Simulation of resonant-tunneling heterostructure devices

Abstract

The resonant-tunneling quantum-well diode is studied by numerical evaluation of the quantum-mechanical density matrix. This approach addresses such aspects of the tunneling problem as the effect of temperature, the transient response of a tunneling device, and the effects of dissipative interactions. The density matrix contains the spatial distribution of electrons and by calculating the time evolution of the density matrix the evolution of the electron density is observed. The density matrix is represented on a finite-difference basis in real space. Its time evolution is obtained by numerically integrating the quantum Liouville equation. To incorporate dissipative effects a simple relaxation term was added to Liouville equation. The boundary conditions were formulated so as to simulate the effects of Ohmic contacts. For the resonant-tunneling diode the simulations show a significant electron density in the quantum well, which builds up in a time on the order of 100 fs, when the structure is biased at resonance. For biases below the resonant value, the electron density in the well remains negligible.