Finite Element Analysis of Strain Effects on Electronic and Transport Properties in Quantum Dots and Wires

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 SixGe1−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.