Interface recombination parameters of atomic-layer ...

Interface recombination parameters of atomic-layer-deposited Al2O3 on crystalline silicon F. Werner, A. Cosceev, and J. Schmidt Citation: J. Appl. Phys. 111, 073710 (2012); doi: 10.1063/1.3700241 View online: http://dx.doi.org/10.1063/1.3700241 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v111/i7 Published by the American Institute of Physics.

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JOURNAL OF APPLIED PHYSICS 111, 073710 (2012)

Interface recombination parameters of atomic-layer-deposited Al2O3 on crystalline silicon F. Werner,1 A. Cosceev,2 and J. Schmidt1 1

Institute for Solar Energy Research Hamelin (ISFH), Am Ohrberg 1, 31860 Emmerthal, Germany Institute of Electronic Materials and Devices, Leibniz University Hanover, Schneiderberg 32, 30167 Hanover, Germany 2

(Received 22 December 2011; accepted 2 March 2012; published online 6 April 2012) We measure the energy-dependent interface recombination parameters at the c-Si/Al2O3 interface using the frequency-dependent conductance technique. The hole capture cross section rp ¼ (4 6 3)  1016 cm2 is energy-independent, whereas the electron capture cross section rn shows a pronounced energy dependence and decreases from (7 6 4)  1015 cm2 at midgap over two orders of magnitude toward the conduction band edge Ec. The capture cross section ratio at midgap is highly asymmetric with rn/rp ¼ 5–70. The interface state density Dit is of the order of 1  1011 eV1 cm2 at midgap. Besides the main defect, a second type of defect with a capture cross section below 1019 cm2 is resolved near the valence band edge. Numerical calculations of the injection-dependent effective surface recombination velocity using the measured interface recombination parameters show an excellent agreement with experimental data measured C 2012 American Institute of Physics. using the photoconductance technique. V [http://dx.doi.org/10.1063/1.3700241] I. INTRODUCTION

Aluminum oxide (Al2O3) deposited by atomic layer deposition (ALD) provides an outstanding level of surface passivation on both n- and p-type crystalline silicon1,2 and is an ideal choice for the surface passivation of silicon solar cells.3,4 The optimization of photovoltaic devices toward higher energy conversion efficiencies profits substantially from numerical device simulations, which rely on experimental data and empirical models to quantify the relevant loss mechanisms in the device. A detailed knowledge of the energy-dependent electron-hole recombination parameters at the c-Si/Al2O3 interface enables highly predictive simulations of the interface recombination processes at the Al2O3passivated solar cell surface, and hence would be of great benefit for the development and improvement of novel highefficiency solar cells. The passivation mechanisms at the c-Si/Al2O3 interface have previously been investigated by many authors,5–8 revealing an excellent level of field-effect passivation due to a high negative fixed charge density Qf of about –1012 to –1013 cm2 and a chemical passivation due to a reduced interface state density of the order of 1011 cm2 eV1 at midgap. These measurements however reveal no information about the recombination dynamics, and hence do not allow a determination of the capture cross sections for electrons and holes. Recently, capture cross sections measured by deeplevel transient spectroscopy (DLTS) have been published for Al2O3 layers deposited by plasma-enhanced chemical vapor deposition (PE-CVD),9 showing similarities to the c-Si/SiO2 interface. To our knowledge, no capture cross section values have yet been reported for Al2O3 deposited by atomic layer deposition. In this paper, we investigate the interface recombination parameters of atomic-layer-deposited Al2O3 on c-Si as a function of energetic position in the silicon bandgap 0021-8979/2012/111(7)/073710/6/$30.00

using frequency-dependent conductance measurements10 on MIS- (metal-insulator-silicon) capacitors. II. SAMPLE PREPARATION

All samples analyzed in this paper are fabricated on RCA-cleaned 280 – 300 lm thick 1.3 – 1.5 Xcm p-type FZ-Si, 280 lm thick 1.5 – 1.6 Xcm n-type FZ-Si, or 225 lm thick 1.0 Xcm n-type FZ-Si wafers, respectively. The MIScapacitor samples for the conductance measurements are coated on one side with an Al2O3 film with thicknesses ranging between 10 and 30 nm. The films are deposited by plasma-assisted ALD in an Oxford Instruments FlexALTM reactor. The samples are annealed for 15 min at 425  C to “activate” the passivation,11 then circular aluminum gate contacts are defined on top of the Al2O3 film by electron gun evaporation through a shadow mask, and a full-area aluminum back contact is evaporated on the noncoated side of the wafer. For measurements of the effective carrier lifetime the RCA-cleaned wafers are passivated on both sides by identical Al2O3 films using the same deposition and annealing parameters as for the MIS-samples. III. MEASUREMENT TECHNIQUES A. Frequency-dependent conductance measurements

Fig. 1(a) shows a sketch of the sample structure and the corresponding electric equivalent circuit. The admittance Ym of the Al/Al2O3/Si capacitor is measured as a function of angular frequency x for a fixed gate bias voltage VG superimposed by a small ac variation dV. By varying VG in subsequent measurements the interface parameters are determined as a function of energetic position in the silicon bandgap, which is given by

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C 2012 American Institute of Physics V

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n-type FZ-Si for an Al2O3 layer thickness of 10 nm (solid symbols). Similar plots are obtained for other gate voltages within the accessible range, on p-type substrates, as well as for different Al2O3 layer thicknesses. The relevant interface recombination parameters, i.e., the interface state density Dit and the capture time constant sn for electrons (on n-type samples) or sp for holes (on p-type samples), respectively, are deduced from the peak of the normalized parallel conductance Gp/x as a function of angular frequency x by the following equations:13 Dit ¼ ðq A fD ðrs ÞÞ1 ½Gp =xpeak ;

(3a)

sn=p ¼ np ðrs Þ=xpeak ;

(3b)

where A is the gate contact area and fD(rs) and np(rs) are correction factors explained below. The capture cross sections rn and rp are related to the capture time constants sn and sp via the following equation:14 rn ¼ ðvth sn ns Þ1 ¼ ðvth sn ni Þ1 expðb½E  Ei Þ; FIG. 1. (a) Sketch of the Al/Al2O3/Si capacitors under investigation (left) and corresponding equivalent circuit of the device (right). (b) Exemplary plots of the normalized parallel conductance Gp/x as a function of angular frequency x for three different gate voltages of VG ¼ 0.36, 0.42, and 0.48 V on 1.5 Xcm n-type FZ-Si for an Al2O3 film thickness of 10 nm. The green curve (open symbols, measured on 1.5 Xcm p-Si near flatband and scaled by a factor of 1/4 to account for the different gate area) illustrates a second type of defect at low frequencies and a deformation of the peak shape at high frequencies.

EðVG Þ ¼ Ei þ qub þ qWs ðVG Þ;

(1)

where Ei is the intrinsic Fermi level, q is the elementary charge, ub is the bulk potential, and Ws(VG) is the voltagedependent surface potential, which is obtained by numerical simulation12and verified by quasi-static capacitance-voltage (C-V) measurements. Especially at high frequencies the series resistance Rs plays a major role in the measurement. Hence, an accurate determination of Rs is mandatory. In accumulation, the space charge capacitance Cs and the interface-trap-related admittance Yit [see Fig. 1(a)] can be neglected, and the MIS-capacitor is dominated by the oxide capacitance Cox. Thus, the equivalent circuit can be simplified and both Rs and Cox can be obtained by a least-square fit of the predicted total admittance to a measurement of Ym(x) in accumulation. The equivalent circuit shown in Fig. 1(a) is then used to extract the equivalent parallel conductance Gp, which is the conductive component of Yit ¼ Gp þ ixCp, from the measured admittance Ym ¼ Gm þ ixCm of the complete system, resulting in the equation13 Gp ¼

ðG2m þ x2 C2m Þ  a ; a2 þ x2 C2m

where

a ¼ Gm  Rs ðG2m þ x2 C2m Þ:

(2)

Figure 1(b) shows exemplary plots of the measured normalized parallel conductance Gp/x as a function of the angular frequency x for three different gate voltages VG on 1.5 Xcm

(4)

where vth ¼ 107 cm/s is the thermal velocity of the charge carriers, ns is the electron concentration at the surface, ni is the intrinsic carrier concentration, b ¼ (kBT)1, kB is the Boltzmann constant, and T is the temperature. For holes, ns is replaced by the hole concentration ps at the surface, sn is replaced by sp, and the negative sign in the exponential function changes to positive. The energy range in the silicon bandgap accessible by this analysis extends roughly between 2 kBT from midgap to within 2 kBT from flatband,10 and the conductance signal is dominated by the majority carrier time constant.10 Therefore, both n- and p-type samples are required to cover both halves of the bandgap. The correction factors fD(rs) and np(rs) in Eq. (3a) account for the effect of a spatially nonuniform surface band bending, which is described as a Gaussian distribution with standard deviation rs around the mean value of surface band bending Ws. Both fD(rs) and np(rs) are known functions of rs, which can be calculated numerically13 and, for realistic values of rs, have values in the range of 0.15–0.35 for fD and 2.0–2.5 for np.13 The parameter rs is calculated from the ratio of experimental Gp/x values at the peak frequency xpeak and its multiples nxpeak.13,15 In this study we use n ¼ 5, or n ¼ 1/5 if the corresponding frequency would otherwise exceed the reliable measurement range. We obtain values of rs ¼ 54 6 7 mV on p-type and 57 6 3 mV on n-type samples, respectively. A spatially inhomogeneous fixed charge density Qf due to randomly distributed charges in the Al2O3 is one possible cause of a nonuniform surface potential. These rs values then correspond to a standard deviation of the fixed charge density distribution of rQ.f < 2  1011 cm2, which is at least one order of magnitude lower than typical values of Qf ¼ 4  1012 cm2 for Al2O3 on c-Si.6 B. Carrier lifetime measurements

The effective carrier lifetime seff was measured as a function of excess carrier density Dn on p- and n-type FZ-Si samples passivated on both sides with Al2O3 layers deposited by

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plasma-assisted ALD. We use a Sinton Instruments WCT120 lifetime tester in both quasi-steady-state and transient mode, in order to cover a wide range of excess carrier densities and to reduce calibration errors in the quasi-steadystate measurement. The effective surface recombination velocity (SRV) Seff is calculated from seff using the equation:16 " # 1 w w2 seff  2 ; (5) Seff ¼  s1 b p D 2 where w is the wafer thickness, D is the minority carrier diffusion constant, and sb is the bulk lifetime. For sb we use an empirical parameterization,17 which accounts for intrinsic radiative and Auger recombination. Further losses, e.g., recombination via bulk defects, are neglected. Hence we obtain an upper limit Seff.max of the surface recombination velocity. IV. RECOMBINATION PARAMETERS AT THE c-Si/Al2O3 INTERFACE

The interface state density Dit obtained by the conductance method using Eq. (3a) is shown in Fig. 2 and compared to Dit values obtained by capacitance-voltage (C-V) analysis.6 Both methods are in excellent agreement and yield Dit values near midgap of (6–20)  1010 eV1 cm2, which are virtually independent of energy over a wide range in the bandgap. For numerical simulations the exponential tails toward the band edges were subtracted, as they are attributed to measurement artifacts in the C-V analysis. The remaining defect distribution is well described by a virtually constant Dit with a small Gaussian-shaped peak around an energy of 0.9 eV above the valence band edge, as indicated by the green line in Fig. 2. Figure 3 shows the capture time constants sp (below midgap) and sn (above midgap) calculated from the peak frequency xpeak using Eq. (3b), and the corresponding capture cross sections rp and rn. The solid green lines in Fig. 3(a) are fits to the experimental data, which intersect at an energy E0 of 40 meV below the intrinsic Fermi energy Ei. This energy corresponds to the symmetry point of the intrinsic

FIG. 2. Interface state density Dit as a function of energetic position E – Ev in the silicon bandgap obtained in this work by the conductance method (blue circles) and in Ref. 6 by capacitance-voltage analysis on n-type (triangles down) and p-type (triangles up) samples for 10 nm of Al2O3 deposited by plasma-assisted ALD. Error bars are shown in red for exemplary data points. The green line marks the defect distribution used for the numerical calculations in Sec. V.

FIG. 3. (a) Capture time constants sp (below midgap) and sn (above midgap) as function of energetic position in the silicon bandgap for the main defect (circles) and a second type of defect (diamonds). The solid green lines are fits to the experimental data; the dotted green lines illustrate the relation s / expð6bEÞ expected from Eq. (4) for constant capture cross sections. (b) Capture cross sections rp and rn of the main defect. The solid green lines were calculated using the fit results from part (a). Error bars are shown in red for exemplary data points.

defects at the Si/SiO2 interface, reported earlier by Fu¨ssel et al.18 to lie 40 meV below midgap, which acts as charge neutrality level ECNL in silicon. We obtain capture cross sections of rn ¼ (7 6 4)  1015 cm2 and rp ¼ (4 6 3)  1016 cm2 at midgap. The asymmetry rn/rp ¼ 5 – 70 mainly originates from the difference of 40 meV between E0 and Ei, which results in a factor of expð2b½Ei  E0 Þ  20 in the midgap ratio of rn/rp. The dotted green lines in Fig. 3(a) illustrate the relation s / expð6bEÞ expected from Eq. (4) for energy-independent capture cross sections, which is well fulfilled for sp in the lower half of the bandgap. Hence, the hole capture cross section rp below midgap is virtually independent of energy, while the electron capture cross section rn above midgap decreases toward the conduction band edge Ec, as illustrated in Fig. 3(b). It should be kept in mind, however, that small variations in the capture time constant lead to a large error in the capture cross section, which could conceal a more pronounced energy dependence of rp. For energies closer to the band edges than shown in Fig. 3 it becomes increasingly important to take into account the limited measurement range of the experimental setup. Capture time constants below 3.5  107 s cannot be resolved in our experimental setup, as the peak frequency lies above the maximum measurement frequency of 1 MHz. Furthermore, at high frequencies the value of Gp is large and inaccuracies in the measurement and in the correction for the series resistance can have a large impact on the shape of the Gp/x peak. This is illustrated by the green open symbols in Fig. 1(b) showing a cut-off of the Gp/x peak at high frequencies. This masks the dependence of xpeak on gate bias, and hence yields apparent capture time constants near the detection limit and practically independent of energy. As a

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consequence, the apparent capture cross-sections seem to decrease exponentially with energy, following the factor expð6bEÞ in Eq. (4). Hence, in this work, we disregard all data where the experimental and numerically computed peak shapes deviate significantly. Over a wide range of energies around midgap, the capture cross sections rn and rp shown in Fig. 3(b) are similar to capture cross sections measured for c-Si passivated with high-quality thermal silicon dioxide (SiO2)19 or Al2O3 deposited by PE-CVD.9 This similarity between Al2O3 and SiO2 is attributed to a thin silicon oxide layer2,6 forming at the c-Si/Al2O3 interface, which presumably dictates the chemical conditions, and hence the recombination parameters, at the interface. For several p-type samples a second peak in the Gp/x vs x curve was identified at low frequencies, as shown by the open green symbols in Fig. 1(b) at low frequencies and the blue diamonds in Fig. 3(a). This peak is attributed to a second type of defect with a unique set of recombination parameters D’it, s’p and r’p, which can only be resolved far from midgap where s’p(E) drops below the maximum detection limit of 5 ms. The corresponding capture cross section r’p can be estimated to be below 1019 cm2 near the valence band edge, and hence at least three orders of magnitude smaller than rp of the main defect, presumably making this second defect less important concerning interface recombination. However, the energy dependence of r’p remains unknown as the second defect could not be resolved at energies closer to midgap. V. EFFECTIVE SURFACE RECOMBINATION VELOCITY

We use an iterative numerical model introduced by Girisch et al.,14 assuming flat quasi-Fermi levels in the space charge region, to calculate the surface band bending Ws, and hence the charge carrier densities ns and ps at the c-Si/Al2O3 interface, for a given total surface charge density QR. In this model Ws is varied until charge neutrality at the interface is reached. For this, the acceptor or donor nature of the interface traps needs to be known in order to correctly calculate traps. An upper the charge density Qit stored in the interface Ð limit of Qit is given by Qit:max ¼ qDit dE ¼ (7–23)  1010 cm2, which only plays a role for small surface charge densities QR. However, reducing QR from –4  1012 cm2 for Al2O3-passivated samples to values near zero, e.g., by corona charging, causes additional uncertainty and lateral variation in QR typically larger than Qit.max. Hence, we neglect Qit in our calculations. The recombination rate via interface traps is then calculated using the Shockley-Read-Hall (SRH)20,21 theory, applying the interface recombination parameters presented in the previous section. The second very shallow defect observed on some of our p-type samples was ignored in our calculations. The interface recombination velocity Sit as a function of excess carrier density Dn is then given by the following equation:14,20  ð   ns ps  n2i Eg ns þ n1 ðEÞ ps þ p1 ðEÞ 1 þ Sit ¼ vth Dit ðEÞ dE; Dn rp ðEÞ rn ðEÞ 0 (6)

J. Appl. Phys. 111, 073710 (2012)

where n1(E) and p1(E) are the energy-dependent SRH-densities for a defect level at energy E.14 However, as the conductance method is only sensitive to majority carriers, the capture cross sections rp and rn are only known in one half of the bandgap. We therefore consider two different models represented in Fig. 4(a): in model A we replace the unknown values of rn/p by the midgap values of rn and rp, in model B rn and rp are assumed to be symmetric with respect to the intrinsic Fermi energy Ei. In addition, we consider a case C where the continuum of interface traps in the silicon bandgap is replaced by a single trap level at midgap, using rn ¼ 7  1015 cm2, rp ¼ 4  1016 cm2, and an interface trap density Nit ¼ 1.3  1011 cm2. Figures 4(b) and 4(c) show calculated Sit(Dn) curves using model A, B, and C for 1.3 Xcm p-Si and 1.6 Xcm n-Si, respectively, in comparison with experimental Seff.max values determined using the photoconductance technique and applying Eq. (5). The fixed charge density is Qf ¼ 4  1012 cm2. Due to the large uncertainty in the interface recombination parameters, the calculated absolute Sit values show a large uncertainty. The contribution of recombination via interface traps given by Sit is well below 5 cm/s for all models, emphasizing the excellent level of field-effect passivation caused by the high negative Qf at the c-Si/Al2O3 interface. Due to the low Sit values below the experimental Seff.max, all models are consistent with our experimental data. A more restrictive constraint might apply if all contributions of bulk recombination to Seff.max are taken into account. The large overlap of the uncertainty ranges, however, makes it appear unlikely that one of the assumed models could be refuted purely based on a comparison with experimental lifetime data. In the following we will hence use model A, which yields up to a factor of 2 higher recombination rates compared to model B.

FIG. 4. (a) Sketch of two models used to continue the capture cross sections beyond the measurement range. (b) and (c) Calculated Sit and experimentally determined Seff.max values as a function of excess carrier density Dn for (b) 1.3 Xcm p-Si and (c) 1.6 Xcm n-Si for model A (solid line), model B (dash-dotted line), and assuming a single trap level at midgap (dashed line). The fixed charge density at the c-Si/Al2O3 interface is Qf ¼ 4  1012 cm2.

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Due to the strong suppression of interface recombination caused by the excellent field-effect passivation, standard Al2O3-passivated lifetime samples are unsuited to compare simulated and experimental lifetime data. We use corona charging as a tool to vary the total surface charge density QR and hence vary the interface recombination rate. For a moderate or low level of field-effect passivation Seff strongly depends on QR and spatial variations of QR have to be taken into account. We assume a Gaussian distribution of the surface charge density with a standard deviation rQ, which initially is given by rQ ¼ 2  1011 cm2 obtained from the conductance measurements. During corona charging rQ is increased by 5% of the deposited corona charge density Qc, which roughly corresponds to the lateral inhomogeneity of Qc over the active sensor area of 6 cm2 of the WCT-120 lifetime tester. Then, Seff(Dn, QR þ DQ) is calculated for a range of charge densities within 2.5 standard deviations around QR and folded with a Gaussian distribution to yield Seff(Dn). The inset in Fig. 5 shows the experimentally determined (black symbols) and numerically calculated (red line) effective SRV Seff for 1.3 Xcm p-type Si as a function of total surface charge density QR given by the sum of fixed charge density Qf ¼ 3.8  1012 cm2 and deposited corona charge density Qc. In this case, Seff is calculated from seff at a fixed excess carrier density of Dn ¼ 1015 cm3. Figure 5 shows the corresponding injection-level-dependent SRV Seff(Dn) for several data points in the inset, with QR values ranging from 3.8  1012 cm2 (bottom) to 0 (top). The calculated Seff values include the interface recombination velocity Sit and,

in order to explain the injection level dependence of the lower plot (QR ¼ 3.8  1012 cm2, black line), an increased recombination in the space charge region with an electron/ hole lifetime of sn0 ¼ 1.5  106 s and sp0 ¼ 1.5  104 s, respectively.22,23 At lower jQRj values interface recombination dominates and recombination in the space charge region becomes negligible. The same type of plot is shown in Fig. 6 for 1.0 Xcm n-type Si. Due to the different surface treatment, however, the electron/hole lifetimes sn0 and sp0 in the space charge region are reduced by a factor of 5. The calculated Seff(Dn) curves are in excellent agreement with the experimental data, taking into account that recombination via bulk defects has been neglected and the experimental data only presents an upper limit Seff.max of the SRV. However, we observe two exceptions: (i) For QR near zero, Seff seems to be systematically overestimated, although calculation and experiment agree within the uncertainty range due to the large uncertainty in the capture cross section values. For QR near zero Seff is sensitive to small changes in QR of the order of 1011 cm2, which is below the smallest charging step of DQc  5  1011 cm2 in our experimental setup. Hence, a slight deviation from QR ¼ 0 or assuming a larger inhomogeneity of the deposited corona charge is expected to lead to a better agreement. (ii) For large values of QR > þ 1012 cm2, Seff is significantly underestimated. We attribute this to damage occurring during corona charging, as the same effect is observed for both p- and n-type samples, and hence is unlikely to be related to the charge polarity. This interpretation is supported by our experimental finding that after

FIG. 5. Calculated (lines) and experimentally determined (symbols) effective SRV Seff for 1.3 Xcm p-Si as a function of excess carrier density Dn for four different surface charge densities QR ranging from 3.8  1012 cm2 (bottom) to 0 (top). The corresponding values of QR are given in the plot. A wider range of surface charge densities is shown in the inset, where Seff at Dn ¼ 1015 cm3 is plotted vs QR.

FIG. 6. Calculated (lines) and experimentally determined (symbols) effective SRV Seff for 1.0 Xcm n-Si as a function of excess carrier density Dn for four different surface charge densities QR ranging from 3.8  1012 cm2 (bottom) to 2  1011 cm2 (top). The corresponding values of QR are given in the plot. A wider range of surface charge densities is shown in the inset, where Seff at Dn ¼ 1015 cm3 is plotted vs QR.

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removal of the corona charges using de-ionized water the carrier lifetime is reduced compared to the initial lifetime of the sample. VI. CONCLUSIONS

In conclusion, the interface between p- and n-type FZ-Si and an amorphous Al2O3 surface passivation layer deposited by plasma-assisted ALD was investigated by conductance measurements. The hole capture cross section in the lower half of the bandgap, rp ¼ (4 6 3)  1016 cm2, was found to be independent of energy. The electron capture cross section rn in the upper half of the bandgap on the other hand shows a pronounced energy dependence and decreases from rn ¼ (7 6 4)  1015 cm2 at midgap over two orders of magnitude toward the conduction band edge Ec. The capture cross section ratio at midgap is highly asymmetric with rn/rp ¼ 5 – 70. The capture cross sections are similar to values reported for SiO2, suggesting a strong influence of the interfacial SiOx layer on the chemical passivation properties. The interface state density Dit shows an excellent agreement with values obtained from capacitance-voltage analysis, yielding Dit values around the middle of the bandgap of the order of 1011 eV1 cm2. A second type of defect was detected, which is considered negligible concerning interface recombination due to its very low r’p < 1019 cm2 near the valence band edge. The injection level dependent surface recombination velocity was calculated numerically based on these interface recombination parameters for Al2O3-passivated samples and compared with experimental data measured at different surface charge densities. The numerical simulations show an excellent agreement to the experimental data for both n- and p-Si and for a wide range of surface charge densities. For small surface charge densities close to zero both experimental and calculated SRVs show a strong dependence on excess carrier density. For large surface charge densities, on the other hand, e.g., for annealed Al2O3passivated c-Si, interface recombination is shown to be effectively suppressed and virtually independent of excess carrier density for both n- and p-Si. ACKNOWLEDGMENTS

Funding was provided by the State of Lower Saxony and the German Ministry for the Environment, Nature

J. Appl. Phys. 111, 073710 (2012)

Conservation and Nuclear Safety (BMU) under contract number 0325050 (“ALD”).

1

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