Practical application of zne-folding concepts in tight-binding calculations

Modern supercell algorithms, such as those used in treating arrays of quantum dots or alloy calculations, are often founded upon local basis representations. Such local basis representations are numerically efficient, allow considerations of systems consisting of millions of atoms, and naturally map into carrier transport simulation algorithms. Even when treating a bulk material, algorithms formulated on a local basis generally cannot produce an Eskd dispersion resembling that of a simple unit cell, due to zone folding. This paper provides an exact method for perfect supercells to unfold the zone folded Eskd diagrams into a meaningful bulk dispersion relation. In addition, a modification to the algorithm for use with imperfect supercells is presented. With this method, questions such as algorithm verification, dispersions in nanowires, and dispersions in finite supercell heterostructures can be addressed

The discretized Schrodinger equation and simple models for semiconductor quantum wells

The discretized Schr¨odinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schr¨odinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schr¨odinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

Full 3D Quantum Transport Simulation of Atomistic Interface Roughness in Silicon Nanowire FETs

The influence of interface roughness scattering (IRS) on the performances of silicon nanowire field-effect transistors (NWFETs) is numerically investigated using a full 3D quantum transport simulator based on the atomistic sp3d5s* tight-binding model. The interface between the silicon and the silicon dioxide layers is generated in a real-space atomistic representation using an experimentally derived autocovariance function (ACVF). The oxide layer is modeled in the virtual crystal approximation (VCA) using fictitious SiO2 atoms. -oriented nanowires with different diameters and randomly generated surface configurations are studied. The experimentally observed ON-current and the threshold voltage is quantitatively captured by the simulation model. The mobility reduction due to IRS is studied through a qualitative comparison of the simulation results with the experimental results

Brillouin-zone Unfolding of Perfect Supercells Having Nonequivalent Primitive Cells Illustrated with a Si/Ge Tight-Binding parameterization

Numerical calculations of nanostructure electronic properties are often based on a nonprimitive rectangular unit cell, because the rectangular geometry allows for both highly efficient algorithms and ease of debugging while having no drawback in calculating quantum dot energy levels or the one-dimensional energy bands of nanowires. Since general nanostructure programs can also handle superlattices, it is natural to apply them to these structures as well, but here problems arise due to the fact that the rectangular unit cell is generally not the primitive cell of the superlattice, so that the resulting E(k) relations must be unfolded to obtain the primitive- cell E(k) curves. If all of the primitive cells in the rectangular unit cell are identical, then the unfolding is reasonably straightforward; if not, the problem becomes more difficult. Here, we provide a method for zone unfolding when the primitive cells in a rectangular cell are not all identical. The method is applied to a Si(4)Ge(4) superlattice using a set of optimized Si and Ge tight-binding strain parameters

Effects of Interface Roughness Scattering on Radio Frequency Performance of Silicon Nanowire Transistors

The effects of an atomistic interface roughness in n-type silicon nanowire transistors (SiNWT) on the radio frequency performance are analyzed. Interface roughness scattering (IRS) is statistically investigated through a three dimensional full-band quantum transport simulation based on the sp3d5s?* tight-binding model. As the diameter of the SiNWT is scaled down below 3 nm, IRS causes a significant reduction of the cut-off frequency. The fluctuations of the conduction band edge due to the rough surface lead to a reflection of electrons through mode-mismatch. This effect reduces the velocity of electrons and hence the transconductance considerably causing a cut-off frequency reduction

Conduction band tight-binding description for silicon applied to phosphorous donors

A tight-binding parametrization for silicon, optimized to correctly reproduce effective masses as well as the reciprocal space positions of the conduction-band minima, is presented. The reliability of the proposed parametrization is assessed by performing systematic comparisons between the descriptions of donor impurities in Si using this parametrization and previously reported ones. The spectral decomposition of the donor wavefunction demonstrates the importance of incorporating full band effects for a reliable representation, and that an incomplete real space description results from a truncated reciprocal space expansion as proposed within the effective mass theory.Comment: 4 pages, 3 figure

Valley Degeneracies in (111) Silicon Quantum Wells

(111) Silicon quantum wells have been studied extensively, yet no convincing explanation exists for the experimentally observed breaking of 6 fold valley degeneracy into 2 and 4 fold degeneracies. Here, systematic sp3d5s* tight-binding and effective mass calculations are presented to show that a typical miscut modulates the energy levels which leads to breaking of 6 fold valley degeneracy into 2 lower and 4 raised valleys. An effective mass based valley-projection model is used to determine the directions of valley-minima in tight-binding calculations of large supercells. Tight-binding calculations are in better agreement with experiments compared to effective mass calculations.Comment: 4 pages, 3 figures, to appear in Applied Physics Letter

Gate induced g-factor control and dimensional transition for donors in multi-valley semiconductors

The dependence of the g-factors of semiconductor donors on applied electric and magnetic fields is of immense importance in spin based quantum computation and in semiconductor spintronics. The donor g-factor Stark shift is sensitive to the orientation of the electric and magnetic fields and strongly influenced by the band-structure and spin-orbit interactions of the host. Using a multimillion atom tight-binding framework the spin-orbit Stark parameters are computed for donors in multi-valley semiconductors, silicon and germanium. Comparison with limited experimental data shows good agreement for a donor in silicon. Results for gate induced transition from 3D to 2D wave function confinement show that the corresponding g-factor shift in Si is experimentally observable.Comment: 4 pages, 4 figure