Authors: E. Atanassov, T. Gurov, A. Karaivanova and M. Nedjalkov
Department of Parallel Algorithms
Institute for Parallel Processing - Bulgarian Academy of Sciences
E-mails:{emanouil, gurov, anet, mixi}@parallel.bas.bg
Abstract body:
SALUTE (Stochastic ALgorithms for Ultra-fast Transport in sEmiconductors) is an MPI
Grid application developed for solving computationally intensive problems in
quantum transport.
Monte Carlo (MC) methods for quantum transport in semiconductors and semiconductor
devices have been actively developed during the last decade. If temporal or spatial
scales become short, the evolution of the semiconductor carriers cannot be
described in terms of the Boltzmann transport [1] and therefore a quantum
description is needed. We note the importance of active investigations in this
field: nowadays nanotechnology provides devices and structures where the carrier
transport occurs at nanometer and femtosecond scales. As a rule quantum problems
are very computationally intensive and require parallel and Grid implementations.
SALUTE is a pilot grid application developed at the Department of Parallel
Algorithms, Institute for Parallel Processing - BAS where the stochastic approach
relies on the numerical MC theory applied to the integral form of the generalized
electron-phonon Wigner equation. The Wigner equation for the nanometer and
femtosecond transport regime is derived from a three equations set model based on
the generalized Wigner function [2]. The full version of the equation poses serious
numerical challenges. Two major formulations (for homogeneous and inhomogeneous
cases) of the equation are studied using SALUTE.
The physical model in the first formulation describes a femtosecond relaxation
process of optically excited electrons which interact with phonons in one-band
semiconductor [3]. The interaction with phonons is switched on after a laser pulse
creates an initial electron distribution. Experimentally, such processes can be
investigated by using ultra-fast spectroscopy, where the relaxation of electrons is
explored during the first hundreds femtoseconds after the optical excitation. In
our model we consider a low-density regime, where the interaction with phonons
dominates the carrier-carrier interaction. In the second formulation we consider a
highly non-equilibrium electron distribution which propagates in a quantum
semiconductor wire [4]. The electrons, which can be initially injected or optically
generated in the wire, begin to interact with three dimensional phonons. The
evolution of such process is quantum, both, in the real space due to the
confinements of the wire, and in the momentum space due to the early stage of the
electron-phonon kinetics. A detailed description of the algorithms can be found in
[5, 6, 7].
Monte Carlo applications are widely perceived as computationally intensive but
naturally parallel. The subsequent growth of computer power, especially that of the
parallel computers and distributed systems, made possible the development of
distributed MC applications performing more and more ambitious calculations.
Compared to the parallel computing environment, a large-scale distributed computing
environment or a Computational Grid has tremendous amount of computational power.
Let us mention the EGEE Grid which today consists of over 18900 CPU in 200 Grid
sites.
SALUTE solves an NP-hard problem concerning the evolution time. On the other hand,
SALUTE consists of Monte Carlo algorithms which are inherently parallel. Thus,
SALUTE is a very good candidate for implementations on MPI-enabled Grid sites. By
using the Grid environment provided by the EGEE project middleware, we were able to
reduce the computing time of Monte Carlo simulations of ultra-fast carrier
transport in semiconductors. The simulations are parallelized on the Grid by
splitting the underlying random number sequences.
Successful tests of the application were performed at several Bulgarian and South
East European EGEE GRID sites using the Resource Broker at IPP-BAS. The MPI version
was MPICH 1.2.6, and the execution was performed on clusters using both pbs and
lcgpbs jobmanagers, i.e. with shared or non-shared home directories. The test
results show excellent parallel efficiency. Obtaining results for larger evolution
times requires more computational power, which means that the application should
run on larger sites or on several sites in parallel. The application can provide
results for other types of semiconductors like Si or for composite materials.
Figure 1. Distribution of optically generated electrons in a quantum wire.
REFERENCES
[1] J. Rammer, Quantum transport theory of electrons in solids: A single-
particle approach, Reviews of Modern Physics, series 63 no 4, 781 - 817, 1991.
[2] M. Nedjalkov, R. Kosik, H. Kosina, and S. Selberherr, A Wigner Equation for
Nanometer and Femtosecond Transport Regime, In: Proceedings of the 2001 First IEEE
Conference on Nanotechnology, (October, Maui, Hawaii), IEEE, 277-281, 2001.
[3] T.V. Gurov, P.A. Whitlock, "An efficient backward Monte Carlo estimator for
solving of a quantum kinetic equation with memory kernel", Mathematics and
Computers in Simulation, Vol. 60, 85-105, 2002.
[4] M. Nedjalkov, T. Gurov, H. Kosina, D. Vasileska. and V. Palankovski,
Femtosecond Evolution of Spatially Inhomogeneous Carrier Excitations: Part I:
Kinetic Approach, to appear in Lecture Notes in Computing Sciences, Springer-Verlag
Berlin Heidelberg, Vol. 3743, (2006)
[5] E. Atanassov, T. Gurov, A. Karaivanova, and M. Nedjalkov, SALUTE – an MPI
GRID Application, in: Proceedings of the 28th International Convetion, MIPRO 2005,
May 30-June 3, Opatija, Croatia, 259 - 262, 2005.
[6] T.V. Gurov, M. Nedjalkov, P.A. Whitlock, H. Kosina and S. Selberherr,
Femtosecond relaxation of hot electrons by phonon emission in presence of electric
field, Physica B, vol 314, p. 301, 2002
[7] T.V. Gurov and I.T. Dimov, A Parallel Monte Carlo Method for Electron
Quantum Kinetic Equation, LNCS, Vol. 2907, Springer-Verlag, 153—160, 2004