Reaction Kinetics Analysis of Treatment Process on Light-Induced Degradation for p-Type Passivated Emitter and Rear Contact Solar Cell Module with Gallium Cz-Si Wafer

Abstract

The light-induced degradation (LID) phenomenon in solar cells reduces power generation output. Previously, a method was developed to prevent LID where a group III impurity that can replace boron is added to the silicon wafer. However, in a subsequent study, performance degradation was observed in gallium-doped solar wafers and cells, and a degradation pattern similar to that occurring in light and elevated temperature-induced degradation (LeTID) was reported. In this study, a 72-cell module was fabricated using gallium-doped PERC cells, and the treatment of the LID process for carrier injection in the range of 1 to 7 A at 130 °C was analyzed using kinetic theory. We selectively heated only the solar cells inside a 72-cell module using a half-bridge resonance circuit for remote heating. To monitor the treatment of LID process in real time, a custom multimeter manufactured using an ACS758 current sensor and a microcomputer was used. Least-squares curve fitting was performed on the measured data using a reaction kinetics model. When the carrier-injection condition was applied to the gallium-doped PERC solar cell module at a temperature of 130 °C, the observed degradation and treatment pattern were similar to LeTID. We assumed that the treatment rate would increase as the size of the injected carrier increased; however, the 5 A condition exhibited the fastest treatment rate. It was deduced that the major factors of change in the overall treatment of the LID process vary depending on the rate of conversion from the LID state to the treatment state. In conclusion, it can be expected that the deterioration state of the gallium-doped solar cell module changes due to the treatment rate that varies depending on the carrier-injection conditions.

1. Introduction

The photovoltaic industry has made considerable efforts to increase the power generation output of solar cells to achieve grid parity and expand the distribution of solar cells. The annual output of solar modules in 2021 was 183 GWp, which is calculated as 173 GWp installed and 10 GWp in storage and in transit by the end of 2021 [1,2]. The cumulative solar module power installed worldwide increased from 756 GWp in 2020 to 940 GWp by the end of 2021 [1,3]. The market price of solar cell modules continues to be issued with a gap larger than that predicted by the PV learning curve [4,5]. In the global solar power market, the proportion of passivated emitter and rear contact (PERC) solar cells using p-type wafers to date has reached 82%. The power generation output of p-PERC crystalline silicon solar cells, which are currently used extensively in industry, has reached 24.0% in notable exceptions and 23.0% in average stabilized efficiency in mass production [1,4,6,7].

Despite the improvement in the power generation output of the solar cell, numerous factors can lead to a decrease in the efficiency in the long term. Among the various causes of this long-term decrease in efficiency, the most noteworthy cause is a phenomenon known as light-induced degradation (LID). The LID phenomenon is frequently observed in the crystalline silicon solar cell industry. In boron-doped crystalline silicon solar cells grown with the Czochralski (Cz) method, boron–oxygen defects activated by carrier injection are considered the most frequently observed LID phenomenon [8,9,10]. The cause of photodegradation is considered to be a boron–oxygen complex (B${}_s$O${}_{2i}$) created by the combination of substitutional boron (B${}_s$) and interstitial oxygen dimer (O${}_{2i}$) diffused inside Cz-Si. Owing to the LID phenomenon, the power generation output of the solar cell may be reduced by approximately 10% based on the overall efficiency, and numerous studies have been conducted to prevent this [11,12,13]. A separately treated degradation phenomenon called light and elevated temperature-induced degradation (LeTID) has been observed in polycrystalline silicon casting blocks [14,15,16]. The LeTID phenomenon was later reported in solar cells using p-type and n-type Cz-Si substrates, and was also found in Fz-Si solar cells [17,18,19,20,21,22].

To prevent the LID of solar cells, adding a group III impurity that can replace boron has been proposed, and gallium is considered as the most promising material [1,23,24,25]. In the case of the impurity implantation method, the effect of preventing LID was partially confirmed. However, due to the difference in segregation coefficient, the deviation of the resistivity value along the length increases during growth of the ingot with the Czochralski method. Considering these problems, the LID prevention technology using gallium doping has hardly been investigated. In addition, the gallium-doped ingot manufacturing technology is protected by a patent; therefore, industrial studies are limited. However, the patent has recently expired. Therefore, recently, major wafer industries have been manufacturing and supplying gallium-doped wafers, and it is expected to replace boron, considering the impact of the LID phenomenon on the high-efficiency solar cell market in the future.

In an early study related to LID prevention technology, it was reported that the injection-dependent minority carrier lifetime in gallium-doped solar cell wafers and solar cells was stable regardless of oxygen concentration when irradiated with light at low temperature [26,27,28]. However, in a subsequent study, degradation was reported in gallium-doped mc-Si PERC solar cells in a smaller amount compared to boron-doped solar cells, and showed a similar reaction to LeTID [29,30,31]. Recently, it has been reported that the change in the minority carrier lifetime has a similar shape as that of LeTID when the firing process is applied to the gallium-doped Cz-Si specimen, and the pattern of the injection-dependent minority carrier lifetime varies depending on the temperature applied to the wafer [32]. In addition, through PL analysis, the degradation characteristics of the gallium-doped Cz-Si PERC solar cell were also reported to be similar to the LeTID type [33]. Although a reaction similar to LeTID was observed in gallium-doped solar wafers and cells, there have been no studies on the degradation characteristics according to the carrier-injection level in the module unit.

In this study, we fabricated a 72-cell solar module using a gallium-doped p-PERC solar cell. In contrast to previous studies, we changed the carrier-injection level applied to the internal circuit of the solar cell module at the same high temperature by using a self-manufactured gallium-doped solar cell module. A stable heat source was applied to the module used in the experiment via a remote heating method using a half-bridge resonance circuit. The change in the electrical characteristics of the gallium-doped PERC solar cell module according to the carrier-injection level was observed in real time. To quantitatively analyze the recorded treatment of light-induced degradation, we defined a cyclic reaction path and analyzed it using a reaction kinetics technique. Our analysis using reaction kinetics revealed that the characteristics observed in LeTID also occurred in the solar cell module unit, which shows characteristics similar to the previously reported results in wafers and cells.

2. Materials and Methods

A three-layer structure that can heat the entire area of a 72-cell solar module was manufactured and used as the apparatus for the treatment of LID, as shown in Figure 1a. As shown in Figure 1b, the temperature distribution of the heated solar module was confirmed using the fabricated apparatus with infrared image analysis. As shown in Figure 2, the apparatus was configured such that the solar cell module could be placed on the coil structure and an AC electromagnetic field could be applied. For the application of a high frequency electromagnetic field, 20 copper coils with a diameter of 0.35 mm were used, and a pseudo-square coil structure with a length of approximately 15 m was fabricated. A half-bridge resonance circuit was fabricated to apply alternating current power to the pseudo-square coil structure, and the oscillation output was 3000 W. To drive the half-bridge resonance circuit, a direct current power of 48 V, 62 A was supplied using a rectifier.

A proportional integral derivative (PID) controller was used to control the heating of the solar cell module; the temperature was measured in a contact-free manner using an infrared thermometer on the backsheet surface of the module. To prevent further heating after the solar cell module temperature reached the target value, a solid-state relay was installed between the rectifier and the half-bridge resonance circuit and was maintained within a temperature error range of <±0.2 °C. A switching mode power supply (SMPS), capable of regulating the voltage, was used as the external power supply to the solar cell module. For real-time observation of the power injected into the solar cell module, a multimeter circuit—capable of measuring voltage and current—was manufactured at our laboratory and data were collected. All electronic signals generated by the equipment were collected using the serial communication method on the main computer, and played the role of PID control and SMPS observation result storage. The advantage of the remote heating method used in this study is that it enables a semi-batch process of the module, quickly heats a large area of the solar cell module, and precisely controls the temperature.

A PERC solar cell was fabricated with a gallium-doped p-type M2 size wafer. Seventy-two solar cells were connected in series to construct a 72-cell gallium-doped solar cell module. External power was supplied through a junction box. The size of the solar cell module was 90 cm × 180 cm × 35 cm, and the total weight including the aluminum frame was 32 kg. Figure 2 shows a cross-sectional view of the solar cell module. A 3 mm-thick front glass and a structure with encapsulant and backsheet were used to protect the solar cell. To use the remote heating device, the solar cell module was mounted such that the front glass was in contact with the induction heating coil surface, as shown in Figure 2. To selectively heat only the cells inside the solar cell module and minimize the interaction of the material with the magnetic field, an induction coil plate made of polycarbonate was used.

The solar cell removes the residual LID of the process through the recovery process (200 °C, 10 min). However, this process was excluded in this study because, under these conditions, the solar cell module has the potential to damage the encapsulant. At room temperature (25 °C), the gallium-doped PERC solar cell module was mounted on the experimental apparatus and the ramp-up process was performed using a remote heating device, as shown in Figure 3. The temperature of the gallium-doped solar cell module was set to 130 °C. When the gallium-doped PERC solar cell module reached a target thermal stability state, an external power source was applied to the solar cell module, and the changes in electrical characteristics were measured and recorded in real time. The external power is applied as a constant voltage (CV) source and is set by changing the voltage from 35 V to 40 V to maintain the carrier-injection condition in the range of 1∼7 A. When the LID phenomenon proceeds under CV, the current must be increased to maintain the same voltage, and the current changes in the opposite direction in the treatment process. To observe the minute changes in voltage generated by individual solar cells inside a solar cell module, it is possible to amplify the change in open-circuit voltage by observing a relatively sensitive measurable current. Finally, after the solar cell treatment process was completed, the external power was cut off and a half-bridge resonance circuit was turned off to block the remote heating of the solar cell module.

Chemical reaction kinetics theory was applied to interpret the degradation and treatment monitoring data of the gallium doping module measured in real time through the treatment of LID equipment [34,35]. The state in which LID does not occur at all in the solar cell module is defined as the initial state A, and the state in which LID has progressed is defined as state B. The metastable state in which the gallium-doped solar cell module was treated from the LID state was defined as the state C, and the measurement results were analyzed under a fully reversible reaction condition assuming a cyclic reaction path in which these three states are interlocked. The governing equation of the reaction kinetics model is as follows:

$$\begin{array}{c}\hfill \frac{{\partial C}_a}{\partial t}=k_3{C}_c-k_{i3}{C}_a-k_1{C}_a+k_{i1}{C}_b\end{array}$$

(1a)

$$\begin{array}{c}\hfill \frac{{\partial C}_b}{\partial t}=k_1{C}_a-k_{i1}{C}_b-k_2{C}_b+k_{i2}{C}_c\end{array}$$

(1b)

$$\begin{array}{c}\hfill \frac{{\partial C}_c}{\partial t}=k_2{C}_b-k_{i2}{C}_c-k_3{C}_c+k_{i3}{C}_a\end{array}$$

(1c)

where $C_a$ denotes the concentration of the state A, and has a value in the range 0∼100%. $C_b$ and $C_c$ denote the concentrations of the states B and C, respectively, and the sum of the concentrations of the three states is always assumed to be 100%. $k_1$, $k_2$, and $k_3$ denote the rate constants of the forward reaction path, and correspond, respectively, to the reaction paths state A→state B, state B→state C, and state C→state A. $k_{i1}$, $k_{i2}$, and $k_{i3}$ denote the rate constants of the reverse reaction path, and each constant corresponds to the opposite direction to the forward reaction path. The governing equation has a nonlinear form; hence, it is impossible to interpret it with a general algebraic method. Therefore, using the eigenvalue method, the governing equation can be developed as follows.

$$\begin{array}{c}\hfill \lambda J_a-k_{i3}{J}_a-k_1{J}_a+k_{i1}{J}_b+k_3{J}_c=0\end{array}$$

(2a)

$$\begin{array}{c}\hfill \lambda J_b+k_1{J}_a-k_{i1}{J}_b-k_2{J}_b+k_{i2}{J}_c=0\end{array}$$

(2b)

$$\begin{array}{c}\hfill \lambda J_c+k_{i3}{J}_a+k_2{J}_b-k_{i2}{J}_c-k_3{J}_c=0\end{array}$$

(2c)

After transforming Equation (2) into a matrix form, simplifying it into a general solution, and then rearranging it with an inverse Laplace transform, the concentration of each state can be described as time changes. To analyze the treatment of the LID process, fitting using a kinetics model was performed, and a mathematical optimization algorithm was developed to obtain a solution of a mathematical model in which three initial state concentrations and six reaction rate constants exist as variables. For the optimization process, the least-squares curve fitting method of the nonlinear equation was used, and an automated code was developed using the MATLAB (R2021) program.

3. Results

The treatment of the LID process of the gallium-doped PERC solar cell 72-cell module was measured in real time, and the results are shown in Figure 4. To compare the initial response form of the LID process, the unit of time was converted into a log function as shown in Figure 4b. Carrier-injection conditions were defined as 1 A, 3 A, 5 A, and 7 A, and a total of four conditions were used. As shown in Figure 4, the position of the max degradation point where the LID and treatment process are compensated changes according to the change in the carrier-injection level. The maximum degradation point has the values of 42.83%, 77.54%, 85.81%, and 64.96% under the conditions of 1 A, 3 A, 5 A, and 7 A, respectively.

As shown in Figure 4, an analysis of the cyclic reaction kinetics was performed using the measured experimental results. The least-squares curve fitting result of the nonlinear equation, calculated using MATLAB, agrees well under all carrier-injection conditions. As shown in Figure 4a, the real-time data, measured under the 1 A condition, agree well with the reaction kinetics model over the entire measurement time. Moreover, the results shown in Figure 4b indicate that the real-time data and the reaction kinetics model agree well near the maximum degradation point, even under the conditions 3 A, 5 A, and 7 A.

Figure 5 shows the results of comparison between each state of the cyclic reaction model according to the carrier-injection conditions. The change in the initial state according to the LID process is shown in Figure 5a; the degradation pattern varies according to the carrier-injection conditions. The rate of LID progress immediately after carrier injection is the fastest under the 7 A condition, and the slowest under the 3 A condition. The defect concentration in the LID state is shown in Figure 5b, where the generation rate and dissociation form of the LID defect vary with the carrier-injection conditions. The LID defect concentration increased the fastest in the 7 A condition, and the LID defect concentration was the highest in the 1 A condition. As shown in Figure 5c, by comparing the treatment of the LID process according to carrier injection through reaction kinetics analysis, the maximum treatment state is predicted as 93.95%, 99.88%, 95.36%, and 98.97% for the conditions of 1 A, 3 A, 5 A, and 7 A, respectively. We also found that the speed of the treatment process was the fastest in the 5 A condition and slowest in the 1 A condition.

4. Discussion

As shown in Figure 4, when carrier injection is performed while a temperature of 130 °C is applied to the gallium-doped PERC solar cell module, degradation and treatment processes similar to LeTID are observed. Although the exact mechanism related to the degradation and treatment of the Ga element cannot be reasonably deduced, an analysis based on the three-state model—the initial state, the LID state, and the treatment state—can be performed. In most previous studies on gallium-doped wafers and solar cells, the change in temperature was considered a major parameter in the analysis. However, in this study, the kinetic characteristics generated during the LID and treatment process were analyzed with respect to the changes in carrier-injection conditions.

To analyze the LID and treatment characteristics of the gallium-doped PERC solar cell module, the real-time current change in the solar cell module was recorded, and is shown in Figure 4. The applied voltage and current of the solar cell module were measured in real time with an ACS758 current sensor and a custom multimeter manufactured using a microcomputer. Because the measured current reaches 7 A, we used a current sensor in the 50 A range. As a result, the error range increased as the carrier-injection condition was lowered, and, as shown in Figure 4, the noise signal increased at 1 A. Nevertheless, these noise signals did not significantly affect the monitoring of the results of the treatment of LID, which had a shape similar to that of LeTID.

As shown in Figure 4, the results measured under the 1 A condition show a typical pattern of degradation and treatment of LeTID, and the trend is in general agreement with the three-state reaction kinetics model. However, the treatment of the LID process takes a considerably long time—567,615 s (157.7 h)—to reach saturation. We assumed that the treatment rate would increase with the size of the injected carrier; however, the treatment rate is fastest under 5 A. As shown in Figure 4, the time it takes for the treatment to reach saturation in the 5 A condition was 39,527 s (10.98 h), 14.4 times shorter than that in the 1 A condition.

To verify the possibility of increasing the treatment rate of LID according to the change of the carrier-injection conditions, we confirmed that the results were different from our expectations when the experiment was conducted under the 7 A condition. As shown in Figure 4, compared with the 3 A condition, the 7 A condition has a lower degradation–treatment compensation point. In summary, the treatment rate of LID does not increase linearly with increasing carrier-injection level, and the treatment rate is maximized at a specific injection range. To quantitatively analyze this phenomenon, the concentration change for each state was derived via the cyclic reaction model, and is shown in Figure 5.

Generally, in the case of a boron-doped PERC solar cell module, the loss form of the initial state (State A) has a form similar to that of the complementary error function (ERFC). As shown in Figure 5a, the form of ERFC was confirmed under 5 A condition. In contrast, in conditions 1 A, 3 A, and 7 A, the point of inflection is added instead of the ERFC type. The occurrence of such an inflection point is judged to be a characteristic of the gallium-doped solar cell module; the reason for this occurrence is the difference in the individual phase transition rate in the three-state model.

The concentration change in the three-state model derived in this study shows how the conversion rate of each state changes in the transient state. The reaction kinetics state can be analyzed through the relative difference between the rate of conversion from the initial state (State A) to the LID state (State B) and the rate of conversion to the treatment state (State C) of the gallium-doped PERC solar cell module. From this viewpoint, as shown in Figure 5c, the speed of the treatment state appears quickly in the 5 A condition. Comparing the results shown in Figure 5b,c, the inflection point does not occur in the 5 A condition because the occurrence of the treatment state increases when the increase in the concentration of the LID state reaches the peak. In contrast, as the rate of treatment is slow in the other conditions, an inflection point is formed at a different location according to each carrier-injected condition.

As shown in Figure 6 and

Table 1. Simulation parameters extracted through the optimization of each injected carrier of the reaction kinetics model for the cyclic reaction path.

Injected Carrier (A)	Initial A State(%)		Initial B State(%)		Initial C State (%)
	k${}_1$	k${}_2$	k${}_3$	k${}_{\mathit{i}1}$	k${}_{\mathit{i}2}$	k${}_{\mathit{i}3}$
1	9.999991		$9.004700\times {10}^{-5}$		$1.037940\times {10}^{-13}$
	$1.467220\times {10}^{-4}$	$3.979100\times {10}^{-7}$	$2.837770\times {10}^{-7}$	$1.208410\times {10}^{-4}$	$2.057160\times {10}^{-7}$	$8.462530\times {10}^{-6}$
3	9.999990		$1.000000\times {10}^{-4}$		$2.220460\times {10}^{-14}$
	$1.790050\times {10}^{-4}$	$2.008830\times {10}^{-5}$	$2.220450\times {10}^{-14}$	$6.062810\times {10}^{-4}$	$2.220450\times {10}^{-14}$	$2.220450\times {10}^{-14}$
5	9.999990		$9.502730\times {10}^{-5}$		$2.696890\times {10}^{-12}$
	$1.664220\times {10}^{-4}$	$3.425730\times {10}^{-4}$	$6.306950\times {10}^{-6}$	$9.275170\times {10}^{-4}$	$3.307060\times {10}^{-6}$	$6.332250\times {10}^{-6}$
7	$9.999990$		$1.000000\times {10}^{-4}$		$2.220480\times {10}^{-14}$
	$6.903940\times {10}^{-4}$	$1.458150\times {10}^{-5}$	$2.220480\times {10}^{-14}$	$1.300000\times {10}^{-03}$	$2.220480\times {10}^{-14}$	$2.220450\times {10}^{-14}$

, to compare the conversion rate for each state in the three-state model, the rate constant extracted by the reaction kinetics model analysis was shown considering the cyclic reaction path with respect to the size of the carrier-injection level. The rate constant for transition from the initial state to the LID state, indicated as $k_1$, has the highest value at 6.9 × 10${}^{-4}$ under the 7 A condition. Therefore, it was deduced that the LID rate was the fastest in the 7 A condition. Moreover, as shown in Figure 5b, this can explain the initial rapid LID defect generation. The recovery ($k_{i1}$) process in which the LID state is restored to the initial state shows a form that increases according to the size of the carrier-injection level. The LID and recovery speed were were seen to have similar values under condition 1 A. However, as the size of the carrier-injection level increased, the recovery speed was larger, and the initial reaction speed was slowed down due to the generation of defects through re-LID.

As can be seen in Figure 6, the rate constant for the conversion from the LID state to the treatment state, $k_2$, has the highest value of 3.43 × 10${}^{-4}$ under the 5 A condition. With an increase in the total amount of carrier injection, the treatment rate can be increased. However, when the level of carrier injection is greater than a certain value, the treatment rate decreases. It is inferred that the major factors of the overall degradation and treatment pattern change of the gallium-doped PERC solar cells module vary depending on the rate of conversion from the LID state to the treatment state. The $k_2$ value for the conversion from LID to treatment in condition 1 A is 3.98 × 10${}^{-7}$, and it is 861 times slower than that in condition 5 A. Under an inappropriate carrier-injection condition of the gallium-doped solar cell module, the rate of treatment is very low because $k_2$ is relatively small compared to the optimal condition. This generates an inflection point as shown in Figure 5a. In conclusion, the treatment rate of the gallium-doped solar cell module depends on the rate $k_2$, which in turn varies according to the carrier-injection conditions.

5. Conclusions

In this study, a 72-cell solar cell module was fabricated using a gallium-doped p-type PERC solar cell, and the dependence of the treatment process on the carrier-injection level applied to the inner circuit of the solar cell module was investigated at a constant temperature. The solar cell module was designed to perform remote heat treatment by arranging it in a coil structure for induction heating. To quantitatively analyze the recorded treatment of the LID process, the cyclic reaction path was defined and analyzed using the reaction kinetics technique. Carrier injection was performed on the gallium-doped PERC solar cell module at a temperature of 130 °C and a pattern of deterioration and treatment process similar to that of LeTID was observed. Real-time measurements showed that the pattern of the treatment process changed according to the carrier-injection conditions. With an increase in the level of carrier injection, although the treatment rate first increased, it decreased after a certain value was reached. The treatment of the LID rate constant (k${}_2$) analyzed through reaction kinetic simulation had a minimum value of 3.98 × 10${}^{-7}$ in the condition of 1 A and a maximum value of 3.43 × 10${}^{-4}$ in the condition of 5 A. Through this quantitative analysis, we believe that the precise physical mechanism may be revealed by defining the detailed reaction relationship for the LID characteristics of the gallium-doped solar cell module, which has only been reported for macroscopic behavior to date.