We use realistic pseudopotentials and a plane-wave basis to study the electronic structure of non-periodic, three-dimensional, 2000-atom (AlAs) n /(GaAs) m (001) superlattices, where the individual layer thicknesses n, m ∈ {1, 2, 3} are randomly selected. We find that while the band gap of the equivalent (n = m = 2) ordered superlattice is indirect, random fluctuations in layer thicknesses lead to a direct gap in the planar Brillouin zone, strong wavefunction localization along the growth direction, short radiative lifetimes, and a significant band-gap reduction, in agreement with experiments on such intentionally grown disordered superlattices. PACS numbers: 73.20.Dx,78.66.-w,71.50.+t Typeset using REVT E X 1 Ordered semiconductor superlattices-produced routinely by epitaxial crystal growth techniques-are widely recognized for their unique electronic and optical properties [1]. To tailor the electronic properties (e.g., through band folding) one aims at growing ordered superlattices (o-SL) with definite values of the thicknesses n and m in (A) n /(G) m . One could, however, deliberately grow a disordered superlattice (d-SL) [2,3], where the individual layer thicknesses n, m, n ′ , m ′ , n ′′ , m ′′ , . . . are selected at random according to a given probability distribution p α (n) (α = A, G). While the electronic structure of an o-SL is characterized by extended states and the formation of mini-bands, a truly one-dimensional disordered system (described, e.g., by the Anderson model) shows carrier localization and absence of dispersion [4,5]. Sasaki et al. [3] grew ∼1000 monolayer (ML) thick AlAs/GaAs d-SL's (i.e., A = AlAs, G = GaAs) with n and m chosen from a set of small integers {1, 2, 3}, viz., p A = p G = p, with p(1) = p(2) = p(3) = 1 3 . Since the average layer thickness is 2 monolayers, one can think of this d-SL as evolving from an (A) 2 /(G) 2 o-SL by random substitution of A 2 and G 2 layers by A 1 , A 3 , G 1 , and G 3 layers ("δ-doping"). Such disordered superlattices have shown surprising and unique optical properties relative to their parent o-SL [3]: (a) strong and initially fast decaying (lifetime τ = 0.25 ns at T = 77 K) photoluminescence (PL) intensity even though the equivalent o-SL has an indirect band gap and thus emits both weakly and slowly, (b) a large red shift (∼60 meV) of the PL peak with respect to the equivalent o-SL, and (c) an order of magnitude slower rate of reduction of the PL intensity with temperature. These unusual properties of d-SL's appear very attractive for optoelectronic applications [3].In modelling the electronic structure of a d-SL [2,6,7], one faces difficulties arising from the existence of two entirely different length scales: (i) The lack of translational symmetry requires the use of unit cells with a macroscopic length N ≈ 1000 ML, equal to the total length of the d-SL (Nd ≈ 300 nm, where d is the monolayer thickness). (ii) The spatial variations of the electron potential, however, occur on a microscopic length scale of about 0.1 nm. While it is possible to re...