Density Functional Theory Calculations Revealing Metal‐like Band Structures for Ultrathin Germanium (111) and (211) Surface Layers

Abstract

To find out if germanium possesses facet-dependent electrical-conductivity properties, surface-state density functional theory (DFT) calculations were performed on one to six layers of germanium (100), (110), (111), and (211) planes. Tunable Ge(100) and Ge(110) planes always present the same semiconducting band structure with a band gap of 0.67 eV expected of bulk germanium. In contrast, one, two, four, and five layers of Ge(111) and Ge(211) plane models show metal-like band structures with continuous density of states (DOS) throughout the entire band. For three and six layers of Ge(111) and Ge(211) plane models, the normal semiconducting band structure was obtained. The plane layers with metal-like band structures also show Ge-Ge bond-length deviations and bond distortions, as well as significantly different 4s and 4p frontier-orbital electron counts and relative percentages integrated over the valence and conduction bands from those of the semiconducting state. These differences should contribute to strikingly dissimilar band structures. The calculation results suggest the observation of facet-dependent electrical-conductivity properties of germanium materials; when making transistors from germanium, the facet effects with shrinking dimensions approaching 3 nm may also need to be considered.

Density Functional Theory Calculations Revealing Metal‐like Band Structures and Work Function Variation for Ultrathin Gallium Arsenide (111) Surface Layers

“…For 3, 6, and 9 GaAs (111) planes, the same DOS plot as that of the unit cell of GaAs returns. This 3‐layer repeating trend is same as those seen in the conductive Si and Ge (111) and (211) plane cases . Band diagrams for 1–9 layers of GaAs (111) planes are given in Figure .…”

“…This 3-layer repeating trend is same as those seen in the conductive Si and Ge (111)a nd (211) plane cases. [11,12] Band diagramsf or 1-9 layers of GaAs (111)p lanes are given in Figure 3.…”

“…[15] Specifically,D FT calculations on tunable numbers of various Si and Ge planesh ave revealed as emiconducting band structure for their (100) and( 111) planes, but metal-like band structures for certain numberso f (111)a nd (211)/(112) plane layers. [11,12] Moreover,t he calculations also show variations in the bond length, bond geometry, and frontier orbital electron distribution between semiconducting and metal-like cases. Taken these deviations together,t he observed facet-dependent physical and chemical properties of semiconductor materials should be quantum mechanical in nature with surface state differencesa tt he orbitall evel.S uch DFT results provide very useful informationh elping us to understandt he origin of semiconductor facet effects.…”

“…Thus, Cu 2 O cubes, octahedra, and rhombic dodecahedra having the same size still display discernably different colors and band gaps . Specifically, DFT calculations on tunable numbers of various Si and Ge planes have revealed a semiconducting band structure for their (100) and (111) planes, but metal‐like band structures for certain numbers of (111) and (211)/(112) plane layers . Moreover, the calculations also show variations in the bond length, bond geometry, and frontier orbital electron distribution between semiconducting and metal‐like cases.…”

“…[8][9][10] The emergence of these semiconductor facet effects should originate from the presence of an ultrathin surface layer with dissimilar band structures for different crystal planesa sr evealed through DFT calculations, such that charge carriers encounter different barrierh eights across ap articular crystal surface. [1][2][3][10][11][12] This ultrathin surface layer should also be respon-sible fort he observation of opticalf acet effects demonstrated in polyhedralC u 2 Oa nd Ag 3 PO 4 nanocrystals, suggesting light absorption of semiconductor crystals actually has bulk and surface components. [13,14] Thus, Cu 2 Oc ubes,o ctahedra, and rhombic dodecahedrah aving the same size still display discernably different colors and band gaps.…”