 
Summary: Engineering Analysis with Boundary Elements 30 (2006) 925939
A Lagrangian approach for quantummechanical electrostatic analysis
of deformable silicon nanostructures
G. Li, N.R. AluruÃ
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology,
University of Illinois at UrbanaChampaign, Urbana, IL 61801, USA
Received 7 January 2006; accepted 12 March 2006
Available online 18 September 2006
Abstract
Semiconductor mechanical components of nanoelectromechanical systems (NEMS) typically undergo deformations when subjected to
electrostatic forces. Computational analysis of electrostatic NEMS requires an electrostatic analysis to compute the electrostatic forces
acting on the nanomechanical structures and a mechanical analysis to compute the deformation of the nanomechanical structures.
Typically, the mechanical analysis is performed by a Lagrangian approach using the undeformed position of the structures. However, the
electrostatic analysis is performed by using the deformed position of the nanostructures. The electrostatic analysis on the deformed
position of the nanostructures requires updating the geometry of the structures during each iteration. In this paper, based on a recently
proposed hybrid BIE/Poisson/Schro¨ dinger approach, we propose Lagrangian formulations for the BIE/Poisson/Schro¨ dinger equations
and solve the coupled Lagrangian BIE/Poisson/Schro¨ dinger's equations selfconsistently using the undeformed position of the
semiconductors to compute the charge distributions on the deformed semiconductors. The proposed approach eliminates the
requirement of updating the geometry and, consequently, significantly simplifies the procedure of coupled electromechanical analysis of
NEMS.
