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Pan Stanford Publishing eBooks

Subquantum Accelerating Universe

Pedro F. González-Dı́az, Alberto Rozas-Fernández

Published Jun 4, 2012• 1 citation
Publisher

Abstract

The necessity of faster and smaller devices is pushing the electronic industry into developing electron devices with solid-state structures of a few nanometers driven by picosecond signals. Electron dynam- ics in such scenarios is in general governed by quantum mechanical laws. This chapter is devoted to discuss how Bohmian mechanics can help us to understand and model the behavior of novel electron devices at the nanometer and picosecond scales. The adaptation of Bohmian mechanics to electron transport in open systems leads to a quantum Monte Carlo algorithm, where randomness appears because of the uncertainties in the number of electrons, their energies, and the initial positions of the (Bohmian) trajectories. A general, versatile, and time-dependent three-dimensional (3D) elec- tron transport simulator for nanoelectronic devices, namedBITLLES (Bohmian Interacting Transport for nonequiLibrium eLEctronic Structures), is presented, showing its ability for a full prediction (direct current [DC], alternating current [AC], fluctuations, etc.) of the electrical characteristics of any nanoelectronic device. See the website http://europe.uab.es/bitlles . As a typical example of the BITLLES capabilities, we discuss the performance of a resonant tunneling diode.

DOI
10.1201/b12311-10

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The necessity of faster and smaller devices is pushing the electronic industry into developing electron devices with solid-state structures of a few nanometers driven by picosecond signals. Electron dynam- ics in such scenarios is in general governed by quantum mechanical laws. This chapter is devoted to discuss how Bohmian mechanics can help us to understand and model the behavior of novel electron devices at the nanometer and picosecond scales. The adaptation of Bohmian mechanics to electron transport in open systems leads to a quantum Monte Carlo algorithm, where randomness appears because of the uncertainties in the number of electrons, their energies, and the initial positions of the (Bohmian) trajectories. A general, versatile, and time-dependent three-dimensional (3D) elec- tron transport simulator for nanoelectronic devices, namedBITLLES (Bohmian Interacting Transport for nonequiLibrium eLEctronic Structures), is presented, showing its ability for a full prediction (direct current [DC], alternating current [AC], fluctuations, etc.) of the electrical characteristics of any nanoelectronic device. See the website http://europe.uab.es/bitlles . As a typical example of the BITLLES capabilities, we discuss the performance of a resonant tunneling diode.
Today, the necessity of faster and smaller devices is pushing the electronic industry into developing electron devices with solid-state structures of few nanometers. In these dimensions electron dynamics are in general governed by quantum mechanical laws. We have recently shown that Bohmian trajectories allow a direct treatment of the many-particle interaction among electrons with an accuracy comparable to DFT techniques. In this article we present a general, versatile and time-dependent 3D quantum electron transport simulator, named BITLLES (Bohmian Interacting Transport in Electronic Structures), based on Bohmian trajectories for nanoelectronic devices. As a numerical example, we show the ability of BITLLES simulator to predict the electrical characteristics (DC, AC and fluctuations) of a Resonant Tunneling Diode.
This chapter discusses how Bohmian mechanics can help us to understand and model the behavior of novel electron device prototypes at the nanometer and picosecond scales. It shows that how Bohmian mechanics can help us in the understanding and designing the upcoming electron device prototypes. The chapter also discusses how Bohmian mechanics can help us to study many-particle quantum electron transport phenomena in nanoelectronic devices and an important advantage of Bohmian mechanics: its ability to treat many-particle systems. It explains the birth of the electronics and its evolution towards nanoelectronics. The chapter also shows that the Bohmian perspective provides useful tools when dealing with the continuous measurement of the electrical current in nanodevices. The former appears at nonzero temperature, where the thermal agitation causes the occupation of energy states to fluctuate. The practical expressions for the computation of the current fluctuations within Bohmian mechanics are quite simple.
With the aim of manufacturing faster and smaller devices, the electronic industry is today entering into the nanoscale and the high frequency regimes. In this particular scenario, the dynamics of the electron charge becomes affected by quantum mechanical laws, both, for its spatial or temporal description. We have recently shown that Bohmian trajectories allow a direct treatment of the time-dependent many-particle interaction among electrons with an accuracy comparable to Density Functional Theory techniques. In addition, Bohmian mechanics, by combining wave functions and trajectories, provides a very simple description on how to describe multi-time measurements in quantum scenarios. Using the previous formalism, in this work we present a general purpose time-dependent 3D quantum electron transport simulator named BITLLES (Bohmian Interacting Transport in large low-dimensional Electronic Structures) especially indicated for AC, transients and noise predictions. As a numerical example of its capabilities, we compute the full electrical characteristics (DC, High frequency and fluctuations) of a Resonant Tunneling Diode.
With the aim of manufacturing faster and smaller devices, the electronic industry is today approaching both the nano and the picosecond scales. In this particular scenario, electron dynamics becomes strongly correlated both in space and time. We have recently shown that Bohmian trajectories allow a direct treatment of the time-dependent many-particle interaction among electrons with accuracy comparable to Density Functional Theory techniques. In this work we present a general purpose time-dependent 3D quantum electron transport simulator based on Bohmian trajectories that we call BITLLES. As a numerical example of its capabilities, we compute the full electrical characteristics (DC, High frequency and fluctuations) of a Resonant Tunneling Diode.
After the seminal work of R. Landauer in 1957 relating the electrical resistance of a conductor to its scattering properties, much progress has been made in our ability to predict the performance of electron devices in the DC (stationary) regime. Computational tools to describe their dynamical behavior (including the AC, transient and noise performance), however, are far from being as trustworthy as would be desired by the electronic industry. While there is no fundamental limitation to correctly modeling the high-frequency quantum transport and its fluctuations, certainly more careful attention must be paid to delicate issues such as overall charge neutrality, total current conservation, or the back action of the measuring apparatus. In this review, we will show how the core ideas behind the Bohmian formulation of quantum mechanics can be exploited to design an efficient Monte Carlo algorithm that provides a quantitative description of electron transport in open quantum systems. By making the most of trajectory-based and wave function methods, the BITLLES simulator, a free software developed by the authors, extends the capabilities that the semi-classical Monte Carlo simulation technique has offered for decades (DC, AC, noise, transients) to the quantum regime.
Moore’s law has been the milestone for electronics improvement, and the cause for the exponential growth in our computational abilities and for reaching nanoscale electron devices. At such dimensions, classical simulation tools must be substituted by quantum ones. Such substitution implies to tackle new fundamental problems. First, the many-body problem makes (almost) impossible the exact simulation of many particles scenarios. Second, the measurement problem is especially relevant in high-frequency scenarios where multi-time measurements are mandatory. Alternatively to the orthodox theory, Bohmian mechanics emerges as a quantum theory which is specially well-equipped for the simulation of high-frequency characteristic of quantum electron devices. The Bohmian theory provides the conditional wave function that guides particles with well-defined positions. In this thesis, I explored quantum transport using Bohmian mechanics, putting special emphasis to graphene, a 2D material with linear bandstructure, which is expected to play an important role in the next future electronics. Differently from other materials, graphene obeys the bispinor Dirac equation, electrons behave as massless particles, exhibiting exotic behaviors, such as the Klein Tunneling effect. During the thesis, the quantum BITLLES simulator has been improved to correctly model electron nanodevices with either linear (by the inclusion of the complex bispinor Dirac equation) or parabolic bandstructures in either ballistic or dissipative (by the inclusion of the complete positive Bohmian scattering approach) systems. Thus, the BITLLES has become the candidate for substituting the versatile semiclassical Monte Carlo approach in the quantum regime, while keeping the versatility to predict DC, AC and noise performances. As practical applications, during the thesis, unexpected scattering probabilities in a Hong-Ou-Mandel experiment were predicted. In addition, different current-voltage characteristics were analyzed. Finally, a new limit (due to the discrete nature of charge) for ultra-small logic applications working at THz frequencies was predicted.