Electronic states and optical properties of GaAs/AlAs and GaAs/vacuum superlattices by the linear combination of bulk bands method

The linear combination of bulk bands method recently introduced by Wang, Franceschetti, and Zunger [Phys. Rev. Lett. 78, 2819 (1997)] is applied to a calculation of energy bands and optical constants of $(\mathrm{GaAs}{)}_n/(\mathrm{AlAs}{)}_n$ and $(\mathrm{GaAs}{)}_n/(\mathrm{vacuum}{)}_n$ (001) superlattices with n ranging from 4 to 20. Empirical pseudopotentials are used for the calculation of the bulk energy bands. Quantum-confinement-induced shifts of critical point energies are calculated and are found to be larger for the GaAs/vacuum system. The $E_1$ peak in the absorption spectra has a blueshift and splits into two peaks for decreasing superlattice period; the $E_2$ transition instead is found to be split for large-period GaAs/AlAs superlattices. The band contribution to linear birefringence of GaAs/AlAs superlattices is calculated and compared with recent experimental results of Sirenko et al. [Phys. Rev. B 60, 8253 (1999)]. The frequency-dependent part reproduces the observed increase with decreasing superlattice period, while the calculated zero-frequency birefringence does not account for the experimental results and points to the importance of local-field effects.