Pierre Albert
email: pierre.albert@usherbrooke.ca

Gwenaelle Hamon

Maite Volatier

Yannick Deshayes

Abdelatif Jaouad

Vincent Aimez

Laurent Bechou

Maxime Darnon

Gwenaëlle Hamon

Maïté Volatier

Laurent Béchou

Towards miniaturization of concentrated photovoltaics (CPV): impact on

Keywords: multijunction solar cells, micro-CPV, microfabrication, perimeter recombination, reliability

I. INTRODUCTION

Concentrated Photovoltaics (CPV) technology relies on the concentration of the sunlight onto small (typically mm 2 to cm 2 ) and highly efficient (III-V-based, typically triple junctions) cells. However, this-technology cost is still too high to be widely adopted. An emerging approach consists in miniaturizing modules dimensions (micro-CPV). Submillimeter multijunction cells are the cores of this innovative technology as they can overcome some of the limitations that make the standard CPV unwelcome. Low-temperature operation is the key for high electrical performance and for an improved reliability. Due to their small dimensions, easier strategies for thermal management can be offered with micro-cells [START_REF] Domínguez | A review of the promises and challenges of micro-concentrator photovoltaics[END_REF]. In addition, smaller cells show less resistive losses thus higher efficiency is theoretically achievable under very high concentration.

Whereas micro-CPV and microcells seem of great interest, some challenges exist. First, fabrication processes must be adapted to provide good performance and high wafer throughput, for which the conventional saw dicing is limiting. Second, perimeter recombination is known to affect electrical characteristics, and an efficient passivation appears to be necessary in order to lower performance losses. This is mitigated by saturation of traps under high-intensity illumination making microcells assuredly good candidates for high-concentration photovoltaics [START_REF] Albert | Front-contacted Multijunction Micro Cells: Fabrication and Characterization[END_REF]. Perimeter effect was also shown to influence the reliability of GaAs 1-mm 2 solar cells, but no investigation focused on impact of size on multijunction solar cells reliability to our knowledge was reported [START_REF] González | Reliability analysis of temperature step-stress tests on III-V high concentrator solar cells[END_REF]. CPV-cells operating conditions are complex (high-intensity light, heat, temperature variations, humidity, etc.) and thus, accelerated ageing tests design is not straightforward. A conventional technique used by the CPV community for simulating cell photogeneration ageing deals with active storage, in which cells are current-biased during the accelerated tests [START_REF] González | Reliability analysis of temperature step-stress tests on III-V high concentrator solar cells[END_REF]- [START_REF] Eltermann | Performance and failure analysis of concentrator solar cells after intensive stressing with thermal, electrical, and combined load[END_REF]. However, such a bias is quite different from operating conditions [START_REF] Espinet-González | Temperature accelerated life test on commercial concentrator III-V triple-junction solar cells and reliability analysis as a function of the operating temperature: Temperature accelerated life test[END_REF]. Passive thermal storage has also been considered but was demonstrated to be more aggressive to CPV cells compared to active storage [START_REF] Eltermann | Performance and failure analysis of concentrator solar cells after intensive stressing with thermal, electrical, and combined load[END_REF]. Therefore, no perfect solution exists and ageing tests need to be considered with hindsight.

In this paper, we propose processes based on microfabrication techniques to fabricate InGaP/(In)GaAs/Ge CPV cells with submillimeter dimensions (down to 0.068 mm 2 ). One-sun characterization of cells from 1 mm 2 to 0.076 mm 2 shows the dependency between electrical performance and cell size, which highlights perimeter recombination. The effect of reducing cell dimensions on long-term performance is also investigated. Two strategies of accelerated ageing tests, based on thermal step stress, are developed: a passive (thermal stress only) and an active (thermal + current stress) test. Whereas the type of test shows different behaviors of performance changes, the 0.076-mm 2 cells have demonstrated a good robustness, higher than the one of 1-mm 2 cells. Finally, the impact of perimeter recombination effect on cells degradation is discussed, as well as the impact of test type on performance.

II. DEVICES FABRICATION

A commercial structure of InGaP/(In)GaAs/Ge was chosen as the building block to develop the fabrication processes. The first step consists in depositing Al-based or Au-based contacts as emitter electrodes to define the front contact grid. Cells are then electrically isolated in individual devices, using inductively coupled plasma etching (ICP) with a combination of SiCl4, Cl2 and H2 [8]. Then, the Al-based or Au-based base contact is deposited by evaporation either on the backside of the wafer or on the front side close to the mesa. Both contact methods lead to the same electrical results [START_REF] Albert | Front-contacted Multijunction Micro Cells: Fabrication and Characterization[END_REF]. Then, an antireflective coating (ARC) made of SiNXHY/SiOXHY is deposited by plasmaenhanced chemical vapor deposition (PECVD). Besides increasing optical absorption of the cell, such ARC permits a passivation effect, which can limit perimeter recombination rate [START_REF] Darnon | Deep germanium etching using time multiplexed plasma etching[END_REF]. The ARC is then opened on metallization to access the electrical contacts. The fabrication processes ends by singulating cells from the wafer. This step is performed by plasma dicing [10]. Indeed, compared to the conventional saw dicing, plasma dicing offers a stress-and-damages-free singulation with flexibility in the desired cell shapes. Moreover, narrow dicing lines offered by such technique (10-µm) allow the wafer yield to be more than doubled with microcells, compared to saw dicing. After this step, devices fabrication is complete and Fig. 2 shows some examples of fabricated front-contacted cells, with various shapes (rectangular, hexagonal or circular active area), dimensions (from 12.25 mm 2 to 0.068 mm 2 ) and contact methods (front or standard contacts).

III. ELECTRICAL PERFORMANCE

Fabricated cells were characterized under one-sun illumination (1000 W/m 2 , AM1.5g, 25 °C) with an Oriel 1A solar simulator. In Fig. 3, current densities (J) of rectangular cells with mesa surface of 1 mm 2 , 0.25 mm 2 and 0.076 mm 2 are plotted along voltage (V). All cells show good characteristics with open-circuit voltage (VOC) > 2.12 V and fill factor (FF) > 82 %. The changes in cell size do not affect the JSC. Extracted FF are between 82.3 % (0.076-mm 2 cell) and 85.4 % (1-mm 2 cell). The slight decrease of FF as the cell size decreases is related to the VOC drop [12]. Indeed, a VOC decrease of 4.4 % can be seen from the plot when cell area is reduced from 1 mm 2 to 0.25 mm 2 . This VOC decline reaches 8.1 % when cell area is reduced from 1 mm 2 to 0.076 mm 2 . All cells were fabricated with the same processes and with the same epitaxial structures, which implies bulk recombination rates are assumed to be the same for all cells. Therefore, the reduction in VOC can be attributed to perimeter recombination effect. Based on a simple one-diode model, one can express VOC of a 3-junction cell as:

𝑉 𝑂𝐶 ≈ ∑ 𝑛 𝑖 𝑘𝑇 𝑞 𝑙𝑛 [ 𝐽 𝐿,𝑖 𝐽 0,𝑖 ] 3 𝑖=1 (1)
where 𝑛 𝑖 is the diode ideality factor of subcell 𝑖, which depends on the recombination processes that occur in the subcell, 𝑘 is the Boltzmann constant, 𝑇 is the temperature, 𝑞 is the electron charge, 𝐽 𝐿,𝑖 is the photogenerated current density of subcell 𝑖 and 𝐽 0,𝑖 is the reverse saturation dark current density of subcell 𝑖. 𝐽 0,𝑖 can be expressed as:

𝐽 0,𝑖 = 𝐽 01,𝑖 + 𝐽 02,𝑠𝑐𝑟,𝑖 + 𝐽 02,𝑝𝑒𝑟,𝑖 (2)
where 𝐽 01,𝑖 is the saturation current density associated with diffusion process in subcell 𝑖, 𝐽 02,𝑠𝑐𝑟,𝑖 is the saturation current density associated with the effects in space charge region in subcell 𝑖 and 𝐽 02,𝑝𝑒𝑟,𝑖 is the saturation current density resulting from recombination at the perimeter of subcell 𝑖 . The latter parameter can be written as:

𝐽 02,𝑝𝑒𝑟,𝑖 = 𝑞𝑛 𝑖 𝑆 0,𝑖 𝐿 𝑆,𝑖 𝐿 𝑝𝑒𝑟 𝐴 (3)
where 𝑆 0,𝑖 is the surface recombination velocity in subcell 𝑖, 𝐿 𝑆,𝑖 is the diffusion length of subcell 𝑖, 𝐿 𝑝𝑒𝑟 is the cell perimeter and 𝐴 is the cell area.

Therefore, the quasi-linear relation between VOC and perimeter-to-area ratio 𝐿 𝑝𝑒𝑟 𝐴 observed on the inset of Fig. 3 indicates that 𝐽 0 of at least one subcell varies linearly with 𝐿 𝑝𝑒𝑟 𝐴 and perimeter recombination is more significative than other contributions to the dark current. This proves the high influence of perimeter recombination on small-dimensions cells performance. Dedicated surface passivation could further limit perimeter recombination rate by efficiently passivating recombination centers. Moreover, perimeter recombination centers become saturated under high-intensity light. In a previous study, we demonstrated that the drop in VOC due to small dimensions turns to be insignificant under high concentration (< 2.0 % under ~1300 X, even in the absence of a passivating ARC) [START_REF] Albert | Front-contacted Multijunction Micro Cells: Fabrication and Characterization[END_REF]. Therefore, microcells are particularly of interest for highly concentrated photovoltaics not only thanks to their reduced resistive losses but also to their better efficiency under higher concentration.

IV. ROBUSTNESS ASSESSMENT

A. Accelerated Test Overview

Accelerated life tests can be divided in two categories: quantitative and qualitative tests. On the one hand, quantitative accelerated life tests aim at extracting a device lifetime, with the mean time to failure (MTTF) for example. This last can be predicted by observing the cumulated failure distribution during accelerated life test and by extrapolating it to the operation conditions, using an adequate model depending on accelerated parameters (I, V, T, …). It is generally performed on a large number of mature devices from a technological point of view. On the other hand, qualitative tests, that are typically highly accelerated life tests (HALT), aim at highlighting failure modes. It is often coupled with failure analysis to determine the physical mechanisms responsible for the failure. Qualitative ageing tests are typically preliminary tests performed with low-maturity technology to give a feedback particularly on the variability of fabrication processes. Step stress ageing tests (SSAT) are HALT that gradually increase a given stress or a combination of stress parameters on the devices. Multiple parameters can be stressing, but the most relevant parameter is temperature, as most degradation mechanisms are affected by thermal effects.

CPV cells, due to the high-intensity light they convert, are often considered to operate at up to 80 °C, with an nominal operating temperature of 65 °C for 1-mm 2 cells operating under 1000 X [START_REF] Espinet-González | Evaluation of the reliability of commercial concentrator triple-junction solar cells by means of accelerated life tests (ALT)[END_REF], [START_REF] Núñez | Evaluation of the reliability of high concentrator GaAs solar cells by means of temperature accelerated aging tests: Reliability of GaAs concentrator solar cells[END_REF]. Besides high temperature, CPV cells are submitted to large photocurrent densities resulting from the high light intensity they convert into electricity under concentration. Therefore, the most common method for simulating photogeneration during accelerated life tests consists in injecting in the cell a current similar to the one generated in operating conditions.

B. Experimental Procedure

In our study, SSAT were designed with a gradual temperature storage (passive stress, PSSAT) in a first case and with a gradual temperature storage together with a constant current injection equivalent to 1000 × ISC (active stress, ASSAT) in a second case. Storage temperature was increased by 20 °C after each week (168 h), from 85 °C to 185 °C (PSSAT) and from 65 °C to 185 °C (ASSAT). Step stress temperature storage profiles are shown in Fig. 4 and parameters are summarized in Table 1. Electrical characterization was performed after each ageing step (see Fig 4) with a Keithley 2420 by removing the cells from the thermal chamber and characterizing them under a one-sun illumination In the PSSAT, six rectangular bare cells of 1 mm 2 , 0.25 mm 2 and 0.076 mm 2 (two per size) were considered. In this case, cells are not singulated and the base contact is located onto the back surface of the Germanium substrate. Cells are bonded on a copper-covered FR4 board with Indium as shown on Fig. 5.a). I-V measurements under one sun are done by contacting cells with probes. In the ASSAT case, rectangular cells (with base contact on the back surface) were fabricated with the same processes as presented previously. However, nine cells (1 mm 2 , 0.25 mm 2 and 0.076 mm 2 , three per area) were saw-diced and mounted on Al carriers. Al-wirebonding was used for the front contact and SAC 305 as die-attach. A thermistor was also assembled on each carrier to control temperature of the package. A photograph of a 0.076-mm 2 cell package is given in Fig. 5.b).

C. Electrical Performance Monitoring

In Fig. 6 performance changes in solar cells of after the PSSAT (step stress thermal storage) are depicted. We observe that all cells were degraded by the ageing test as a global decline in PMPP/PMPP0 occurs. The PMPP/PMPP0 is finally extracted between 0.825 (0.076-mm 2 cell A) and 0.957 (1-mm 2 cell B) and no catastrophic failure were observed. This validates the relative robustness of the developed fabrication processes for all cell dimensions. In addition, a clear dependence between cell size and PMPP changes can be observed. Indeed, a trend appears for which the smaller cells are more affected by the PMPP/PMPP0 decrease. The difference in PMPP/PMPP0 due to cell size can be identified as soon as the first ageing step at 85 °C. The gap due to cell size is extending until the 125-°C step. This indicates that degradation processes that affect cells by their size occur at relatively low temperature After 125 °C, changes in PMPP/PMPP0 are very similar, within 5.5 %, regardless the cell size. These processes also affect the VOC as can be seen in the bottom part of the same figure. Based on (1) and ( 2), VOC monitoring can give information on the recombination processes. We can observe on the VOC/VOC0 plot that changes follow the same trend as the one observed for PMPP/PMPP0. Indeed, at the end of the PSSAT, VOC/VOC0 clearly depends on cell dimensions with a low value of 0.908 for the 0.076-mm 2 cell and a high value of 0.983 for the 1-mm 2 cell. These results indicate an increasing impact of recombination with the miniaturization of the cells after PSSAT. However, results are very encouraging for this non-mature technology as no catastrophic failure was observed, even with the high stress level induced by the ageing test. (1-mm 2 cell) and 0.972 (0.076-mm 2 cell), which is higher than the ones observed in the PSSAT, confirming the robustness of the fabricated cells. We can notice that besides fluctuations, no clear trend of variations with cell size can be observed on the PMPP/PMPP0 plot. However, whereas the VOC of all cells is affected, it can be seen that the one of 1-mm 2 cells is slightly more affected (i.e. decrease of 1.4 %) by ageing and VOC/VOC0 ratio is equal to 0.972 for 1-mm 2 cell A' and 0.986 for 1-mm 2 cell A' by the end of the ASSAT. Considering that quite high stressing conditions have been considered (TASSAT = 185 °C and a constant current injection of 1000×ISC), very small variations of the electrical parameters have been observed. Whereas the effect of cell size on PMPP is not so clear than for PSSAT, microcells and larger cells have shown very good robustness under ASSAT. The difference between PSSAT and ASSAT can be explained by more aggressive stress conditions for thermal storage only, as previously reported by Eltermann et al, or by the thermal step at 230 °C required for cells mounting process used for ASSAT that may have slightly modified the cells [START_REF] Eltermann | Performance and failure analysis of concentrator solar cells after intensive stressing with thermal, electrical, and combined load[END_REF].

V. CONCLUSION & DISCUSSION

In this work, cells were fabricated with microfabrication processes to allow various geometries and dimensions down to 0.068 mm 2 , with standard or front base contacts. The use of microelectronics-inspired processes allowed high wafer throughput. Performance of the smaller cells are affected by perimeter recombination, which dominate the recombination mechanisms that take place in the cells. A VOC drop of 8.1 % under one sun was measured when reducing cell area from 1 mm 2 to 0.076 mm 2 but becomes negligible under high concentration illumination.

A study of the robustness of the fabricated cells was also performed. Both passive and active step stress accelerated tests (PSSAT and ASSAT) were considered and designed to investigate the impact of the cell size on their long-term performance. Whereas no catastrophic failure was observed, higher performance changes occurred in the PSSAT with a minimum PMMP/PMMP0 of 0.825 at the end of the test (up to 185 °C). Similarly, Eltermann et al. have shown that thermal storage only, compared to thermal storage coupled with current injection and current injection only, led to the most severe degradation of the CPV cells [START_REF] Eltermann | Performance and failure analysis of concentrator solar cells after intensive stressing with thermal, electrical, and combined load[END_REF]. However, using current injection in ageing tests is often considered as a correct stressing method by the CPV community to simulate photogeneration. These combined stresses aim at better highlighting degradation mechanisms susceptible to appear in real-conditions operation, with a current flowing through the junctions and contacts. Using this technique, we have shown a very promising minimum PMMP/PMMP0 of 0.931 at the end of the ASSAT. These results are very encouraging although active ageing may create degradations different from the ones related to nominalconditions operation. Indeed, it was shown that current injection generates a very different current density distribution in the cell structure [START_REF] Espinet-González | Temperature accelerated life test on commercial concentrator III-V triple-junction solar cells and reliability analysis as a function of the operating temperature: Temperature accelerated life test[END_REF]. This may overstress some part while being too gentle on other and lead to degradation dissimilarities. However, no failure analysis was intended in this robustness investigation work. It was finally demonstrated a globally higher robustness of the smallest cells (0.076 mm 2 ) with a maximum PMMP/PMMP0 of 0.972 at the end of the ASSAT (185 °C). From the results obtained in our study, a similar a lifespan in operating conditions for microcells compared to larger cells is expected. Further works will include a comprehensive analysis of the measured degradations.

Fig. 1 .

 1 Fig. 1. Major steps for fabrication of solar cells with a) front contacts and b) standard contacts.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Images of fabricated solar cells with front contacts (top) and standard contacts (bottom). Cell area ranges from 12.25 mm 2 to 0.068 mm 2

Fig. 4 .

 4 Fig. 4. Stress profiles and I-V measurement occurencies in PSSAT and ASSAT

Fig. 7 Fig. 5 .

 75 Fig. 7 illustrates the effects of ASSAT (step stress thermal storage + current injection ≡ 1000×ISC) on the electrical performances of cells, depending on their size. In the top part of Fig. 7, we observe a global decrease of the PMPP/PMPP0, proving that all cells were degraded by the ASSAT. The final values for PMPP/PMPP0 are comprised between 0.931

Fig. 6 .

 6 Fig. 6. Performance changes of cells with various size along temperature of the passive step stress ageing test (PSSAT). Top: Variations of the maximal power PMPP, relative to the initial value PMPP0 and bottom: variations of the open-circuit voltage VOC, relative to the initial value VOC0.

ACKNOWLEDGMENT LN2 is an International Research Laboratory (UMI 3463) between Université de Sherbrooke, CNRS Université de Lyon (INSA, Centrale, CPE) and Université Grenoble Alpes. It is supported by the Fonds de Recherche du Québec Nature et Technologie (FRQNT). The support of Quebec MEI-PROMPT, NSERC and STACE is also acknowledged.