文档介绍：JOURNAL OF APPLIED PHYSICS VOLUME 84, NUMBER 7 1 OCTOBER 1998
Finite element analysis of strain effects on electronic and transport
properties in quantum dots and wires
H. T. Johnson, L. B. Freund, C. D. Akyu¨z, and A. Zaslavsky
Division of Engineering, Brown University, Providence, Rhode Island 02912
͑Received 30 April 1998; accepted for publication 6 July 1998͒
Lattice mismatch in epitaxial layered heterostructures with small characteristic lengths induces
large, spatially nonuniform strains. ponents of the strain tensor have been shown
experimentally to affect the electronic properties of semiconductor structures. Here, a technique is
presented for calculating the influence of strain on electronic properties. First, the linear elastic
strain in a quantum dot or wire is determined by a finite element calculation. A strain-induced
potential field that shifts and couples the valence subbands in the structure is then determined from
deformation potential theory. The time-independent Schro¨dinger equation, including the
nonuniform strain-induced potential and a potential due to the heterostructure layers, is then solved,
also by means of the finite element method. The solution consists of the wave functions and energies
of states confined to the active region of the structure; these are the features which govern the
electronic and transport properties of devices. As examples, two SixGe1Ϫx submicron resonant
tunneling devices, a quantum wire with two-dimensional confinement and a quantum dot with
three-dimensional confinement, are analyzed. Experimentally measured resonant tunneling current
peaks corresponding to the valence subbands in the material are modeled by generating densities of
confined states in the structures. Size position-dependent strain effects are examined for
both devices. In both the quantum dot and the quantum wire, the strain effects on the wave functions
and energies of confined states are evident in the calculated