Development of a Nanoelectronic 3-D (NEMO 3-D) Simulator for Multimillion Atom Simulations and Its Application to Alloyed Quantum Dots

Material layers with a thickness of a few nanometers are common-place in today’s semiconductor devices. Before long, device fabrication methods will reach a point at which the other two device dimensions are scaled down to few tens of nanometers. The total atom count in such deca-nano devices is reduced to a few million. Only a small finite number of “free” electrons will operate such nano-scale devices due to quantized electron energies and electron charge. This work demonstrates that the simulation of electronic structure and electron transport on these length scales must not only be fundamentally quantum mechanical, but it must also include the atomic granularity of the device. Various elements of the theoretical, numerical, and software foundation of the prototype development of a Nanoelectronic Modeling tool (NEMO 3-D) which enables this class of device simulation on Beowulf cluster computers are presented. The electronic system is represented in a sparse complex Hamiltonian matrix of the order of hundreds of millions. A custom parallel matrix vector multiply algorithm that is coupled to a Lanczos and/or Rayleigh- Ritz eigenvalue solver has been developed. Benchmarks of the parallel electronic structure and the parallel strain calculation performed on various Beowulf cluster computers and a SGI Origin 2000 are presented. The Beowulf cluster benchmarks show that the competition for memory access on dual CPU PC boards renders the utility of one of the CPUs useless, if the memory usage per node is about 1-2 GB. A new strain treatment for the sp3s∗ and sp3d5s∗ tight-binding models is developed and parameterized for bulk material properties of GaAs and InAs. The utility of the new tool is demonstrated by an atomistic analysis of the effects of disorder in alloys. In particular bulk InxGa1−xAs and In0.6Ga0.4As quantum dots are examined. The quantum dot simulations show that the random atom configurations in the alloy, without any size or shape variations can lead to optical transition energy variations of several meV. The electron and hole wave functions show significant spatial variations due to spatial disorder indicating variations in electron and hole localization