† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant No. 11547151).
The lowest energies which make Cu, In, Ga, and Se atoms composing Cu(In, Ga)Se2 (CIGS) material displaced from their lattice sites are evaluated, respectively. The non-ionizing energy loss (NIEL) for electron in CIGS material is calculated analytically using the Mott differential cross section. The relation of the introduction rate (k) of the recombination centers to NIEL is modified, then the values of k at different electron energies are calculated. Degradation modeling of CIGS thin-film solar cells irradiated with various-energy electrons is performed according to the characterization of solar cells and the recombination centers. The validity of the modeling approach is verified by comparison with the experimental data.
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
![]() | 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 JSC(λ) at a given wavelength is the sum of the photocurrent density generated in the depletion region (DR) JDR(λ) and in the quasi-neutral region (QNR) JQNR(λ) as
The total short circuit current density JSC when the sunlight with a spectral distribution F0(λ) is incident on the solar cells is found by integrating Eq. (
Taking into account the surface recombination at the CdS/CIGS interface, under zero-bias, JDR(λ) can be written as[13,15]
By considering the recombination at the back surface of the CIGS layer, JQNR(λ) is given by[15]
![](cpb_25_9_098402/cpb160865ieqn1.gif)
The basic solar cells equation incorporating recombination losses is expressed as
In the condition of open circuit, V = VOC (open circuit voltage), J = 0. According to Eq. (
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 (Tm) is more than the displacement energy (Td). The Td 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 Tm can be given by[17]
Figure
Figure
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. (
Substituting the values of k and NIEL for 1-MeV and 3-MeV electron in Eq. (
In order to predict the degradation of CIGS solar cells, the physical parameters of solar cells used in calculations are listed in Table
![]() | Table 1. The physical parameters of CIGS solar cells. . |
Figure
![]() | 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. 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.
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