Wigner-Boltzmann Particle Simulations

Computational tools for simulation of electronic devices bring to the semiconductor industry a considerable reduction of the development costs. The classical era of device simulation in terms of charge transport and electrical behavior can be characterized by the keywords `Boltzmann equation` and `Silicon`. However, the nano-era of semiconductor devices involves novel materials and architectures, along with a number of novel phenomena which must be taken into account. While some of them can be described in classical terms, others, being dominant at nanometer and femtosecond scales, require multi-dimensional quantum description capable of taking into account both, purely coherent processes such as quantization and tunneling, as well as phase breaking processes of interactions with the lattice. The aim of this project is threefold: (i)Upgrade of the in-home VMC particle simulator to a multi-dimensional, parallel, self-consistent, stationaryransient ensemble Monte Carlo routine with statistical enhancement. According the road-map for VMC this is a necessary step for a further expansion of the simulator towards complex physical models imposed by novel materials and structures. (ii)Development of a two-dimensional particle quantum simulator based on the WIgner ENSemble (WIENS) union. (iii)Further development of WIENS as a union of theoretical and numerical approaches and algorithms for particle simulation of quantum phenomena in nanostructures. The evolution principle is the common linking element for these activities. The single-particle simulator VMC accounts for most cubic semiconductors. The material modules related to band structures, phonon scattering models, and alloy compositions will be adopted directly by the ensemble counterpart. The quantum simulator is built as an extension of the two-dimensional ensemble routine re-utilizing the models for boundary conditions, particle evolution, and estimators for physical averages. The algorithms and parameter settings of WIENS are used consistently with the particle generation-annihilation scheme to construct the Wigner part of the code. The classical and Wigner simulators are applied for simulation of actual devices where Boltzmann or quantum-dissipative conditions of transport dominate the device behavior. The work on WIENS continues to address still open physical and numerical issues related to the Wigner picture of statistical mechanics, which are resolved by theoretical analysis and numerical experiments. An idea is pursued for the cases where the transport is close to coherent or is determined by processes of dissipation. Under the assumption that the Wigner function in the considered limiting case is known, we theoretically and numerically investigate the equation for the corresponding correction. The approach involves an interface with other numerical methods which are efficient in providing the limiting solution. Active collaboration with groups from the home and international institutions is envisaged.

The aim of FWF Project P21685-N22 is to develop a union of theoretical and numerical approaches for a particle-based simulation of quantum phenomena in nanostructures. While the particle concept is inherent to classical mechanics and particle-based models provide deep insight into phenomena governing generations of microelectronic devices, the emerging nanoelectronics require wave-based quantum mechanics. Nevertheless, the particle concept may be retained in the quantum world through use of the Wigner function, interpreted as a quantum analog of the classical distribution function. This correspondence is further expanded in what forms the basic theoretical pillar of ViennaWD: a model explaining the quantum evolution through generation/annihilation (g/a) of positive and negative particles. A very important project outcome is the result that the g/a process is a stochastic alternative to Newton's acceleration. It follows that the model bridges purely quantum with classical evolution: a wide range of phenomena existing between these ultimate transport regimes may be addressed, such as processes of decoherence: the environment-induced transition from a quantum to a classical state. Flagship project results are obtained from the Wigner study of an electron state Decoherence (WD) due to crystal lattice vibrations (phonons). These impact technologically important disciplines like nanoelectronics and quantum computing. It is shown that the domination of classical or quantum behavior depends on the scales of the involved physical quantities. A notion called scaling theorem is derived, which gives deep insight in the way of destruction of the quantum information and explains why the current nanometer transistors may be still modeled by classical methods. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the WignerBoltzmann evolution is demonstrated. Numerical studies of the role of the interfaces on the formation of the electron state in nanotransitors show that e.g. rough but specular surfaces preserve the time reversability while flat but diffusive surfaces causes decoherence. Applications to trapping/scattering electron dynamics around oxide/channel centers of two dimensional nanoscale MOSFETs revealed quantum effects like non-locality, blocking of channel regions and capture constants. This established the model as a powerful research tool and answers the basic challenge of the project: quantum particle simulations beyond 1D structures. Optimization and large scale MPI parallelization have been successfully completed to address precision, memory and run time aspects preparing the method for stationary, self-consistent applications. The ViennaWD union is implemented in algorithms that form a suite of particle-based simulation tools, publicly available at http://viennawd.sourceforge.net/