Collisionless space-charge limited currents in semiconductors with nonparabolic bands

Abstract

The current-voltage relation for space-charge limited collisionless flow is computed for a model semiconductor with a hyperbolic band structure as deduced from two-band <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{k} \cdot \bar{p}</tex> perturbation theory. The expected current is reduced significantly below the constant effective mass value for voltages in excess of the bandgap, and the high-voltage asymptotic relation is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</tex> rather than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V^{3/2}</tex> .