Band Gap Anomaly in Ternary Chalcopyrites and Optical Bowing in Binary Semiconductor Alloys

Abstract

The lowest optical band gaps E(x) of semiconductor alloys1–4 AXB1-xC are usually smaller than the concentration (x) weighted average Ē(x) = xEAC + (l-x)EBC of the band gaps EAC and EBC of the end-point AC and BC semiconductors. The upward concave non-linearity in E(x) can be characterized by the bowing parameter b, defined by E(x) = Ē(x) − bx(l-x). Optical bowing has been often analyzed4–6 as arizing from a combination of two types of phenomena. Much like in the filed of Mott-Anderson metal- nonmetal transition, these are: (i) effects due to electron-electron and electron-core interactions which are already present in a fictitiously ordered (“virtual”) crystal, and (ii) effects due to disorder, e.g. compositional disorder (an additional form of disorder can arize from clustering). We refere to these two contributions to the experimental bowing bexp as bI and bII, respectively. Traditionally, bI was evaluated4–7 from the Virtual Crystal Approximation (VCA), where it was assumed that the chemical and structural identies of AC and BC are lost in the alloy, and replaced by an average lattice constant ā(x) with a corresponding (single) average anion-cation bond length RVCA(X)the reason that VCA gives a finite bowing is that most band structure methods show the band energies to be nonlinear functions of the potential parameters. We may express this as EAC pVAC + qU2 AC +…, where p and q are coefficients and VAC, and UAC are potential parameters. For example, in the pseudopotential perturbation theory the X gap of a zincblende semiconductor is EAC ~ 2VAC (220) + a2/2π V2 AC (111), and VAC(hkl) are potential form factors.