Open Problems in Quantum Simulationin Ultra‐Submicron Devices

Abstract

Quantum transport is becoming more significant as device size shrinks. For example, as device sizes are scaled below 0.1 tm, the number of impurities becomes quite small, so that they are no longer homogeneously distributed throughout the device volume and the carriers are localized into quantum boxes, in that self-energy corrections produced by locally high carrier densities will lead to quantum dot formation. This leads to the need to discuss transport through an array of such quantum structures. Here, we discuss several issues which must be considered in treating the transport through such devices.

The onset of quantization in ultra-submicron semiconductor devices

“…Indeed, the previous success of Monte Carlo suggests that one might hope to find a trajectory-based Monte Carlo, nondeterministic picture for the Schrödinger equation and/or the density-matrix Liouville equation if these problems are overcome. However, the clear point is that it will no longer be adequate to consider the electron as a point particle in these future device simulations, and new approaches to kinetic pictures for transport are needed [1]. On the other hand, initial approaches can still utilize the particle picture providing that the real potential is replaced with the effective potential, with the smoothing arising from the size associated with the electron's wave packet.…”

“…1). We earlier argued about the need to properly introduce decoherence effects for the carriers in order to bound the device properties within the active region [1]. If the decoherence is introduced by adding an imaginary potential term to the Hamiltonian only in the contact regions, the size of this potential is inversely proportional to the phase coherence lifetime τ φ .…”

“…In this regime, the transport is expected to be dominated by quantum effects throughout the active region, even though quantum transport is not well established within a consistent conceptual framework [1]. Nevertheless, several approaches to simulation of semiconductor devices have appeared in which the transport is handled quantum mechanically [2].…”

Effective potentials and the onset of quantization in ultrasmall MOSFETs

“…Moreover, the effective potential carries the entire quantization effects, which arise from the non-zero size of the electron wavepacket. This means that the effective potential is already of a nature to be used for mixed wavefunctions, whereas the density gradient approaches have severe problems in this case, particularly near nodal points of the composite wavefunction [3]. By judicious choice of the extent of the wavepacket, excellent fit can be obtained for the quantum parameters in e.g.…”

“…In this regime, the transport is expected to be dominated by quantum effects throughout the active region, even though quantum transport is not well-established within a consistent conceptual framework [3]. Nevertheless, several approaches to simulation of semiconductor devices have appeared in which the transport is handled quantum mechanically [4].…”