Self-consistent analysis of resonant tunneling in a two-barrier–one-well microstructure

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Abstract
A self-consistent solution to the resonant tunneling problem is presented based on the simultaneous solution of the time-independent Schrödinger equation with the Poisson equation. The solution is obtained from a piecewise linear matching of Airy functions. The model is used to explore the effects of the self-consistent electron charge on the transmissivity and current-voltage characteristics of a double-barrier single-well GaAs-AlGaAs device. It is found that the self-consistent potential always acts to shift the negative differential resistance onset voltage to large positive values. The self-consistent field effectively acts to screen the positive applied voltage. Therefore, the effects of the self-consistent field can essentially be modeled by a smaller applied positive bias. It is further found that the effects of the self-consistent field are most prevalent at high temperatures, ∼300 K, and at high dopings, >1.0×1018. It is necessary to include the self-consistent effects then when designing resonant tunneling structures within these constraints.