Finite element analysis of strain effects on electronic and transport properties in quantum dots and wires

Abstract

Lattice mismatch in epitaxial layered heterostructures with small characteristic lengths induces large, spatially nonuniform strains. The components 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 Schrödinger 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 wavefunctions 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 Si x Ge 1−x 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 and composition dependent strain effects are examined for both devices. In both the quantum dot and the quantum wire, the strain effects on the wavefunctions and energies of confined states are evident in the calculated densities of confined states in the structures, which are found to be consistent with experimentally measured tunneling current/voltage curves for resonant tunneling diodes.1

Optical schemes for quantum computation in quantum dot molecules

“…These include a full pseudopotential calculation, 67,68,69 finite element analysis, 70 plane wave expansion 71 and the use of finite differences. 72 We employ a similar strategy to that in Refs.…”

Quantum field induced strains in nanostructures and prospects for optical actuation

“…Andreev et al, 1999;Bellaiche et al, 1996;Bernard and Zunger, 1994;Cusack et al, 1996;Davies, 2000;Davies et al, 2002;Downes et al, 1997;Ellaway and Faux, 2002;Glas, 2001;Grundmann et al, 1995;Jiang and Singh, 1997;Johnson and Freund, 2001;Johnson et al, 1998;Keating, 1966;Korkusinski and Hawrylak, 2001;Makeev and Madhukar, 2003;Martin, 1970;Migliorato et al, 2002;Nishi et al, 1994;Pan and Yang, 2001;Pearson and Faux, 2000;Pryor, 1998;Pryor et al, 1998;Pryor et al, 1997;Romanov et al, 2001;Shin et al, 2003;Stillinger and Weber, 1985;Tadic et al, 2002;Yang et al, 1997;Yu and Madhukar, 1997a,b). The envelope function approach is attractive, simple and physically intuitive and thus widely used for both bulk semiconductors and nanostructures.…”

“…This coupling between strain and electronic structure, particularly in quantum dots where elastic fields are highly nonuniform, has been widely studied, and is relevant for many emerging applications (e.g. Jiang and Singh, 1997;Johnson et al, 1998;Stier et al, 1999). In particular, the reader is referred 0020-7683/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved.…”

Meshfree implementation for the real‐space electronic‐structure calculation of crystalline solids

“…At this scale, it is well known that mechanical analysis is often crucial in examining the electronic, magnetic, optical and transport properties of materials [1][2][3][4][5][6]. For example, the strain analysis of a quantum dot is essential for the studies of its electronic structure and transport properties [1,[4][5][6]. Simulation procedures for quantum heterostructures typically consist of modelling the strain-induced potential and solving the Schrödinger equation with the appropriate Hamiltonain.…”