The present work considers the electronic spectra of a simple two-dimension
al (2D) cubic crystal and a three-dimensional (3D) GaAs crystal when a cons
tant electric field is applied. The 2D case is treated within the empirical
tight-binding (TB) model, taking one s-orbital per atom and accounting for
the interactions with neighbours up to fourth order. For the 3D case a sem
iempirical sp(3)s* TB model is used, taking into account the spin and first
neighbours. The local densities of states (LDOSs) have been calculated for
different field intensities, showing that for a sufficiently strong field
the 2D LDOS turns into the ID LDOS corresponding to chains perpendicular to
the field orientation. This is a novel observation achieved through the us
e of neighbours farther than the first. The 3D LDOS of a GaAs crystal proje
cted by a strong field on the [001] direction is found to coincide with the
2D LDOS of an isolated atomic layer.