We present a pseudopotential approach to the calculation of the excitonic spectrum of semiconductor quantum dots. Starting from a many-body expansion of the exciton wave functions in terms of singlesubstitution Slater determinants constructed from pseudopotential single-particle wave functions, our method permits an accurate and detailed treatment of the intraconfiguration electron-hole Coulomb and exchange interactions, while correlation effects can be included in a controlled fashion by allowing interconfiguration coupling. We calculate the exciton fine structure of InP and CdSe nanocrystals in the strong-confinement regime. We find a different size dependence for the electron-hole exchange interaction than previously assumed ͑i.e., R Ϫ2 instead of R Ϫ3). Our calculated exciton fine structure is compared with recent experimental results obtained by size-selective optical spectroscopies. ͓S0163-1829͑99͒00227-1͔

We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens shaped InAs quantum dots within the "linear combination of bulk bands" method. We present a detailed comparison with experiment, including quantities such as the single particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole and electron hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.

We present a comparison of the 8-band k-p and empirical pseudopotential approaches to describing the electronic structure of pyramidal InAs/GaAs self-assembled quantum dots. We find a generally good agreement between the two methods. The most significant shortcomings found in the k-p calculation are ͑i͒ a reduced splitting of the electron p states ͑3 vs 24 meV͒, ͑ii͒ an incorrect in-plane polarization ratio for electron-hole dipole transitions ͑0.97 vs 1.24͒, and ͑iii͒ an over confinement of both electron ͑48 meV͒ and hole states ͑52 meV͒, resulting in a band gap error of 100 meV. We introduce a ''linear combination of bulk bands'' technique which produces results similar to a full direct diagonalization pseudopotential calculation, at a cost similar to the k-p method.

While (InAs) n /(GaSb) n ͑001͒ superlattices are semiconducting for nϽn c Ϸ28 ML, for nϾn c the InAs electron level e InAs is below the GaSb hole level h GaSb , so the system is converted to a nominal semimetal. At nonzero in-plane wave vectors (k ʈ 0), however, the wave functions e InAs and h GaSb have the same symmetry, so they anticross. This opens up a ''hybridization gap'' at some k ʈ ϭk ʈ *. Using a pseudopotential plane-wave approach as well as a ͑pseudopotential fit͒ eight-band k•p approach, we predict the hybridization gap and its properties such as wave-function localization and out-of-plane dispersion. We find that recent model calculations underestimate this gap severely.

The conditions under which the band gaps of free standing and embedded semiconductor quantum dots are direct or indirect are discussed. Semiconductor quantum dots are classified into three categories; (i) free standing dots, (ii) dots embedded in a direct gap matrix, and (iii) dots embedded in an indirect gap matrix. For each category, qualitative predictions are first discussed, followed by the results of both recent experiments and state of the art pseudopotential calculations. We show that: • Free standing dots of InP, InAs, and CdSe will remain direct for all sizes, while dots made of GaAs and InSb will turn indirect below a critical size. • Dots embedded within a direct gap matrix material will either stay direct (InAs/GaAs at zero pressure) or will become indirect at a critical size (InSb/ InP). • Dots embedded within an indirect gap matrix material will exhibit a transition to indirect gap for sufficiently small dots (GaAs/AlAs and InP/ GaP quantum well) or will be always indirect (InP/GaP dots, InAs/GaAs above 43 kbar pressure and GeSi/Si dots). In indirect nanostructures, charge separation can occur with electrons and holes localized on different materials (flat InP/GaP quantum well) or with electrons and holes localized in different layers of the same material (concentric cylindrical GaAs/AlAs layers).