Three-dimensional analysis of the electronic structure of cylindrical vertical quantum dots

We present a detailed analysis of single-electron charging effects in cylindrical vertical quantum dots (CVQD's). Emphasis is placed on three-dimensional (3D) device effects that induce appreciable features in the quantized electron spectrum and in the addition energy spectrum of CVQD's. A potential model based on a 3D analytical solution of the Poisson equation provides intuitive physical insight into the variation of the eigenspectrum as a function of the potential nonparabolicity. This analytical model is in good qualitative agreement with a fall 3D self-consistent quantum simulation of single-electron charging in quantized CVQD's based on the density-functional theory. Hence we show that the-spin sequences realized in filling the third and fourth electronic shells are a sensitive function of the potential nonparabolicity arising from the 3D CVQD geometry, and varying with applied gate bias. Within this "atomic shell" model, the addition energy spectrum reflects the influence of 3D device effects and is not necessarily a signature of a particular spin-filling sequence.