Extended Hückel theory for band structure, chemistry, and transport. II. Silicon

Abstract

In this second paper, we develop transferable semi-empirical parameters for the technologically important material, silicon, using Extended Hückel Theory (EHT) to calculate its electronic structure. The EHT-parameters are optimized to experimental target values of the band dispersion of bulk-silicon. We obtain a very good quantitative match to the bandstructure characteristics such as bandedges and effective masses, which are competitive with the values obtained within an sp 3 d 5 s * orthogonal-tight binding model for silicon 9 . The transferability of the parameters is investigated applying them to different physical and chemical environments by calculating the bandstructure of two reconstructed surfaces with different orientations: Si(100) (2x1) and Si(111) (2x1). The reproduced π-and π * -surface bands agree in part quantitatively with DFT-GW calculations and PES/IPES experiments demonstrating their robustness to environmental changes. We further apply the silicon-parameters to describe the 1D band dispersion of a unrelaxed rectangular silicon nanowire (SiNW) and demonstrate the EHT-approach of surface passivation using hydrogen. Our EHT-parameters thus provide a quantitative model of bulk-silicon and silicon-based materials such as contacts and surfaces, which are essential ingredients towards a quantitative quantum transport simulation through silicon-based heterostructures.

Extended Hückel theory for band structure, chemistry, and transport. I. Carbon nanotubes

“…We show that the same bulk-optimized EHT parameters ͑onsite energies and AObasis functions͒ are transferable to small diameter CNT band structures, capturing even curvature-induced band gap effects for larger than 1%-3% tube deformation, in quantitative agreement with STS data. Furthermore, surface chemical effects are examined through the study of nanotube based carbon monoxide sensors whose alteration of electronic structure upon molecular adsorption compares favorably with ab initio calculations of da Silva et al 24 In our follow-up paper, 25 we will demonstrate a similar transferability between bulk silicon and various silicon surfaces and apply the EHT methodology to unreconstructed silicon nanowires. Taken together, the wide variety of these examples illustrates the range of transferability of EHT parameters, which we believe makes extended Hückel theory a useful practical tool for electronic structure and quantum transport.…”

“…This makes EHT a good compromise between accuracy and practicality. In our follow-up paper, 25 we will demonstrate the applicability of EHT to modeling silicon, including its transferability between bulk and multiple surface band structures of reconstructed silicon surfaces and also for nanowires. Applying this approach has allowed us to quantitatively explain and in some cases even predict interesting experimental results involving molecular conductors on silicon.…”

Semiempirical model for nanoscale device simulations

“…Examples of semiempirical transport models are methods based on SlaterKoster tight-binding parameters 6,7 and extended Hückel ͑EH͒ parameters. [8][9][10][11][12][13][14] The ab initio models have the advantage of predictive power and can often give reasonable results for systems where there is no prior experimental data. However, the use of the Kohn-Sham one-particle states as quasiparticles is questionable, and it is well known that for many systems the energies of the unoccupied levels are rather poorly described within DFT.…”

Si(100)-2 × 1-H dimer rows contrast inversion in low-temperature scanning tunneling microscope images

“…STM images were computed using the surface Green-function matching (SGFM) method [27] with an extended Hückel molecular orbital (EHMO) Hamiltonian [28] tuned to match HSE06 density functional theory band structures [29]. The STM junction was modeled as a semi-infinite W(111) slab, a Si-terminated STM tip, a five-layer Si(100):H surface, and the semi-infinite Si(100) bulk, as illustrated in Fig.…”