GNU Archimedes

Not to be confused with Archimedes (CAD).

GNU Archimedes

Original author(s)	Jean Michel Sellier
Developer(s)	GNU project
Stable release	2.0.0
Operating system	GNU/Linux, UNIX
Type	TCAD
License	GPL
Website	Official website

Archimedes is a TCAD package for use by engineers to design and simulate submicron and mesoscopic semiconductor devices. Archimedes is free software and thus it can be copied, modified and redistributed under GPL. Archimedes uses the Ensemble Monte Carlo method and is able to simulate physics effects and transport for electrons and heavy holes in Silicon, Germanium, GaAs, InSb, AlSb, AlAs , AlxInxSb, AlxIn(1-x)Sb, AlP, AlSb, GaP, GaSb, InP and their compounds (III-V semiconductor materials), along with Silicon Oxide. Applied and/or self-consistent electrostatic and magnetic fields are handled with the Poisson and Faraday equations.

The GNU project has announced on May 2012 that the software package Aeneas will be substituted by Archimedes, making this one the GNU package for Monte Carlo semiconductor devices simulations.

Introduction

Archimedes is the GNU package for semiconductor device simulations that has been released for the first time on 2005 under GPL. It has been created by Jean Michel Sellier who is, since then, the leader of the project and the main developer. It is a Free software and thus it can be copied, modified and redistributed under GPL. This is the one of the big advantages of using Archimedes.

Archimedes belongs to the well-known family of TCAD software, i.e. tools utilized to assist the development of technologically relevant products. In particular, this package assists engineers in designing and simulating submicron and mesoscopic semiconductor devices. In a next-future version Archimedes will also be able to simulate nanodevices, using the Wigner Monte Carlo formalism (an experimental release can be found at ). Today Archimedes is used in several big companies for simulation and production purposes.

Archimedes is also useful for teaching purposes since everybody can access the sources, modify and test them. Today, it is used for teaching courses in several hundreds universities all around the world. Furthermore, a simplified version, developed for students, is available on nanoHUB.org.

The Ensemble Monte Carlo method is the method that Archimedes uses to simulate and predict the behavior of a devices. Being the Monte Carlo very stable and reliable, Archimedes can be used to know the characteristics of a device even before this last is built.

The physics and geometry of a device is described simply by a script, which makes, in this sense, Archimedes a powerful tool for the simulation of quite general semiconductor devices.

Archimedes is able to simulate a plenty of physics effects and transport for electrons and heavy holes in Silicon, Germanium, GaAs, InSb, AlSb, AlAs , AlxInxSb, AlxIn(1-x)Sb, AlP, AlSb, GaP, GaSb, InP and their compounds (III-V semiconductor materials), along with Silicon Oxide, the applied and/or self-consistent electrostatic and magnetic fields by means of Poisson and Faraday equation. It is, also, able to deal with heterostructures.

The Ethical Motivations, a New Paradigma in Science

Archimedes has been created after observing the situation of semiconductor simulations around the world. One easily observes that the all codes developed for simulation are usually not free and/or proprietary codes. That is a very bad situation, at least for academic purposes, since it forces people to reinvent the wheel every time a piece of code is needed. This surely slows down the progress of Science (imagine you had to rediscover the Newtonian laws every time you need them...).

The actual situation is that we have a huge amount of papers describing a lot of numerical methods for advanced simulations of semiconductor devices, but nobody can access a single code on which to build new and even more advanced methods.

So, today, every university (and even every group in a university) has its own Monte Carlo simulator, its own NEGF simulator and so on.. Would not it be better if we could avoid this incredible duplication of efforts all around the world?

That is why Archimedes has been created.

Boltzmann transport equation

The Boltzmann transport equation model has been the main tool used in the analysis of transport in semiconductors. The BTE equation is given by:

${\frac {\partial f}{\partial t}}+{\frac {1}{\hbar }}\nabla _{k}E(k)\nabla _{r}f+{\frac {qF(r)}{\hbar }}\nabla _{k}f=\left[{\frac {\partial f}{\partial t}}\right]_{\mathrm {collision} }$

$v={\frac {1}{\hbar }}\nabla _{k}E(k)$

The distribution function, f, is a dimensionless function which is used to extract all observable of interest and gives a full depiction of electron distribution in both real and k-space. Further, it physically represents the probability of particle occupation of energy k at position r and time t. In addition, due to being a seven-dimensional integro-differential equation (six dimensions in the phase space and one in time) the solution to the BTE is cumbersome and can be solved in closed analytical form under very special restrictions. Numerically, solution to the BTE is employed using either a deterministic method or a stochastic method. Deterministic method solution is based on a grid-based numerical method such as the spherical harmonics approach, whereas the Monte Carlo is the stochastic approach used to solve the BTE.

Monte Carlo method

The semiclassical Monte Carlo method is a statistical method used to yield exact solution to the Boltzmann transport equation which includes complex band structure and scattering processes. This approach is semiclassical for the reason that scattering mechanisms are treated quantum mechanically using the Fermi's Golden Rule, whereas the transport between scattering events is treated using the classical particle notion. The Monte Carlo model in essence tracks the particle trajectory at each free flight and chooses a corresponding scattering mechanism stochastically. Two of the great advantages of semiclassical Monte Carlo are its capability to provide accurate quantum mechanical treatment of various distinct scattering mechanisms within the scattering terms, and the absence of assumption about the form of carrier distribution in energy or k-space. The semiclassical equation describing the motion of an electron is

${\frac {dr}{dt}}={\frac {1}{\hbar }}\nabla _{k}E(k)$

${\frac {dk}{dt}}={\frac {qF(r)}{\hbar }}$

where F is the electric field, E(k) is the energy dispersion relation, and k is the momentum wave vector. To solve the above equation, one needs strong knowledge of the band structure (E(k)). The E(k) relation describes how the particle moves inside the device, in addition to depicting useful information necessary for transport such as the density of states (DOS) and the particle velocity. A Full-band E(K) relation can be obtained using the semi-empirical pseudopotential method.

4-graphs plot of a Silicon diode simulated using Archimedes.

4-graphs plot of a Silicon MESFET simulated using Archimedes.

Example 1: Silicon Diode

A simple 2D diode simulation using Archimedes is reported in order to show the reliability of the package. The diode is a simple n+-n-n+ structure, the channel length being equal to 0.4 micron. The diode has two n+ regions of 0.3 micron (i.e. the total length is 1.0 micron ). The density in the doping regions are n+=1.e23/m^3 and n=1.e21/m^3 respectively. The applied voltage is equal to 2.0 Volts.

The device is totally defined by means of an input deck in ASCII format.

Example 2: Silicon MESFET

A 2D Silicon MESFET simulation using Archimedes is presented. Archimedes takes into account all the relevant scattering mechanisms.

External links

• Official website
• nano-archimedes website
• draft of a complete manual
• nanoHUB website
• user manual