Local density of states for solids in an electric field

The local densities of states (LDOSs) in electrified simple cubic crystals have been studied within the semi-empirical tight-binding (TB) model. One-d imensional (1D), two-dimensional.(2D) and three-dimensional (3D) cases are investigated, taking into account first neighbours and one band, when an ex ternal constant electric field with arbitrary direction is applied. The inc reasing strength of the field in a given direction turns smoothly the LDOSs of an n-dimensional crystal (n = 1, 2, 3) into the LDOSs of an (n - 1)-dim ensional crystal. The Wannier-Stark ladder phenomenon for crystals of diffe rent dimensionalities is discussed and the role of the electric field stren gth for the effective crystal dimension is assessed. The LDOSs are calculat ed by means of a new convolution technique which allows to compute the resu lts faster than any conventional method.