements presented in this work have been performed with 1.1 ms pulses. It must be noted that the amplitude of the b-TRMC signal (i.e., the signal height after the end of the pulse) reflects the convolution of the generation function of excess charge carriers with an average of the relevant decay processes during the pulse characterized by the effective differential lifetime.
G(x, t) = f(t) · g(x).
(7)
For the experiments presented here the shape of the excitation function f(t) for the pulsed excitation (TRMC) can be considered as a delta function because all decay processes are much slower than the duration of the excitation pulse. In the case of modulated excitation, the generation function Gmod (x,t) is composed of two parts, a dc-part representing the bias illumination and an ac-part coming from the modulation. Gmod (x, t) = gdc (x) + gac (x) · ei τ ,
(8)
where is the frequency of the modulation. The evolution of the b-TRMC signal is also composed of a dc and an ac-part. Here, the pulse is not a delta function anymore. Already during the excitation, excess charge carrier decay occurs. Evolution of the number of excess charge carriers (n(t)) as a function of the time is given by n(t) = n0 e−t/τ ,
(9)
where τ is in this case a differential effective lifetime τ diff .14 The differential character of b-TRMC at low bias level implies that the signal decay is exponential as given by Eq. (9), if the differential lifetime is smaller than the inverse of the pulse repetition frequency. Only excitation by photons with energy larger than the band gap will be considered. So an equal concentration of electrons (n0 (t)) and holes (p0 (t)) is generated. The spatial distribution of the electron hole pairs (g(x)) generated is given by Beers law assuming that for semiconductors the quantum efficiency is unity. So the density of electron-hole pairs generated by a monochromatic light of wavelength λ in a sample with absorption coefficient α λ with a photon density Iλ is given by n0 (x, t) = p0 (x, t) = (1 − R) · f (t) · Iλ · αλ · e−αx , (10) where the factor (1 − R) takes the reflection of the incident light into account and multiple reflections are neglected. III. EVALUATION OF THE EXPERIMENTS
TRMC, FRMC, and b-TRMC measurements were performed to compare the effect induced by two different kinds of coatings (a-SiNx :H or Al2 O3 ) on silicon substrates. Previously to the interpretation of the measurements some words must be said about the methods for a better understanding.
B. FRMC
The differential FRMC lifetime τ diff is obtained by fitting the FRMC signal with Eq. (6). Another way to obtain the differential lifetime is by the use of the phase shift between the reflected microwave power and the light excitation as a function of the modulation frequency,13 tan ϕ(ω) = ωτdiff .
(11)
With ϕ the phase shift at frequency ω. This method will not be used in the present work. Due to the bias light, FRMC measurements give the differential lifetime for a specific intensity of illumination, i.e., stationary concentration of excess charge carriers. A third way to analyze the data is to use the amplitude (A) of the FRMC signal, i.e., the FRMC signal height as the frequency tends to zero. A is proportional to the stationary concentration of excess charge carriers induced by the modulation: A = Cn = CGτdiff .
(12)
With G the generation of excess charge carriers, τ diff the differential lifetime of excess charge carriers, and C is a constant.
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065105-4
Klein et al.
Rev. Sci. Instrum. 85, 065105 (2014)
FIG. 2. b-TRMC signal induced by 1064 nm light of p-Si covered with Al2 O3 (full markers) and a-SiNx :H (hollow markers) coating deposited on p Si (130 cm, 350 μm) for different bias intensities as indicated on the graph. Lines are the exponential fits of the curves.
This equation can be used as a simple verification in order to avoid errors due to the measurement device. To determine the lifetime, a fit with Eq. (6) must be preferred. C. TRMC
For TRMC measurements induced by 1064 nm light pulses as presented here the theory developed for the principal mode in Refs. 4 and 7 is used. It must be noted that the TRMC amplitude, i.e., the (maximum) signal height after the excitation, is proportional to the number of photons of the excitation light absorbed if decay processes during the excitation of about 10 ns can be neglected. For a more sound interpretation of the TRMC results complementary SPV measurements were performed as described previously.15 The SPV measurements are induced by 532 nm (10 ns FWHM) pulses. The usual sign convention for the SPV signal is used where positive signals refer to a positive charge at the surface.15 The theory of excess charge carrier kinetics for TRMC measurements is given in Refs. 4 and 7.
pSi/Al2 O3 system whereas for higher bias power the lifetime of the pSi/a-SiNx :H system is larger. It must be noted that b-TRMC (and also FRMC) measurements of pSi/Al2 O3 at 17 mW cm–2 have not been performed because they were felt to be of less importance due to the only minor change of the behavior in this range. More important is the observation that at higher bias level (68 and 135 mW cm−2 ) the b-TRMC signal of the pSi/a-SiNx :H system is no longer characterized by an exponential decay. This is explained by the high excess charge carrier concentration corresponding to the modulation depth of 5% at these power densities of the excitation density. Consequently, the approximation of small perturbation and so Eq. (1) is no longer valid and/or the lifetime is too long compared to the pulse repetition frequency. For the pSi/Al2 O3 system the concentration of excess charge carriers is much larger and the lifetime much smaller at the same power densities. So for this system the bTRMC signal is exponential. TABLE II. Differential lifetimes obtained by FRMC and b-TRMC measurements for an Al2 O3 and a-SiNx :H coating on a p Si substrate(130 cm, 350 μm) under different bias intensities. Al2 O3 coating
IV. RESULTS AND DISCUSSION A. p-type silicon substrate
b-TRMC measurements of pSi/Al2 O3 (full markers) and pSi/a-SiNx :H (empty markers) performed at 1064 nm bias excitation are shown in Fig. 2. The corresponding differential lifetimes are listed in Table II. For both systems the differential lifetimes increase strongly with increasing bias power, i.e., stationary excess charge carrier concentration. At low bias intensity (
