Valence Force Field Theory Research Articles

Spectroscopic analysis of Sn doped Se–Te glassy alloy

Structural adaptation in Sn doped Se–Te glassy alloy has been investigated using infrared (IR) and Raman spectroscopy. The Raman and IR spectra of Se30Te70−xSnx (x=0, 1.5, 2.5 and 4.5) glassy alloy have been recorded in the frequency range of 100–1000cm−1 and 30–700cm−1, respectively. Various structural parameters are investigated in the light of existing models as a function of average coordination number ⟨r⟩ and with valence force field theory by using force constants. The molecular model approach has been employed to analyze the spectral data. A right/left shift in the Raman/IR spectra has been observed with an increase in Sn concentration. The increase in the intensity of the observed vibrational bands with Sn content has been explained in terms of increase in absorption centers. Further, it is found that the addition of Sn results in the formation of Sn–Se bonds, favored by chemical ordered network model, accountable for the cross linking and formation of tetrahedral arrangement in the glassy network. The increase in average coordination and average constraints with Sn contents also support the cross linking of chalcogen atom in the glassy network.

Microscopic phonon theory of Si/Ge nanocrystals

Microscopic phonon theory of semiconductor nanocrystals (NCs) is reviewed in this paper. Phonon modes of Si and Ge NCs with various sizes of up to 7 nm are investigated by valence force field theory. Phonon modes in spherical SiGe alloy NCs approximately 3.6 nm (containing 1147 atoms) in size have been investigated as a function of the Si concentration. Phonon density-of-states, quantum confinement effects, as well as Raman intensities are discussed.

Band-edge alignment ofSiGe∕Siquantum wells andSiGe∕Siself-assembled islands

We report on the energy band gap and band lineup of $\mathrm{SiGe}∕\mathrm{Si}$ heterostructures either in the case of coherently strained quantum wells or in the case of $\mathrm{SiGe}∕\mathrm{Si}$ self-assembled islands. We take into account the strain field and the quantum confinement effects through an accurate description of the conduction band including the $\ensuremath{\Delta}$ and $L$ bands. The strain field is calculated using a microscopic valence force field theory. The conduction-band diagram and energies are obtained from a 30-band $\mathbf{k}∙\mathbf{p}$ Hamiltonian accounting for the strain through the Bir-Pikus Hamiltonian. The band-edge description is first given for biaxially strained pseudomorphic $\mathrm{SiGe}$ layers. In $\mathrm{SiGe}$ quantum wells grown on relaxed silicon, the band line-up switches from type I to type II depending on the value of the average valence band offset. Applying the 30-band formalism to the case of heterostructures grown on relaxed silicon germanium buffer layers indicates that a better agreement with experimental data is obtained for a valence-band offset value $\mathrm{\ensuremath{\Delta}}{E}_{v}=0.54x$ where $x$ is the Ge composition. For this parameter, a type-II band lineup is thus expected for all compositions of pseudomorphic $\mathrm{SiGe}$/relaxed Si heterostructures. For $\mathrm{GeSi}∕\mathrm{Si}$ islands, we take into account the strain relaxation in the surrounding Si matrix. A type-II band lineup is predicted for all Ge compositions. The near-infrared interband recombination energy of the islands is calculated as a function of their $\mathrm{SiGe}$ composition.

Ge/Si self-assembled Islands for Photonics Applications

ABSTRACTWe first present an analysis of the band line-up in the case of SiGe/Si quantum wells and in the case of SiGe/Si self-assembled islands. The conduction and valence band diagrams are obtained from a 30 band k.p Hamiltonian which allows to describe simultaneously conduction and valence band states. The strain field is obtained from a microscopic valence force field theory. The band edge alignment is strongly dependent on the input parameters for this heterosystem. We determine the average valence band offset from photoluminescence measurements of heterostructures grown on relaxed SiGe buffer layers. A type II band line-up is calculated for all Ge compositions in the case of two-dimensional quantum wells and SiGe/Si self-assembled islands. The 30-band formalism allows the determination of the near-infrared interband recombination energy as a function of the self-assembled island structural parameters. We then present recent results obtained by embedding SiGe/Si self-assembled islands in two-dimensional photonic crystals. The photoluminescence of GeSi islands acts as an internal probe to characterize the optical properties of silicon-based two-dimensional photonic crystals designed for the near-infrared spectral range. Cavities, defect-free photonic crystals operated at the second Bragg order and two-dimensional photonic crystals fabricated on top of one-dimensional Bragg mirrors (2D + 1D) are described. We show that, in the case of 2D +1D structures, we can control the quality factor of optical modes at the second Bragg order by matching the resonance conditions and controlling the thickness of the layers. Photonic crystals with pure Ge layers are finally described.

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO 2 glass

A short survey has been made on the extensive work that is being done on the pressure derivatives of the second order elastic constants (SOEC) to ascertain various properties of substances. Hence an attempt has been made to correlate the pressure derivatives to some properties of the substances. Thus some equations have been derived to correlate the Grüneisen parameter which is evaluated from Schofield's equations and Bhatia-Singh's (BS) parameters. They have been used to compute the longitudinal ( γ g L) and transverse ( γ g T) Grüneisen constants. γ g L calculated by different methods agree well with experiment. γ g T obtained from BS parameters gives rather higher value while Schofield's equations give results in agreement with experiment. The DeLaunay–Nath–Smith (DNS) equation has been used to derive a relation to compute γ g el (elastic). A method has been extended to calculate the third order elastic constants (TOEC) and it is found to give excellent values of TOECs in agreement with experiment. The absorption band position of TeO 2 has been predicted to occur at 276 cm −1. The phonon dispersion curves have been calculated through BS equations for TeO 2. Several other properties of TeO 2 have been computed such as thermal Grüneisen parameter γ g th, its pressure derivatives ( γ g th)′≡(d γ g th/d P), the pressure variation of bulk modulus C 1≡(d K T /d P) T and its pressure derivatives that is (d C 1/d P) T which is in turn related to ( γ g th)′, the heat capacity at constant volume C V, and the second Grüneisen constant Q. In some cases we calculated these quantities by different methods and the agreement between them is good. Besides we evaluated δ T AG the Anderson Grüneisen parameter. Another important aspect of the present investigations is the formulation of the potential function (PF) of TeO 2 from which we calculated SOECs and these are found to be in excellent agreement with experiment. All other properties mentioned already have also been calculated through the use of the newly formulated PF and the calculated values obtained through various other equations are in good agreement with those obtained from PF. According to valence force field (VFF) all atomic forces can be resolved into bond bending β and bond stretching α forces. It is shown that TeO 2 does not satisfy Martins unity rule. Hence it is concluded that there is an effective dynamic charge on Te in TeO 2. Using the experimental elastic constants the bond bending force β and bond stretching force α and also their pressure derivatives have been evaluated. In addition the reststrauhlen optic frequency ω has been calculated. A self consistent check has been made by evaluating C 44 through the calculated values of α and β.

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

A short survey has been made on the extensive work that is being done on the pressure derivatives of the second order elastic constants (SOEC) to ascertain various properties of substances. Hence an attempt has been made to correlate the pressure derivatives to some properties of the substances. Thus some equations have been derived to correlate the Grüneisen parameter which is evaluated from Schofield's equations and Bhatia-Singh's (BS) parameters. They have been used to compute the longitudinal (γgL) and transverse (γgT) Grüneisen constants. γgL calculated by different methods agree well with experiment. γgT obtained from BS parameters gives rather higher value while Schofield's equations give results in agreement with experiment. The DeLaunay–Nath–Smith (DNS) equation has been used to derive a relation to compute γgel (elastic). A method has been extended to calculate the third order elastic constants (TOEC) and it is found to give excellent values of TOECs in agreement with experiment. The absorption band position of TeO2 has been predicted to occur at 276 cm−1. The phonon dispersion curves have been calculated through BS equations for TeO2. Several other properties of TeO2 have been computed such as thermal Grüneisen parameter γgth, its pressure derivatives (γgth)′≡(dγgth/dP), the pressure variation of bulk modulus C1≡(dKT/dP)T and its pressure derivatives that is (dC1/dP)T which is in turn related to (γgth)′, the heat capacity at constant volume CV, and the second Grüneisen constant Q. In some cases we calculated these quantities by different methods and the agreement between them is good. Besides we evaluated δTAG the Anderson Grüneisen parameter. Another important aspect of the present investigations is the formulation of the potential function (PF) of TeO2 from which we calculated SOECs and these are found to be in excellent agreement with experiment. All other properties mentioned already have also been calculated through the use of the newly formulated PF and the calculated values obtained through various other equations are in good agreement with those obtained from PF. According to valence force field (VFF) all atomic forces can be resolved into bond bending β and bond stretching α forces. It is shown that TeO2 does not satisfy Martins unity rule. Hence it is concluded that there is an effective dynamic charge on Te in TeO2. Using the experimental elastic constants the bond bending force β and bond stretching force α and also their pressure derivatives have been evaluated. In addition the reststrauhlen optic frequency ω has been calculated. A self consistent check has been made by evaluating C44 through the calculated values of α and β.

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

Application of valence force field theory, tight binding approximation and Girifalco potential in the study of thermodynamic and elastic properties of C 60 in detail

In this paper we calculated the second order elastic constants (SOECs) of C 60 using tight binding approximation (TBA) and valence force field theory (VFFT). To the SOECs obtained from Girifalco potential we added the contribution of Coloumb forces obtained through Martins prescription and the corrected values so obtained compare favorably with those of TBA and VFFT and also with literature values. We also derived the pressure derivatives of SOECs obtained through TBA and VFFT. In addition we calculated bond stretching force constant ∝ and bond bending force constants β and also their pressure derivatives. The ratio ∝/β compares favorably with several compounds for which these calculations have been made. The longitudinal ω L and transverse ω T frequencies have been calculated by two different methods. The calculated band positions are in satisfactory agreement with each other. Even though C 60 is not isotropic, sample calculations of γ g L and γ g T have been made so as to have an insight into these quantities. A second method due to Bhatia and Singh has also been applied to calculate these quantities. But this method gives a high γ g T value while it gives a good γ g L value. Reasons for this high value of γ g T have been discussed. The longitudinal ω L and transverse ω T frequencies of C 60 have been calculated through the use of calculated elastic constants. We also used the Nath–Smith–De Launey equation to calculate the band position. The calculated and observed band absorption position agree well. The calculated ω T value has been used to compute K T the bulk modulus with a modified Szigete's equation taking into consideration the existence of a small amount of Coloumb forces and the calculated value is found to be in good agreement with Duclose value. The effective charge on C 60 has been obtained through Martin's equation and the elastic constant C 44 has been evaluated through Martin's prescription. The effective charge found to be 0.21 e is in satisfactory agreement with that of Lu et al. [24] who found the effective charge to be 0.27 e. The pressure derivative of γ g th, the thermal Grüneisen constant has been evaluated and also through the second derivative of η and δ, the Bhatia Singh's parameters and the value is found to be −0.01 Kbar −1 and this value of γ′ g has been used to evaluate the second Grüneisen constant Q and the Anderson Grüneisen constant δ T AG. A new equation has been derived through the use of the derivative of SOECs C 11 ′ and η′ to evaluate γ g th which is found to be in good agreement with the measured value. The pressure derivative of bulk modulus ( K T) has been calculated. The estimated heat capacity is in fair agreement with experiment and the calculated value of K T using the computed value of ω T is found to be in reasonable agreement with that modified by Szigeti equation.

EXAFS study of the local structure in compounds

Extended X-ray absorption fine structure (EXAFS) was used to obtain information about the local structure in CdSxSe1−x compounds. These compounds show interesting optical and electronic properties controllable by varying the stoichiometry of the mixed anion system. For x ranging from 1 to 0, these compounds crystallize in the wurtzite structure and the lattice parameters closely follow Vegard's law. For the coordination shells, a complete set of values was obtained from measurements at the K edge of sulphur and selenium and at cadmium K, LI and LIII edges. A large relaxation of the bond length was observed, in agreement with previous measurements on ternary zinc blende systems and with the predictions of valence force field theory. The presence of sulphur second neighbours around selenium atoms was evidenced. This eliminates the possibility of CdSe clustering on the scale of a few atomic cells.

Anharmonic Properties of Ultrasounds in Diamond-Type Crystals and Quartz Plate under an Intense Exicitation

The harmonic generation due to the third-order elastic (TOE) constants in germanium and gallium arsenide, and the nonlinear current-jump effect due to the fourth-order elastic constants in a quartz plate have been investigated. The complete TOE constants were determined from the measurement using an optical interferometer and from the values derived from the valence-force field theory. They showed a good agreement with those obtained by other experimental techniques. A phenomenon analogous to the hybride optical bistability was observed in a thickness-shear mode quartz resonator, and this was analyzed in terms of an equivalent nonlinear network.