Minority carrier lifetime in indium doped silicon for photovoltaics

For photovoltaics, switching the p‐type dopant in silicon wafers from boron to indium may be advantageous as boron plays an important role in the light‐induced degradation mechanism. With the continuous Czochralski crystal growth process it is now possible to produce indium doped silicon substrates with the required doping levels for solar cells. This study aims to understand factors controlling the minority carrier lifetime in such substrates with a view to enabling the quantification of the possible benefits of indium doped material. Experiments are performed using temperature‐dependent Hall effect and injection‐dependent carrier lifetime measurements. The recombination rate is found to vary linearly with the concentration of un‐ionized indium which exists in the sample at room temperature due to indium's relatively deep acceptor level at 0.15 eV from the valence band. Lifetime in indium doped silicon is also shown to degrade rapidly under illumination, but to a level substantially higher than in equivalent boron doped silicon samples. A window of opportunity exists in which the minority carrier lifetime in degraded indium doped silicon is higher than the equivalent boron doped silicon, indicating it may be suitable as the base material for front contact photovoltaic cells.


| INTRODUCTION
The vast majority of photovoltaic (PV) solar cells are made from boron doped p-type silicon substrates. Such substrates are potentially susceptible to light-induced degradation (LID) due to the formation of a recombination centre containing boron and oxygen, 1 which can result in cell conversion efficiency reductions of~10% (relative).
Oxygen in silicon usually originates from the silica crucibles which contain the melt. Whilst low oxygen concentrations can be achieved by modifying the Czochralski process with magnetic fields (~3 × 10 17 cm −3 ) 2 or novel processes such as NeoGrowth (~4 × 10 17 cm −3 ) 3 , the production of such crystals is relatively expensive or immature. Float-zone silicon (FZ-Si) has lower oxygen concentrations than Cz-Si or mc-Si (usually <5 × 10 15 cm −3 ) but comes with other lifetime stability issues probably due to complexes associated with intrinsic point defects 4 and is also much more expensive. Using n-type substrates is generally beneficial from the perspective of bulk lifetime, 5 but this requires modifications to standard p-type cell processes such as diffusions, electrical contact schemes, and surface passivation.
Creation of p-type substrates by doping silicon with group III elements other than boron (such as aluminium, gallium, or indium) may provide a route to reducing or eliminating LID. Aluminium is unlikely to be a viable bulk dopant, as aluminium-oxygen complexes exhibit strong recombination activity. 6 Gallium doped silicon exhibits stable high lifetimes upon illumination 7,8 so could be a viable alternative.
Indium doped silicon has been studied since the 1950s. 9 Historically, indium doped crystal growth research has been in the context of the development of infrared detectors 10,11 for which the challenge is to get a high concentration of indium. Crystal growth is challenging due to the relatively low segregation coefficient of indium, 10,12,13 evaporation of indium from the melt, 12 and the clustering or precipitation of indium at high concentrations. 11,12,14,15 Photovoltaic devices generally require lower levels of indium doping than infrared detectors, and recent work has shown that 200 mm diameter indium doped silicon wafers with PV-relevant doping levels can be grown on an industrial scale. 13 Passivated emitter and rear cells (PERC) made from indium doped silicon substrates have an efficiency of >20% even after exposure to light levels which would result in substantial LID in boron doped cells. 16 It is also noted that indium's relative scarcity is unlikely to limit the commercial deployment of indium doped silicon. Based on solar irradiance of 1000 Wm −2 , 1 TW of silicon PV peak capacity equates to 5 × 10 9 m 2 of 20% efficient silicon PV cells. If these are 180 μm thick, the required volume of silicon for 1 TW capacity is 9 × 10 5 m 3 . The indium doping level will bẽ 10 16 cm −3 , which is around 2 × 10 −7 of the silicon volume, so the volume of indium required for this level of deployment is 0.18 m 3 . The density of indium is 7310 kg/m 3 , which means that only 1300 kg of indium is required for 1 TW peak of indium doped silicon deployment, which is a tiny fraction of the world's total indium reserves of >356 000 000 kg. 17 The challenge with the deployment of indium doped silicon arises from indium's relatively deep acceptor level, which optical measurements reveal to be at E V + 0.15 to E V + 0.16 eV. 9,[18][19][20][21] For shallow acceptors, such as boron, aluminium, and gallium, it is often reasonable to assume complete ionization at room temperature. With indium doping, this approximation is not valid, so not only does the doping level change with temperature, but the un-ionized indium has the potential to act as a recombination centre. The aim of this paper is to understand factors which control the minority carrier lifetime (henceforth just "lifetime") in indium doped silicon for PV applications. We use temperature-dependent Hall effect measurements to determine the concentration of ionized indium, and make injection-dependent lifetime measurements on the same material.
We correlate lifetime measurements with indium levels to establish the relationship between lifetime and the levels of ionized and unionized indium. By analysing the injection dependence of the lifetime, we extract the relevant defect parameters and hence enable general parameterization of lifetime in indium doped silicon. As there are apparent conflicts in the literature regarding whether indium doped silicon itself experiences LID, 16,22-24 we perform LID experiments. We compare the final lifetimes to those expected for boron doped silicon with equivalent doping and oxygen concentrations after complete boron-oxygen LID to assess the viability of indium doped silicon in PV applications.

| EXPERIMENTAL METHODS
Seven indium doped mono-crystalline silicon wafers grown by the continuous Czochralski process were studied. Samples for characterization were laser cut from 156 mm diameter pseudo squares, which were initially~190 μm thick. Interstitial oxygen and, in some cases, substitutional carbon concentrations were measured by infrared spectroscopy in sections of the ingot from which the wafers used were taken. The maximum and minimum values measured are given in Table 1, and concentrations in the wafers studied lie in this range.
For Hall effect measurements, the Van der Pauw method with contacts at the corners of 10 mm × 10 mm square samples was used.
Contacts were formed by evaporation of aluminium followed by a 10 min anneal at 450°C in a nitrogen atmosphere. Hall effect measurements were made from 100 K up to 320 K, which was the maximum operational temperature of the system.
The main set of samples for lifetime measurements (40 mm × 40 mm) first underwent a chemical etch which typically removed~30 μm of material from each side. Samples were then subjected to room temperature superacid-derived surface passivation 25,26 which used a thin film formed from a solution of bis(trifluoromethane)sulfonimide (TFSI) dissolved in anhydrous 1,2-dichloroethane using a procedure described in detail by Grant et al. 25 The advantage of this scheme over dielectrics is that it avoids possible ambiguities associated with annealing, external gettering, and possible hydrogenation which typically occur with dielectric passivation. 27 We expect excellent surface passivation from the superacid-derived scheme and have previously shown surface recombination velocities (SRVs) of 2.7 ± 1 cms −1 for 1 Ωcm and 0.63 ± 0.07 cms −1 for 10 Ωcm boron doped silicon. 25 Lifetimes were measured at room temperature (~25°C) by photoconductance measurements conducted with a Sinton WCT-120 lifetime tester. Errors in lifetime measurements were taken as 5%, as guided by a reproducibility study. 28 Based on information in Table 1, it is noted that the level of compensation in some samples is as high as 2.2, which according to Schindler et al 29 would lead to a reduction in mobility of around 10%. This relatively small change is ignored in the measurement of lifetimes presented in this paper.
Samples with superacid-derived passivation were also characterized by photoluminescence (PL) imaging 30 using a BT Imaging LIS-L1 PL system with a photon flux of 2.6 × 10 17 cm −2 s −1 .
A second set of lifetime samples cut from the same indium doped wafers was used for LID experiments. Such experiments required surface passivation with better temporal stability than the superacid-derived scheme, and we opt for Al 2 O 3 deposited by atomic layer deposition (ALD) rather than SiN x as the latter has its own instabilities under illumination. 31,32 Float-zone silicon samples (360 μm thick, 2 Ωcm, n-type) were also passivated to demonstrate the stability of the surface passivation under illumination. Samples were subjected to a thorough surface preparation procedure involving a dip in HF (2%), an RCA 1 clean (H 2 O, H 2 O 2 (30%), NH 4 OH (30%) in the ratio 5:1:1) at 75°C for 5 minutes, a dip in HF (2%), a tetramethylammonium hydroxide etch at 80°C for 10 minutes, a dip in HF (2%), an RCA 2 clean (H 2 O, H 2 O 2 (30%), HCl (37%) in the ratio 5:1:1) at 75°C for 10 minutes, and a final HF dip (2%).
The samples, which were typically 180 μm thick after the pretreatment, were then pulled dry from the final HF dip (ie, no rinsing) and were immediately transferred to a Veeco Fiji G2 ALD system where they were rapidly put under vacuum to prevent surface oxi- and where p is the hole concentration (temperature dependent), N d is the total donor concentration, N a is the total acceptor concentration, g is the spin degeneracy, N v is the density of states in the valence band, E a is the energy level of the acceptor above the valence band, k is Boltzmann's constant, and T is absolute temperature. It should be noted that the definition of p * 1 in Equation (2) is different to the definition of p 1 used in lifetime measurements later in this paper as it includes the degeneracy factor (g) which is commonly included for Hall effect studies. Rearranging Equation (1) and solving as a quadratic in p gives the positive root: Equation (3) is therefore used to fit the temperature-dependent hole concentration data from the Hall effect measurements assuming the main indium level is the only acceptor state. Figure 2 shows the results of this fitting for three samples. In all cases, we take E a is varied in the range 0.152 to 0.159 eV to achieve the best fit to the experimental data. The key parameters resulting from the fit are N a (the total indium concentration) and N d (the compensating donor concentration), and these are listed in Table 1 for all the samples.
The un-ionized indium concentration at 298 K is calculated as N a − p 298K and is also shown in Table 1.
The key point is that at room temperature there is a substantial concentration of both ionized and un-ionized indium in all samples, with the ionization level ranging from approximately 32% to 53%.

| Measured lifetime data
The measured lifetimes in as-received samples with superacid-derived passivation are plotted in  is a slight hint of these in Sample In-7 (top left), but their impact on bulk lifetime appears to be fairly small in the samples studied.

| Correlation of recombination with indium
To establish a possible correlation between lifetime and indium doping, the intrinsic lifetime given by the parameterization of Richter et al 39 was removed from the measured lifetime according to The residual lifetime, τ residual , will still include a small contribution from other recombination processes not related to indium, τ other . Figure 5 shows the correlation between τ residual and both the ionized (p 298K ) and un-ionized (N a − p 298K ) indium concentrations at 10 15 and 10 16 cm −3 injections. There is an approximately linear relationship between recombination and un-ionized indium.
If the un-ionized indium acts as a recombination centre, then the recombination rate can be expressed according to where α n is the capture coefficient for electrons at the un-ionized indium centre (the capture coefficient is the product of the capture cross section and the thermal velocity). The linear fits to the black circles in Figure 5 are in accordance with Equation (5) Equation (1) at 298 K can be rewritten as Substituting Equation (7) into Equation (5) gives If the compensating donor concentration is small, then Equation (8) simplifies to Equation (9) implies that if recombination is via un-ionized indium, a quadratic dependence on recombination rate with p 298K is expected for samples which are not significantly compensated. The results presented in Figure 5 show approximate quadratic behaviour, with deviation from this most likely due to the level of compensation being non-negligible in some samples (see Table 1 and Equation (8)

| Analysis of the lifetime injection dependence
To provide a deeper understanding of the recombination activity in indium doped silicon, the injection-dependent lifetime data were analysed using a linear version of Shockley-Read-Hall (SRH) statistics which has been described in detail previously. 41,42 For a p-type semiconductor, the lifetime is plotted as a function of the ratio of the total electron concentration to the total hole concentration. When appropriate, the lifetime curve can then be fitted with an integer number of independent SRH centres where the lifetime due to the ith SRH recombination centre varies according to where α ni is the capture coefficient for electrons, N i is the concentration of the recombination centre, Q i ¼ α ni α pi where α pi is the capture coefficient for holes, p 0 is the hole concentration (taken as p 298K here), . The variables n i and p i are the SRH densities for electrons and holes, respectively. By convention for lifetime measurements, the spin degeneracies used for SRH densities in Hall effect measurements (eg, for p * 1 in Equation (2)) are omitted, and so and : (12) where N c is the density of states in the conduction band, N v is the density of states in the valence band, and E Ti is the energy level of the trap relative the edge of the conduction band (E c ) or the valence band (E v ).
The residual lifetime from experiment can be fitted using an integer number of independent SRH centres each with lifetimes varying in accordance with Equation (10) combined according to Figure 6 shows that the residual lifetime in indium doped samples plotted against X approximates to linear as X increases. In accordance with Equation (10), this suggests that one SRH centre dominates the recombination in indium doped silicon at relatively high X. At lower values of X, the lifetime curves in Figure 6 bend downwards, which implies the existence of at least one other SRH centre in the samples.
To fit the curves shown in Figure 6, we adopt a two independent SRH centre approach and fit the data in accordance with Equation (13). We arbitrarily refer to the state dominant at high injection as State 1 and  Figure 6, it is clear that its concentration is dependent on the indium level in some way. A correlation between recombination rate and the un-ionized indium concentration was found in Figure 5. If State 1 is due to un-ionized indium, then taking the X = 1 limit of Equation (10) where τ n1X → 1 is the X = 1 limit of the State 1 fit to the experimental data. Figure 7(a) is a plot in accordance with Equation (14)  respect to X and normalizing this by the X = 1 limit gives the following expression which is independent of state density:  The degradation is not due to degradation of the surface passivation as measurements of float-zone silicon control samples also shown in Figure 8(a) show a stable lifetime within experimental error. In indium doped silicon, substantial lifetime degradation occurs in <1 second, with the lifetime then decaying to a steady state in a few minutes.
As suggested by Möller and Lauer, 22 we find that a 200°C anneal reverses the LID, and, as shown in Figure 8(a), the lifetime then again degrades under illumination at approximately the same rate as on previous degradation cycles.
The motivation for using indium doped silicon would be to replace boron doped silicon which is well known to degrade under illumination. 43 It is therefore important to compare the degraded lifetimes in indium doped silicon with boron doped equivalents. For such a comparison, we use the parameterization of degraded lifetime in boron doped silicon from Bothe et al. 44 Noting the comments of Niewelt et al, 45 this provides a reasonable comparison to our data as it refers to the as-delivered state, and our samples did not undergo a high temperature diffusion step which can strongly affect the effective concentration of the recombination centre which forms under LID. In  Table 1. Importantly, in all cases, the degraded lifetime is higher in the indium doped material than in the boron doped samples with a lifetime limited by the boron-oxygen defect.

| Factors controlling lifetime
Our work clearly shows that the lifetime in as-received indium doped silicon is in some way dependent on the doping level of the sample. In Figure 3, we see a well-ordered family of lifetime curves. All the samples considered have relatively low doping levels and, even with excellent surface passivation, the lifetimes measured are well below those expected from intrinsic (Auger and radiative band-to-band) recombination. 39 The results presented in Figure 5 show that the lifetime varies linearly with the un-ionized indium concentration and with the square of the ionized indium concentration (subject to the limitations of this analysis in compensated material). Analysis in Figure 7(b) enables an energy level close to that expected for indium to be extracted from the injection-dependent lifetime data. We therefore conclude that the un-ionized indium gives rise to the main recombination centre which controls lifetime in our indium doped silicon samples.
In previous studies, indium doped silicon is often found to contain a shallower defect (sometimes called the "X-centre") at around E V + 0.11 eV. 11,33,34,46,47 An initial study by Baron et al 33 found this defect to scale with the total indium concentration, and to exist in float-zone as well as Czochralski silicon thus probably ruling out the involvement of oxygen. 33 A later study showed a correlation with carbon concentration so it was concluded that the level was due to a substitutional carbon-indium pair, 47   occurring much more slowly than in our samples. 22

| Use of indium doped silicon in solar cells
This study has shown that indium doped silicon has the potential to offer higher carrier lifetimes than degraded boron doped equivalent 852 MURPHY ET AL. samples at room temperature, even after LID that occurs in indium doped samples. It is however noted that processes to regenerate boron doped silicon after boron-oxygen LID exist, 49,50 and application of similar processes to indium doped silicon may provide effective results. It is also important to note that a solar cell in service will typically operate above room temperature. Our Hall effect data ( Figure 1) show that indium is not fully ionized at room temperature, so raising the temperature will increase the ionized indium concentration and hence reduce the un-ionized indium acting as a recombination centre. This means that the minority carrier lifetime should increase with temperature, but it is noted that to achieve a full temperature-dependent parameterization of lifetime in indium doped silicon it would be necessary to determine the temperature dependence of the electron and hole capture coefficients. Furthermore, because of the relatively deep acceptor state of indium, the effective doping level of an indium doped silicon substrate will change as the cell temperature changes. This is fundamentally unavoidable, and this variation may cause challenges for the optimization of other aspects of the cell manufacturing processes. This limitation also means that indium doped silicon may only be of use in front junction solar cells, such as PERC designs which have already been demonstrated. 16 Rear contact cells (eg, interdigitated back contact cells) require carrier lifetimes of several milliseconds or greater, 51 and even with the lowest indium level studied here (sample In-7), the un-ionized indium level limits the lifetime to below 2 ms (below 1 ms after LID).

| CONCLUSIONS
The electronic properties of indium doped silicon grown by the continuous Czochralski process have been studied systematically to