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.

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.

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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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The iterative Monte Carlo method—a general time-dependent approach for partial differential equations that can deal with general initial and boundary conditions—is utilised to numerically solve Wigner equation. Monte Carlo techniques scale incredibly well on parallel machines, allowing the simulation of comparatively very complex systems. We have discussed about Monte Carlo simulations in detail in March issue of EFY.

The Wigner formalism is nowadays applied to a plethora of different situations. For example, recently it has been utilised in the field of simulation of semiconductor devices, post-CMOS design and quantum chemistry (Wigner DFT and many-body techniques), among others. nano-archimedes software is based on this Wigner formalism and could be used in advanced research in these areas.

Signed particle formulation to be introduced into nano-archimedes
The latest development in nano-archimedes is based on a brand new formulation of quantum mechanics called signed particle formulation, which is currently under review. This is an important generalisation of Wigner MC method provided with a physical interpretation. In this novel formulation, a quantum system is described in terms of virtual Newtonian field-less particles that can interact with a potential by means of creation and annihilation of particles only.


Being a very intuitive approach, thus easy to implement, the signed particle formulation proves to be more convenient than other approaches in certain cases of quantum system simulations. “Even though the signed particle formulation is mathematically equivalent to other formulations, such as Schrödinger and Wigner, it has strong advantages to be intuitive, highly parallelisable and easy to extend to situations such as inelastic scattering,” says J.M. Sellier.

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Download latest version of the software: click here

Boosting up scientific innovations
In the initial days of research, there are times when we do not know where to start the work. If we consider the semiconductor industry, researches around the world have been so advanced that we are now dealing in nano-scale sizes. Unfortunately, the people who are new to this field of research have to begin their work from scratch, as every work will be patented and not available freely. This will waste a lot of time, effort and money.

Providing the source codes of Archimedes and nano-archimedes as open source is a positive step in this regard, as more researchers could benefit from it and could spend their time more fruitfully. Let us hope this step from the developers will inspire other researchers to release more free scientific codes, and thereby enhance more scientific advancements in the society.

The author is an electronics enthusiast from Kerala



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