Localization and Band Gap Pinning in Semiconductor Superlattices with Layer Thickness Fluctuations

We consider (AlAs)n/(GaAs)n superlattices with random thickness fluctuations Δn around the nominal period n. Using three-dimensional pseudopotential plane-wave band theory, we show that i) any amount Δn/n of thickness fluctuations leads to band edge wave function localization, ii) for small Δn/n the SL band gap is pinned at the gap level produced by a single layer with "wrong" thickness n + Δn, iii) the bound states due to monolayer thickness fluctuations lead to significant band gap reductions, e.g., in n = 2, 4, 6, and 10 monolayer SLs the reductions are 166, 67, 29, and 14 meV for 111 SLs, and 133, 64, 36, and 27 meV for 001 SLs, iv) 001 AlAs/GaAs SLs with monolayer thickness fluctuations have a direct band gap, while the ideal 001 SLs are indirect for n < 4.