Electric-field distribution in a quantum superlattice with an injecting contact: Exact solution

A very simple model describing steady-state electron transport along a quantum superlattice of a finite length taking into account an arbitrary electrical characteristic of the injecting contact is considered. In the singleminiband approximation, exact formulas for the spatial distribution of the electric field in the superlattice are derived for different types of contact. Conditions under which the field is uniform are identified. Analytical expressions for the current-voltage characteristics are obtained. In the context of the developed theory, the possibility of attaining uniform-field conditions in a diode structure with a natural silicon-carbide superlattice is discussed.