Direct-to-Indirect Crossover in Semiconductor Alloys: A First-Order Phase Transition?

Abstract

We study the direct-to-indirect gap crossover in Al Gal, As alloys driven by Al addition, in analogy with temperature-induced phase transitions. The adopted real-space formalism incorporates occupational disorder in a realistic manner: different atomic configurations, accommodated in a supercell, are generated and solved independently.We perform a systematic study of the scaling of calculated gap properties of Al Gal As alloys with the cell size, and consider system sizes ranging from 64 to 8000 atoms. Extrapolation to infinite system size follows scaling laws appropriate for firstorder phase transitions, and allows an accurate determination of the crossover composition x, .The current development of electronic structure calculations allows for large systems to be treated and solved, in particular, taking into account surface effects, impurities, and disorder over relatively extended regions in

Semiconductor Hetrostructures with Non-Ideal Interfaces: Electronic Structure and Optical Properties

“…The magnitude of f determines, in an alloy or quantum well, if the gap is direct (dipole-allowed transitions, f T 0 or indirect (dipoleforbidden transitions, f 0 [9,10]. Within the tight-binding formalism, the dipole moment hvj p jci is easily calculated as [21] hvj…”

“…In the past few years, we have developed such a method and subsequently applied it to a variety of problems involving III±V based semiconductor systems, including random [9,10] and partially ordered [11] alloys, ideal quntum wells (QWs) and superlat-tices [12], interdiffusion [13], roughness [14] and segregation [15] effects in quantum wells. As described below, the method is based on a combination of an empirical tightbinding model with statistical ensemble averages in large supercells.…”

Optical effects of interdiffusion in GaAs/AlAs heterostructures: Atomic scale calculations

“…The inhomogeneous alloying present in the diffusion region is treated microscopically according to a recently developed formalism. 4 Ensembles of supercells, each cell containing up to ϳ10 4 atoms with periodic boundary conditions, are used to simulate the structures. Physical properties of the macroscopic system are identified with the ensemble averages performed over numerically generated representative structures.…”

“…The electronic properties of the heterostructure are calculated within the tight-binding small crystal formalism. 4,5 We adopt orthorhombic cells with dimensions N x ϭN y (ϭN ʈ ) and N z . Periodic boundary conditions are imposed, and for each L and W the value of N z is taken to be sufficiently large to guarantee convergence of the composition profiles and of the calculated electronic properties to the infinitely wide AlAs separators situation.…”

“…3. 7 Data points just above L C with large error bars are characteristic of finite-size effects, 4 and converge to zero as the cell size increases. Figure 3 shows a remarkable collapse of the oscillator strength data for 10ϽWϽ14 ͑well widths between ϳ30 and 40 Å͒ onto a single curve.…”