Localization and band-gap pinning in semiconductor superlattices with layer-thickness fluctuations

We consider (AlAs)_n/(GaAs)_n superlattices with random thickness fluctuations Delta-n around the nominal period n. Using three-dimensional pseudopotential plane-wave band theory, we show that (i) any amount Delta-n/n of thickness fluctuations leads to band-edge wavefunction localization, (ii) for small Delta-n/n the SL band gap is pinned at the gap level produced by a single layer with ``wrong thickness n + Delta-n, (iii) the bound states due to monolayer thickness fluctuations lead to significant band-gap reductions, (iv) <001> AlAs/GaAs SLs with monolayer thickness fluctuations have a direct band gap, while the ideal <001> SLs are indirect for n<4.