Annealing Effects on GaAs/Ge Solar Cell after 150keV Proton Irradiation

Radiation-induced defects are responsible for solar cell degradation. The effects of radiation and annealing on the defects of a GaAs/Ge solar cell are modeled and analyzed in this paper. The electrical performance and spectral response of solar cells irradiated with 150 keV proton are examined. Then, thermal annealing was carried out at 120°C. We found that the proportion of defect recovery after annealing decreases with increasing irradiation fluence. The minority carrier lifetime increases with decreasing defect concentration, which means that the electrical performance of the solar cell is improved. We calculated the defect concentration and minority carrier lifetime with numerical simulation and modeled an improved annealing kinetic equation with experimental results.


Introduction
Space radiation produced damage in solar cells, which will limit the capability and lifetime of satellites. In order to mitigate the space radiation damage, the mechanisms of radiation-induced degradation of the solar cell have been heavily studied [1][2][3][4][5]. It is clear that interactions between energetic particles and nucleus result displacement damage and induce lattice defects in materials. Defects act as recombination centers in the band gap and have a significant impact on the minority carrier lifetime, a parameter that determines the electric performance of solar cells [6][7][8][9][10][11][12][13][14].
The minority carrier lifetime for solar cells is extremely sensitive to defects and increases with the decrease of defect concentration [15][16][17]. Defects in semiconductor material can be recovered via thermal annealing. There are two ways to anneal cell damage, postirradiation annealing and continuous annealing. Continuous annealing means that solar cells are radiated at a high temperature that the defects are produced by irradiation and recovered by thermal annealing simultaneously. Some results show that continuous anneal-ing could reduce the concentration of defects above a certain temperature [13,18]. In earth orbit, the solar array will be heated to above 100°C [19,20], and the recovery of radiation defects will be more rapid with the high temperature. Therefore, it is necessary to consider the effect of temperature on radiation defects when studying the radiation degradation of solar cells.
In this paper, single-junction GaAs/Ge solar cells were irradiated with 150 keV proton, and the irradiated solar cells were annealed at 120°C. Then, we used an improved defect annealing kinetic equation to calculate the defect concentration. And based on the defect concentration, the simulation of short-circuit current during the annealing process was in good agreement with the experimental results.

Experimental
The samples used in this work are GaAs/Ge single-junction solar cells manufactured by metal organic chemical vapor deposition (MOCVD). The cell size is 10 × 10 mm 2 , and the structure is shown in Figure 1. The samples were irradiated with 150 keV proton under vacuum at room temperature, and the irradiation fluence is listed in Table  I-V characteristics and spectral response (also called external quantum efficiency (EQE)) were measured under AM0 conditions (0.1367 W/cm 2 ) at 25°C. The cell surface reflectance was measured simultaneously with EQE on a Quantum Efficiency Tester (model: Enlitech QE-R). Thermal annealing was carried out at 120°C, and meanwhile, the short-circuit current was measured every ten minutes in situ.

Results and Discussion
3.1. Degradation Behaviors of Electrical Properties. The I-V characteristics of the GaAs/Ge solar cell irradiated with various fluence were shown in Figure 2. Clearly, the performance of the solar cell was declined with increasing irradiation fluence. The normalized degradation of I SC , V OC , and P max versus fluence was shown in Figure 3(a). It can be seen from Figure 3(a) that when fluence is smaller than 1 × 10 11 cm -2 , the degradation of V OC is more serious than that of I SC . When fluence increases to 5e11 cm -2 , I SC decreased quickly while V OC is almost unchanged. This unusual decrease of I SC can be explained by the degradation of EQE with fluence which is shown in Figure 3(b). EQE in short wavelength (λ < 650 nm) declined more severe than that in long wavelength (λ > 650 nm) when the irradiated fluence is 5e11 cm -2 .

Simulation of I SC Degradation
Behaviors. The steadystate operating characteristics of solar cells can be described by the minority carrier diffusion equations [21] The meaning of all parameters is shown in Table 2.
The current density of emitter, base, and space charge regions can be deduced from the above minority carrier diffusion equations [21,22]: International Journal of Photoenergy The meaning and value of parameters in the above formula are shown in Table 3. Among them, minority carrier diffusion length L e /L b and simplified surface recombination rate s e /s b are related to the minority carrier lifetime, which means that these parameters will change with the minority carrier lifetime. In addition, some parameters related to wavelength are shown as a graph, in which F is the photon flux incident cell surface and FðλÞ = ϕðλÞ · λ/hc. In this equation, ϕðλÞ is an air mass zero reference spectrum developed by the American Society for Testing and Materials [23]. α is the photon absorption rate of GaAs; here, what we used was the experimental value published by Aspnes et al. [24]. R is surface reflectivity of the solar cell. These wavelength-dependent parameters are shown in Figures 4 and 5.
The short-circuit current density J sc is the sum of contributions from each of the three regions listed in Equation (2), which can be expressed as where Eg is bandgap, for GaAs is 1.424 eV, corresponding to the wavelength of 871 nm. According to Equations (2) and (3), J sc is a function of minority carrier lifetime τ, a parameter commonly used to evaluate solar cell performance. An effective minority carrier lifetime is given as where τ r , τ nr , and τ Auger represent the minority carrier lifetime of radiative, nonradiative (SRH reorganization), and Auger recombination, respectively. For unirradiated GaAs solar cells, τ r is about 40 ns, τ nr is 870 ns [25], and τ Auger is usually ignored for its effect is much smaller than that of the other two recombination mechanisms. The nonradiative recombination minority carrier lifetime decreases with increasing defect concentration: where σ is defect capture cross-section with a value of 4 × 10 −13 cm 2 , v th is thermal velocity of the carriers with   [6], and N is the concentration of defects, N = kφ and k = βE niel , in which φ is fluence, k is the introduction rate (the number of defects induced by the incident particle), β is a constant coefficient and its value is 3:76 × 10 3 g/MeV/cm 3 [11,26], and E niel (nonionizing energy loss) for 150 keV proton is 0.259 MeV·cm 2 /g [27], so k of 150 keV proton is 974 cm -1 . In fact, irradiation will produce a series of defects with different defect energy levels in the forbidden band, in which deep defect energy levels can function as significant recombination centers. Here, k refers to the introduction rate of these defects, whose energy levels are near Ev+0.71 and Ec-0.71. Thus, the effective minority carrier lifetime can be expressed as We calculated the defect concentration and minority carrier lifetime with 150 keV proton fluence (seen in Figure 6) by Equation (6). Here, the introduction rate is a constant; that is,     International Journal of Photoenergy there is no correlation between two independent incidents. So, the defects are increasing linearly with irradiation fluence, and the minority carrier lifetime is also decreasing continuously.
To verify the accuracy and parameter settings of Equation (2), we substitute the correspondence between minority carrier lifetime and fluence into Equation (2); the result is shown in Figure 7. In addition, the normalized I SC vs. fluence fitted with I/I 0 = 1 − A × logð1 + φ/φ 0 Þ is also shown in Figure 7, where the fitting parameter A is 0.2879 and φ 0 is 2:8663 × 10 10 cm -2 . Mean square error of fitting results and numerical calculation results compared with the experimental data, respectively, are 25% and 19%.

Thermal
Annealing. Studies show that after thermal annealing, the irradiation damage of solar cells will be partially recovered [18,28]. Figure 8 shows that the normalized I SC increases at an annealing temperature of 120°C. The normalized factor in this figure is I SC before irradiation at 120°C, for the short-circuit current will increase with temperature [29,30]. The fact that I SC increases with annealing time indicates that the radiation damage is recovered by thermal annealing.
The annealing kinetics of radiation defects can be expressed as [7,31] where t is annealing time, α is the annealing rate, and dN/dt is the annealing efficiency. Obviously dN/dt is decreasing with the defect concentration. N can be obtained by integrating Equation (7) [7]: where N 0 is the initial defect concentration before annealing. According to Equation (8), defect concentration will decrease continuously until all defects are recovered. That is to say, the defects related in Equation (8) are all recoverable radiation defects. However, experiments show that some radiation defects are stable at the annealing temperature and the defects are partially recovered after thermal annealing [7,9,18,32]. Accordingly, the radiation-induced defects can be divided into two types; that is, defects can be or cannot be recovered by annealing. Based on this fact, Equation (8) can be rewritten as where p is the proportion of defects cannot be recovered. Figure 8 shows the fitted results with I SC and Equation (9). The annealing rate α, proportion of stable defects p, defect concentration, and minority carrier lifetime before and after annealing are shown in Table 4. The annealing rate α is 5:167 × 10 −4 s -1 in this annealing condition. As shown in Figure 9, p increases with irradiation fluence and increases quickly at lower irradiation fluences, then becomes saturated at higher irradiation fluences. This means that the higher the irradiation fluence, the smaller the proportion of defects that can be recovered after annealing. That is because point defects tend to cluster with increasing irradiation fluence and clustered defects are more difficult to be recovered. The defect concentration after annealing is decreased dramatically compared to the defects before annealing. Based on the defect concentration and Equation (5), the minority carrier lifetime before and after annealing can be calculated as listed in

Conclusion
The degradation of GaAs solar cells in electrical properties can be enhanced by increasing the proton fluence. However, it can be improved in the process of thermal annealing. The short-circuit current after irradiation and annealing can be studied by the minority diffusion equation. Based on the experiment results and theoretical analysis, an improved annealing kinetic equation is carried out. I SC calculated by the minority diffusion equation and the improved annealing formula agrees well with the experimental results. From our analyzation, the defects can be partially recovered after annealing. Furthermore, the proportion of stable defects is the defects unrecovered after annealing increases with increasing irradiation fluence for the reason of clustered defects. The minority carrier lifetime increases dramatically in this annealing experiment.

Data Availability
The data used to support the findings of this study are included within the article.

Additional Points
Highlights. (i) Defect concentration and minority carrier lifetime are modeled and analyzed after irradiation and during thermal annealing. (ii) The annealing kinetic equation is developed to describe the defect change.

Conflicts of Interest
The authors declare that they have no conflicts of interest.