Electron radiation–induced degradation of GaAs solar cells with different architectures

The effects of electron irradiation on the performance of GaAs solar cells with a range of architectures is studied. Solar cells with shallow and deep junction designs processed on the native wafer as well as into a thin‐film were irradiated by 1‐MeV electrons with fluence up to 1×1015 e−/cm2. The degradation of the cell performance due to irradiation was studied experimentally and theoretically using model simulations, and a coherent set of minority carriers' lifetime damage constants was derived. The solar cell performance degradation primarily depends on the junction depth and the thickness of the active layers, whereas the material damage shows to be insensitive to the cell architecture and fabrication steps. The modeling study has pointed out that besides the reduction of carriers lifetime, the electron irradiation strongly affects the quality of hetero‐interfaces, an effect scarcely addressed in the literature. It is demonstrated that linear increase with the electron fluence of the surface recombination velocity at the front and rear hetero‐interfaces of the solar cell accurately describes the degradation of the spectral response and of the dark current characteristic upon irradiation. A shallow junction solar cell processed into a thin‐film device has the lowest sensitivity to electron radiation, showing an efficiency at the end of life equivalent to 82% of the beginning‐of‐life efficiency.

possibility of applying a back reflector, thin-film devices require smaller active layer thicknesses, further reducing costs related to both the weight and the growth of the epitaxial layers. The reflectivity of the rear mirror in high-quality materials has also been proven important to maximize photon recycling, which in turn increases the open circuit voltage and therefore the efficiency of the devices. [16][17][18][19][20][21] In these structures, the bottom subcell consists of thin-film GaAs, which has demonstrated the highest conversion efficiency among all types of single junction solar cells. 1 Additionally to back contact design strategies, 22-24 the position of the junction in GaAs cells has been identified as an important parameter, showing that a device with the junction closer to the bottom of n-on-p cells allows for operation in the radiative recombination regime. 20,25,26 This type of cell, therefore, has a higher open circuit voltage and is preferred over the standard structure with a junction located closer to the front. But even though the deep junction design allows for better performance at the beginning-of-life, its resilience in the space environment is expected to be lower than that of the conventional shallow junction design. 27,28 The most challenging aspects for solar cells in space are the exposure to particle irradiation and the temperature cycling. Because of the copper commonly applied as the flexible carrier for thin-film GaAs cells, degradation related to copper diffusion is a potential problem for devices with this architecture. It has been shown that the effects of copper-diffusion are temperature dependent, and for temperatures below 200 • C, it does not reduce the cell performance in drastic degrees, provided the absence of damages induced by thermal stress, such as cracks or bends. 29 The level of irradiation that cells would face throughout their entire lifetime in space depends on the type of mission. Based on the hypothesis that the permanent displacement damage produced by the incidence of charged particles is the main aspect that degrades the device performance in space, the mission equivalent damage from electrons, protons, ions, and neutrons of different energies can be averaged by a certain electron fluence. 30-33 Geostationary orbit missions (GEO) usually last for 15 years, and the damage created by the irradiation environment is equivalent to that obtained by a fluence of 1 × 10 15 1-MeV electrons/cm 2 . For low earth orbit (LEO) missions, which last for approximate 10 years at a lower altitude, the equivalent fluences are five to 10 times lower.
The recombination centers formed in GaAs solar cells under irradiation have been studied in depth 30,31,33-36 and the implications of the junction position with lifetime degradation have been discussed. 27,28 It is generally understood that irradiation reduces the minority carriers' diffusion length, and therefore the average distance that these carriers have to travel before reaching the p−n junction directly affect the cells resilience to the space environment. A systematic study of different architectures, however, has not yet been reported, and there is a lack of consistency between the previously reported minority carriers' lifetime degradation constants. Furthermore, in view of the current trend of developing thin and ultra-thin radiation-hard solar cells, 14  In the current study, the possible influence of electron irradiation on hetero-interfaces of GaAs solar cells is systematically investigated. For this purpose, GaAs cells with different junction depths with respect to the hetero-interfaces, both on their native substrates and pro-

Device model
The solar cells subjected to 1-MeV irradiation have been analyzed based on the 1D analytical Hovel model 39 and its extended version for thin-film solar cells with back-side reflector. 40 The model formulation is rather general and well suited to describe different solar cell designs provided that material and geometry parameters are changed accordingly. A schematic depiction of the modeled structure and corresponding variables used in this study are shown in Figure 3, where X E and X B denote the thickness of the emitter and base layers, respectively, and W denotes the width of the depleted region across the junction.
where the radiative lifetime is given as ,rad = 1∕BN AB(DE) , B being the microscopic radiative recombination rate of the semiconductor, and N AB , N DE the acceptor and donor doping density in the base and emitter.
For the sake of thermodynamic consistency, the coefficient B is calculated by integrating the spontaneous emission rate associated with the GaAs absorption profile used in the CPS and is found to be 6.22×10 −10 cm 3 /s. Photon recycling is modeled through the photon recycling factor f PR , calculated according to the model reported by Steiner et al. 19 For the solar cells in this study the calculated f PR ranges from approx-imately 0.78 for the substrate based cells to 0.93 for the thin-film devices. Finally, ,SRH characterizes the non-radiative recombination lifetime. At the microscopic level, ,SRH results from electron-hole recombination and generation events through defect states whose rates can be modeled according to the classical Shockley-Read-Hall theory. Multiple defects can be taken into account, provided that they can be considered independent, characterized by their own density, energy and capture time constants. Under the assumption of low-level injection, exploited in this work, this yields a constant effective lifetime, ,SRH , independent of the injection level and dominated by the defect state with higher rates, i.e. those generally located close to mid-gap. 43 Therefore, in the present work, ,SRH was used as a fitting parameter and no a priori hypothesis was done on the nature and characteristics of the defect levels.
After de-embedding the possible influence of the parasitic series and shunt resistances, the dark J − V characteristic (J dark ) of the solar cell can be modeled by two diodes in parallel 25 : where J 01 and J 02 are the reverse saturation current densities of the 1kT and 2kT components, respectively, and q, k, and T the electron charge, Boltzmann constant and temperature. The ratio between the two components of the dark current is voltage dependent, with non-radiative recombination in the perimeter of the cell and in the space-charge region dominating at low voltages (the 2kT region) and recombination in the quasi-neutral regions (QNR) dominating at higher voltages (the 1kT region). According to the junction diffusion theory, J 01 arises from the bulk and interface recombination of minority carriers in the base and emitter QNR regions 39 and is given by with each component given by and where d B and d E are the thickness of the QNR of the base and emitter with intrinsic carrier density n 2 i,B and n 2 i,E , respectively. The intrinsic carrier density is computed taking into account the bandgap narrowing effect in the highly doped regions. In particular, the bandgap narrowing significantly affects the QNR recombination current in the highly doped base and emitter layer of the DJ and SJ cells, respectively.
We have assumed bandgap shrinkage E g ≈ 2 × 10 −11 N 1∕2 AB eV for p-type GaAs 44 and E g ≈ 2 × 10 −8 N 1∕3 DE for n-type GaAs. 45 The J 02 dark current component involves non radiative recombination mechanisms in the space charge region that can usually be modeled according to the Shockley-Read-Hall theory, 40,46 with analytical or semi-analytical formulations available under the assumption of a single mid-gap defect level 46 and for the more realistic case of multiple trap levels. 33

Overview of the performance at BOL and upon irradiation
The average photovoltaic cell parameters measured at BOL for the different device architectures are reported in Table 2 and compared with the simulated values. When corrected to the active area, the solar cells present efficiencies close to 25% under AM1.5G, and close to 21.5% under AM0 (1367 W/m 2 at 28 • C). The produced thin-film solar cells mounted on a metal foil present a specific power above 1200 W/kg, and when combined with light weight mounting systems and flexible protective coatings for space application they show the potential to reach a module specific power above 400 W/kg. 2 In order to identify the four model parameters S p , S n , p , and n before and after irradiation, EQE spectra, illuminated and dark J − V parameters at BOL and upon irradiation were considered. The  Table 2 are very representative of the measured values and indicate a good quality of the epitaxial layers. The measured V oc values are all within 1% of the simulated values, and a slightly larger variation is seen for the J sc , probably due to a non-perfect deposition of the ARC layers, which can directly affect the experimentally obtained current. Note that the J sc values of the TF cells are significantly lower than that of the SB cells because their grid coverage is much higher. When J sc is corrected for the effective exposed area, the values are comparable.
The effect that the electron irradiation has on the illuminated J − V parameters is expressed in terms of the remaining factor with respect to the BOL values, defined as Parameter∕Parameter BOL . The average experimentally determined remaining factors from J sc and V oc are shown in Figure 4A  The modeled efficiency remaining factors match the measured values within 5% relative, as shown in Table 3. The remaining efficiencies are clearly higher for SJ than for DJ cells, and are higher for both geometries in a thin-film design than when they are substrate based,   (1) and accounting -whenever needed -for an imperfect passivation at the window and BSF interfaces. Following this approach specifically

Analysis at BOL
The  Note. At BOL, the values of n (p) and L n (p) are the nominal ones and only S n and S p are used as fitting parameters. At EOL, both lifetime and surface recombination velocity are used as fitting parameters. The values presented in parentheses may be affected by a large error.  Table 5.
whereas for thin QNR (L p(n) ≫ d E(B) ), J 01 is dominated by surface recombination and Equations (3a) to (3c) reduce to The SJ design presents a strongly asymmetric doping (N DE ∕N AB = 100), and therefore, the base dark current component tends to be highly dominant ( Figure 8A). On the other hand, in the DJ design  Table 5). This indicates a significant contribution to J 01 from the base layer. In fact, as can be verified in Figure 8B  A/cm 2 ) that is attributed to an S n comparatively higher than that of the SB structure, as also observed for the DJ cells.
Overall, it turns out that in both DJ and SJ geometries p and S p are the predominant factors affecting the EQE at BOL, while n and S n mainly influence the V oc through the recombination current in the p-type QNR region.

Analysis of bulk and interface radiation damage
In order to simulate the cell performance after intermediate electron irradiation doses, the decrease of the SRH lifetime ,SRH with radiation is modeled as 1  The degradation of S p and S n is considered to be linearly dependent on the fluence and expressed by where S (BOL) is the value of S at BOL and K S is the interface damage rate, deduced from the best CPS model fit to the experimental data. In the SJ cells, most of the photogenerated free carriers, therefore, only have to diffuse over a short distance to the pn-junction to be drifted towards the right electrode and be collected. This is particularly true for carriers generated by short wavelength light. For longer wavelengths a smaller fraction of the light is able to penetrate deeper into the cell and consequently generates some minority carriers deeper in the base, which have to travel further before reaching the pn-junction.
Therefore, the short wavelength photocurrent is mostly sustained by the thin emitter, whereas most of the long wavelength photocurrent is supported by the thick base. Electrons generated deeper in Differently from the SJ cells, in DJ cells all the minority carriers photogenerated in the emitter (except for the small fraction generated deeper in the cell) have to diffuse over a long distance before reaching the pn-junction. Therefore, the degradation of p and S p in the emitter reduces the collection efficiency over the entire wavelength range in the DJ cell (see Figure 6), resulting in a significant reduction of J sc , whereas the impact of the base parameters is restricted to the longer wavelength region and turns out to be completely marginal. In fact, the significant asymmetry of the spectral response between the short and the long wavelength ranges observed for the DJ cells after irradiation can only be correctly modeled if an increased S p is assumed, supporting the approach described in Equation (7).
In summary, the EQE upon irradiation is influenced mainly by the lifetime in the emitter for DJ cells and by the lifetime in both emitter and base for SJ cells. Moreover, the observed increase in S p in both SJ and DJ cells upon irradiation indicates a degradation in the emitter-window hetero-interface quality.
The study of the dark J − V characteristics upon irradiation (see    6 Values for the radiation induced damage rates deduced from the J − V and EQE measurements of the cells geometry, as can be observed in Figure 8, and is quite insensitive to n as long as the L n ∕d B ratio remains higher than one. Therefore, the electron lifetime cannot be reliably extracted.
In order to determine the damage rates, an approach was taken in which initially K p and K n were assumed to be the same for all configurations and then adjusted by closely fitting the model outcomes to the measured EQE, average illuminated J − V parameters and dark J − V curves. The fitted EOL values for , L and S resulting from this approach are depicted in the right portion of Table 4. Because the depletion region in the DJ solar cells is much closer to the base-BSF hetero-interface, the increase in S n is the limiting mechanism to the performance for this geometry, rather than the decrease in n , and the values for K n cannot be deduced. Therefore, the n values shown in Table 4 for the DJ cell are set equal to those extracted from the analysis of the SJ cells. Conversely, in the SJ solar cells the junction distance to the rear interface is so large that the increase in S n is hardly relevant to the performance, and therefore the values for K S n cannot be determined. The extracted values of K p , K n , K S p and K S n for the various cell geometries under study are stated in Table 6.
The hypothesis of a linear dependence of the recombination velocities with irradiation fluence provides a very good agreement between measured and simulated values of J sc , V oc and for the whole fluence range, as seen from the detailed comparison of measured and simulated data in Figure 4 and in Table 3. Overall, the observed degradation of the performance of the solar cells upon irradiation is satisfactorily simulated assuming similar lifetime damage rates for electrons and holes for all the architectures of the solar cells, indicating that the material radiation damage is probably not affected by the device geometry or the fabrication steps. The identified values for the lifetime damage constant of minority electrons and holes are in good agreement with previous studies. 27 ,47 In particular, taking into account the carriers' diffusivity, the ratio K n ∕K p corresponds to a ratio in terms of diffusion length damage constant of about one tenth, inferring a damage rate for the diffusion length in n-type GaAs about ten times larger than that one in p-type GaAs, as theoretically predicted by Yamaguchi et al. 27 The thickness of the active layers and the position of the depletion region are shown to be the determinant parameters with regards to the radiation resistance of the cells. Thin-film devices present the big advantage of having a back reflector that allows the thickness of the active layers to be significantly reduced. Therefore, a shallow junction solar cell processed into a thin-film geometry is found to be the best structure for space applications. The MOCVD growth of hetero-interfaces such as GaAs/AlInP and GaAs/InGaP has been shown to be a challenge in the past. [49][50][51][52] A meticulous control of chemical composition, material inter-diffusion and surface segregation is necessary in order to prevent the formation of mixed compounds that reduce the abruptness of the interfaces. The fact that interface recombination velocity is affected by irradiation indicates that it is an important aspect to be optimized, with the potential to further increase the resilience of the TF -SJ devices under irradiation. to the device geometry or fabrication steps. The incidence of electrons introduces lattice defects in the cells that act as recombination centers, directly impacting carrier lifetimes. Because for the DJ cells at EOL the hole diffusion length is smaller than the emitter thickness, the collection of generated carriers is strongly reduced, and this geometry presents a much larger decrease of J sc when compared to SJ devices.

CONCLUSIONS
Therefore, we find that DJ cells in the present configuration are not suited for space application.
Most importantly, however, the modeling study has pointed out that besides the reduction of the lifetime of the carriers, the electron irradiation strongly affects the quality of hetero-interfaces, characterized by a linear increase in the interface recombination velocity.
The current study shows that the degradation of the window-emitter and base-BSF hetero-interfaces quality is responsible for a significant increase of the diffusion component of the dark current, and consequently for the reduction of V oc . Therefore, it is a critical aspect which deserves further investigation since it can become the bottleneck for the optimization of the cell radiation tolerance.
A shallow junction solar cell processed into a thin-film geometry is found to be the best structure for space applications, presenting an EOL average efficiency that is 82% of the BOL value. The presence of a rear reflector in the thin-film geometry allows the design of thinner devices that show the potential to further increase the BOL performance and the resilience under irradiation, provided that the interface radiation hardness can also be improved.