Semiconductor devices – primarily logic transistors and memory cells – have now been successfully scaled down in size for half a century, which brought about the increased performance and reduced costs making electronics ubiquitous in our daily lives. However, the long-predicted limits to scaling imposed by physics are now rapidly being approached and the need for novel device concepts is becoming a pressing issue. In this pursuit of novel concepts for nanoelectronics, simulation tools will further gain in importance and play a fundamental role to help understand and explore the feasibility of new materials, devices and systems.
Up to now, the effects of quantum mechanics have mostly been accounted for, instead of harnessed, in the design of nanoelectronic devices. A better understanding and practical grasp of quantum mechanics has opened the door to using quantum principles to engineer devices and systems. The need for simulation tools to help understand and design such quantum devices is of utmost importance. The simulation of electron transport in a semiconductor presents a fundamental simulation capability for nanoelectronics research and is approached in this work using the Wigner-Boltzmann equation.
The Wigner formalism provides a more intuitive description of quantum mechanics, compared to operator mechanics, since it is formulated in the phase space with functions and variables, which allows the adoption of models and analogies from semi-classical transport. The most important consequence of this is the ability to augment the Wigner quantum transport equation with Boltzmann scattering models, which yields the Wigner-Boltzmann equation.
The consideration of scattering in quantum transport is essential to study the decoherence of entangled electron states, which can represent qubits – the fundamental building blocks for quantum computing. The simulation of time-resolved quantum transport can help to understand highly miniaturized circuits dominated by quantum effects, which exhibit behaviour, e.g. oscillations, that cannot be explained using classical circuit theory. Currently, the only computationally viable formalism for scattering-aware, time-resolved quantum transport is found in the Wigner-Boltzmann equation.
This work presents a simulation tool which solves the equation in two dimensions using a Monte Carlo approach, based on particles with an affinity which carries the quantum information – the signed-particle method. The progress that has been made in recent years regarding, especially, computational issues, algorithms and their practical implementation is reported here.
The algorithms presented in this work represent the current state of the art for the signed-particle method and have been implemented in the Wigner Ensemble Monte Carlo tool, which forms part of the freely available ViennaWD simulation suite, to serve as a reference implementation.
The developed simulator allows the study of single electrons represented as wavepackets. First investigations of the dynamic behaviour and manipulation of such wavepackets is shown, using the concept of electrostatic lenses. An application of such a lens to improve the drive-current in a nano-scaled channel is demonstrated.