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  μ s 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  μ s, 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  μ s. Therefore, τ _eff (1323  μ s) 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  μ s (at least) to 140  μ s 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.

Table 1.

Table 1.

Table 1. All wafers with different processes. Group Process τ eff/μ s 1 ALD 20-nm Al2O3 + SiNxa 1926 2 SiNx 1323 3 Oxidizationb + HF + SiNx 193 4 Oxidization + HF + KOH + SiNx 30 5 Oxidization + HF + KOH + SC-2c + SiNx 140 a) Plasma-enhanced chemical vapor deposition 80-nm SiNx. b) 950  ° C 30  min in dry oxygen ambient. c) HCl:H2O2:DI water = 1:1:6 (80  ° C; 15  min) + dilute HF + DI water.

Table 1. All wafers with different processes.

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  μ m and 300  μ m, respectively. The gap between emitter and BSF is defined to be 50  μ m 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  μ m to 50  μ m for various lifetimes are simulated and the main parameters used in the model are listed in Table  2.

Fig.  1.

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	Fig.  1. Schematic view of the simulated structure of IBC solar cell.

Table 2.

Table 2.

Table 2. Parameters used in simulation. Substrate     Doping type n     Doping concentration 1.56× 1015/cm− 3     Thickness 250  μ m Surface recombination     Sfront 10  cm/s     Sback 10  cm/s Impurity doping     Implant dose of emitter 3× 1015/cm− 2     Implant energy of emitter 90  keV     Implant dose of BSF 1× 1015  cm− 2     Implant energy of BSF 150  keV     Implant dose of FSF 2× 1013  cm− 2     Implant energy of FSF 20  keV Antireflection layer     Refractive index of SiOx 1.5     Thickness of SiOx 105  nm     Refractive index of SiNx 2.6     Thickness of SiNx 55  nm Measurement     Spectrum AM 1.5G     Incidence angle 90°     Testing voltage 0 ∼ 0.75  V

Table 2. Parameters used in simulation.

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.

Fig.  2.

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	Fig.  2. Variations of open-circuit voltage with wafer thickness for various bulk lifetimes, calculated by (a) the TCAD model of IBC solar cells, and (b) simple model of hole generation and diffusion. (c) Process of generation and diffusion of holes.

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  μ m to 150  μ m, then V_oc decreases to 640.125  mV as the wafer thickness further decreases to 50  μ m. 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 Ψ ₀(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  μ m to 50  μ m. 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-μ s 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  μ m to 250  μ m and then decreases to 32.64  mA/cm² with the wafer thickness further decreasing to 50  μ m. 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  μ s, 125  μ s, and 62.5  μ s when the wafer thickness values are 150  μ m, 100  μ m, and 100  μ m, 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  μ s 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 Δ λ _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-μ s 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-μ s 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  μ s for 50-μ m 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  μ m, 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  μ s) substrates, diffusion length is 285  μ m, which is smaller than the thickness of 300-μ m 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  μ m, 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  μ s, the maximum EFF can be obtained by optimizing wafer thickness for various τ _bulk values. For example, the optimized thickness values are 300  μ m, 250  μ m, 200  μ m, and 150  μ m for the τ _bulk values of 1  ms, 500  μ s, 250  μ s, and 125  μ s, respectively.

Fig.  3.

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	Fig.  3. (a) Variations of TCAD simulated short circuit current density with wafer thickness with τ bulk decreasing, (b) variations of calculated EQE of IBC solar cells with substrate thickness for 2-ms τ bulk, (c) variations of calculated EQE of IBC solar cells with substrate thickness for 62.5-μ s τ bulk, and (d) variations of integrated EQE with substrate thickness for 62.5-μ s τ bulk.

Fig.  4.

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	Fig.  4. Variations of calculated efficiency with wafer thickness for various substrate lifetimes.

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  μ s) 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.