The first mono-crystalline silicon solar cell with passivated emitter rear contact (PERC) configuration was proposed in 1989^[1]. Compared with the conventional aluminum back surface field (Al-BSF) silicon solar cell, PERC has a rear surface passivation layer such as Al₂O₃/SiN_x stacked thin films and local Al-BSF contact^[2]. The stacked Al₂O₃/SiN_x thin films on the rear surface effectively reduce the recombination of carriers through the combination of chemical and field passivation^{[3, 4]}. The metal paste is in partial contact with the silicon material on the rear side, which reduces the recombination area at the metal/oxide interface and thus further improves the open circuit voltage (V_OC)^{[5, 6]}. Consequently, the V_OC and short circuit current (J_SC) of PERC are higher than that of Al-BSF solar cells, in which the rear passivation layers are absent^[7]. Moreover, this partial contact design alleviates the bowing effect due to the mismatch of thermal expansion coefficients between aluminum and silicon that exists in the Al-BSF devices^[8]. Although a light-induced degradation of efficiency is an important issue for PERC solar cells^[9], elaborate stabilization has recently been developed to significantly suppress the degradation^{[10, 11]}.

In 2019, the average mass-production efficiency of p-type mono-crystalline PERC solar cells has reached around 22%, which is 1.2% higher than that of Al-BSF solar cells^{[12, 13]}. At the beginning of 2019, LONGi Solar has announced that it has received a mono-crystalline silicon PERC laboratory efficiency at 24.06%^[14]. This is the first time that the efficiency of mono-crystalline silicon PERC solar cells has exceeded 24% in commercial dimensions. This new world record and its compatibility with conventional Al-BSF product line provide a great potential of the PERC solar cell to become dominant in the upcoming market. However, there is little technical information on this achievement. In this work, a p-type mono-crystalline silicon PERC solar cell was numerically studied in terms of surface passivation of the emitter, and the quality of silicon wafer and metal electrodes, based on data from the production line and literature. A feasible way to achieve 24% efficiency of PERC solar cell using mass production technology is proposed. In addition, the efficiency loss sources between 24% and the ultimate limit of 29% are analyzed using free energy loss analysis to illustrate the space for further improvement. This is expected to provide a guideline for the design and manufacture of high efficiency mono-crystalline silicon PERC solar cells.

The PERC solar cell is simulated by Quokka 2 software, which solves the charge carrier transport in a quasi-neutral silicon device^[15]. This approach employs simplifications, featuring conductive boundaries and quasi-neutrality condition to the general semiconductor carrier transport model^[15]. The conductive boundary condition omits the need to solve the general set of semiconductor equations, consisting of one transport equation for minority and majority carriers and Poisson’s equation for the electric potential^[15-17]. The model of charge carrier transport as described by three coupled differential equations^[18] can be simplified and therefore solely solved by a set of two differential equations. These simplifications are well validated to not impose notable loss of generality or accuracy for wafer-based silicon solar cell devices^[15].

Fig. 1(a) shows a digital camera image of a PERC solar cell with five busbars from our product line. The simulation model (Fig. 1(b)) is configured based on the products. The width of simulated solar cell is 200 μm. The solar cell features a front selective emitter (SE) configuration. The emitter is passivated with a double-layered SiN_x thin films, in which the refractive index (@632 nm) and thickness of the bottom SiN_x are 2.41/15 nm and the top SiN_x are 2.09/70 nm, respectively. Al₂O₃/double-layered SiN_x stacked thin films are deposited on the rear side, in which the thickness of Al₂O₃ is 8 nm and the refractive index and thickness of SiN_x are 2.03/15 nm, 1.98/135 nm, respectively. The generation profile of light to electrical carriers is simulated by Module Ray Tracer from PV Lighthouse, Sunsolve^[19].

Table 1 lists the initial parameters of the PERC reference cell, which includes the data acquired from the production line and literatures. Based on the data in Table 1, a 21.90% efficiency reference PERC solar cell is obtained by simulation, which is similar with the mass-produced efficiency as shown in Fig. 2.

Based on the simulated 21.90% PERC reference solar cell, potential improvements from surface passivation, silicon wafer quality and metal grid line are studied using data from the literature to pave the way for PERC solar cells beyond 24%. In PERC solar cells, the front double-layered SiN_x thin films act not only as antireflection layers but also as a passivation layer. This passivation layer has a significant increase on the electrical properties of the solar cell, especially the V_OC and J_SC. The passivation performance is reflected by the reverse saturation current density (J_0E) in the simulated model. The relationship between the recombination current density (J_rec) and J_0E is given by^[23]

$ {J_{{\rm{rec}}}} = {J_{{\rm{0E}}}}{\left(\frac{np}{n_{\rm{i,eff}}^{\rm{2}}- 1}\right)}, $  (1)

where n and p represent the concentration of electrons and holes, respectively, and n_i,eff represents the effective intrinsic carrier concentration. According to the Eq. (1), reducing the J_0E will lead a lower the J_rec and a better passivation performance.

In an ideal case, the relationship between V_OC, J_SC and J_rec can be expressed by^[24]

$ {V_{\rm{OC}}} = \frac{{KT}}{q}{\rm{ln}}\left( {{\rm{1 + }}\frac{{{J_{{\rm{ph}}}}}}{{{J_{{\rm{rec}}}}}}} \right), $  (2)

$ {J_{{\rm{SC}}}} = {J_{{\rm{rec}}}}\left[ {{\rm{exp}}\left( {\frac{{qv}}{{nKT}}} \right) - 1} \right] - {J_{{\rm{ph}}}}, $  (3)

where J_ph is the photocurrent density, K the Boltzmann constant, T the thermodynamic temperature, q the electron charge, and v the voltage. According to the Eqs. (2) and (3), the V_OC and J_SC increase as the recombination current J_rec decreases. Therefore, an excellent passivation layer can effectively increase the V_OC and J_SC of the cell. In the reference cell, a double-layered SiN_x having different refractive indices is selected as the front surface passivation layer based on our production line. Besides the double-layered SiN_x, Huang et al. systematically studied the passivation mechanism and performance of stacked PECVD SiO_xN_y/SiN_x, thermally grown SiO₂/SiN_x, thermally grown SiO₂/ALD Al₂O₃/SiN_x and ALD Al₂O₃/SiN_x^[25] thin films. According to these results, the relationships between the sheet resistance of n⁺ emitter and the J_0E after passivation using these four types stacked thin films are summarized in Fig. 3^{[25, 26]}. It is seen that the emitters with a higher sheet resistance can be passivated much better. SiO₂/Al₂O₃/SiN_x and SiO₂/SiN_x have better passivation performance than the SiO_xN_y/SiN_x and Al₂O₃/SiN_x, which delivers a J_0E as low as 20 fA/cm² as the sheet resistance increased to 120 Ω/□. The Al₂O₃/SiN_x stacked film has a poor passivation performance on n⁺ emitter due to the high effective negative charge density (Q_eff = −2.4 × 10 ¹² cm⁻²) in Al₂O₃^[25]. This will repel photogenerated electrons and then result in depletion or weak inversion of the charge carriers under a high surface doping concentration condition^{[25, 27]}, and in turn an increased recombination at the n⁺ emitter. For the SiO₂/Al₂O₃/SiN_x stacked film, the introduction of SiO₂ layer not only brings a low negative charge density (Q_eff = −2.1 × 10 ¹¹ cm⁻²) but also results in a very low interface state density (D_it = 10¹⁰ eV⁻¹·cm⁻²) because of the superior ability of SiO₂ in passivating the dangling bonds on Si surface^[28], which is also called chemical passivation. The excellent passivation result of SiO₂/SiN_x stacked film (Q_eff = 2 × 10¹¹ cm⁻²) can also be attributed to the superior chemical passivation of SiO₂ which is similar to SiO₂/Al₂O₃/SiN_x. The SiO_xN_y/SiN_x stacked film (Q_eff = 1.2 × 10¹² cm⁻²) has a higher interface state density (D_it = 6.1 × 10¹¹ eV⁻¹·cm⁻²)^[29] and so results in a poor chemical passivation compared to SiO₂/SiN_x stacked film^[26].

Fig. 4 compares the electrical properties of the four types of stacked films (SiO₂/Al₂O₃/SiN_x, SiO₂/SiN_x, SiO_xN_y/SiN_x and Al₂O₃/SiN_x) that are used in the PERC model. The thickness and refractive index of the double-layered SiN_x and the simulation parameters are consistent with the reference cell, while all SiO₂, SiO_xN_y, Al₂O₃ in the four stacked films are 7 nm. It is seen that the V_OC and FF are positive dependent on the J_0E. Although a lower J_0E can benefit photocurrent, the optical parasitic loss seems dominant and leads to decreased J_SC. Eventually, the device using SiO₂/SiN_x has the highest efficiency of 22.22%, which is 0.32% higher than that of the reference cell, while the cell using Al₂O₃/SiN_x has the lowest simulated efficiency of 21.35%. Therefore, in the subsequent optimization process, SiO₂/SiN_x stacked film is selected as the emitter passivation layer.

A silicon wafer with high carrier lifetime is of great benefit for improving solar cell efficiency. The carrier lifetime is inversely proportional to the recombination rate (R). The R, as a comprehensive result of Auger, radiative and Shockley-Read-Hall (SRH) recombination, which can be expressed as^[24]

$ R = {R_{{\rm{Auger}}}}{\rm{ + }}{B_{{\rm{rad}}}}pn{\rm{ + }}{R_{{\rm{SRH}}}}{\rm{ + }}{\tau _{{\rm{b,fixed}}}}{\rm{(}}n-{n_{\rm{0}}}{\rm{),}} $  (4)

where R_Auger is the Auger recombination rate derived from the research of Richter^[30]. The radiative recombination is described by the product of hole concentration p, electron concentration n and radiative recombination coefficient B_rad. SRH recombination is given by^{[31, 32]}

$ {R_{{\rm{SRH}}}}{\rm{ = }}\frac{{np-n_{{\rm{i,eff}}}^{\rm{2}}}}{{{\tau _{{\rm{p0}}}}\left( {{n_{\rm{1}}}{\rm{ + }}n} \right){\rm{ + }}{\tau _{{\rm{n0}}}}\left( {{p_{\rm{1}}}{\rm{ + }}p} \right)}}, $  (5)

where n₁ = n_i,eff exp[(E_t− E_i)/kT], p₁ = n_i,eff exp[−(E_t− E_i)/kT], E_t is the defect level, E_i is the intrinsic level, and τ_n0 and τ_p0 represent the lifetime of electrons and holes, respectively. τ_n0/p0 = (v_thσN_t)⁻¹, where the average thermal motion rate v_th = 1.1 × 10⁷ cm/s, σ is the capture section of the defect recombination center for electron/hole, and N_t is the defect concentration. The last part in the Eq. (4) represents for the recombination caused by a fixed; that is, injection independent, bulk minority carrier lifetime τ_b,fixed.

In boron-doped p-type silicon wafers, the BO complex defect is an important SRH recombination center affecting carrier lifetime of the silicon wafer. Fig. 5 shows the carrier lifetime of p-type silicon wafer of varying resistivity under different conditions of BO complex activity. The intrinsic limit solid curve^[33] represents the BO complex-free status while the dashed line and dotted line are the deactivated BO conditions obtained by Walter et al.^[34] and Schmidt et al.^[35], respectively. It can be clearly seen that the carrier lifetime can be improved through the effective BO deactivated process.

Based on the relationship between wafer resistivity and carrier lifetime shown in Fig. 5, the electrical performance for different wafer resistivity is simulated in Fig. 6. Furthermore, in Fig. 6, the results from Refs. [33–35] are labeled as sample As, Bs and Cs, respectively. It can be seen that the efficiencies, V_OC and J_SC of all samples increase with increasing wafer resistivity over the range of 0.5–1.5 Ω·cm. When the wafer resistivity increases further, V_OC and J_SC saturate gradually for both of Bs and Cs, while efficiencies of Bs show slight decreasing and efficiencies of Cs become saturated. These trends for efficiencies, V_OC and J_SC are similar with the experimental results^[36]. In contrast to the increasing trend of FF in literature 36, all of the FF results for different samples in Fig. 6 show a decreasing trend. This discrepancy can be attributed to the special injection dependence of bulk lifetime. To get the highest solar cell efficiency, the optimum value of the wafer resistivity is around 1.5 Ω·cm. When taking the intrinsic limit lifetime (6200 μs)^[33], the maximum efficiency of the cell is 22.19%, which is 0.29% higher than that of the reference cell. When the silicon wafer is subjected to an optimum BO deactivated process (2500 μs)^[34], the highest efficiency of the cell is 22.13%, which is 0.23% higher than that of the reference cell. When the silicon wafer is subjected to a general BO deactivated process(430 μs)^[35], the maximum efficiency of the cell is 21.85%, which is 0.05% lower than the reference cell. This indicates that a suitable BO “passivation” process is very important to achieve a high-efficiency PERC solar cell. The subsequent optimization process is based on p-type silicon wafer with the resistivity of 1.5 Ω·cm and a corresponding carrier lifetime of 2500 μs.

In the reference cell, the front grid line uses mainstream five busbars (BB) technology. The busbar width is 700 μm, while the width and pitch size of fingers are 38 and 1600 μm, respectively. The width of the busbars and the fingers are converted to a whole optical shading width of 57.7 μm with a shading factor of 0.69^[37]. A shading factor is used to define the effective width of fingers, which can be reduced due to the reflection into the cell through the edges of the fingers and the total internal reflection at the air/glass interface^{[37, 38]}.

In order to further reduce the series resistance of the cell and improve efficiency, multi-busbar technology (MBB) is expected developed rapidly^[39]. The increase in the number of busbars can shorten the conduction distance of the current in the fingers, which effectively reduces the resistance loss and improves the efficiency of the cell. In addition, MBB can reduce the usage amount of silver paste by greatly reducing the width of busbars^[40].

In the current industrial production of PERC solar cells, Ag paste is generally used in the front screen printing while Al paste is used on the rear side. A multilayer material with higher density and higher conductivity using nickel, copper and other metals based on the electrolysis principle is also used in the metallization scheme^[41]. Compared with the traditional screen-print Ag paste, this technology can achieve a thinner grid line and a lower contact resistivity, which can effectively improve the cell efficiency. A comparison of resistivity and contact resistivity of different metal electrode is shown in Table 2.

In the simulation optimization, the front grid line of PERC adopts a 12 BB design. By calculating the total optical shading area of the metal electrodes, combined with the busbar and finger width of 300 and 38 μm for 12 BB technology and the shading factor of 0.69^[37], the corresponding shading width is 32.6 μm. The front metal electrode is deposited by electroplating Ni/Cu with a contact resistivity of 0.1 mΩ·cm².

Fig. 7 summarizes the three optimization steps of the PERC solar cell. The first step is the n⁺ emitter passivation optimization. According to different passivation layers, the cell using SiO₂/SiN_x has the highest simulated efficiency, followed by SiO₂/Al₂O₃/SiN_x, SiO_xN_y/SiN_x and Al₂O₃/SiN_x. When using a SiO₂/SiN_x passivation layer, the surface J_0E reaches as low as 20 fA/cm² and the cell efficiency reaches 22.22%, which is 0.32% higher than the reference cell. An optimized bulk resistivity of 1.5 Ω·cm is obtained in the second step. The star, rhombic and circle in step (2) are electrical parameters that are based on silicon wafers with carrier lifetimes of 6200, 2500 and 430 μs, respectively, which are described in Fig. 4. When the carrier lifetime is taken as 6200 μs, the simulation efficiency of the cell is 23.13%, which is considered as the limiting efficiency in this step. When the carrier lifetime is 2500 μs, the simulation efficiency of the cell is 22.98%. The third step is the optimization of the metal electrodes based on a carrier lifetime of 2500 μs. The hollow stars represent the 23.76% efficiency based on the 12 BB technology by which the shading width reduces from 57.7 to 32.6 μm. If the screen-print Ag paste is furtherly replaced by the electroplated Ni/Cu electrode with lower contact resistivity of 0.1 mΩ·cm² and width of 32.6 μm, the efficiency can be improved to 24.04% thanks to the significant improvement of FF of up to 81.24%, while the V_OC and J_SC remain constant. These results are represented by solid hollow stars, as shown in Fig. 7.

Based on the free energy loss analysis (FELA) simulation, Fig. 8 shows the analysis of the efficiency loss sources of PERC solar cell between the efficiency of 24.04% and the ultimate limit efficiency of 29% based on the Shockley–Queisser model^[42-44]. The recombination loss is the largest (2.73%), followed by the optical loss (1.42%), and finally the ohmic loss (0.81%). Further analysis has found that the individual loss due to the recombination of SRH and intrinsic carriers in the silicon wafer is the largest (0.61%), followed by the individual loss from surface reflection (0.54%), and then from parasitic absorption (0.51%). These individual losses sum up to an efficiency of 27.51% rather than to the ultimate limit of 29%. The rest efficiency gap is due to the synergistic effect that the increase of J_SC will result in increasing V_OC, and hence will increase the efficiency. The synergistic efficiency enhancement over the whole ohmic improvements and optical improvements are only 0.03% and 0.18%, respectively, while the synergistic efficiency enhancement over the whole recombination improvements is as high as 1.49%.

A reference PERC solar cell with 21.90% efficiency is obtained from numerical simulation based on the data from the production line. Its electrical properties are well coincided with that of the practical solar cell. Based on the reference cell, the performance as a function of surface passivation, quality of silicon wafer and metal electrodes was systematically discussed. By comparing the passivation layers, SiO₂/SiN_x stacked thin films are considered to be the best candidates for the passivation of n⁺ emitters because of their low optical parasitic loss and excellent passivation properties. By considering both the passivation of BO complex and the relationship between resistivity and minority carrier lifetime, silicon wafers with resistivity of 1.5 Ω·cm and carrier lifetime of 2500 μs are preferred. For metal electrodes, the 12 BB technology and Ni/Cu electrode are employed with an optimal shading width of 32.6 μm and contact resistivity of 0.1 mΩ·cm². Finally, a PERC model with an efficiency of 24.04% is obtained. In addition, an analysis of the efficiency loss sources from the 24.04% simulated efficiency to the 29% ultimate limit of PERC solar cell is performed. It can be seen that there is still much room for optimization in terms of surface reflection loss, absorption loss and SRH recombination loss. Therefore, this work is expected to give a guideline for the design and manufacture of high-efficiency PERC solar cells.

This work was supported by the National Natural Science Foundation of China (No. 61504155).