 
Summary: Combined semiclassical and effectivemass Schrödinger approach for multiscale analysis
of semiconductor nanostructures
Yang Xu and N. R. Aluru*
Beckman Institute for Advanced Science and Technology, University of Illinois at UrbanaChampaign, Urbana, Illinois 61801, USA
Received 26 December 2006; published 3 August 2007
A multiscale model, seamlessly combining semiclassical and quantummechanical theories, is proposed for
electrostatic analysis of semiconductor nanostructures. A quantum potential criterion is used to determine if a
local region in the semiconductor is semiclassical or quantum mechanical. If the local physical model is
semiclassical, the charge density is directly computed by the semiclassical theory. If the local physical model
is quantum mechanical, the charge density is calculated by using the theory of local density of states LDOS .
The LDOS is efficiently calculated from the Green's function by using Haydock's recursion method where the
Green's function is expressed as a continued fraction based on the local effectivemass Schrödinger Hamil
tonian. Once the charge density is determined, a Poisson equation is solved selfconsistently to determine the
electronic properties. The accuracy and efficiency of the multiscale method are demonstrated by considering
examples from nanoelectromechanical systems NEMS and nanoelectronics. Furthermore, the regions where
quantummechanical effects are significant are identified for the NEMS and nanoelectronic device structures.
DOI: 10.1103/PhysRevB.76.075304 PACS number s : 85.30.De, 85.85. j, 85.35. p, 41.20.Cv
I. INTRODUCTION
Semiconductor nanostructures, such as nanoelectrome
chanical systems NEMS , semiconductor heterostructures,
