Analysis of the interdigitated back contact solar cells: The n-type substrate lifetime and wafer thickness^*

For the silicon solar cells, pursuing higher energy conversion efficiency on thinner Si wafer is the future development trend for the photovoltaic industry.^[1] Hence, the interdigitated-back contact (IBC) solar cell based on n-type Si wafer has attracted extensive attention due to its high efficiency of up to 24%, as realized in the large area 125 mm× 125 mm.^[2] The absence of the front metal contacts of IBC solar cell allows the full light illumination without any shading loss. On the back side of the cell, there are p⁺ -emitter, n⁺ -base and metallization contacts, which require the complex fabrication processing including several mask and alignment steps, high temperature oxidation and diffusion processes, such as boron (B) and phosphorus (P) diffusion.^[3] For IBC structure, the photon-generated carriers need to transport through the whole thickness of wafer and then separate and collect by the p⁺ -emitter and n⁺ -base on the back side of the cell. Generally, in order to obtain high conversion efficiency, the diffusion length of the minority carriers should be at least four times the thickness value of the cell.^[4,5] However, as is well known, the n-Si wafer with high τ_bulk (> 1 ms) and good surface passivation, i.e., the low surface recombination velocity s_eff (SRV), can be easily degraded during the above-mentioned complex fabrication processing. For example, for the high temperature oxidation (> 950 °C) and boron diffusion (> 1000 ° C), if there is contamination during the processing, then the recombination center can be activated and the bulk lifetime can be greatly degraded in a time range from millisecond to several microseconds. Even for the surface recombination velocity s_eff is very low, the photon-generated carriers, which transport from the wafer's front surface to the back, can extensively recombine via those bulk centers due to contaminations. Recently, it was found that if careful fabrication process is not controlled, then oxidation induced stacking faults (OSFs) can form during the high temperature fabrication processing, which obviously reduces the final τ_bulk of n-Si wafer.^[6] Thus, the measured effective minority lifetime τ_eff, which generally includes τ_bulk and surface lifetime τ_surf (equal to wafer thickness SRV divided by W), is very low even if the τ_surf is high. Hence, the fabrication processing such as n-Si wafer cleaning, surface passivation and boron & phosphorous diffusion should be handled very carefully. But to date, to our knowledge, there are no systematic research reports on the influence of n-Si wafer's τ_bulk degradation on the characteristic of IBC solar cell. Accordingly, it is necessary to clarify the influence of τ_bulk change on the performance of IBC solar cell when the wafer thickness scales down.

In this paper, combining with our experimental data, we systematically study the effect of change in bulk lifetime on the property of IBC solar cell when the wafer thickness scales down by using 2D technology computer aided design software (2D TCAD),^[7] which is widely used in solar cell simulation.^[8] During the simulation, in order to highlight the effect of bulk lifetime on the device property, we assume that the whole IBC solar cell has good front and back surface passivation with SRV S = 10 cm/s (in fact, this can be obtained by good Al₂O₃ or SiO₂ passivation).^[9] Based on the results of the 2D TCAD simulation, the key factors are discussed and clarified for the n-Si IBC solar cell with scaling down the thickness. It is helpful for fabricating the future cost-effective IBC solar cell of high efficiency with using the thinner wafer.

In this work, we will first investigate the influence of high temperature process on lifetime. The n-type FZ 〈100〉 silicon wafers with 5 Ω·cm resistivity were cleaned using the standard RCA procedure.^[10] Then, we divided all of the wafers into five groups with different process listed in Table 1. After all of the processes, Semilab PV2000A was used to determine lifetime. From the results, we could find that the τ_eff values of groups 1 and 2 (without high temperature process) both excess 1 ms after passivation. Al₂O₃/SiN_x double passivation was more effective than SiN_x passivation for n-type silicon due to field effect passivation.^[9] Group 3 was processed in oxygen ambient using a conventional quartz furnace, and a 23-nm SiO₂ layer was achieved under the condition of 950 °C and 30 min. Then, we removed the oxide layer by dilute HF, and a new SiN_x layer was deposited by PECVD for passivation. Compared with group 2, the τ_eff is much lower than that of group 3, which was subjected to an extra thermal oxidation process. In order to exclude the effect of silicon surface defect on τ_bulk, group 4 experienced the same process as group 3 except inserting additional KOH etch between HF dip and SiN_x deposition. An unexpected result was achieved, the τ_eff of group 4 was only 30 μs which was much lower than τ_eff of group 3. A possible reason was that the residual K⁺ ion moved from surface into the inside of silicon in the PECVD SiN_x process (300 °C). Therefore, SC-2 solution (HCl:H₂O₂:DI water = 1:1:6) was used to remove the K⁺ ion in group 5. The τ_eff of group 5 after all processes was 140 μs, this value was similar to the τ_eff of group 3 and proved that the high temperature oxidization process leads to the decrease of τ_eff. The same problem appears in other high temperature processes, such as boron and phosphorus diffusion, which cannot be avoided in traditional production process of solar cells. From group 1, we verified that the τ_bulk of our substrate exceeded 1926 μs. Therefore, τ_eff (1323 μs) was mainly determined by τ_surf for SiN_x passivation in group 2. For group 5, the wafers were also passivated by SiN_x but suffered oxidation process in contrast to group 2, τ_eff was determined by τ_bulk. Consequently, τ_bulk decreases from 1926 μs (at least) to 140 μs due to the high temperature process. In the next section, we will add these experimental results to our simulation to investigate the influence of high temperature process on the performance of an IBC solar cell.

The 2D TCAD tool is used to simulate the operation of IBC solar cells when τ_bulk decreases. As a pathway to reducing the dependence of IBC solar cells on τ_bulk, reducing the variation of wafer thickness with τ_bulk is also simulated. The investigated device structure is shown in Fig. 1 in which the back emitter, the back surface field (BSF), and the front surface field (FSF) are formed by ion implantation. Implant energy and implant dose are given in Table 1. The simulated region is defined between the centre of two neighboring contacts of emitter and base. The widths of emitter and BSF are fixed to be 1700 μm and 300 μm, respectively. The gap between emitter and BSF is defined to be 50 μm to reduce the shunt current. To improve the light absorption, a two-layer (SiO₂/SiN_x) AR coating is used on the front side of device. In order to accurately simulate the IBC solar cells, the effects including carrier concentration dependent SRH recombination, Auger recombination, carrier concentration dependent mobility, band-gap narrowing are taken into account in the model. Moreover, the Fermi–Dirac statistics are used to simplify the calculation. Since we focus on the effect of wafer thickness variation on the performance of IBC solar cells, the recombination rate of the front surface and back surface is 10 cm/s for assuming excellent passivation. In the model, the doping concentration of N-type silicon wafer is defined to be 1.56× 10¹⁵ cm⁻³ as commonly used for solar cell application. Devices with wafer thickness values changing from 300 μm to 50 μm for various lifetimes are simulated and the main parameters used in the model are listed in Table 2.

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Figure 2(a) shows the dependences of V_oc of IBC solar cells on wafer thickness with τ_bulk decreasing. It can be clearly seen from the figure that V_oc is not affected by wafer thickness for the substrate with high τ_bulk. However, V_oc drops off considerably with increasing wafer thickness when the τ_bulk becomes low. This phenomenon can be explained by one ideal-diode model as given by^[11]

where N_D, n_i, p are the doping concentration of the substrate, the intrinsic carrier concentration, and the injected hole concentration in emitter region, respectively; k is Boltzmann's constant; T is absolute temperature; and, q is the charge on an electron. For the substrate with low τ_bulk, the hole generated on the front side of device can be easily lost due to the large SRH recombination. Therefore, for the thicker substrate, few holes can reach the emitter, resulting in the lower value of V_oc.

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The inset of Fig. 2(a) shows the V_oc as a function of wafer thickness with the τ_bulk value of 2 ms. It can be seen that the value of V_oc slightly increases from 640.3 mV to 640.7 mV as the wafer thickness decreases from 300 μm to 150 μm, then V_oc decreases to 640.125 mV as the wafer thickness further decreases to 50 μm. This phenomenon can be explained by considering the holes transport from front surface to back emitter, as shown in Fig. 2(c). The holes excited by the photons within the absorption depth can reach the back emitter by diffusion. In this process, the concentration of photon-generated holes is dependent on the photon flux density and the distance from front surface x as given by

where Ψ₀(λ) is the photon flux density incident on the front surface and is the absorption coefficient. The concentration of holes which reach the back emitter for each wavelength by diffusion p_d(λ) can be calculated from the following equation:

where W is the wafer thickness and is the diffuse length of holes.

The total photon-generated holes reaching the back emitter can then be calculated by integrating the left-side of Eq. (3) with respect to all involved wavelength and the V_oc can be obtained by combining Eqs. (1), (2), and (3). Figure 2(b) shows the calculated results. Compared with the results obtained by the TCAD model, the V_oc exhibits a similar behavior as a function of wafer thickness and τ_bulk. Therefore, the model involving hole generation and diffusion can well explain the effect of wafer thickness on V_oc for different substrate lifetimes. The difference between these results achieved by the two methods arise as the horizontal transmission of holes and back reflection are ignored in the calculations.

Figure 3(a) shows the variations of J_sc of IBC solar cells with wafer thickness as τ_bulk decreases. For the substrate with 2 ms τ_bulk, the value of J_sc gradually decreases from 37.39 mA/cm² to 32.74 mA/cm² as the wafer thickness decreases from 300 μm to 50 μm. The same behavior is found for the substrate with 1 ms τ_bulk.

However, the values of J_sc exhibit different wafer thickness dependences as the τ_bulk further decreases. For example, for the substrate with 500-μs lifetime, the value of J_sc increases from 35.62 mA/cm² to 35.81 mA/cm² first with the wafer thickness decreasing from 300 μm to 250 μm and then decreases to 32.64 mA/cm² with the wafer thickness further decreasing to 50 μm. The same behavior is found for the solar cells using the substrate with lower τ_bulk. The maximum values of J_sc are observed to be 34.77 mA/cm², 33.6 mA/cm², and 32.49 mA/cm² for the τ_bulk values of 250 μs, 125 μs, and 62.5 μs when the wafer thickness values are 150 μm, 100 μm, and 100 μm, respectively.

To explain this phenomenon, the calculated values of external quantum efficiency (EQE) of IBC cells with various wafer thickness values for the τ_bulk of 2 ms and 62.5 μs are plotted in Figs. 3(b) and 3(c), respectively. It can be seen that the EQE begins to decrease quickly as the absorption depth becomes longer than wafer thickness at a specific wavelength. This wavelength is defined as critical wavelength λ_c hereafter, and the values of λ_c are variable corresponding to different wafer thickness values.

For the substrate with 2-ms τ_bulk, the EQE at the wavelength ranging from 500 nm to the λ_c changes a little with wafer thickness. Therefore, J_sc is mainly determined by the value of λ_c. A higher λ_c will increase the absorption of photons at the wavelength within the Δλ_c, hence more carriers can be generated. Figure 3(b) shows that the λ_c shifts to the longer wavelength as the wafer thickness increases, which results in increasing J_sc for thicker wafer. The same principle can be applied to the substrate with 1-ms τ_bulk.

For the substrate with 62.5-μs τ_bulk, the wavelength λ_i is determined as the curves intersect where the EQE values of two IBC solar cells with different substrate thickness are equal. The figure indicates that the EQE decreases as the wafer thickness increases at the wavelength shorter than λ_i due to the recombination of electrons and holes. However, at the wavelength longer than λ_i, the EQE increases with wafer thickness decreasing as the result of the increase in absorption of long wavelength photons. Therefore, when wafer thickness increases, the change of J_sc is determined by compromising between the decreasing of the integrated value of EQE for wavelength lower than λ_i and the increasing of integrated value of EQE for wavelength higher than λ_i. To quantify the relationship of EQE with wafer thickness for 62.5-μs substrate, the integrated values of EQE are plotted in Fig. 3(d). The change of J_sc with wafer thickness is also shown in Fig. 3(d). The same changes tend to verify our point of view.

The fill-factor (FF) of IBC solar cells is also affected by both τ_bulk and wafer thickness. Our simulation results show that the shunt resistance decreases with τ_bulk decreasing, which results in the decreasing of FF for a given wafer thickness. For example, FF changes from 67.7% to 63.5% as lifetime decreases from 2 ms to 62.5 μs for 50-μm substrate. Moreover, for a given τ_bulk, the series resistance increases and the shunt resistance decreases with the wafer thickness scaling down, both leading to the decrease in FF.

Figure 4 shows the variations of final efficiency (EFF) with wafer thickness for various τ_bulk values of substrate. For the high τ_bulk (such as 2 ms) substrates, reducing substrate thickness causes the decrease in EFF. Diffusion coefficient in silicon substrate is 13 cm²/s,^[12] 2-ms τ_bulk makes diffusion length reach 1612 μm, which is much larger than the thickness of substrate. Therefore, bulk recombination is not the limiting factor in the performance of IBC solar cells, and the absorption of photons will decrease when a thinner substrate is used. For the low τ_bulk (such as 62.5 μs) substrates, diffusion length is 285 μm, which is smaller than the thickness of 300-μm substrate. Reducing substrate thickness will increase the number of minority carriers (holes) which can reach the rear surface of IBC solar cells; therefore, the EFF increases at first. When the thickness of substrate is below 100 μm, the influence of reducing photon-absorption on performance of IBC solar cells exceeds that of increasing holes; therefore, the EFF decreases when substrate continues to scale down. For the substrate with τ_bulk value between 2 ms and 62.5 μs, the maximum EFF can be obtained by optimizing wafer thickness for various τ_bulk values. For example, the optimized thickness values are 300 μm, 250 μm, 200 μm, and 150 μm for the τ_bulk values of 1 ms, 500 μs, 250 μs, and 125 μs, respectively.

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During the simulation, in order to highlight the influence of bulk lifetime on the device properties, we assume that the whole IBC solar cell has a good front and back surface passivation with S = 10 cm/s. In this situation, τ_eff is determined by τ_bulk, which can be explain by the following equation^[13]

where W is the thickness of the substrate. In fact, the above conclusions on τ_bulk should be changed into the ones on τ_eff in consideration of S. If S = 100 cm/s, for the high τ_bulk (such as 2 ms) substrate, τ_eff is determined by surface (S and W), EFF will decrease more quickly as W decreases because τ_eff also decreases. For the low τ_bulk (such 62.5 μs) substrate, τ_eff is determined first by τ_bulk, then by surface as W decreases. Therefore, bulk recombination will increase for low W and EFF may increase directly as W scales down.

In order to clearly illustrate the influence of τ_bulk decreasing and wafer thickness scaling down on the performance of IBC solar cells, a 2D simulation tool TCAD is used to calculate the changes of V_oc, J_sc, FF, and EFF of IBC solar cells with τ_bulk values and wafer thickness. For a substrate with high τ_bulk, the V_oc first slightly increases then falls as wafer thickness decreases. However, for a substrate with low τ_bulk, the V_oc increases linearly as wafer thickness scales down. We use a physical model which combines the absorption of photons and diffusion of holes to explain this tendency. For a substrate with high τ_bulk, J_sc decreases as the wafer thickness decreases. For the substrate with low τ_bulk, the J_sc first increases and then falls as wafer thickness scales down. Different changes of EQE curves with various thickness values for different τ_bulk values are plotted to explain this phenomenon. Moreover, FF decreases as the values of both τ_bulk and wafer thickness reduce. The effects of V_oc, J_sc, and FF induce the EFF to change with substrate lifetime and wafer thickness. The influence of reducing τ_bulk on IBC solar cells becomes increasingly weaker as wafer thickness scales down due to the reduced absorption of light for long wavelengths. Therefore, an optimizing light trapping technology needs to be developed to prevent EFF from decreasing.