3-D atomistic nanoelectronic modeling on high performance clusters: multimillion atom simulations

Electronic device scaling is ultimately limited by atomic dimensions. The simulation of electronic structure and electron transport on these length scales must be fundamentally quantum mechanical. This leads to computational models that account for fundamental physical interactions using an atomistic basis and tax even the largest available supercomputer when simulating measurable devices. The prototype development of a software tool that enables this class of simulation is presented. Realistically sized structures contain one million to tens of millions of atoms that need to be represented with an appropriate basis. The resulting sparse complex Hamiltonian matrix is of the order to tens of millions. A custom matrix–vector multiplication algorithm that is coupled to a Lanczos and/or Rayleigh–Ritz eigenvalue solver has been developed and ported to a Beowulf cluster as well as an Origin 2000. First benchmarking results of these algorithms as well as the first results of quantum dot simulations are reported.