Theoretical comparison of electron real-space transfer in classical and quantum two-dimensional heterostructure systems

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Abstract
We present a comparison of the effect of real‐space transfer on the electron drift velocities in both classical heterostructure systems, those in which spatial quantization effects do not occur, and in two‐dimensional heterostructure systems using an ensemble Monte Carlo simulation. The calculations for the two‐dimensional system are based on a first‐principles formulation of electron transport in a triangular quantum well system using an ensemble Monte Carlo code tailored to include the basic physics of two‐dimensional systems. In addition, we present an analysis, again based on a complete ensemble Monte Carlo simulation, of real‐space transfer from classical systems, ones in which no two‐dimensional gas is formed at the heterointerface. Electron drift velocities within the classical system greater than that possible in the constitutive bulk materials are thwarted by either real‐space transfer out of the high mobility material into the adjacent low mobility material or k‐space transfer within the narrow gap material itself. In contrast, higher electron drift velocities than that achievable in the bulk occur in a system in which two‐dimensional effects are present. In this case, when the electrons are confined within the two‐dimensional gas, their corresponding drift velocities are somewhat larger than within the bulk three‐dimensional system. We conclude that in electronic devices in which the electric field is applied parallel to the heterostructure layers, that the highest steady‐state electron velocities are achieved for transport within the two‐dimensional gas. In structures in which either a two‐dimensional system is not present or the carriers all reside outside of the quantized states, the steady‐state electron drift velocity is always less than or equal to the corresponding velocity in the bulk material due to the combined actions of real‐space and k‐space transfer.