Piezoelectric field effects on electron density in a δ-doped AlGaAs/InyGa1-yAs/GaAs pseudomorphic HEMT

We have calculated the low-temperature electron density in a -doped AlGaAs/InGaAs/GaAs heterostructure in the presence of a piezoelectric field. Growth of a strained InGaAs layer on (N11) GaAs substrates causes a piezoelectric field to be built into the quantum well of a pseudomorphic high electron mobility transistor (HEMT). The presence of this field modifies the electronic properties of strained-layer heterostructures. A self-consistent analysis is made of these -doping systems to solve simultaneously the Schrödinger and Poisson equations taking into account exchange-correlation and strain effects. Thus, we have found the confining potential, the electron density, the subband energies, the eigenenvelope wavefunctions, and the Fermi-energy level in the quantum well. We have studied the effects of the InGaAs channel width and the indium composition on the electron density. Our results show a larger increase of the electron density when the calculated value is for a (111) GaAs substrate rather than for equivalent (001) and (311) substrates. We have also investigated the effects of the environmental Al concentration seen by the Si -doped on the electron density. PACS 71.76     

The crystal and molecular structures of 3,3,6,6-Tetramethylbicyclo[2.2.1]heptane-2,5-dione and 6,6-Dibromo-1,3,3-Trimethylbicyclo[2.2.2] octane-2,5-dione

The X-ray crystal structures of two bicyclic diketones have been determined. 3,3,6,6-Tetramethylbicyclo[2.2.1]heptane-2,5-dione, C₁₁H₁₆O₂ (A), is monoclinic,C2/c (No. 15), with cell dimensionsa=9.071(3),b=9.748(5),c=12.322(6)Å,=110.15(3)°, andZ=4. The structure was determined by direct methods and refined toR ₁=0.065,R ₂=0.052 for 570 reflections. 6,6-Dibromo-1,3,3-trimethylbicyclo[2.2.2]octane-2,5-dione, C₁₁H₁₄Br₂O₂ (D), is orthorhombic,Pcab, (No. 61), with cell dimensionsa=11.206(3),b=18.818(6),c=11.695(4) Å, andZ=8. The structure was solved by the heavy-atom method and refined toR ₁=0.070,R ₂=0.065 for 1210 reflections. Bond lengths and angles within both structures do not differ from those in similar structures. The opening up of the internal ring angle of the ketone inA (vs. a normal bicyclo[2.2.1]heptane) and the consequent decrease of the adjacent internal ring angle brings the ketone carbon atoms nearer to the hydrogen atoms of the bridging methylene group.     

Modelling investigation on the thermal conductivity of pure liquid,vapour, and supercritical refrigerants and their mixtures by using Heyen EOS

This work presents a literature survey of the available data regarding the thermal conductivity of refrigerants. About 31 pure refrigerants that contain 7127 data points are selected for the temperature range of 91.35–580.00 K, a pressure range of (0.000111-500) bar, and thermal conductivity range of (0.007–0.27) W m^?1 K^?1 containing liquid, vapour, and supercritical phases. Seven binary and three ternary mixtures are also collected both in liquid and vapour phases with an overall of 803 data points. Based on the similarity between the pressure-volume-temperature and Tλ (thermal conductivity) P diagrams, the thermal conductivity model based on Heyen equation of state has been developed for pure refrigerants and their mixtures. The genetic algorithm is used to determine the adjustable parameters of the model. The calculation results prove that this proposed model can reproduce and predict thermal conductivity of refrigerants with good accuracy (overall AAD = 6.85% for pure compounds, AAD = 6.14% for binary mixtures and AAD = 9.32% for ternary mixtures).     

Fermi edge singularity evidence from photoluminescence spectroscopy of AlGaAs/InGaAs/GaAs pseudomorphic HEMTs grown on (3 1 1)A GaAs substrates

InGaAs/AlGaAs/GaAs pseudomorphic high electron mobility transistor (P-HEMT) structures were grown by Molecular Beam Epitaxy (MBE) on (3 1 1)A GaAs substrates with different well widths, and studied by photoluminescence (PL) spectroscopy as a function of temperature and excitation density.The PL spectra are dominated by one or two spectral bands, corresponding, respectively, to one or two populated electron sub-bands in the InGaAs quantum well. An enhancement of PL intensity at the Fermi level energy (E_F) in the high-energy tail of the PL peak is clearly observed and associated with the Fermi edge singularity (FES). This is practically detected at the same energy for all samples, in contrast with energy transitions in the InGaAs channel, which are shifted to lower energy with increasing channel thickness. PL spectra at low temperature and low excitation density are used to optically determine the density of the two-dimensional electron gas (2DEG) in the InGaAs channel for different thicknesses. The results show an enhancement of the 2DEG density when the well width increases, in good agreement with our previous theoretical study.     

Dynamic 1H NMR study around the carbon-carbon single bond and partial carbon-carbon double bond in the two particular phosphorus ylides and in an enaminoester

Herein, a series of separate dynamic (1)H NMR effects are reported at different temperatures within a particular enaminoester involving a phenanthridine. These effects are attributed to restricted rotation around the two single bonds such as carbon-carbon (H(a)-C-C-H(b)) and nitrogen-carbon (NCCOOCH(3)). Activation energies (E(a)) for these interconversion processes in their rotational isomers are equal to 20 and 20 ± 1 kJ mol(-1), respectively. In addition, three dynamic (1)H NMR effects are investigated at different temperatures for a particular phosphorus ylide involving a 2-indolinone around the carbon-carbon single bond (H-C-C-PPh(3)) within the two Z- and E-rotational isomers and partial carbon-carbon double bond (OCH(3)-C=C-PPh(3)). Activation energies (E(a)) for these interconversion processes in rotational isomers are equal to 53, 63 and 73 ± 1 kJ mol(-1) , respectively. This behavior was also observed for other phosphorus ylide containing 2-mercaptobenzoxazole around the carbon-carbon single bond and partial carbon-carbon double bond with their relevant activation energies containing 13, 10 and 75 ± 1 kJ mol(-1), respectively.     

Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients

In the literature, sensitivity analysis of linear programming (LP) has been widely studied. However, only some very simple and special cases were considered when right-hand side (RHS) parameters or objective function coefficients (OFC) correlate to each other. In the presence of correlation when one parameter changes, other parameters vary, too. Here principal component analysis is used to convert the correlation of the LP homogenous parameters into functional relations. Then, using the derivatives of the functional relations, it is possible to perform classical sensitivity analysis for the LP with correlation among RHS parameters or OFC. The validity of the devised method is corroborated by open literature examples having correlation among homogenous parameters.     

A variational approach to difference equations

In this paper, we are concerned with the existence of at least three distinct solutions for nonlinear difference equations with Dirichlet boundary conditions. The proof of the main result is based on variational methods. We also provide an example in order to illustrate the main results.