A general solution to the Schrödinger–Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure

A general, system-independent, formulation of the parabolic Schrödinger–Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrödinger–Poisson equation.     

Strain-induced metal to semiconductor transition in ultra-small diameter single-wall carbon nanotubes

Under a large tensile strain near fracture limit, the band structures of single-wall carbon nanotubes (SWCNTs) with diameter less than 0.5 nm begin a metal to semiconductor transition and these ultra-small SWCNTs can normally maintain their metallicities. The band gap behavior of these SWCNTs intrinsically originates from the long axial direct bond lengths and the severe curvature. The gap opening comes mainly from the transfer of pπ electrons. And the localized π and σ states can result in a lower electrical conductivity. This band gap behavior suggests that it has potential to find applications in nano-electromechanical system.     

The electronic structure of pentacene revisited

Recently, there have been reports of the valence band photoemission of pentacene films grown on various substrates with particular emphasis on the highest occupied molecular orbital (HOMO) and its dispersion. In various works, evidence for HOMO band dispersion as high as 0.5 eV, even for polycrystalline films, has been presented. In apparent contradiction to these results, we have previously reported a band dispersion of only 50 meV, measured on a well characterised film with a single polymorph and single crystalline orientation, 5A(0 2 2). Here, we first present the two-dimensional momentum distribution of the HOMO of a 5A(0 2 2) film. Then the development of the valence band spectra for films grown at room temperature and low temperature are compared, and we show that morphological aspects can lead to the apparent observation of high HOMO dispersion. Finally, with the aid of the two-dimensional momentum distribution of the HOMO, we show that a reasonably large dispersion (0.25 eV) does indeed exist in 5A(0 2 2).     

Synthesis and characterizations of two anhydrous metal borophosphates: M2BP3O12 (M=Fe, In)

Two members of M^III₂BP₃O₁₂ borophosphates, namely Fe₂BP₃O₁₂ and In₂BP₃O₁₂, were synthesized by the solid-state method and characterized by the X-ray single crystal diffraction, the powder diffraction and the electron microscopy. They both crystallize in the hexagonal system, space group P6(3)/m (no. 176) and feature 3D architectures, build up of the M₂O₉ units and B(PO₄)₃ groups via sharing the corners; however, they are not isomorphic for the different crystallographically distinct atomic positions. Optical property measurements of both compounds and magnetic susceptibility measurements of Fe₂BP₃O₁₂ also have been performed. Moreover, in order to gain further insights into the relationship between physical properties and band structure of the M^III₂BP₃O₁₂ borophosphates, theoretical calculations based on density functional theory (DFT) were performed using the total-energy code CASTEP.     

A theoretical study of band structure properties for III–V nitrides quantum wells

Reliable and precise knowledge about the strain and composition effects on the band structure properties is crucial for the optimization of InGaN based heterostructures for electronic and optoelectronic device applications. AlInGaN as quaternary barrier material permits to control the band gap and the lattice constant independently. Using the model solid theory and the multi-band k.p interaction model, we investigate the composition effects on band offsets and band structure for pseudomorphic Ga_1−xIn_xN/Al_zIn_yGa_1−y−zN (0 0 1) heterointerfaces having zinc-blende structure. The results show that both conduction and valence band states are strongly modified while varying In and Al contents in the well and barrier materials. Furthermore, it is found that using AlInGaN as the barrier material allows the design of heterostructures including InGaN wells with tensile, zero or compressive strain. Such results give new insights for III-nitride compounds based applications and especially may guide the design of white-light emission diodes.     

Electronic band structure of InPxSb1−x alloys

The investigation of optoelectronic properties of zinc-blende InP_xSb_1−x, semiconducting alloys by pseudopotential calculations is studied. The scheme uses the local empirical pseudopotential method, which involves the disorder effect into the virtual crystal approximation by introducing an effective potential disorder. Various quantities for the alloy of interest are calculated. The obtained results show a reasonable agreement with the available experimental data. Special attention has also been given to the compositional dependence of these studied quantities.     

Two-parameter extended Hubbard Hamiltonian with supersymmetry

We investigate under which circumstances extended Hubbard models, including bond-charge, exchange, and pair-hopping terms, are invariant under gl (2,1) superalgebra. This happens for a two-parameter Hamiltonian which includes as particular cases the t - J, the EKS and the one-parameter BGLZ Hamiltonians, all integrable in one dimension. We show that the two parameter Hamiltonian can be recasted as the sum of the BGLZ Hamiltonian plus the graded permutation operator of electronic states on neighbouring sites. The integrability of the corresponding one-dimensional model is discussed. Received: 17 February 1998 / Received in final form: 6 March 1998 / Accepted: 17 April 1998     

Effects of relativistic motion of electrons on the chemistry of gold and platinum

Experimental evidence proving the unique stabilization of the 6s orbital in platinum and gold is presented. The conclusions are drawn from the chemical reactivities, of both elements, as well as from structural and spectroscopic features of selected compounds. In particular, the opening of a band gap in transparent CsAu and Cs₂Pt, backed by band structure calculations, are regarded conclusive indications of Au⁻ and Pt²⁻ to exist as closed shell species in these compounds.     

Diamagnetism of some quasi-two-dimensional graphites and multiwall carbon nanotubes

The diamagnetic susceptibility (DMS) of quasi-two-dimensional graphites (QTDGs) and multiwall carbon nanotubes (MWCNs) was measured at 4–950 K. The DMS of these carbons was explained by means of the band model of QTDG. The high average DMS value of QTDGs and MWCNs is associated with DMS normal to graphene sheets: the orbital diamagnetism of 2D conduction carriers. The DMS values along the sheets and nanotubes axes are close to the atomic one, i.e. they are 2 orders of magnitude less than those normal to the sheets and to MWCNs axes.     

Scaling properties of a tetragonal photonic crystal design having a large complete bandgap

Photonic crystal structures (PCs) of tetragonal lattice type are introduced and studied. They feature complete three-dimensional (3D) photonic bandgaps (PBGs). The PC design is based on two systems of ordered, parallel pores being perpendicular to each other. For increasing pore radii, the pore systems interpenetrate and an inverted woodpile geometry arises. The size of the 3D bandgaps depends on the ratio of the cell parameters L_x, L_y, and L_z, the pore radii and the refractive index of the dielectric material. If realized as a silicon/air structure, the maximum 3D gap is larger than 25%. A possible fabrication route for the near-infrared is based on 2D macroporous silicon where perpendicular pores are drilled, e.g., by focused-ion-beam etching. The dispersion behaviour of the PCs is theoretically analysed (band structures, density-of-states), systematically varying all relevant parameters. The optimization of the PBG sizes as well as a possible tunability of the PBG energies are discussed.