Phonon-assisted tunneling in Schottky barriers

Experimental current-voltage characteristics and their temperature dependencies for AlGaAs Schottky barrier structures are shown to be in agreement with the recent theory of phonon-assisted tunneling.     

The second harmonic generation in semiconductors in the DC magnetic field

The second harmonic radiation in millimeter wave region is found in semiconductors in the absence of the dc electric field. The observed resonant maximum of radiation intensity is shown to be related to the excitation of the free-electron plasma oscillations in the dc magnetic field.     

Periodic density functional theory investigation of the uranyl ion sorption on the TiO2 rutile (110) face

Periodic density functional theory calculations have been performed in order to study the uranyl ion sorption on the TiO2 rutile (110) face. From experimental measurements, two uranyl surface complexes have been observed and the two corresponding sorption sites have been identified. However, from a crystallographic point of view, three different sorption sites can be considered on this face. The corresponding three surface bidentate complexes were modeled and optimized, and their relative energies were calculated. Only 5 kJ/mol separates the two most stable structures, which correspond to the experimental ones. The third surface complex is nearly 10 kJ/mol less stable, in agreement with the fact that it was not observed experimentally.     

Matricially free random variables

We show that the framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called matricial freeness, can be viewed as a concept which not only leads to a natural generalization of freeness, but also underlies other fundamental types of noncommutative independence, such as monotone independence and boolean independence. At the same time, the sums of matricially free random variables, called random pseudomatrices, are closely related to random matrices. The main results presented in this paper concern the standard and tracial central limit theorems for random pseudomatrices and the corresponding limit distributions which can be viewed as matricial semicircle laws.     

On the Brillouin delta function of cubic and hexagonal lattices

In many problems of solid state physics one faces the task of integrating functions over polyhedra. This is necessary, for example, for the form factor in the theory of scattering, the Wannier function in band theory, and the Brillouin delta function in pseudocontinuum theory of crystal lattices. The integrands of these quantities are of similar form; the last two require integration over Brillouin zones. In the paper the properties of the Brillouin delta function are shortly rewieved. This function allows, in pseudocontinuum theory, the establishment of a unique relationship between functions of discrete and continuous arguments.A method of simplifying the integration of functions over polyhedra is proposed. The method is based on dividing a polyhedron into simplexes and calculating the integral in new barycentric coordinates. This method is applyied to the calculation of Brillouin delta functions for body centred and face centred cubic crystals. Explicit formulae for hexagonal and orthorhombic lattices are also given and discussed.     

Ethylene-promoted intermolecular enyne metathesis

[reaction: see text] Intermolecular enyne metathesis between functional group-rich alkynes and vinyl ethers was promoted by ethylene cometathesis. The concentration of ethylene was optimized to suppress the competing formation of butadiene through background ethylene metathesis. The role of ethylene appears to be both protective and rate enhancing.     

Ring-opening reactions of 3-substituted 1-azabicyclo[1.1.0]butane with dichlorocarbene

Reaction of 3-ethyl-1-azabicyclo[1.1.0]butane ( 1a ) with chloroform-potassium tert-butoxide afforded a ring-opened product, 1,1-dichloro-2-aza-4-ethylpenta-1,4-diene ( 4a ), which was characterized via conversion to the corresponding N-substituted 5-chloro-1,2,3,4-tetrazole, Sa . Reaction of 3-phenyl-1-azabicyclo-[1.1.0]butane ( 1b ) with “Seyferth's reagent” (PhHgCCl₂Br) afforded 1,1-dichloro-2-aza-4-phenylpenta-1,4-diene ( 4b ), which also was characterized via conversion to a tetrazole derivative, i.e., 5b . Finally, the reaction of 1b with dichlorocarbene generated under phase transfer conditions (chloroform-sodium hydroxide-TEBA) was studied. At short reaction times (0.5 hour), the major reaction product was 4b . However, at longer reaction times (20–30 hours), two secondary products, 8 and 9 , were formed which resulted via subsequent dichlorocyclopropanation of 4b .     

Rationalization of the stereochemistry of an addition of dialkyl phosphites to certain chiral aldimines: The experimental and theoretical approach

The absolute configuration of an α‐P stereogenic center in two diastereomeric O,O‐dialkyl α‐aminophosphonates ( 3 ), arising from an induced 1,3‐asymmetric phosphite addition to the CN bond of furfural‐derived Schiff bases ( 1 ), was established from single product ¹H NMR data. Such spectra were interpreted with anisotropic shielding in relation to the AM1 and MNDO/d structures of 3 ; the former ones turned out to be closer to the obtained experimental results (¹H NMR spectra of 3 , crystallographic database study). Since favored 3‐21G geometries of starting imines 1 were modeled as well, it was inferred that a stereochemical outcome of this reaction is governed by Cram selectivity. © 2002 Wiley Periodicals, Inc. Heteroatom Chem 13:120–125, 2002; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/hc.10005     

Synthesis of 1,4‐phenylene‐bis‐aminomethanephosphonates: The stereochemical aspect

The synthesis of new 1,4‐phenylene‐bis‐(N‐alkylaminomethane)‐bis‐phosphonates 3Aa–3Da by the addition of dialkyl or diaryl phosphites to the azomethine bond of 1,4‐phenylene Schiff bases is reported. Some NMR studies on the stereochemistry of dialkyl phosphite addition to terephthalic bis‐imines showing the exclusive formation of the meso‐form are presented. The mechanism and the origin of such a high stereoselectivity are discussed. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:144–151, 2000     

Monte Carlo Modeling of Phonon-assisted Carrier Transport in Cubic and Hexagonal Gallium Nitride

Monte Carlo method is employed for the calculations of electron and hole transport characteristics of cubic and hexagonal GaN at T = 300 K in the fields of E ≤ 1000 kV/cm⁻¹. It is shown that electron drift velocity and mobility is heavily reduced in hexagonal crystals due to additional phonon modes (~ 26 meV) and by fast electron scattering between the lowest Γ₁ valley and the minimally (~ 400 meV) up-shifted Γ₃ valley. Intervalley scattering is mediated most efficiently by the low-energy (~ 2 meV) acoustic phonons. The randomizing scattering is even more pronounced in p-type crystals where the sub-bands of light and heavy holes merge at the Γ-point of Brillouin zone. Cubic phase crystals are concluded to be advantageous for ultrafast electronic and photonics device performance because electron drift mobility is higher by an order of magnitude, and the hole mobility is several times higher than those in hexagonal phase.