The Mechanism of Hot Spots Caused by Avalanche Breakdown in Gallium-Doped PERC Solar Cells

Abstract

Gallium-doped p-type passivated emitter and rear contact (PERC) solar cells, which eliminate light-induced degradation (LID) and reduce the impact of light- and elevated-temperature-induced degradation (LeTID), have completely replaced boron-doped p-type PERC cells. However, in previous experiments, we found hot spots in the center of gallium-doped PERC solar cells. In this study, it was found that gallium-doped PERC cells had uneven resistivity, which caused hot spots brought about by the avalanche breakdown of PN junctions. There were significant hot spots in the center of the tested cells, with an average resistivity of 0.4–0.5 Ωcm and nonuniformity greater than 30%, or at an average resistivity of 0.5–0.6 Ωcm with nonuniformity greater than 40%. In this paper we describe and study in detail hot spots triggered by the uneven resistivity of gallium-doped cells and analyze the causes and related influencing factors, thereby providing guidance and a reference for the improvement of the performance and reliability of gallium-doped PERC solar cells.

1. Introduction

If a solar cell is fully or partly shaded in a photovoltaic module by, for example, leaves or other detritus, it can be reverse-biased to voltages up to 15 V depending on the module structure and can dissipate up to approximately one-third (for three incorporated bypass diodes) of the module’s maximum output power [1]. When the power dissipation is concentrated in a small area, local overheating will occur in the cells, which will eventually lead to hot spots in the module. Studies by Jordan [2] and Zhen [3] have shown that hot spots in a photovoltaic module represent one of the main factors causing module performance degradation and reliability failure.

Boron-doped monocrystalline silicon passivated emitter and rear contact (PERC) cells have significant light-induced degradation (LID) [4,5] and light- and elevated-temperature-induced degradation (LeTID) problems [6,7]. Although the LID caused by boron–oxygen (B-O) defects can be eliminated by regeneration [8,9], the process incurs additional costs and increases the cell fabrication time. Gallium-doped silicon wafers do not contain B-O defects, can effectively eliminate the impact of LID [10,11], and are less affected by LeTID, according to various studies [12,13]. Hence, gallium-doped silicon wafers have gradually replaced boron-doped silicon wafers in the production of PERC solar cells.

Recently, we observed a phenomenon of hot spots at the center of the gallium-doped p-type PERC cells in our experiments, but no such phenomenon has been found in boron-doped p-type PERC cells. Numerous studies are underway to improve the performance and reduce the hot spots mainly in boron-doped cells. There are two directions regarding hot spot research: the cell and the module. The cell aspect is mainly focused on the defects that cause hot spots [14,15,16] and test methods [17,18,19] to facilitate the timely and effective analysis and screening of hot spot cells; the module aspect aims to reduce the power consumption of hot spots as much as possible when the phenomenon occurs [20,21,22]. However, there has been no research on the hot spot phenomenon in Ga-doped solar cells. With the trend toward larger cells [23], some studies have indicated that the application of large silicon wafers will make the impact of hot spots more severe [24]. Therefore, it is imperative to study the emerging central hot spots in gallium-doped PERC cells with respect to the large-scale application and large-size development of gallium-doped p-type silicon wafers.

In this paper we provide a systematic and in-depth study of the performance effects of the central hot spots in gallium-doped PERC cells. The reverse I–V curves and hot spot tests of gallium-doped PERC cells with different resistivities indicate that the central hot spots were caused by the avalanche breakdown of the cell junctions; the lower the resistivity, the more likely that breakdown occurred, and the greater the proportion of central hot spots. Further research on the intrawafer resistivity distribution of gallium-doped silicon wafers showed that poor intrawafer resistivity uniformity was an important factor causing hot spots in the cells. Significant hot spots were found at an average resistivity of 0.4–0.5 Ωcm and a nonuniformity greater than 30%, or with an average resistivity of 0.5–0.6 Ωcm and a nonuniformity greater than 40% in the gallium-doped PERC cells. In addition, it was found that the surface-textured structure and emitter sheet resistance of gallium-doped PERC cells also affect the reverse breakdown characteristics and may lead to more severe hot spots. Finally, the breakdown that caused the hot spots was simulated using the EDA platform, which revealed that wafer resistivity, surface texture, and emitter sheet resistance of the cells all influenced the distribution of the electric field in the junctions at the reverse bias, leading to different cell reverse breakdown and hot spot performances.

2. Results and Discussion

2.1. Cell Hard Breakdown

The dark reverse I–V curves of each group of cells were obtained using an I–V tester. Figure 1a shows a typical dark reverse I–V curve, indicating that the reverse breakdown voltage had a significant upward trend as the resistivity of the cell increased from 0.40.5 Ωcm to 0.8–1.0 Ωcm.

Fischer recommends using the following formula to calculate the breakdown voltage, denoted as V_BD [25]:

$$\begin{gathered} V_{BD}=-\frac{{\epsilon }_{si}}{2q{N}_A}{E}_c^2 \\ {E}_c=-4010{\left(N_A\right)}^{1/8} \end{gathered}$$

${\epsilon }_{Si}$ is the dielectric constant of the silicon, $N_A$ is the base doping concentration of the p-type silicon, q is the element charge, and $E_c$ is the critical field, which can be approximated in the equation.

It can be seen from the above formula that the breakdown voltage followed a downward trend as the base doping concentration increased, consistent with our experimental test results. However, we found that the calculated breakdown voltage was significantly higher than the experimental value under the same wafer base doping concentration. For example, the calculated breakdown voltage was between 17 and 21 V for a resistivity of 0.4–0.5 Ωcm, which was higher than the test value of 12–15 V. The reasons for the difference in breakdown voltage values are discussed further in Section 2.3. In addition, the breakdown voltage exhibited a downward trend when the diffusion sheet resistance increased from 100 Ω/sq to 150 Ω/sq.

In order to reduce the recombination in the emitter and improve the efficiency, the diffusion sheet resistance should be increased to 190 Ω/sq or higher [23]. Further, attention should be paid to the impact of the sheet resistance on the breakdown characteristics of gallium-doped PERC solar cells.

The PN junction breakdown is mainly categorized into an avalanche breakdown (impact ionization) and a tunneling breakdown, in which the avalanche breakdown voltage is positively correlated with the temperature, and the tunneling breakdown and temperature are negatively correlated. Hence, the type of cell breakdown can be distinguished by measuring the reverse I–V curves at different temperatures [26]. Figure 1b shows the dark reverse I–V curves of the gallium-doped PERC cells at a resistivity of 0.4–0.5 Ωcm and a diffusion sheet resistance of 100 Ω/sq at different temperatures. As the temperature increased from 20 °C to 40 °C, the breakdown voltage exhibited an obvious upward tendency, indicating a positive correlation. Therefore, the experimental results indicate that the reverse breakdown of the Ga-doped PERC solar cells was mainly caused by an avalanche breakdown.

2.2. Hot Spot Analysis

Cell hot spots were tested using the cetisPV-IR package (I–V measuring system). Figure 2a shows the maximum equilibrium temperature increase ($Max.∆T_{eq.}$) of the tested gallium-doped PERC cell with different resistivities and diffusion sheet resistances at a reverse bias voltage of −15 V. It can be seen from the figure that as the resistivity decreased from 0.8–1.0 Ωcm to 0.4–0.5 Ωcm, the average value of $Max∆T_{eq.}$ increased significantly, from 4.8 °C to 57 °C, for a sheet resistance of 100 Ω/sq. The temperature rose sharply under the −15V bias, and the potential risk of cell hot spots increased significantly. Combined with the reverse I–V test results in Section 2.1, it can be seen that the low-resistivity gallium-doped PERC cell exhibited a significant breakdown at −15 V, and its reverse current increased significantly, causing the temperature of the cell to rise. In addition, Figure 2a shows that the lower the resistivity of the gallium-doped PERC cell, the greater the variation range of $Max.∆T_{eq.}$, among which the variation range of $Max.∆T_{eq.}$ at a resistivity of 0.4–0.5 Ωcm reached 160 °C. It can be seen from the figure that the $Max.∆T_{eq.}$ values of cells with similar resistivity were quite different when the resistivity was less than 0.6 Ωcm, making it difficult to explain the above phenomenon only in terms of the average resistivity. After increasing the sheet resistance of the cells from 100 Ω/sq to 150 Ω/sq, the $Max.∆T_{eq.}$ of the group with a resistivity of 0.4–0.5 Ωcm changed from 57 °C to 67.3 °C, an increase of approximately 10 °C on average, while the group with a resistivity of 0.8–1.0 Ωcm exhibited little change. Further, $Max.∆T_{eq.}$ increased with the diffusion sheet resistance, and the lower the wafer resistivity, the greater the increase was. For the gallium-doped PERC cells, the diffusion process involving a high sheet resistance reduced the breakdown voltage and increased the hot spot risk at the same time. Figure 2b shows a scatter plot between the reverse leakage and $Max.∆T_{eq.}$ of cells under −15 V reverse bias when the resistivity was 0.4–0.5 Ωcm, and the diffusion sheet resistance values were 100 Ω/sq and 150 Ω/sq. It can be seen that there was some correlation between the reverse leakage current and $Max.∆T_{eq.}$ in the trend, but the correlation was weak. Therefore, the large increase in $Max.∆T_{eq.}$ in some cells could not simply be attributed to the increase in the leakage current caused by the reverse breakdown leakage when the resistivity was less than 0.6 Ωcm.

For further analysis of the resistivity data of the gallium-doped PERC cells, we tested the resistivity distribution in the wafer. The graph on the left in Figure 3a shows the scanning path during the resistivity test, where a total of 840 datapoints were scanned, and the graph on the right shows the plot of the resistivity versus the scan path as displayed after scanning. The wafer resistivity is the average value of all the scan points, and the resistivity uniformity is defined as the scan maximum value minus the minimum value divided by the mean value. Because of the low segregation coefficient of the gallium in silicon, the resistivity of the experimental gallium-doped silicon wafer exhibited an increasing trend from the center to the edge, where the central resistivity was lower than the average value of the wafer resistivity. Figure 3b shows the trend of $Max.∆T_{eq.}$ and the maximum and minimum resistivity with respect to the resistivity uniformity, when the resistivity was 0.4–0.5 Ωcm, and the sheet resistance was 100 Ω/sq. It can be seen that when the resistivity values were similar to each other, $Max.∆T_{eq.}$ increased greatly from 20 °C to approximately 180 °C, as the resistivity uniformity changed from 14% to 49%, and the minimum resistivity decreased from 0.44 Ωcm to 0.34 Ωcm. Figure 3c presents a graph showing the variation in $Max.∆T_{eq.}$ with respect to the resistivity uniformity of the gallium-doped PERC cells with different resistivities. The lower the resistivity, the worse the resistivity uniformity, and the greater the rise in $Max.∆T_{eq.}$. It can be seen that as the resistivity decreased, the more significantly $Max.∆T_{eq.}$ was affected by the uniformity of the resistivity. From the overall results of the experimental gallium-doped PERC cells at a sheet resistance of 100 Ω/sq, the cell temperature increased by more than 80 °C above the operating temperature when the uniformity for the 0.5–0.6 Ωcm resistivity was greater than 40% and when the uniformity of the 0.4–0.5 Ωcm resistivity cells was higher than 30%, significantly increasing the risk of cell hot spots. We found that the resistivity uniformity of the low-resistivity gallium-doped PERC cells had a decisive impact on $Max.∆T_{eq.}$, and the more uneven the resistivity distribution, the greater the risk of hot spots.

Figure 4 maps the equilibrium temperature increase ($∆T_{eq.}$) of the gallium-doped PERC cells with a resistivity of 0.4–0.5 Ωcm and a sheet resistance of 100 Ω/sq under different resistivity uniformities, which shows that the locations of $Max.∆T_{eq.}$ were concentrated at the center of the cells, consistent with the position of the lowest resistivity shown in Figure 3a. As the uniformity changed from 14% to 49%, $∆T_{eq.}$ at the center increased significantly, while no obvious differences were observed at other positions. Combined with the conclusion in Figure 3, it is obvious that the central resistivity decreased significantly as the resistivity uniformity deteriorated, and the difference between the central and surrounding resistivities intensified. The avalanche breakdown occurred first in the central low-resistivity region of the gallium-doped PERC cell, concentrating the breakdown currents in the central region. Therefore, the overall reverse current change was not obvious, but a high-density reverse current region formed at the center as the breakdown point shrank, generating a large amount of Joule heat and forming an obvious central hot spot in the gallium-doped PERC cell.

2.3. Finite Element Analysis (FEA) Modeling of the Ion Impact Breakdown

From the above analysis, it can be concluded that the avalanche breakdown in the center of a gallium-doped PERC cell with uneven resistivity led to a high risk of hot spots in this type of low-resistivity solar cell. The reverse breakdown of the cell PN junctions was further simulated and analyzed using an EDA multiphysics simulation platform. The carrier-generation rate G of the PN junction avalanche breakdown impact ionization can be expressed as [27]:

$$G=\frac{{\alpha }_n}{q}\left|J_n\right|+\frac{{\alpha }_p}{q}\left|J_p\right|$$

where $J_n$ and $J_p$ are the current densities of the electrons and holes, respectively, and ${\alpha }_n$ and ${\alpha }_p$ are the ionization rates of the electrons and holes, respectively, where the ionization rates in the simulations are based on the Okuto–Crowel model [28]. The resistivity of the p-type silicon wafers in the simulation was set to three types: $4.3\times {〖10〗}^{16}/\left({\mathrm{c}\mathrm{m}}^3\right(0.4\mathsf{\Omega }\mathrm{c}\mathrm{m}\left)\right),2.7\times {〖10〗}^{16}/\left({\mathrm{c}\mathrm{m}}^3\right(0.6\mathsf{\Omega }\mathrm{c}\mathrm{m}\left)\right)$, and $1.7\times {10}^{16}/{\mathrm{c}\mathrm{m}}^3$ (0.9 Ωcm), and their n+ emitter profiles were set to high doping (the error function distribution of the surface concentration was $5\times {10}^{20}/{\mathrm{c}\mathrm{m}}^3$, and the junction depth was 0.25 µm) and low doping (the error function distribution of the surface concentration was $3\times {10}^{20}/{\mathrm{c}\mathrm{m}}^3$, and its junction depth was 0.2 µm).

Figure 5a shows the simulated inverse I–V curves of the cells with different resistivities, when the cell surface was a plane and a pyramid for n+ emitter high doping, where the simulated inverse I–V curve for the pyramid surface was close to that of the test in Figure 1a. When the resistivity increased from 0.4 Ωcm to 0.9 Ωcm, the simulated breakdown voltage rose significantly. In contrast, the breakdown voltage of the simulated planar surface was significantly higher than that of the pyramid surface and was similar to Fischer’s theoretical voltage value. It can be seen that the surface-textured structure resulted in the difference in the breakdown voltage discussed in Section 2.1. Figure 5b shows the simulated electric field distribution of cells with different resistivities and pyramid surfaces under a −14 V reverse bias for the high-doping case. As the resistivity increased from 0.4 Ωcm to 0.9 Ωcm, the depletion layer width of the reverse-biased PN junction increased significantly, and its electric field strength decreased significantly, so the high-resistivity cell had extremely strong breakdown resistance. Figure 5c shows the simulated electric field distribution under −14V reverse bias under high doping at a resistivity of 0.4 Ωcm for the planar and pyramid surfaces. When the surface had a planar structure, the electric field was uniformly distributed across the entire surface, but when the surface had a pyramid structure, the electric field intensity increased rapidly from the top to the bottom of the pyramid. The electric field strength at the base of the pyramid structure was much larger than that of the planar structure under the same reverse bias voltage, similar to the electrostatic tip effect caused by the etch tips in polysilicon described by Bauer [29], and a strong electrostatic tip effect was also generated at the bottom of the pyramid. This was the reason for the significant drop in the breakdown voltage of the surface-textured structure. It can be argued from the above that changes in the resistivity and surface structure of the silicon wafers significantly affected the breakdown characteristics of the PERC solar cells. Therefore, for the Ga-doped PERC cells with different silicon wafer resistivities and surface structures, there were differences in the reverse breakdown leakage in the central low-resistivity region, resulting in different thermal effects.

Figure 6a shows the simulated reverse I–V curves of a p-type silicon wafer at different resistivities with a high-doped and low-doped pyramid surface. With the increase in the emitter doping concentration, the breakdown voltage showed an obvious rising trend, such that the greater the resistivity, the more obvious the effect of the doping. Figure 6b shows the simulated electric field distribution at 0.4 Ωcm for the pyramid surface under high doping and low doping. It can be seen that the change in the doping concentration had an influence on the electric field, as the electric field strength at the bottom of the pyramid decreased when the doping concentration rose. Therefore, a high sheet resistance processing of gallium-doped PERC cells increased the electric field strength during the reverse bias, thereby reducing the cell breakdown voltage, increasing the likelihood of hot spots.

3. Materials and Methods

The cell sample process flow for the hot spot comparison test is described as follows.

3.1. Wafer Grouping

The experiment used < 1 0 0 >-orientation gallium-doped single-crystal large-size silicon wafers with a resistivity of 0.4–1.0 Ωcm, a thickness of 155–165 μm, and an area of 182 mm × 182 mm, which were categorized into four groups according to the resistivity: Group 1 with 400 pcs of 0.4–0.5 Ωcm, Group 2 with 400 pcs of 0.5–0.6 Ωcm, Group 3 with 400 pcs of 0.6–0.7 Ωcm, and Group 4 with 400 pcs of 0.8–1.0 Ωcm.

3.2. Cell Fabrication

Figure 7 shows the fabrication flow chart for the experimental gallium-doped PERC cells, where the preparation process was divided into two phases: the “front-end process” and the “back-end process”.

3.2.1. Front-End Process: Texturing to Diffusing

The silicon wafers were textured and cleansed using groove-type alkaline texturing equipment (BatchTex, RENA Technologies GmbH, Gütenbach, Germany) to form double-sided pyramid-textured surfaces; then, each group of silicon wafers with different resistivities were divided into divided into two smaller groups and diffused using POCl₃ diffusion sources in a low-pressure diffusion furnace (NAURA HORIS D8478AL, NAURA, Beijing, China), to form n+ emitters with sheet resistances of 150 Ω/sq and 100 Ω/sq.

3.2.2. Back-End Process: Selective Emitter Formation and Metallization

The diffused silicon wafers with a sheet resistance of 150 Ω/sq were selectively doped with a laser doping device (SE-DY80, DR laser) to prepare an n++ selective emitter region with a sheet resistance of approximately 105 Ω/sq; then, the 150 Ω/sq and 100 Ω/sq groups were simultaneously back-polished and removed from the front-side phosphosilicate glass (PSG) layers in an inline-type wet bench (InOxSide, RENA Technologies GmbH, Gütenbach, Germany), where the front-side emitters were thermally oxidized using a furnace tube (DOA-420, JJWC). Subsequently, Al₂O₃/SiNx films were layer-deposited on the back of the wafers, SiNx antireflection films were deposited on the front of the wafers using PECVD equipment (T-ALOX, Hanwha corporation, Seoul, Korea), and the Al₂O₃/SiNx stack films were locally removed with laser equipment (AL-D90, DR laser) at the contact position of the back electrode. Finally, silver and aluminum pastes were printed on the front and back of the cells, respectively, using screen-printing equipment (MX XDLSP 4P3D, MAXWELL) followed by a fast-firing process.

3.3. Cell Hot Spot Characterization

The resistivity of the gallium-doped silicon wafers was tested, and the wafers were sorted according to their resistivity using screening equipment (Measuring-System HE-WI-06s, Hennecke Systems GmbH, Frankfurt, Germany); the reverse I–V curves of the cells were measured in the dark with a cell I–V tester (cetisPV-IUCT -1800, H.A.L.M. GmbH, Frankfurt, Germany).

The hot spots of the cells under reverse bias were tested with the cetisPV-IR package integrated in the I–V test instrument designed for measuring the thermal images of the solar cells together with the I–V measuring system. The temperature measurement algorithm was based on the convoluting power dissipation images measured with infrared thermography using specially designed point spread functions [8]. We obtained the mapping image of the equilibrium temperature increase (${∆T}_{eq.}$) and the maximum equilibrium temperature increase (${Max.∆T}_{eq.}$) of the cell using this equipment.

4. Conclusions

In this study, hot spots caused by the reverse avalanche breakdown of gallium-doped PERC cells were investigated. We observed a clear relationship between hot spots and wafer resistivities. The poor resistivity uniformity of gallium-doped cells was the most important factor causing reverse breakdown hot spots; that is, the lower the resistivity and the poorer the resistivity uniformity, the greater the risk of hot spots. The diffusion sheet resistance of the gallium-doped PERC cells also affected the hot spots, and the risk increased when the gallium-doped PERC cells had a high sheet resistance.

The simulation results show that the experimental reverse breakdown voltage was lower than the theoretical value due to the electrostatic tip effect brought about by the pyramid-textured structure. The electric field strength in the depletion region could be reduced, and the reverse breakdown voltage of the cells could be effectively enhanced through the increase in silicon wafer resistivity and the reduction in diffusion sheet resistance. Thus, the anti-hot-spot performance of the photovoltaic cell itself can be improved by optimizing the base resistivity, sheet resistance, and surface-texture structure.

We systematically and innovatively studied the effect of gallium-doped PERC cell resistivity on cell breakdown characteristics and cell hot spots, providing meaningful guidelines for maintaining the reliability of gallium-doped photovoltaic cells and their components. The current research was mainly focused on the cell, and further analysis and research will be conducted regarding the key influencing factors on new types of cells and modules encapsulated to attempt to improve the long-term reliability.