Cu(In, Ga)Se₂ (CIGS) thin-film solar cells have been considered as one of the most promising candidates for space application, having high efficiency exceeding 21%, lightweight, flexible and high radiation tolerance.^[1,2] Exposure to the space radiation environment degrades the performance of solar cells, even causing the failure of the space mission.^[3,4] Consequently, it is extremely important to predict the degradation of solar cells induced by electron and proton.

Previous studies on the degradation of CIGS solar cells were based on ground test and space flight experiment.^[5,6] Essentially, the degradation of solar cells induced by electron irradiation is directly related to the concentrations of the recombination centers, which can be detected and identified among all the defects by photoluminescence.^[7,8] In order to improve the radiation resistance of solar cells, the study on injection-enhanced annealing of electron irradiation-induced defects was carried out by temperature-dependent photoluminescence.^[9,10] However, the experimental characterization is time consuming and can be very expensive. As a result, a modeling method was proposed to predict the degradation of solar cells based on classical semiconductor equations.^[11] The key of this method is the determination of the introduction rates (k) of the recombination centers, but the values of k at several specific electron energies are merely provided for CIGS solar cells. In order to predict the degradation of CIGS solar cells systematically, the values of k need to be given for various-energy electrons. This purpose can be achieved by obtaining non-ionizing energy loss (NIEL), which is analogous to the linear energy transfer or stopping power for ionization events.^[11,12]

In this paper, firstly, the electron-induced NIEL in the CIGS material is computed by an analytic method. Secondly, the values of k for different energy electrons are confirmed by NIEL. Finally, the degradation of CIGS solar cells irradiated with various-energy electrons is predicted by a theoretical calculation according to the characterization of solar cells and the recombination centers.

In this work, CIGS solar cells which have an average bandgap energy of around 1.16 eV (corresponding to Ga/(Ga + In) ≈ 0.24) are chosen as the research object. Figure 1(a) shows the schematic cross-section of a typical CIGS solar cell which consists of an antireflection layer, transparent conducting oxide (TCO), a CdS buffer layer, a CIGS absorber layer, an Mo layer as a back contact and substrate.^[13] Generally, the CIGS solar cells are considered as a one-side abrupt heterojunction, for which the depletion region is virtually located in the lightly doped CIGS layer (see Fig. 1(b)) and the photoelectric conversion almost takes place in this layer.^[14]

Fig. 1.

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	Fig. 1. (a) Typical structure for CIGS solar cells. (b) Schematic band diagram of CIGS solar cells under zero-bias voltage condition.

Therefore, the short circuit current density J_SC(λ) at a given wavelength is the sum of the photocurrent density generated in the depletion region (DR) J_DR(λ) and in the quasi-neutral region (QNR) J_QNR(λ) as

The total short circuit current density J_SC when the sunlight with a spectral distribution F₀(λ) is incident on the solar cells is found by integrating Eq. (1) as

Taking into account the surface recombination at the CdS/CIGS interface, under zero-bias, J_DR(λ) can be written as^[13,15]

By considering the recombination at the back surface of the CIGS layer, J_QNR(λ) is given by^[15]

The basic solar cells equation incorporating recombination losses is expressed as

In the condition of open circuit, V = V_OC (open circuit voltage), J = 0. According to Eq. (5), the relation of V_OC to J_SC can be derived as follows:

Recombination centers cause the performance degradation of solar cells by reducing the minority carrier lifetime^[15]

The NIEL is a quantity that describes the rate of energy loss due to atomic displacements when particles traverse a certain material. Atomic displacements can be produced only if the maximum transferred energy (T_m) is more than the displacement energy (T_d). The T_d was calculated as being 9.8 eV, 15.6 eV, 12.4 eV, and 28.5 eV for Cu, In, Ga, and Se atoms in CIGS material, respectively.^[16] The T_m can be given by^[17]

Figure 2 shows the variation of T_m versus E for Cu, In, Ga, and Se atoms in CIGS material, respectively. It is noted that T_m increases with the increase of E. According to T_d for Cu, In, Ga, and Se atoms, electron energy can be divided into five regions: (i) E ≤∼ 0.23 MeV, no vacancies are produced, (ii) ∼ 0.23 MeV < E ≤∼ 0.30 MeV, only Cu vacancies (V_Cu) are probably produced, (iii) ∼ 0.30 MeV < E ≤∼ 0.53 MeV, Cu and Ga vacancies (V_Cu and V_Ga) are probably produced, (iv) ∼ 0.53 MeV < E ≤∼ 0.63 MeV, Cu, In and Ga vacancies (V_Cu, V_In and V_Ga) are probably produced, (v) E >∼ 0.63 MeV, Cu, In, Ga, and Se vacancies (V_Cu, V_In, V_Ga, and V_Se) are probably produced.

Fig. 2.

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	Fig. 2. Maximum transferred energy of Cu, In, Ga, Se atoms composing CIGS material.

Figure 3 shows the electron NIEL for Cu, In, Ga, Se atoms and CuIn_0.76Ga_0.24Se₂ compound. The electron NIEL is calculated by an analytic method using the Mott differential cross section, then NIEL for the CuIn_xGa_1−xSe₂ compound can be estimated by the ratio of atoms in this material as^[17]

Fig. 3.

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	Fig. 3. NIEL of Cu, In, Ga, Se atoms and CuIn0.76Ga0.24Se2 compound.

The correlation between the introduction rate (k) and NIEL can be written as^[11]

For 1-MeV electron, k = 0.02 cm^−1[18] and NIEL = 1.2 × 10⁻⁵ MeV · cm² · g⁻¹. Hence, β = 1.67 × 10³ g · MeV⁻¹· cm⁻³. For 3-MeV electron, NIEL = 3.99 × 10⁻⁵ MeV· cm² · g⁻¹. According to Eq. (12), k = 0.07 cm⁻¹ is obviously different from the value (0.2 cm⁻¹) in Ref. [18]. Therefore, by analogy to the relation of the displacement damage dose to electron NIEL,^[19] k is modified as follows:

Substituting the values of k and NIEL for 1-MeV and 3-MeV electron in Eq. (13), we obtain n = 1.91 and β = 1.67 × 10³ g · MeV⁻¹· cm⁻³. Therefore, using Eq. (13), more values of k at different electron energy can be calculated. Figure 4 shows the dependence of k versus electron energy. As seen in Fig. 4, the rate k increases with electron energy increasing, but the rate of increase gradually decreases.

Fig. 4.

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	Fig. 4. The introduction rate of recombination centers for different energy electron irradiation.

In order to predict the degradation of CIGS solar cells, the physical parameters of solar cells used in calculations are listed in Table 1.

Table 1.

Table 1.

Table 1. The physical parameters of CIGS solar cells. . Symbol Parameter Value μn electron mobility 20 cm2 · V−1 · s−1a μp hole mobility 30 cm2 · V−1 · s−1a R reflectivity Ref.[13] α absorption coefficient Ref.[13] NC effective density of states in the conduction band 2.2 × 1018 cm−3b NV effective density of states in the valence band 1.8 × 1019 cm−3b NA doping concentration 2 × 1016 cm−3 τ0 minority carrier lifetime 100 ns σ minority carrier trapping cross section 3 × 10−16 cm2 ν thermal velocity of carriers 4 × 107 cm/s a Ref. [13] b Ref. [20].

Table 1. The physical parameters of CIGS solar cells. .

Figure 5 shows the degradation of normalized short circuit current for CIGS solar cells under 1-MeV electron and 4-MeV proton (k = 1000 cm^−1[18]) irradiation. Figure 6 shows the degradation of open circuit voltage for CIGS solar cells under various-energy electron irradiation, and also presents the experimental data taken from Ref. [18] for 1-MeV and 3-MeV electrons. As shown in Figs. 5 and 6, the degradation curves obtained from calculations show good agreement with experimental data. This ensures the validity of the modelling method and the accuracy of calculations.

Fig. 5.

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	Fig. 5. Normalized short circuit current of CIGS solar cells irradiated with 1-MeV electron and 4-MeV proton. Curves are the results of calculations, and symbols are experimental data taken from Ref. [18].

Fig. 6.

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	Fig. 6. Normalized open circuit voltage of CIGS solar cells irradiated with various-energy electrons. Curves are the results of calculations, and symbols are experimental data taken from Ref. [18].

When electron energy E ≤ ∼0.23 MeV, no vacancies are produced and the performance of CIGS solar cells will not degrade. Electron NIEL for CIGS material is calculated analytically. The relation of k to NIEL is modified, and the values of k for various-energy electrons are given. The degradation of CIGS solar cells under various-energy electron irradiation is predicted by a theoretical calculation. Accuracy of prediction can be ensured by the fact that the degradation curves obtained from the theoretical calculation are in good agreement with the experimental data.