Effect of Concentration Fluctuations on Material Properties of Disordered Alloys

Abstract

Alloying compound AX with another compound BX is widely used to tune material properties. For disordered alloys, due to the lack of periodicity, it has been challenging to calculate and study their material properties. Special quasi-random structure (SQS) method has been developed and widely used to treat this issue by matching averaged atomic correlation functions to those of ideal random alloys, enabling accurate predictions of macroscopic material properties such as total energy and volume. However, in AxB1-x alloys, statistically allowed local concentration fluctuations can give rise to defect-like minority configurations, such as bulk-like AX or BX regions in the extreme, which could strongly affect calculation of some of the material properties such as semiconductor bandgap, if it is not defined properly, leading to significant discrepancies between theory and experiment. In this work, taking the bandgap as an example, we demonstrate that the calculated alloy bandgap can be significantly underestimated in standard SQS calculations when the SQS cell size is increased to improve the structural model and the bandgap is defined conventionally as the energy difference between the lowest unoccupied state and the highest occupied state, because the rare event motifs can lead to wavefunction localization and become the dominant factor in determining the "bandgap", contrary to experiment. To be consistent with experiment, we show that the bandgap of the alloy should be extracted from the majority configurations using a density-of-states fitting (DOSF) method. This DOSF approach resolves the long-standing issue of calculating electronic structure of disordered semiconductor alloys. Similar approaches should also be developed to treat material properties that depends on localized alloy wavefunctions.

Figures (4)

• Figure 1: (a)Theoretical bandgap $E_g^{\text{LUS-HOS}}$ as a function of atom number $N_{\text{atom}}$ in a SQS cell and (b) experimental measured bandgap as a function of cooling rate in disordered Zn_0.5Sn_0.5P alloys. The theoretical and experimental bandgap values are from Ref. 2014-PRB-ZnSnP22012-APL-ZnSnP2-disorder2015-PRB-unconvergence2017-JPCC-ZnSnP2-expt-LRO1987-JMR-ZnSnP2-expt2015-PSSC-ZnSnP2. Red hexagram marker denotes the bandgap from this work.
• Figure 2: (a) Schematic of the nearest-neighbor tetrahedron $A_2B_{2}$ and second-nearest-neighbor polyhedron $A_6B_{6}$. (b) Orbital coupling diagram of the ZnSnP2 compound. (c) Band alignment of $\Gamma_{15}$ and $\Gamma_1$ showing the effect of varying nearest-neighbor tetrahedra from Zn2Sn2 to Zn4Sn0/Zn0Sn4, and second-nearest-neighbor polyhedra from Zn6Sn6 to Zn12Sn0/Zn0Sn12, with the nearest tetrahedra fixed at Zn4Sn0/Zn0Sn4.
• Figure 3: Density of states (DOS) for (a) 64-atom and (b) 512-atom supercells of disordered Zn_0.5Sn_0.5P alloys. Blue crosses indicate the selected fitting points, while the red line represents the fitting trend. Charge distributions at the highest occupied state (HOS) and the lowest unoccupied state (LUS) are shown above the respective DOS panels.
• Figure 4: (a) Total energy $E$ relative to the order structure and (b) bandgap $E_g^{\text{LUS-HOS}}$ and $E_{\text{g}}^{\text{DOS}}$ as functions of atom number $N_{\text{atom}}$ in random Zn_0.5Sn_0.5P supercells. (c) $E$ and (d) $E_g^{\text{LUS-HOS}}$ and $E_{\text{g}}^{\text{DOS}}$ as functions of long-range order $\eta$ in 512-atom supercells. Black star markers denote the experimental bandgaps of Zn_0.5Sn_0.5P from Ref. 2017-JPCC-ZnSnP2-expt-LRO.