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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 Inx Ga1−x As and
In0.6 Ga0.4 As 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.
Keywords: quantum dot, alloy, nanoelectronic, sparse matrix-vector multiplication, tight-binding,
optical transition, simulation.

If you reference this work in a publication, please cite as follows:

This work has been published at Gerhard Klimeck, Fabiano Oyafuso, Timothy B. Boykin, R. Chris Bowen, and Paul von Allmen, Computer Modeling in Engineering and Science (CMES) Volume 3, No. 5 pp 601-642 (2002).

• Klimeck, Gerhard; Boykin, Timothy (2008), "Development of a Nanoelectronic 3-D (NEMO 3-D ) Simulator for Multimillion Atom Simulations and Its Application to Alloyed Quantum Dots ," http://www.nanohub.org/resources/3819/.

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1. disorder
2. nanoelectronics
3. parallel programming
4. performance
5. quantum dots
6. software development
7. tight-binding