Quantifying the Effect of Nanofeature Size on the Electrical Performance of Black Silicon Emitter by Nanoscale Modeling

—Nanostructured black silicon (b-Si) surfaces with an extremely low reﬂectance are a promising light-trapping solution for silicon solar cells. However, it is challenging to develop a high-efﬁciency front-junction b-Si solar cell due to the inferior electrical performance of b-Si emitters, which outweighs any optical gain. This article uses three-dimensional numerical nanoscale simulations, which are corroborated with experiment results, to investigate the effect of the surface nanofeature sizes on the b-Si emitter performance in terms of the sheet resistance (R sheet ) and the saturation current density (J 0e ). We show that the speciﬁc surface area (SSA) is an effective parameter to evaluate the nanofeature size. A shallow surface nanofeature with a large SSA will contribute to a better electrical performance. We will show that b-Si emitter R sheet measured by a four-point probe is not a measure of the doping level in the nanofeature, but is ruled by the doping level in the underlying substrate region. We also show that a small nanofeature with SSA > 100 µ m -1 and height < 100 nm can lead to a relatively low J 0e (33 fA/cm 2 lower than the best b-Si results reported in the literature) by suppressing surface minority carrier density and minimizing the total Auger recombination loss.

mass spectrometry [5], and photo-electrocatalysis [6]- [9]. B-Si also shows great potential in solar cell applications, as was demonstrated for interdigitated-back-contact solar cells with an undiffused low-reflectance b-Si front surface [10]- [12]. This application benefits from the atomic-layer-deposited conformal thin films, which overcome b-Si surface passivation challenges [13]- [16]. Moreover, it has been found that there will be an effective reduction of surface recombination loss due to the enhanced field-effect for undiffused b-Si surfaces passivated with charged thin films [13], [17], [18]. However, for applying the low-reflectance b-Si on front-junction solar cells, there are no reported efficiencies higher than 20%. This is attributed to the inferior electrical performance which outweighs the gain in optical performance [19], [20].
Several attempts have been made to understand and optimize b-Si emitters in order to improve their electrical performance. Zhong et al. [20] reviewed the empirical investigations for suppressing the recombination losses in b-Si emitters and concluded that the root causes of the inferior electrical performance were the high surface recombination loss due to the enlarged surface area and also the severe emitter Auger recombination loss caused by the increased emitter volume with a higher post-diffusion doping level. As this problematic enhanced diffusion is also attributed to the enlarged surface area, one of the widely used optimization methods is reducing the heights of the surface nanofeatures and thus decreasing the surface area [21], [22]. Moreover, the surface morphology optimization can make b-Si emitters achieve comparable or even better electrical performance than the conventional microtextures [23]- [25], even though sacrificing some optical gains. However, how the nanofeature size affects the dopant distribution and subsequently affects the recombination losses are still unknown. Recently, Scardera et al. extended the specific surface area (SSA) concept, typically used for nanoparticles, to surface textures with nanofeatures. SSA was defined as the ratio of the surface area to the volume of the nanofeature. It was found that the measured sheet resistance (R sheet ) of the b-Si emitter was independent of both the surface area and the surface morphology, but exhibited a strong correlation with SSA [26]. However, current one-dimensional (1-D) and 2-D R sheet theories based on the dopant concentration cannot fully explain such an outcome [26] and, thus, it is doubtful whether the R sheet measured by the four-point-probe method is a reliable indicator for comparing b-Si doping levels.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Fig. 1. Schematic of the simulated structure with the front-side texture, the front-side n + diffused region, the front-side SiN x passivation layer and the rear-side Al 2 O 3 passivation layer.
A comprehensive investigation into the effect of nanoscale surface morphologies on b-Si electrical properties will be shown in this article. We will investigate the POCl 3 -diffused frontjunction device structure which, for example, is used in the industry-dominant passivated emitter and rear cell (PERC). We will present a systematic 3-D nanoscale simulation approach, corroborated using experimental results, to investigate the POCl 3 diffusion and the corresponding electrical performance. We will show how the b-Si nanofeature size influences the doping profile. We will investigate the characteristics of lateral conductance in the b-Si emitter and the correlation between the measured b-Si R sheet and the doping level. We will subsequently examine the emerging role of SSA optimization in suppressing emitter Auger recombination, Shockley-Read-Hall (SRH) recombination, and the doping-related surface recombination by investigating the emitter saturation current density (J 0e ). Finally, the simulation results will be compared with empirical results, and the effects of nanofeature size on the optical performance will be discussed as well.

A. Simulation Overview and Experiment Information
In this article, the 3-D numerical simulations were performed using the process simulation module [27] and the device simulation module [28] in Synopsys Sentaurus TCAD, which solves the fully coupled set of differential equations based on the transport models (the charged-pair dopant transport model for diffusion simulations and the drift-diffusion carrier transport model for device simulations). The front-side POCl 3 diffusion simulations were simplified as the nonmoving-boundary processes using the two-phase segregation model, i.e., the phosphorus atoms diffused from the 40 nm phosphosilicate glass (PSG) layer into the 180 μm p-type Si substrate directly without the in-situ Si etching. Hence, the surface morphology will not be modified after the diffusion. The PSG layers were then removed and the emitter surfaces were covered with uniform 40 nm SiN x passivation layers. Also, the rear undiffused planar surfaces were covered with uniform 20 nm Al 2 O 3 passivation layers for the subsequent device simulations, as shown in Fig. 1. The simulations of the electrical performance were based on the drift-diffusion carrier transport model with the 3-D Poisson's equation, Fermi-Dirac statistics, Schenk's band gap narrowing model [29] and Philips unified mobility model [30]. For the R sheet simulations, the current injection had a 0.01 V contact potential difference. For the J 0e simulations, the optical injection was under quasi-steadystate conditions with a uniform generation. The simulated unit sample had a full-size thickness (180 μm) while the length and width were modelled in the nanoscale, i.e., the unit sample was a long bar extending along with the entire wafer thickness. The full-size sample simulation was achieved by setting periodical boundaries for the unit sample side-walls. More simulation details are listed in the Supplementary Material, and the models used in this article will be discussed in the following sections.
The experiment results used in this article were reproduced from our previous work [26]. The b-Si samples were fabricated by 2-min and 16-min reactive-ion etching (RIE-2min and RIE-16min) using an SPTS Pegasus System. The nanofeatures were assumed to be conical. The modeling dimensions were based on the measured surface areas and nanofeature height distributions using a Bruker ICON Atomic Force Microscope. The diffusion recipes used in the simulations were identical to the ones used in the experiments, i.e., an 865°C nonoxidation recipe [26]. The doping profiles of planar samples were measured by Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) using an IonTOF TOF.SIMS 5 and also measured by electrochemical capacitance voltage (ECV) profiling using a WEP CPV21 ECV-Profiling. Field-emission scanning electron microscope (SEM) measurements also confirmed the surface morphology and the 2-D doping distributions were monitored with SEM dopant contrast imaging (SEMDCI) using an FEI Nova NanoSEM 450 system. The R sheet samples were measured by the four-point-probe method using a Sunlab Sherrescan. The surface reflectance was measured by the spectrophotometer using a PerkinElmer 1050. More experiment details can be found in [26].

B. Diffusion Modeling
In the POCl 3 diffusion simulations, the charged-pair diffusion model, which is one of the widely used models [31], solved the continuity equations for the charged dopant-defect pairs, i.e., phosphorus-vacancy (PV) and phosphorus-interstitial (PI) pairs with various charge states [27]. It can be generally expressed as where C total P is the total P concentration, D P X c is the effective diffusivity of PV or PI pairs (defect X is V or I) at defect charge state c, n is the electron density, n i is the intrinsic carrier density, and k X is the coefficient determined by the defect concentration. The electrically active P concentration C active P was determined by the solid dopant activation models [27] C active where C SS0 P is the solid solubility of P in an Arrhenius equation, k B is the Boltzmann constant, T is the temperature (k B T in eV), and the multiplication factor f = 2.5 is a fitting parameter. It should be noted that the solubility limit used in this article could be relatively high due to the lack of measured surface dopant concentration. The C active P in the heavily doped surface was assumed according to the doping profile fitting. It was assumed that the inactive P was the interstitial P atom as a single type of defect and its concentration can be calculated by (4)

C. Sheet Resistance Modeling
The sheet resistance R sheet implies the characteristic lateral conductance for the emitter. The first principle definition of R sheet for planar semiconductors is where n and p are the electron and hole densities, μ n and μ p are the carrier mobilities, and x e is the depth from the surface (x = 0) to the metallurgical junction. However, (5) can only determine the local R sheet in 1-D. Therefore, it should be extended to a 3-D equation to calculate the average R sheet for a b-Si emitter where A proj is the projected area of the b-Si surface.R sheet can be regarded as an average value of calculated R sheet based on the dopant distribution. Moreover, we propose a novel parallelcontact simulation method to determine the effective R sheet , which mimics the one-direction lateral current injection in the four-point-probe measurement. As shown in Fig. 2, this method was based on the fundamental lateral resistance equation for a cuboid emitter whereρ is the average resistivity, L is the length, and W is the width. The depth of the side-wall contact was identical to the depth of the metallurgical junction x e . According to (5), it can be derived that R sheet =ρ /x e , thus, the lateral resistance R will be equal to R sheet when L = W . In this way, the onedirection lateral current could be injected into the unit wafer and the measured lateral resistance was independent of the size of the unit wafer. This method can be extended to a b-Si unit wafer. However, the injected current will be multidirectional within the nanofeature. Virtual contacts, in which the contact resistance is zero and contact recombination velocities equal to the carrier thermal velocities, were used in the parallel-contact simulations.

D. Emitter Saturation Current Density Modeling
The emitter saturation current density J 0e was used to evaluate the recombination losses. In this article, J 0e was determined by the lifetime conversion method (known as Kane and Swanson's method) under the conductive boundary assumption, i.e., the carrier generation in the emitter region was negligible, and the emitter and surface regions were lumped as a conductive boundary [32]. The standard equation is where τ ef f is the effective lifetime, τ base is the base lifetime, which is determined by the base SRH, Auger, and radiative recombination losses τ SRV,r is the rear surface lifetime, which is determined by the rear surface recombination velocity (SRV) and carrier densities, τ e is the lumped front boundary lifetime determined by the recombination losses in the emitter and the corresponding surface, N dop is the base doping, Δn is the excess carrier concentration in the flat-band region, n i,ef f is the effective intrinsic carrier density, and W is the wafer thickness. Since the total J 0e is a combination of the effective recombination mechanisms in the boundary these recombination components J 0e,x can be individually calculated by the corresponding average recombination ratesŪ e,x in the emitter region, based on (8) and given that τ For the Auger component J 0e,Auger , the recombination rate U e,Auger was determined from Richter's model [33]. For the SRH component J 0e,SRH , it was assumed that the emitter SRH recombination was only caused by the inactive P as a single type of defect. The recombination rate U e,SRH was determined by where v the and v thh are the carrier thermal velocities, σ n and σ p are the carrier capture cross sections, and n 1 and p 1 are the thermal emission of carriers from the defect energy. Given that n + n 1 p + p 1 for an n-type emitter and n n 1 due to the negligible thermal emission, (11) can be simplified as It was assumed that the σ p for the inactive P was 7.5×10 -18 cm 2 [34]. For the surface component J 0e,SRV,f with the heavily doped n-type surface as well as the high-fixed-charge accumulation condition, the surface recombination rate U e,SRV,f was mainly determined by the intrinsic surface recombination velocity of the minority carrier (S p0 ) and the surface minority carrier density (p s ) based on the SRH model for a single defect energy [35] where the S p0 depended on the surface active P concentration C active P surf and it was parameterized by Altermatt's model [36].

A. Enhanced Area Factor and Specific Surface Area for Black Silicon
The ratio of the surface area (the lateral surface area of a cone) to the projected area (the base circle area of a cone), or enhanced area factor (EAF), is the most widely used morphology parameter in qualifying the b-Si electrical performance. The total number of surface defects and the diffused silicon area will scale with EAF, thus enhancing defect recombination at the enlarged surface as well as Auger recombination in the emitter. However, in our previous work, we showed that nanofeatures of different sizes could have an identical EAF but exhibit significantly different postdiffusion R sheet values, and that in some cases, such values were independent of EAF [26]. Therefore, employing a better metric to evaluate nanofeature sizes is essential for b-Si studies.
In this article, we used SSA to quantify the nanofeature size. It is defined as the ratio of the nanofeature surface area to the nanofeature volume [26], where a larger nanofeature will have a smaller SSA for a given EAF condition, as shown in Fig. 3(a). Fig. 3(b) shows the effects of conical nanofeature base radii and heights on the SSA values. As SSA is a relative size metric associated with the surface area, it would be more meaningful to investigate the nanofeatures with different SSA values but similar EAF values when studying the effects of sizes. Typically, the b-Si surfaces applied in solar cells will have an EAF ranging from 2 to 10 [1], [19], [37]. We assumed that RIE textures were composed of conical nanofeatures, and as a result, the SSA was in a range from around 10 μm −1 to 430 μm -1 , as shown in Fig. 3(b). In this article, we referred to shallow RIE b-Si textures as those having small nanofeatures with a height of < 100 nm and an SSA of > 100 μm -1 , referred to moderate RIE b-Si textures as those having moderate nanofeatures with a height of 100 nm-300 nm and an SSA of 20 μm -1 -100 μm -1 , and referred to deep RIE b-Si textures as those having large nanofeatures with a height of > 300 nm and an SSA of < 20 μm -1 .

B. Effects of Nanofeature Size on Doping Profile
This section will discuss how the nanofeature sizes influence doping by investigating the doping profiles of planar reference, RIE-2min and RIE-16min samples. In our previous work, we find that the b-Si R sheet measured by the four-point-probe method increases with an increasing nanofeature size. Diffusion simulations also indicate that a larger conical nanofeature has a higher concentration of active P dopant C active P at the tip and lower doping at the base of the nanofeature. We propose that there will be limited current flowing in the heavily doped tip of the nanofeature. Thus, the doping level in the underlying substrate plays an essential role in the lateral emitter conductance [26]. The detailed simulation results and analysis for this finding will be shown in Section III-C. This section will revisit the diffusion simulations of the conical nanofeatures and provide a more detailed analysis of both the active and inactive P atom distributions. This analysis will then be extended to investigate the lateral conductance (see Section III-C) and recombination behaviors (see Section III-D) of conical nanofeatures. The nanofeature dimensions, EAF and SSA of the investigated b-Si samples are shown in Fig. 3(b). The nanofeature dimensions used for these simulations were based on the height and slant angle distributions determined from atomic force microscope (AFM) [26]. Fig. 4(a)-(c) shows the cross-sectional SEMDCI results along with the corresponding simulated C active P distributions for the planar, RIE-2min and RIE-16min conditions, respectively. The RIE conditions both exhibit heavily doped near-surface regions as well as deeper metallurgical junction depths compared to the planar sample. Furthermore, the shallow texture (RIE-2min) has a higher doping level in the underlying substrate and a deeper junction depth compared to the deep texture (RIE-16min).  On the other hand, for the deep b-Si texture (RIE-16min), the doping level increases significantly from the bottom to the peak of the nanofeature, resulting in an extremely high dopant concentration at the tip region. This can be attributed to the diffusion length of the P atoms not being sufficient to reach the bottom of the nanofeature. In addition, the dopants diffused from the side-wall will perturb the diffusion process. The diffusion of P atoms in the heavily doped region relies on charged vacancies. Since the P concentration at the tip will be much larger than Fig. 5. Simulated and measured sheet resistance R sheet . The experiment results were reproduced from [26] and the average values for each set of data are indicated. The effective R sheet was determined by the parallel-contact simulation. The calculated R sheet by the first principle is the average of local R sheet values of each b-Si sample determined by (6). Since the ECV measurement had a maximum ±4.3% error and the result of diffusion simulation had a ±6.2% uncertainty due to the profile fitting error and the uncertainty of the surface dopant concentration, it is assumed that the simulated sheet resistance result will have a ±10.5% uncertainty, as shown by error bars. the concentration of charged vacancies in the nanofeature (the P atoms from the side-wall will also diffuse to the tip), the P atoms at the tip will not efficiently diffuse. Consequently, there will be a dopant accumulation in the tip region. This leads to the number of dopants diffused into the underlying substrate being lower. Therefore, the metallurgical junction depth with reference to the bottom of the deep texture (RIE-16min) is more shallow than that of the shallow texture (RIE-2min), even though the RIE-16min sample has a larger EAF. Fig. 4(g)-(i) shows the corresponding distributions of inactive P atoms. The b-Si samples have a wider distribution of inactive P atoms and also higher inactive P concentrations C inactive P in the emitters than the planar reference sample. In addition, compared to the shallow texture (RIE-2min), the C inactive P of the deep texture (RIE-16min) is generally larger and the C inactive P in its tip region is an order of magnitude higher at around 1×10 21 cm -3 . This can be attributed to the P atom accumulation in the tip region and the P solubility limit. A region with a high concentration of inactive P atoms is known as a "dead layer", where the high concentration of inactive P is in the form of interstitial P atoms, inactive P clusters and SiP precipitates. As we do not know the fractions of such components in the "dead layer", it is assumed that the inactive P atoms are a single type of effective defect with a hole capture cross-section σ p = 7.5×10 -18 cm 2 [34]. This assumption will be employed later in Section III-D when investigating SRH recombination loss due to such defects.

C. Effects of Nanofeature Size on Sheet Resistance
In this section, we will investigate the effects of nanofeature sizes on the sheet resistance R sheet. Fig. 5 shows the measured R sheet from four-point-probe measurements, the corresponding simulation results of the effective R sheet determined using the parallel-contact method, and the calculated R sheet values based on the simulated dopant distributions using (6). It can be seen that the b-Si samples had a lower measured R sheet than the planar reference sample and that the shallow texture (RIE-2min) has the lowest measured R sheet . The simulation results by the parallel-contact-method show a relatively good agreement with the experiment results. However, the R sheet of the deep texture (RIE-16min) calculated using (6) has a significant discrepancy with the corresponding experiment result and it incorrectly predicts that the R sheet of the RIE-16min sample would be lower than the RIE-2min sample. This can be attributed to the dopant distribution, as discussed in Section III-B, i.e., the planar sample has the lowest dopant concentration while the RIE-16min sample has the highest doped nanofeatures with a large volume. However, the shallow texture (RIE-2min), in fact, had the lowest measured R sheet . This implies that the dopant concentration can not simply explain the measured R sheet results. Fig. 6 shows the simulated local current density J local of the planar and b-Si samples during current injection in the parallel-contact method with 0.01 V contact potential difference. For all cases, it can be seen that most of the current flow through the top portion of the underlying substrate and the J local decreases with increasing depth into the substrate. This is caused by the reduction of dopant concentration, as shown in Fig. 4, and consequently, the corresponding conductivity decreases. Contrarily, although the dopant concentration is relatively high in the nanofeatures, the J local decreases as the height increases and reaches the lowest value at the tip of the nanofeature. Fig. 7 shows the line scans inside the nanofeatures from the tips to the underlying substrate. These results confirm the strong correlation between the J local and the dopant concentration in the underlying substrate for all samples. However, the J local has a dramatic decrease in the nanofeature even though the dopant concentration keeps increasing from the bottom to the tip of the cone. The extremely low J local in the tip regions can be explained by the current path length in the 3-D structure, i.e., the current will not always take the path with the highest dopant concentration (where the conductivity is the highest) since the total conductance is a function of the conductivity and the path length. It can be concluded that the doping level in the underlying substrate predominantly determines the effective lateral conductance and the effective R sheet of a b-Si emitter, regardless of the doping level in the nanofeature. This can explain the significant difference between the calculated and effective R sheet for the large nanofeature (RIE-16min) in Fig. 5. This also explains why the difference of the calculated and effective R sheet is, to the contrary, insignificant for the RIE-2min sample where the volume of the heavily doped nanofeature is much smaller than that of the underlying emitter. Moreover, the simulation results reveal that the effective R sheet acquired from the four-point-probe method is predominantly an indicator of the doping level in the underlying substrate below the nanofeature.

D. Effects of Nanofeature Size on Emitter Saturation Current Density
In this section, we will study the effects of nanofeature size on each recombination mechanism by investigating the J 0e of simulated samples with a lifetime structure, as shown in Fig. 1. We will investigate a wide range of cone sizes from the nanoscale to the microscale. To eliminate the effects of surface area, all cones had a fixed EAF = 2.2. Fig. 8 shows the simulated J 0e results, including the fractions of different recombination mechanisms. The smallest nanofeature sample (SSA = 232 μm -1 ) and the planar reference sample show a very similar J 0e result. The largest microfeature condition (SSA = 3 μm -1 ) has a 2 μm height, which is close to the surface morphologies fabricated with conventional texturing methods. Fig. 8 indicates that as the nanofeature size increases, the total recombination loss rises. When the cone size is increased to the microscale, the highest J 0e = 178 fA/cm 2 was obtained, which is smaller than the theoretical highest J 0e = 206 fA/cm 2 calculated from the product of the planar reference J 0e and the EAF value. Such a lower result is also observed in micropyramidal samples. McIntosh and Johnson reviewed the reported J 0e values for micropyramidal samples and found that the J 0e increased with a factor < 1.73 (the EAF for pyramidal textures) for heavily diffused samples (planar reference R sheet < 100 Ω/ ). This was attributed to a nonconformal emitter region [38], which is consistent with the simulation results presented in this section. It should be noted that since we only focus on the dopant-associated recombination caused by the morphology variation, the effects of the crystal Fig. 8. J 0e components for varying cone sizes. The EAF value was fixed at 2.2 for all cones on the textured surfaces. It was assumed that the local S p0 at the Si-SiN x interface depends on the surface dopant concentration C active P surf . The Auger components in the cone and underlying substrate are also individually shown.
orientations and the surface stress on the recombination losses were not considered in this article. Fig. 9(a) shows the average P concentration in the nanofeatures and the underlying substrate, which relates to the SRH and Auger recombination losses. As the nanofeature size increases, the total P concentration decreases for the nanocone region and the underlying substrate region. Fig. 9(b) shows the corresponding number of P atoms of Fig. 9(a) calculated for the same unit sample dimensions with an identical projected area (380 nm × 380 nm), which reveals the effects of the nanofeature volume on the P distribution. It is indicated that as the nanofeature size increases, the total number of P atoms decreases in the underlying substrate region while the number in the nanocone increases. Fig. 8 indicates that the SRH recombination loss due to the inactive P atoms is insignificant even though the inactive P concentration is high in the nanofeature, as shown in Fig. 4. This results from the strong charge carrier population control in the heavily doped nanofeature, i.e., the minority carrier density available for SRH recombination is very low due to the high doping level and the carrier consumption by Auger recombination and surface recombination.
Moreover, Fig. 8 also reveals the influence of nanofeature size on the Auger recombination. When the surface texture is relatively shallow (SSA > 77 μm -1 and height < 84 nm), the predominant Auger recombination occurs in the underlying substrate with a relatively high dopant concentration. When the nanofeature size increases, the Auger recombination loss in the nanocone J 0e,Auger,cone rises with an increasing proportion of the nanofeature J 0e . This can also be attributed to the effects of the nanofeature volume, i.e., the increasing nanofeature volume leads to the increasing total number of dopants in this region, as shown in Fig. 9(b). Therefore, there is more Auger recombination occurring in the nanofeature. However, to achieve the lowest total Auger recombination loss, the nanofeature size should be moderate to balance the Auger recombination losses in the nanofeature and the underlying substrate. The optimal  nanofeature size with the lowest Auger recombination loss in this article with an EAF of 2.2 had a SSA = 46 μm -1 and height = 140 nm. Fig. 10 shows the effects of nanofeature size on the surface active P concentrations C active P surf , which relate to the surface recombination loss. The average C active P surf decreases as the nanofeature size increases, which means there will be an effective surface dopant enhancement only when the nanofeature size is sufficiently small, even though the C active P surf was extremely high at the tip region for the large nanofeature. Fig. 11 shows the corresponding surface minority carrier density p s of Fig. 10 for the planar reference and a small nanofeature case (SSA = 232 μm -1 ). It indicates that the p s at the nanofeature surface is much lower than the planar reference and a lot lower than the expectation according to the increase in surface doping shown in Fig. 10. In particular, p s is reduced by over three orders of magnitude in the tip of the nanofeature. This can be attributed to the fact that the doping profile is significantly deeper from the nanofeature surface than from the planar surface, resulting in a more effective carrier population control [39]. This is similar to the enhanced charge-assisted carrier control by the effective space charge region compression for the lightly doped b-Si samples [17]. The decrease in p s at the nanofeature surface more than compensates for the increase in S p0 at the highly doped surface and, subsequently, the surface recombination loss determined by the product of p s and S p0 (13) increases with a factor less than the EAF. This explains why the J 0e,SRV,f of the small nanofeature is comparable to that of the planar reference sample in Fig. 8. As the nanofeature size increases, this effect will become less pronounced, and J 0e,SRV,f will start to scale with EAF.
It can be concluded that the surface morphology optimization strategy will depend on the diffusion level and surface passivation performance. For the heavily-doped b-Si emitters with predominant Auger recombination loss, a moderate nanofeature (SSA = 46 μm -1 and height = 140 nm) size is beneficial as such a size will contribute to the reduction of the total Auger recombination loss from 41 fA/cm 2 for the planar reference to 36 fA/cm 2 for the b-Si sample. For the b-Si emitters with comparable Auger recombination and surface recombination losses, such as the example shown in Fig. 8, the simulation results indicate that a low total recombination loss will be achievable when the nanofeature is small, i.e., 108 fA/cm 2 for the b-Si sample with EAF = 2.2 compared to 97 fA/cm 2 for the planar reference.

E. Optimization of B-Si Emitters
In this section, we will compare the electrical performance and optical performance of reference and the RIE b-Si samples. We will also discuss the potential influences of b-Si nanofeature size on the performance of solar cells.
The effects of surface nanotexture on the dopant-related electrical properties (R sheet and J 0e ) for various diffusion recipes are shown in Fig. 12. These empirical b-Si results were for a deep RIE nanotexture with large surface nanofeatures (SSA < 20 μm -1 ). It should be noted that the field-effect passivation in these b-Si and planar reference samples was enhanced by corona charge deposition. Therefore, the surface recombination losses were relatively low and the predominant J 0e component was due to Auger recombination. Fig. 12 shows that when an identical diffusion recipe is employed for b-Si and planar reference samples, the nanotextured sample will have a higher J 0e but a lower R sheet , which results from the doping enhancement in the b-Si emitter as discussed in Sections III-B-III-D. According to the comparison of the J 0e -R sheet slopes, it can be found that the effects of diffusion recipes on the electrical properties for the large-nanofeature b-Si are very similar when R sheet of the planar reference samples are < 180 Ω/ , i.e., the ratios of the R sheet reduction and the corresponding J 0e increase are similar for all cases. It should be noted that although the diffusion recipe used in the simulations causes heavier doping and thus the simulated R sheet is lower than those from the literature, the simulated J 0e is lower than the empirical J 0e as the simulated cones have a lower EAF and consequently lower surface recombination loss. Moreover, the simulation results reveal that the R sheet can be further reduced with an even lower degree of J 0e increase by using a shallow b-Si texture. As discussed in Sections III-C and III-D, this is plausible given that a relatively small nanofeature (SSA > 20 μm -1 ) can enhance the doping in the underlying substrate region, which relates to the lateral conductance improvement directly. Although this will also increase the Auger recombination compared to the planar reference emitter to some extent, it will be still lower than that for a heavily doped large nanofeature.
It should also be noted that the optical performance of shallow nanofeatures would need to be verified before incorporating them into a solar cell. Ideally optical simulations of our simulated nanocone features would be performed, but such investigations are beyond the scope of this article. However, we have previously shown that while deep RIE textures do exhibit very low weighted average reflectance (WAR), RIE texture with an EAF of 2.3, which is close to the EAF of our simulated shallow nanotexture, exhibited a significantly lower WAR than random pyramids (RPD) [26]. Although a deep RIE nanotexture with large EAF can have a near-zero reflectance without antireflection coating, the collection efficiency could be problematic [40], which outweighs the optical gains and leads to a low external quantum efficiency [42]. On the other hand, a shallow nanotextured can be combined with a microtexture to form a hierarchical structure which has a better optical performance and also a high collection efficiency [43]- [45]. As such, any final optimization strategy should consider all aspects for the development of high-efficiency front-junction b-Si solar cells.

IV. CONCLUSION
The effects of nanofeature sizes on the electrical performance of b-Si emitters were investigated by numerical simulations using Synopsys Sentaurus TCAD. It was revealed that the surface nanotexture would lead to a doping enhancement in the underlying substrate region for small nanofeatures. However, such enhancement will be suppressed for large nanofeatures, while there will be an extremely high dopant concentration within such nanofeatures, especially at the tip region. It was subsequently found that this heavily doped nanofeature will barely affect the lateral conductance during a R sheet measurement by the four-point-probe method. The lateral conductance is mainly determined by the doping level in the underlying substrate region. Hence, this can explain why Scardera et al. [26] observed that the measured R sheet will be smaller as the nanofeature size decreases. This also indicates that the measured R sheet by the four-point-probe method can be regarded as mainly an indicator of underlying substrate doping level when comparing b-Si emitters. Our simulation results also reveal that the predominant recombination mechanisms in the b-Si emitters were surface recombination and Auger recombination. Although the concentration of inactive P, which is one kind of SRH recombination center, is high in the nanofeature, the SRH recombination by such defects will be effectively suppressed due to the low concentration of minority carriers. Moreover, a small nanofeature will lead to less Auger recombination loss due to a small volume of the heavily-doped surface texture. The surface recombination velocity will be also lower as such a nanofeature will have a high surface dopant concentration and a deep dopant profile, which contribute to a low surface minority carrier density and the density at the tip can be even lower than 2×10 10 cm -3 at 5×10 16 cm -3 injection condition. As we have suggested that SSA is a more comprehensive metric than EAF for the comparison of different surface morphologies [26], we further prove that SSA is a good indicator of b-Si emitter electrical performance in this article. We conclude that a shallow nanotexture with SSA > 100 μm -1 and height < 100 nm should be chosen for R sheet and J 0e optimization. However, to determine the best b-Si nanotexture design for the application of front-junction solar cells, the effects of SSA on the optical performance and the collection efficiency should also be investigated in future work.