Theory of space-charge-limited ballistic currents in nanostructures of different dimensionalities

A new unified approach to the description of ballistic unipolar-injection currents is proposed for nanostructures of different dimensionalities. It is shown that in the case of three-dimensional (3D), two-dimensional (2D), and one-dimensional (1D) structures the problem can be reduced to a nonlinear integral equation with a dimensionless parameter determining the coefficient of the universal current-voltage characteristic. The existence of a maximum for this parameter, which is analogous to the Bursian limit for a vacuum diode, is proven for each dimensionality. The current-voltage characteristics and the potential and charge distributions are calculated for 3D, 2D, and 1D structures.