Simple one-dimensional model for electronic structure calculation of unbiased and biased silicon quantum dots in Coulomb blockade applications

This article presents a simple one-dimensional (1D) model of electronic structure calculation able to treat quantum dots (QDs) under bias voltage. With a view to investigating complex Coulomb blockade devices with multiple QDs, this model aims at providing accurate information on the QD eigenstates within reasonable and optimized computation time. First, the electronic structure of an unbiased QD is obtained from a self-consistent solution of the coupled Schrodinger/Poisson equations as a function of the dot size and the charging state. By comparison with three-dimensional (3D) calculations of total energy at given QD volume, we found that the 1D spherical approximation appears to be very good for a wide range of dot shapes. We develop two techniques to include the effect of external 3D bias potential that breaks the symmetry: (i) a perturbation method and (ii) an expansion of the wave function on the eigenstates of the unbiased dot. If the validity of the first technique is limited to small dots and/or low bias voltage, the latter gives excellent results over a wide range of dot sizes and bias voltages. The results obtained for a single dot device using this 1D model are carefully and successfully compared with a full 3D calculation. (C) 2003 American Institute of Physics.