The I2-II-IV-VI4 series of quaternary chalcogenides semiconductors have drawn wide interest for their potential application as solar-cell absorbers. In this paper, we present a study of electronic and optical properties of the equilibrium kesterite structure (KS) of Cu2ZnGeS4 (CZGS) calculated by means of the full potential linearized augmented plane wave method. For this purpose, we used the Wien2k code based on the density functional theory with the generalized gradient approximation (GGA), modified Becke-Johnson exchange potential (mBJ) and the Hubbard potential U. The TB-mBJ is used alone or combined with U (TB-mBJ, and TB-mBJ+U). The results are compared with other theoretical results and the available experimental ones. The obtained results show that the top of the valence band is mainly composed by the Cu d orbital while the bottom of the conduction band is a mixture of Ge s and S p states. It was found that KS-CZGS has a direct band gap of 0.3, 1.8 and 2.0 eV using GGA, GGA+TB-mBJ and GGA+TB-mBJ+U, respectively. It is observed that states exist above the Fermi level (0 eV) with a width of 0.3 and 0.2 eV when we use GGA and GGA+TB-mBJ, while these states come down under the Fermi level when using GGA+TB-mBJ+U. The optical properties are calculated and an almost isotropic behavior is found in contrast to the reported properties of the stannite phase. This behavior can be linked to the charge density and the structure.
The model of multiple trapping into energy-distributed states is a successful tool to describe the transport of nonequilibrium charge carriers in amorphous semiconductors. Under certain conditions, the model leads to anomalous diffusion equations that contain time fractional derivatives. From this perspective, the multiple-trapping model can be used to interpret fractional transport equations, formulate initial and boundary conditions for them, and to construct numerical methods for solving fractional kinetic equations. Here, we shortly review the application of fractional multiple-trapping equations to problems of transient photoconductivity relaxation and transit–time dispersion in the time-of-flight experiment and discuss the connection of the multiple-trapping model with generalized fractional kinetic equations. Different types of charge leakage are discussed. The tempered fractional relaxation is obtained for recombination via localized states and distributed order equations arise for the non-exponential density of states presented as a weighted mixture of exponential functions. Analytical solutions for photocurrent decay in transient photoconductivity and time-of-flight experiments are provided for several simplified situations.
The identification, in our earlier papers, of the discrete energy levels in stabilized a-Se indicate that doping with As in the limit of 0.2-0.5% suppresses the shallow defect and increases the density of the deep one. It may be added at this point that an undesirable decrease in the hole lifetime τ was found to accompany the introduction of As in the a-Se lattice, which was attributed to a new hole trap. More analysis is clearly needed to resolve these questions. For these reasons we have developed a technique to calculate the lifetime. The obtained results confirm the image of the density of states near the valance band.
This paper is devoted to investigating the description of the q-deformed multiple-trapping equation for charge carrier transport in amorphous semiconductors. For this, we at first modified the multi–trapping model (MTM) of charge carriers in amorphous semiconductors from time-of-flight (TOF) transient photo-current in the framework of the q-derivative formalism, and then, we have constructed, our simulated current by using a method based on the Laplace method. This method is implemented in a program proposed recently by [14] which allows us to construct a current using the Padé approximation expansion.
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