Thermal Stimulation of Reverse Breakdown in CIGS Solar Cells

The underlying mechanisms of the initial stages of hot-spot and therefore defect creation due to reverse breakdown in Cu(In,Ga)S$\text{e}_{2}$ solar cells are not well understood. We test the thesis, that permanent damage is created due to a positive feedback loop of local temperature enhancing the local current and vice versa, resulting in a thermal runaway. We present experiments on reverse stress with simultaneously introducing local heat. Depending on the temperature profile of the introduced heat, the local current density is enhanced and leads to a gain in the local temperature. This feedback loop is shown to lead to reverse breakdown, causing permanent damage.

on irregularities like pits and leads to a reduction of the shunt resistance of the device [2]. Nevertheless, with the improvement of the material quality, it has been shown that reverse breakdown does not necessarily lead to permanent defects and degradation in industrial c-Si modules [3]. Modern c-Si PV modules are known to be resilient against performance degradation due to partial shading. With the use of bypass diodes or an architecture to reduce the reverse junction breakdown voltage, the temporary loss in power output can be further reduced [4], [5].
For thin-film technologies, a stronger impact is often observed. Reverse stress applied to hydrogenated amorphous silicon (a-Si:H) solar cells can lead to the creation of hot-spots and reduced shunt resistance [6]. However, the impact of hot-spot damage on a-Si:H module performance varies (i.e., it is not always noticeable) [7]. Furthermore, thermal runaway due to reverse stress can result in glass cracking, encapsulation discoloration, and "cell erosion" [8]. Partial shading of cadmium telluride (CdTe) modules is known to cause performance degradation due to the creation of hot-spots and permanent defects [9], [10]. Furthermore, reverse stress on CdTe modules can lead to hot-spot propagation enhancing the performance loss due to excessive shunting [11].
The review article by Bakker et al. provided a detailed overview of the current status of research on reverse bias damage in CIGS solar cells [12]. The impact of partial shading respectively reverse bias conditions on CIGS module or cell performance is comprehensively documented in literature [9], [10], [13], [14], [15], [16], [17]. An early report on the effects of reverse stress on CIGS solar cells describes the creation of hotspots [13]. Furthermore, Westin et al. described the formation of "wormlike damages," caused by hot-spots propagating through the cell. Electrically the defects reduce the shunt resistance of the cells, thus reducing the fill factor and the overall performance of the device. In general, the propagation of hot-spots under reverse bias conditions, creating worm-like defects in CIGS solar cells respectively modules, is described in literature in great detail [11], [18], [19], [20], [21]. Johnston et al. [11] and Palmiotti et al. [18] further showed that local shunt paths, verified using dark lock-in thermography while limiting the reverse current, act as "seeds" for wormlike defects when the reverse current limit is increased. The works of Johnston et al. and Palmiotti et al., therefore, correlated the formation of worm-like defects to previously present shunt paths in the device like film pinholes or voids.
While the impact of partial shading respectively reverse bias conditions on (as well as the associated propagation of wormlike defects in) CIGS cells and modules are well described, the initial stages of local reverse breakdown are not well depicted in literature. Local reverse breakdown associated with the creation of hot-spots and local defects is also known to occur without prior indication due to visible defects in electroluminescence (EL) and dark lock-in thermography (DLIT) images [10], [11], [15], [18]. The exact mechanism leading to junction breakdown in CIGS solar cells is not well understood. The breakdown current in CIGS solar cells is strongly temperature-and irradiation dependent [22], [23]. The temperature dependency of the breakdown voltage is inconsistent with the Zener and avalanche breakdown mechanisms [22]. For this reason, Szaniawski et al. [22] suggested trap-assisted tunneling transport through the buffer layer. Such a Poole-Frenkel transport mechanism would imply a thermally activated breakdown current, in line with experimental results. However, Poole-Frenkel transport alone cannot explain the observed light enhanced breakdown [22].
In this article, we test the thesis that a positive feedback loop based on the local temperature stands at the root of the formation of reverse bias hot-spots in CIGS solar cells. Such a positive feedback effect leading to a thermal runaway was previously theoretically described by Karpov [24] and Nardone et al. [25]. As the breakdown current in CIGS cells is thermally activated, a locally enhanced temperature is expected to enhance the local current density under reverse bias conditions in turn leading to a local increase in temperature closing a positive feedback loop. If the loop gain exceeds one, the system becomes unstable and a runaway is triggered, leading to permanent damage. In this work, we present experimental evidence to the existence of such a positive feedback effect in CIGS solar cells.
In order to test this thesis, we introduce the concept of "hot-spot stress," where we locally heat a solar cell (without any indication on present defects or weak spots) with a laser to investigate the interaction between a laser-induced hot-spot and reverse bias stress. We expose the solar cell to a moderate reverse bias (not yet leading to damage), to hot-spot stress alone, and to reverse bias and hot-spot stress combined. During the experiments, the evolution of the temperature distribution within the solar cell is recorded with a thermography camera.

A. Samples and Setup
The used substrates are cut from industrial semifabricated and nonencapsulated CIGS modules. The modules consist of a ZnO/CdS/Cu(In,Ga)Se2/Mo layer stack, where the CIGS is prepared by coevaporation [26]. Each substrate consists of 17 cells with a dimension of 8.0 × 0.4 cm 2 = 3.2 cm 2 . We sacrificed every second cell to create contacts to individual cells, thus, obtaining substrates with nine individually contacted cells. The experiments are conducted on unencapsulated solar cells and the substrates are stored under dark conditions in a nitrogen environment before the experiments. Further, we will also refer to a single solar cell as a sample.  applies a constant reverse current and tracks the voltage. The hotspot stress is applied with a 200-mW Laser with a wavelength of 671 nm (Model MRL-III from Changchun New Industries Optoelectronics Technology Co., Ltd.). The Laser is focused on the backside of the sample (molybdenum back contact layer through substrate glass) with an microscope objective. This way we introduce heat directly to the thin-film solar cell stack. As the molybdenum is opaque, the laser does not induce a photo-current (which we also verified experimentally). The focus is adjusted by varying the distance between microscope objective and sample. The laser power can be reduced with different neutral density filters. A shutter is placed in the optical path of the laser to reduce instabilities in the laser output power during the warm-up phase. The thermal response of the solar cell on reverse respectively hot-spot stress is measured with an InfraTec Image IR 9300 thermographic camera with a resolution of 1280 × 1024 pixels. The detector is made of Indium Antimonide (InSb), which captures radiation in the spectral range between 2.0 and 5.7 μm. The whole system (laser, shutter, thermographic camera, and SMU) is controlled using a PC and a Meilhaus electronic modular measuring and control system. A simplified illustration of the setup is shown in Fig. 1.

B. Experiment
In our experiment, we study the interaction between heat and local reverse breakdown effects in CIGS by intentionally creating a laser-induced hot-spot in a sample without prior indication of local defects. To accurately monitor the temperature in the samples, we first conduct experiments to calibrate the thermographic surface temperature measurement.
Subsequently, we expose CIGS samples 1) to laser-induced hot-spots (i.e., hot-spot stress); 2) to a constant reverse current only (i.e., reverse stress); and 3) to combined hot-spot and reverse stress. Furthermore, we investigate the influence of the size of the laser hot-spot by varying the laser focus and intensity (using neutral density filters). Thus, we obtain two different temperature profiles in the laser hot-spot (i.e., a broader temperature profile with a high maximum temperature and a narrower temperature profile with an in comparison lower maximum temperature). For all experiments, we record a movie with the thermographic camera at a frame rate of 100 frames per second. The dark IV characteristics of the samples are measured before, between and after the applied stress tests.

A. Thermographic Temperature Measurement
For an accurate temperature measurement, we need to correct the thermographic images for the effective emissivity of the Mo/CIGS/CdS/i-ZnO/ZnO:Al layer stack CIGS . For the emissivity correction, we used the IRBIS3 professional software. This correction assumes a homogeneous ambient temperature and takes into account the spectral sensitivity of the camera and the resulting differences in sensitivity for different temperatures.
To estimate CIGS , we used a substrate without scribing lines (i.e., only consisting of the CIGS solar cell stack Mo/CIGS/CdS/i-ZnO/ZnO:Al). We applied a coated aluminum foil to one half of the CIGS substrate. The coated foil has a known emissivity fc ≈97% and a high thermal conductivity. The substrate is heated to three different temperatures with a hot plate. The known emissivity fc is used as a reference and the high thermal conductivity ensures nearly equal surface temperatures of the foil-covered half and the uncovered half of the CIGS substrates. The hot plate temperatures used for this experiment are 50 • C, 70 • C, and 90 • C. The ambient temperature is measured with a PT100 temperature sensor to 21.7 • C.
In the thermographic images (one image for each hot plate temperature setting), we define two areas along the edge between the foil-covered half and the uncovered half of the CIGS substrate. Both areas are 5 × 198 = 990 pixel (≈ 4.5 mm 2 ) large, and directly adjacent to ensure the surface temperatures in both areas are nearly identical. For the foil-covered half, we set in the IRBIS3 professional software, the known emissivity fc and the measured ambient temperature of 21.7 • C. Thus, we directly measure the mean surface temperature of the foil-covered CIGS area, T fc for all three images. We again set the ambient temperature to the measured 21.7 • C and vary CIGS such that we obtain the best agreement in mean temperature at the uncovered area as at the foil covered area. Fig. 2 shows the temperature difference ΔT = T CIGS − T fc between the mean surface temperatures of the uncovered and foil-covered CIGS areas versus the T fc for three different CIGS . As the temperature difference is expected to be 0K, we find CIGS = 48% to be a good estimate for the effective emissivity of the Mo/CIGS/CdS/i-ZnO/ZnO:Al layer stack. Fig. 2. Temperature difference ΔT between CIGS surface temperature T CIGS and foil-covered CIGS surface temperature T fc as a function of T fc . We evaluate ΔT for three different CIGS . For an effective CIGS emissivity CIGS = 48%, the measured temperature difference is within ±0.25 K over a temperature range from 45 to 75 • C. Fig. 3. Thermographic image of sample #1 after 15 s exposure of the sample to the laser (left) and zoom-in on the laser-induced hot-spot (right). The magnified area is depicted with the blue box. Along the yellow line, the temperature profile (see Fig. 4) of the hot-spot of sample #1 is extracted.

B. Reverse Bias and Hot-Spot Stress
We first investigate the impact of the laser-induced hot-spot alone. Fig. 3 shows an exemplary thermographic image of sample #1 during a hot-spot stress (in total 30 s exposure) experiment after 15 s exposure to the laser. The temperature distribution is nearly homogeneous over the cell area except for the induced hot-spot. The yellow line in Fig. 3 is used to extract a hot-spot temperature profile (as shown in Fig. 4). In all experiments, the measurement of the absolute temperature is corrected with an emissivity of 48% and an ambient temperature of 20 • C.
We varied laser focus and intensity to obtain two different steady state temperature profiles. Fig. 4 shows the exemplary temperature profiles of sample #1 (small hot-spot) and sample #2 (large hot-spot) after 15 s exposure of the sample to the laser. The small hot-spot is obtained with a neutral density filter, which Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. reduces the beam intensity to 25%, and a good focus on the sample. The large hot-spot is obtained with the full intensity but out of focus. The maximum absolute temperature in the small hot-spot is approximately 140 • C. The maximum absolute temperature in the large hot-spot is approximately 235 • C. Note that the total incident laser power is 4 times larger for the large hot-spot compared to the small hot-spot. The Full Width Half Maximum (FWHM) of the large hot-spot is 0.49 mm and of the small hot-spot the FWHM is 0.20 mm. In total, nine samples were stressed with a small hot-spot and nine samples were stressed with a large hot-spot. After each test, we compared the dark IV characteristics before and after the hot-spot stress and found no significant changes for all used samples (i.e., hot-spot stress alone does not change the electrical properties of the sample).
In a second experiment, we investigate the impact of a reverse (current) stress. The reverse stress was applied for 10 s with a constant reverse current of 10 or 15 mA per cell (current densities of 3.1 and 4.7 mAcm −2 , respectively). After the applied reverse stress, six samples showed a decreased shunt resistance due to permanent defects (shunts) created by local hot-spots. None of the hot-spots are created at the location, where the heat is introduced in the previous experiment (hot-spot stress). These six samples are not considered in the remaining experiments.
The thermographic videos for the remaining 12 samples show a nearly homogeneous increase in temperature (homogeneous heat generation) over the cell area (not shown). From the comparison of the dark IV characteristics before and after the reverse stress, we observe an increase in shunt resistance. We attribute this effect to metastabilities in the CIGS [27], [28]. Since the 12 samples did not show performance degradation due to reverse stress solely, we call them "resilient against reverse stress". Seven of the 12 samples are previously stressed with a small hot-spot and 5 of the 12 samples are previously stressed with a large hot-spot. This results in an unequal sample quantity for the final experiment. An overview of the samples is presented in Table I. In a final experiment, we apply reverse stress for 30 s. After 10 s, the laser shutter is opened, and for the remaining 20 s, combined reverse and hot-spot stress is applied. Fig. 5 shows the evolution of the mean temperature for the cell area, excluding the hot-spot T mean (green line), in sample #1 (exemplary for  5. Development of the mean temperature T mean of the solar cell excluding the hot-spot area (green) during simultaneous reverse bias and hot-spot stress and comparison of maximum temperature T max development within the hot-spot due to hot-spot stress (Laser) and simultaneous reverse stress (black) and hot-spot stress solely (blue) for sample #1 (small hot-spot).
samples stressed with small, focused hot-spot; see the temperature profile in Fig. 4). A circle around the hot-spot maximum with a radius of 28 pixels was defined to exclude the hot-spot area. The reverse stress (−15 mA) during the first 10 s leads to a nearly homogeneous temperature increase over the cell area (not shown), which is reflected in an increase of about 0.4 • C in the mean temperature. After 10 s, the shutter opens and the cell area excluding the laser hot-spot cools down. After 15 s, (i.e., 5 s after the shutter opened), the mean temperature in the cell area excluding the laser spot increases again.
Also shown in Fig. 5 is the evolution of the maximum temperature in the hot-spot area (black line). After 10 s, the laser shutter was opened and the laser induced hot-spot rapidly heats up. We observe a rapid increase in the maximum temperature from about 26 • C to more than 260 • C in about 3 s (note that with the used camera settings, we cannot measure temperatures beyond 260 • C, i.e., the camera is overexposed in the hot-spot area). For comparison, we also show in Fig. 5 the maximum temperature evolution for hot-spot stress alone, without reverse bias stress (blue line). With only hot-spot stress, the maximum temperature reaches approximately 140 • C, i.e., much lower than with the combined stress.
The experiment with combined hot-spot and reverse bias stress produces two remarkable results. First, of all the laser hot-spot reaches much higher temperatures than without simultaneous reverse bias stress. Furthermore, the cell area excluding the hot-spot cools down directly after the shutter opens. This shows the laser hot-spot leads to a redistribution of the power dissipation due to reverse stress over the cell area. More power is dissipated within the laser hot-spot and less in the remainder of the cell. This effect clearly shows a change in the local electric properties since a local hot-spot pulls more electrical power into the hot-spot. Note that the overall power dissipation in the cell Fig. 6. Comparison of the dark IV characteristics of sample #1 (red, small hot-spot) and sample #2 (black, large hot-spot) immediately before (dashed line) and after (solid line) the experiment with reverse stress and simultaneous hot-spot stress. Fig. 7. Development of the mean temperature T mean of the solar cell excluding the hot-spot area (green) during simultaneous reverse bias and hot-spot stress and comparison of maximum temperature T max development within the hot-spot due to hot-spot stress (Laser) and simultaneous reverse stress (black) and hot-spot stress solely (blue) for sample #2 (large hot-spot).
decreases after the shutter opens as the absolute value of the reverse bias voltage decreases from 5.8 to 1.8 V. The redistribution, and overall reduction in dissipated electrical power, initially, leads to a reduction in the cell temperature excluding the laser hot-spot. The subsequent increase in temperature after 15 s is attributed to heat diffusing out of the laser hot-spot area.
The dark IV characteristics after the experiment show a decrease in shunt resistance (also indicated by the voltage drop during the experiment) as can be seen exemplary for sample #1 in Fig. 6 (red lines). Thus, the combined reverse bias and hot-spot stress lead to permanent damage to the cell. All samples with small laser hot-spots (in total seven samples) exhibit similar results as shown for sample #1 (i.e., we measure a higher maximum temperature in the hot-spot in the experiment with combined stress in comparison to the experiment with hot-spot stress alone; we observe the voltage drop and the redistribution of heat generation in the cell area and we verify the decreased shunt resistance after the experiment due to the comparison of the dark IV characteristics). Fig. 7 shows the same experiment with simultaneous hot-spot and reverse bias stress, this time using the larger hot-spot (see the temperature profile in Fig. 4) exemplary for sample #2. The first 10 seconds of the experiment (−15 mA reverse stress) leads, similar to the previous shown experiment, to a nearly homogeneous temperature increase over the cell area (increase of about 0.4 • C in the mean temperature excluding the laser hot-spot area). After the shutter opens, however, we do not observe any cooling in the cell area excluding the laser hot-spot, nor do we observe significantly higher maximum temperatures in the hot-spot as compared to the experiment without simultaneous reverse bias stress. We do observe the increase in temperature over the whole cell area accelerates, which we attribute to heat diffusion out of the defined laser hot-spot area. Also, the absolute reverse bias voltage does not show a decrease (stays constant at 5.9 V). The dark IV characteristics after the experiment show a similar increase in shunt resistance as samples stressed with a reverse current alone as shown exemplary for sample #2 in Fig. 6. We conclude no significant redistribution of the electrical power takes place with the large hot-spot and, therefore, the combined reverse and large hot-spot stress do not noticeably change the local electric properties, let alone do not create a shunt in the device. All five samples exposed to combined reverse and hot-spot stress with a large hot-spot show similar results, regarding maximum temperature in the hot-spot, no visible voltage drop and no redistribution of heat generation as well as regarding the increase in shunt resistance (comparison of dark IV characteristics).
The experiments with the small hot-spots show that the combination of reverse stress and locally induced heat can lead to a change of the local electrical properties. Further, the experiments show that a cell without indication of any previously present defects, resilient to the applied reverse current stress, can be drawn into reverse breakdown inducing local heat. The experiments with the large hot-spots at the same time show that inducing a higher absolute local temperature combined with reverse stress cannot be sufficient to noticeably change the local electrical properties as long as the heat is induced on a larger area.
The total amount of heat induced in the large laser hot-spot is 4 times larger as compared with the small laser hot-spot. Therefore, the larger hot-spot induces a larger change in overall conductivity of the cell compared to the small hot-spot and is expected to pull more current into the hot-spot. At the same time, however, the induced heat is distributed over a larger area leading to a larger share of the cell area experiencing a change in conductivity. While the reverse stress is current driven and, therefore, the applied reverse current is limited, the larger hot-spot is expected to exhibit a lower current density in comparison to the smaller hot-spot. Thus, the loop gain of a possible positive feedback effect between local temperature and local current is expected to be lower for a larger hot-spot.
The maximum temperature in the induced large hot-spot exceeds the maximum temperature in the induced small hot-spot. Therefore, the creation of permanent damage in the experiment with the small hot-spot cannot be explained with a crucial temperature in the hot-spot alone. Thus, the experimental results confirm that a positive feedback effect of local heat and local current is present in CIGS solar cells under reverse bias conditions and can further lead to hot-spot formation and reverse bias damage. The loop gain of the positive feedback is larger in case only a small area is heated, thus a small local defect is more likely to trigger a thermal runaway than a large defect.

IV. CONCLUSION
In this article, we introduced a novel experiment to study the formation of reverse bias hot-spots in thin-film CIGS solar cells. In the experiment, we introduced laser induced hot-spots with two different temperature distributions. Using this experiment, we showed that a positive feedback loop exists in CIGS solar cells, where local heat generation and a local increase in temperature could lead to a higher local current and higher electrical power dissipation under reverse bias conditions. Furthermore, we showed that this effect may lead to a thermal runaway effect leading to permanent damage to the cell. The effect depended strongly on how localized heat was induced, where a small hot-spot exhibited a larger loop gain and was more likely to lead to a thermal runaway.