The role of heterointerfaces and subgap energy states on transport mechanisms in silicon heterojunction solar cells

The contact resistivity is a key parameter to reach high conversion efficiency in solar cells, especially in architectures based on the so‐called carrier‐selective contacts. The importance of contact resistivity relies on the evaluation of the quality of charge collection from the absorber bulk through adjacent electrodes. The electrode usually consists of a stack of layers entailing complex charge transport processes. This is especially the case of silicon heterojunction (SHJ) contacts. Although it is known that in thin‐film silicon, the transport is based on subgap energy states, the mechanisms of charge collection in SHJ systems is not fully understood yet. Here, we analyse the physical mechanisms driving the exchange of charge among SHJ layers with the support of rigorous numerical simulations that reasonably replicate experimental results. We observe a connection between recombination and collection of carriers. Simulation results reveal that charge transport depends on the alignment and the nature of energy states at heterointerfaces. Our results demonstrate that transport based on direct energy transitions is more efficient than transport based on subgap energy states. Particularly, for positive charge collection, energy states associated to dangling bonds support the charge exchange more efficiently than tail states. The conditions for optimal carrier collection rely on the Fermi energy of the layers, in terms of activation energy of doped layers and carrier concentration of transparent conductive oxide. We observe that fill factor (FF) above 86% concurrently with 750‐mV open circuit voltage can be attained in SHJ solar cells with ρc lower than 45 mΩ·cm2 for p‐contact and 20 mΩ·cm2 for the n‐contact. Furthermore, for achieving optimal contact resistivity, we provide engineering guidelines that are valid for a wide range of silicon materials from amorphous to nanocrystalline layers.

consists of a stack of layers entailing complex charge transport processes. This is especially the case of silicon heterojunction (SHJ) contacts. Although it is known that in thin-film silicon, the transport is based on subgap energy states, the mechanisms of charge collection in SHJ systems is not fully understood yet. Here, we analyse the physical mechanisms driving the exchange of charge among SHJ layers with the support of rigorous numerical simulations that reasonably replicate experimental results.
We observe a connection between recombination and collection of carriers. Simulation results reveal that charge transport depends on the alignment and the nature of energy states at heterointerfaces. Our results demonstrate that transport based on direct energy transitions is more efficient than transport based on subgap energy states. Particularly, for positive charge collection, energy states associated to dangling bonds support the charge exchange more efficiently than tail states. The conditions for optimal carrier collection rely on the Fermi energy of the layers, in terms of activation energy of doped layers and carrier concentration of transparent conductive oxide. We observe that fill factor (FF) above 86% concurrently with 750-mV open circuit voltage can be attained in SHJ solar cells with ρ c lower than 45 mΩ·cm 2 for p-contact and 20 mΩ·cm 2 for the n-contact. Furthermore, for achieving optimal contact resistivity, we provide engineering guidelines that are valid for a wide range of silicon materials from amorphous to nanocrystalline layers. as bulk absorber with thin-film silicon technology as transport stacks for high efficiency based on carrier-selective contacts (CSC). SHJ contact stack typically consists of hydrogenated intrinsic amorphous silicon (i-a-Si:H) layer followed by a doped thin-film silicon [1][2][3][4] (eventually alloyed with oxygen [5][6][7][8][9][10][11][12][13][14] or carbon [15][16][17] ) and a transparent conductive oxide (TCO). The purpose of these layers is to provide the so-called contact selectivity by inducing an electric potential inside the c-Si for carrier separation that allows the collection of one type of carriers while repelling the other. Brendel and Peibst 18 proposed the quantification of the selectivity by using a parameter that is inversely proportional to recombination parameter (J 0 ) 19 and contact resistivity (ρ c ).
Similarly, the selective transport 20 is defined as the ratio of local generation (current) between collecting and no-collecting carriers. 21 In fact, high selectivity values reflect high quality of CSC and vice versa, requiring both low J 0 and ρ c values or high current of collecting carriers and minimal current of no-collecting carriers. Accordingly, ρ c entails the complex electronic transport of carriers, governed by potential barriers and energy discontinuities at interfaces, [22][23][24][25] which are related to the flow of collecting carriers. Additionally, for SHJ contact stack endowed with thin-film silicon layers, ρ c includes charge transport processes through subgap energy states. [26][27][28][29][30][31] Altogether, owing to the complexity of SHJ contact stacks, the driving mechanisms of charge transport in SHJ solar cells are not fully understood, yet. In this respect, rigorous advanced simulation tools can elucidate such physical phenomena.
Besides, Adachi et al. 32 demonstrated that reducing carrier recombination also increases the fill factor (FF), thus revealing a link between recombination and resistive losses. This insight anticipated the world-record c-Si conversion efficiency above 26% by combining high passivation quality with low contact resistance. 33 Similarly, research groups reported that in SHJ solar cells, high efficiency depends not only on outstanding passivation but also on low ρ c [34][35][36][37] In particular, Lachenal et al. 36 and Lee et al. 38 demonstrated remarkable efficiency improvements by minimizing ρ c . For practical purposes, it is worth noting that among all available techniques for measuring ρ c , the most straightforward is the transfer length method (TLM). 25,37 Experimentally, 1,34-36 it has been proved that minimizing ρ c of SHJ contact stack system is crucial to reach high efficiency devices. Hence, it is of great interest to investigate the charge transfer mechanisms leading to ρ c .
In this context, the use of advanced simulations tools is imperative to understand charge transfer mechanisms and their relation to ρ c and recombination. In this work, based on rigorous TCAD simulations, we present an analysis of the competitive physical mechanisms driving ρ c for SHJ contact systems. Accordingly, we analyse the transport processes as charge transfer mechanisms supported by not only energy states in conduction or valence band but also subgap states surrounding heterointerfaces. Then, to evaluate the connection between recombination and transport, we deploy and simulate the same SHJ layers in interdigitated back contact (IBC) devices to correlate ρ c , V OC and FF. Finally, we provide practical insights to reduce ρ c , thus providing guidelines for improving not only IBC devices but also other solar cell architectures based on SHJ approach. The first results and validation of this investigation were presented in Procel et al. 39

| CONTACT RESISTIVITY AND TRANSPORT MECHANISMS
To elucidate the intertwined effects of the transport processes, we use contact resistance (ρ c ) as indicator of transport quality. Figure 1A depicts a schematic of TLM measurement structure that consists of two equivalent contacts stack featuring a contact resistance (R c ), separated by a known distance (L). Subsequently, from dark current density-voltage (J-V) curves, calculated for different L, we extract R c with its equivalent ρ c as well as the contribution of the semiconductor resistance (R b ) with the equivalent sheet resistance. 40 In particular, we F I G U R E 1 (A) Schematic of transfer length method (TLM) structures for contact resistivity (ρ c ) calculation. Contact resistance (R c ) comprises the whole contact stack, from c-Si bulk: i-a-Si (yellow)/doped a-Si (red: n-type, green: p-type)/transparent conductive oxide (TCO) (light blue)/ metal (grey) (thicknesses are not in scale). R c is extracted from current density-voltage (J-V) curves evaluated for different semiconductor resistance (R b ) by changing the contact gap (L). (B) Equivalent lumped resistors indicating resistive losses in (interdigitated back contact [IBC]) silicon heterojunction (SHJ) devices: contact resistance for n-(R cn ) and p-contact (R cp ) and bulk resistance (R bulk ) [Colour figure can be viewed at wileyonlinelibrary.com] analyse IBC devices featuring 96% of TCO/metal area coverage to highlight the charge collection through thin-film silicon layers and heterointerfaces up to metal neglecting any effect of the lateral path inside the contact stack. 21 Therefore, ρ c allows for calculating the contact resistance contribution in IBC-SHJ devices (see Figure 1B): R cn for n-contact and R cp for the p-contact. For a proper evaluation of ρ c , the doping type of the base is assumed to have the same doping type of the contact layer stack under analysis, 37,41 thus avoiding currentblocking effects due to reverse polarization of p-n junction. To assess the transport mechanisms through a TLM structure, we firstly analyse the energy band diagram, as Figure 2 shows. Interestingly, ρ c is a measurable parameter that describes the local generation of collecting carriers through the complete contact stack, including (i) c-Si carrier accumulation at interfaces with transport stacks (band bending); In p-contact case (see Figure 2B), the current flow (J) is based on the movement of positive charges along the valence band of c-Si, i-a-Si:H and p-layer (holes) and TCO conduction band (electrons). In particular, the transport of holes in the valence band is based on DT and TE. At p-layer/TCO interface, the transition from holes to electrons and vice versa from (to) the valence band of p-layer to (from) conduction band of TCO is based on band-to-band tunnelling (B2BT) 46 or TAT. B2BT processes are possible with the proper band alignment of valence band of p-layer with conduction band of TCO across equivalent energy states. Such condition is fulfilled if the activation energy (E a ) of p-layer is lower than the energy gap between TCO conduction band and Fermi energy. Besides, subgap energy states also act as carrier reservoir for charge transfer or charge trapping within capture and emission processes (recombination), also known as TAT. 45,47 Furthermore, the dynamics of capture and emission processes is driven by the Fermi energy relative to defect energy distribution for equivalent capture and emission probability that enables charge transfer mechanisms. 45,48 Hence, material parameters associated to Fermilevel energy, such as E a for doped layers and N TCO , ultimately drive the transport of charges through SHJ contact stack. the transport processes described in Section 2. J-V curves in dark conditions (0 < V < 1 V) are evaluated for different contact spacing to calculate ρ c , emulating TLM process. In case of no perfectly linear J-V curve, we limit the voltage range to less than 0.15 V, for which the J-V characteristic is sufficiently linear. 40 To evaluate the contact stack system, we focus our study on material parameters related to Fermi-level energy: E a for doped layers and TCO carrier concentration (N TCO ), assuming N TCO as active dopants. E a is a measurable parameter describing the energy difference between Fermi level and conduction (valence) band in n-type (p-type) silicon thin-film layers, whereas N TCO establishes the Fermi-energy position relative to the TCO conduction band. Accordingly, low E a values mean more doping whereas higher N TCO values imply low work function. Experimentally, low E a values typically correspond to nanocrystalline silicon material whereas high values correspond to amorphous silicon layers. To adjust E a in the doped layer, we use a constant doping in addition to energy states distribution as described in Table 1. We consider reasonably attainable values of E a from 20 up to 350 meV for n-contact and from 30 to 450 meV for p-contact.

| SIMULATION APPROACH
TCO is modelled on the basis of ITO parameters as degenerate semiconductor 55 with corresponding values reported in Table 1. Additionally, we include the evaluation of N TCO effect for a range of values from 1 × 10 19 up to 1 × 10 21 cm −3 . It is worth noting that transport processes through heterointerfaces in the electrode stack are almost insensitive to parameters reported in Table 1 as explained in Section 2.
Therefore, we assume constant such parameters within our analysis, Summary of models input parameters and material parameters used in simulations in order to concisely evaluate the transport mechanisms at contact layers.
Subsequently, to understand the relation of ρ c with recombination and solar cell external parameters, we performed numerical simulations of IBC structure 21 (see Figure 1B Similarly, we consider negligible lateral transport inside bulk, by using relatively small but still realistic 320 μm half pitch. It is worth noting that this approach can be potentially extended to any system of materials based on silicon alloys (e.g., SiO x or SiC x ) or even using multilayer stacks as reported in Procel et al. 21 In this work, however, we simulate fully amorphous or nanocrystalline Si layers.
At last, we assume in this work as ohmic the TCO/metal contact in order to emphasize the effect of transport mechanisms explained in Section 2.

| RESULTS AND DISCUSSION
As discussed in Section 2, E a together with N TCO strongly affect the carrier transport and, therefore, ρ c in SHJ contact stacks. Accordingly,  . Accordingly, Figure 3B shows which mechanism, B2BT or TAT, is dominant in the range of parameters investigated.

| p-Contact
T A B L E 2 Summary of geometrical parameters for transfer length method (TLM) and interdigitated back contact (IBC) device   In case of charge transport based on TAT processes (see Figure 3B), we observe that ρ c values increase by lowering N TCO . In particular, for N TCO < 2 × 10 19 cm −3 , ρ c exhibits minimal values for 220 < E a < 320 meV. This interesting behaviour is explained by looking into the energy of states with similar energy to Fermi energy in Figure 4. As discussed in Section 2, the energy level of subgap states is crucial to define if the state can be charged or discharged in certain conditions. 27 Indeed, energy states with equivalent energy to Fermi level exhibit 50% probability to capture or emit a carrier enabling them for charge transport as TAT processes. Therefore, more active states for TAT mechanism are those located close to Fermi energy and surrounding p-layer/TCO interface ( Figure 5). In particular, according to our simulations, active energy states are located up to 10 nm from inside p-layer from TCO interface. Figure Table 3 summarizes the transition processes for valence band TSs and DBSs dominating the charge transfer from p-layer to TCO. These transitions correspond to capture processes exhibiting recombination behaviour as Figure 5 graphically reports. (Table 1). N Tc , N Tv and N DB stand for tail states (TSs) at conduction band (E C ), valence band (E V ) and dangling bonds, respectively. trap-assisted tunnelling (TAT) is enabled by TSs when Fermi energy is lower than 0.5 eV with respect to valence band energy of p-layer at p-layer/transparent conductive oxide (TCO) interface (see Figure 3B). If Fermi energy has a value higher than 0. According to Figure 3A  The effect of c-Si band bending is apparent by looking at V OC trend in

| n-Contact
As discussed in Section 2, collection of charge through the n-contact implies TAT, TE or DT. Figure 8 shows Furthermore, we observe generally low ρ c Figure 8 values with a maximum value of 10 3 mΩ·cm 2 . This value is two order of magnitude lower than the maximum achieved for p-type contact (see Figure 3A).
Here, the charge transfer through n-contact stack occurs only in the conduction band (see Figure 2). Low Concerning J SC , we observed a variation of less than 0.04 mA/cm 2 due to transport processes. In this respect, J SC depends mostly on light management approach rather than transport mechanisms.
Hence, optimizing ρ c highlights the path for enhancing IBC conversion efficiency. It is worth noting that also other SHJ architectures can be evaluated, but considering more specialized analysis focussed on front contact layers, that additionally include lateral transport inside and surrounding the front contact stack.

| CONCLUSIONS
We have analysed the physical mechanisms driving the charge exchange in SHJ contact systems by advanced electrical modelling of TLM contact stacks. We studied the dominating mechanisms that govern contact resistivity (ρ c ) for both p-and n-type contact stacks by Regarding n-contact, our calculations show that ρ c is more determined by E a than N TCO . In general, decreasing E a while increasing N TCO results on minimal ρ c values. By comparing ρ c in p-and n-contact, for p-contact, ρ c changes about five orders of magnitude by varying E a and N TCO whereas n-contact ρ c varies only two orders of magnitude.
Such a difference reveals that p-contact is more sensitive to layer properties and therefore requires more effort to be optimized. As guideline for optimal contact stack design, we calculated the minimal