Quantized space-charge waves in quasi-2D

Abstract

Hot-electron transport theory of standard semiconductor layered structures predicts the occurrence of negative differential resistance (NDR) associated with inter-valley electron transfer, negative effective mass, and real-space transfer. An analysis of the growth of quantized space-charge waves in single and double heterostructures in which no real-space transfer occurs is presented. It is shown that, in contrast to the situation in bulk material, growth is a complicated function of wave-vector because of quantization effects. As a consequence, growth is limited by quantization effects and diffusion to small wave-vectors. To illustrate the effect of quantization clearly, the analysis is limited to growth within the lowest sub-band. In spite of quantization differences, a quantitative comparison can be made by a simple rescaling. Growth is shown to be severely limited to small wave-vectors and its rate turns out to be independent of the details of quantization, being that for extreme confinement. The rate maximizes for a wave-vector of about 4 × 105 cm−1 corresponding to a frequency of 700 GHz. The criterion for domain formation in GaN systems becomes n02L≥1020cm-3, where n0 is the areal density of electrons and L is the sample length. As far as growth rate is concerned, the restriction to the lowest sub-band represents a worst-case scenario.