Wednesday, June 26, 2024

nano-archimedes: A GNU Package for Nano-World Simulations

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In this article we will talk about nano-archimedes, yet another technology computer aided design (TCAD) software. The tool is based on Wigner equation, a convenient formulation of quantum mechanics in terms of phase-space and two many-body approaches, density functional theory (DFT) and a novel time-dependent ab-initio method.

Generally speaking, nano-archimedes can be used for the simulation of various technology-relevant situations that involve dynamics of electrons, such as transport in nanometer-scale semiconductor devices (for example, nanodevices) as well as dynamics of many-body problems in quantum chemistry (for example, molecular electronics).

The source code, written in C language, is a truly cross-platform code that can be compiled on a huge variety of machines (serial and parallel) without any particular effort. The first release of the software was made early this year under GPL version 3.

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Jean Michel Sellier, the main developer of nano-archimedes, put up every effort to free up more codes on quantum simulations so that a new user could have advanced researches in this area, instead of spending time coding from scratch.

Simulation of a wave packet in proximity of Coulombic potential using nano-archimedes
Simulation of a wave packet in proximity of Coulombic potential using nano-archimedes

Where nano-archimedes finds its applications
Before going deep into the approaches used for this software, let us take a look at some areas where nano-archimedes could be conveniently used.

Simulating post-CMOS designs. We are now in the so-called post- complementary metal oxide semiconductor (CMOS) era. With the continuous process of miniaturisation, the semiconductor’s active length has reduced to nanometers. At these scales quantum effects get prominent and the behaviour is quite different from what classical devices (like CMOS transistors) were designed for. Thus we require a new design paradigm that exploits the typical phenomena of quantum mechanics. The gap between theoretical comprehension and rapidly-advancing experiments can be effectively bridged with the help of quantum simulations using this software.

Practical design and optimisation of realistic solotronic devices. With advances in technology, modern electronics have the capability of manipulating single dopant atoms in semiconductor materials with atomic precision. These advancements took the name and shape as a unique branch of electronics called solotronics. Again, the theoretical comprehension cannot keep in pace with the experimental advancements that would eventually prevent the practical design and optimisation of solotronic devices. There is an increased demand for TCAD software that would help in a meaningful study of solotronic designs, which require a time-dependent, full quantum, multi-dimensional model, even in the relatively simpler case of ballistic regime. nano-archimedes is a free open source option that could ideally, and easily, fill up this space.

Simulating chemical systems. Researchers working in applied atomic physics and quantum chemistry try simulating quantum chemical systems like atoms and molecules with the help of quantum mechanical models. For determination of chemical properties of such a system, their electronic structure should be calculated. This involves numerical simulation of the quantum many-body problem, one of the most computationally-demanding and difficult problems in applied physics.

A pseudo-potential model computes the effective potential consisting of a super position of the core electrons and nucleus potentials. This model can thus be used to reduce the original problem to the simulation of valence electrons only. This modelling could be effectively done by Wigner formalism used in this software.

Ab-initio simulations of the quantum many-body problem
The term ab-initio simulations refers to simulations based on the first principles of quantum mechanics. These simulations are considered to be comparatively difficult and drained immense computational resources. Despite this, a lot of research interests exist in this area. Scientists believe that the tools developed on ab-initio principles can assist in various ways that can significantly improve various aspects of human life. The tool could make notable contributions, for instance, in the designing of new drugs, new materials and in the development of new information-processing technologies such as quantum computing devices.

nano-archimedes is based on the many-body Wigner equation, a sophisticated (and yet, very intuitive) formalism that allows ab-initio (Monte Carlo) simulations in phase-space, even for strongly-correlated systems.

Wigner formalism
Wigner formalism is a time-dependent, full quantum, multi-dimensional model based on the concept of a quasi-distribution function defined in phase-space. The approach is very intuitive and totally equivalent to the well-known Schrödinger model. In this model, an invertible Wigner-Weyl transform exists, which converts wave functions into quasi-distribution functions, and vice-versa. From this angle the situation is not any different from classical mechanics, where different formalisms like Newtonian, Lagrangian and Hamiltonian exist, and can be more or less convenient, depending on the system under consideration.

A system in Wigner formalism is described in terms of a quasi-distribution function defined in the phase-space of n-particles. Hence, we can consider this formalism as a very intuitive approach that is closer to the way experimentalists perform their experiments. Wigner equation allows simulation of many-body quantum systems in a time-dependent, multi-dimensional fashion. This allows scientists to simulate ground and excited states.



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