Quantum Transport Theory of Resonant Tunneling Devices

Abstract

The ability to fabricate semiconductor heterostructures on the scale of a few atomic layers has led to the development of devices which exploit the quantum-mechanical wave properties of electrons in their operation. The quantum device which has recieved the most attention recently is the quantum-well resonant-tunneling diode (RTD).^1,2 This device shows a negative-resistance characteristic which is quantum-mechanical in origin, and is potentially a very fast device. Most of the theoretical work on this device has employed the formal theory of scattering, focusing on the behavior of pure quantum states which are asymptotically plane waves. While this approach should adequately describe the device under stationary conditions, it is poorly equipped to treat any sort of time-varying behavior. The reason for this is that the behavior of the RTD, and indeed any electronic device, is manifestly time-irreversible, and a proper notion of irreversibility cannot be introduced into pure-state quantum mechanics. A pure quantum state cannot evolve time-irreversibly. Models which attempt to introduce such behavior inevitably violate some fundamental physical law, usually the continuity equation. However, transitions between quantum states may proceed irreversibly if the system of interest interacts with an external system having a continuum of states. Such processes may be consistently described in terms of statistically mixed states, which are represented most simply by the single-particle density matrix.³ A description of a many-particle system in terms of such a single-particle distribution is generally termed a kinetic theory.⁴ The present paper describes such a theory of electron devices which incorporates quantum coherence effects (including tunneling).