Direct and exchange-correlation carrier interaction effects in a resonant tunnel diode

Abstract

Results are presented of a density functional calculation of the effects due to both electron-electron direct and exchange-correlation interactions on the effective, single-electron potential, the conduction electron density profile, the device transmission coefficient, and the current-voltage characteristics of a GaAs-AlGaAs quantum-well tunnel diode. The calculation proceeds by self-consistently solving the Kohn–Sham and Poisson equations, accounting for the strong, electric-field-induced nonequilibrium effects by employing a spatially varying chemical potential which is essential for maintaining net charge neutrality. The exchange potential used is the Dirac local-density approximation and the correlation potential is determined from the Wigner interpolation formula. The results show a number of interesting effects: it is found that the direct, electrostatic repulsion due to the buildup of charge within the spacer layers extends far beyond the device, well into the contact layers. Furthermore, the depression of carrier density within the quantum well leads to a reduction in the exchange-correlation screening of the direct interaction. Consequently, the total band bending in the vicinity of the device is enhanced by the exchange-correlation interaction, a result in contradiction with a previous Hartree–Fock calculation [K. Bandara and D. Coon, Appl. Phys. Lett. 53, 1865 (1988)]. In the case of a resonantly biased quantum well, the formation of an exchange-correlation hole due to the population of the resonant level within the quantum well is also observed. Finally, elastic scattering effects have been modeled by including random noise in the barrier conduction band. This causes a broadening of the resonant level within the quantum well, which in turn leads to an enhanced current flow through the overbiased device, although this enhancement is not as large as that seen experimentally. This suggests that the enhanced current flow in the overbiased device is likely to be due to inelastic scattering processes that are not included in this model.