Simulation of Mesoscopic Devices with Bohm Trajectories and Wavepackets

Abstract

Following the idea that the great amount of information extracted from “realistic” Monte Carlo (MC) simulations helps to understand and improve the performance of eletron devices, we present a new proposal for the MC simulation of electronic transport in mesoscopic devices where quantum mechanical (QM) effects are important. In particular, we have developed a one-dimensional self-consistent quantum MC simulator to show the viability of our proposal by applying it to analyze static and dynamic properties of resonant tunneling diodes (RTD).

Our proposal can be explained (understood) from simple and intuitive physical ideas. We use Bohm trajectories to describe the quantum dynamics of electrons in the active region of the device. Among the various causal formulations of QM, the most widely known is the one due to Bohm [1],[2] that assures that the measurable results of standard quantum mechanics are perfectly reproduced by averaging the Bohm trajectories with adequate relative weights. Our simulator [3] defines a QM window (QW) which includes the double-barrier of the RTD, and restricts the QM treatment (i.e. each electron associated to a Bohm trajectory) to this window. Outside the QW, where the potential changes smoothly in the scale of the de Broglie wavelength of the carriers, the classical MC technique is used to simulate the electron transport.

On the other hand, we will also explain that in spite of the simplicity (from a physical point of view) of our proposal, it can be demonstrated that our model provides a particular solution of the Liouville equation. In this regard, we will present a deconstruction of our proposal in terms of the density matrix [4]. So, we can conclude that our proposal is a simple and intuitive way for solving the Liouville equation, at the same level, as the classical MC method provides a simple and intuitive solution of the Boltzman equation.We will also show some results for a typical RTD. The obtained results qualitatively resemble those obtained with other approaches when no scattering is considered. In particular, within our proposal we can define a new phase-space distribution (positive defined everywhere) that is quite similar to the Wigner distribution function. In conclusion, we will present a RTD simulation based on causal trajectories and we will show several examples to discuss the profit of the information (static and dynamic) extracted from it and the viability of our proposal.