Electron-hole alignment in InAs/GaAs self-assembled quantum dots: Effects of chemical composition and dot shape

We investigate theoretically the effects of chemical composition and shape on the electronic states in InAs/GaAs self-assembled quantum dots, by using an eight-band strain-dependent $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian. For a number of InAs dots with different shapes, and especially with different gallium concentration profiles, we found various ranges of separation between electrons and holes. We show that gallium diffusion changes the confining potential for both electrons and holes through the strain profile in the dots, leading to totally different hole states from those in pure InAs dots. We also compute the electron-hole separation as a function of electron and hole energy levels. For the same gallium concentration profile, pyramidal dots exhibit the inverted alignment with the largest electron-hole separation compared with other two types, truncated-pyramidal and lens-shaped dots. Our calculations agree well with recent experiments [P.W. Fry et al., Phys. Rev. Lett. 84, 733 (2000)].