Theory of hole resonant tunneling in quantum-well structures

A method of studying the hole resonant tunneling in quantum wells is proposed. Because of the band-mixing effect at ${\mathit{k}}_{\mathrm{\parallel }}$≠0,, the heavy and light holes can transform into each other in the process of tunneling. The transmission coefficients including h-h (heavy to heavy hole), h-l (heavy to light hole), l-l (light to light hole), and l-h are calculated as functions of hole energies, parallel wave vectors ${\mathit{k}}_{\mathrm{\parallel }}$, and electric-field bias. The resonant energies are consistent with the energies of bound states in the same quantum well. After the difference in the effective-mass parameters in the two materials is taken into account, the theoretical results are in agreement with those of the experiments. The theoretical method developed in the paper is applicable to the study of various kinds of tunneling transmission and subband structure problems in superlattices.