Ab initio calculation of the deformation potentials for intervalley phonons in silicon

The fully self-consistent first-principles calculations of electron scattering from short-wavelength phonons between lower valleys in the conduction band of a silicon crystal are carried out for the first time. The calculations of the lattice constant, the electron and phonon spectra, and the scattering probabilities are performed in the framework of a unified approach within the electron density functional theory. The theory contains no phenomenological assumptions regarding the relative position of minima in the conduction band, effective masses of carriers, interatomic forces, and scattering probabilities. The electron-phonon coupling constants (deformation potentials) for symmetry-allowed f and g transitions are calculated. The calculated constants lie in the range of values measured in different experiments involving intervalley transitions in silicon.     

Ab initio calculations of the deformation potentials for intervalley phonon-assisted transitions in АIIIВV crystals with sphalerite structure

Completely self-consistent ab initio calculations of scattering of electrons between the lowest minima of the conduction band by short-wavelength phonons are performed for the first time for a group of А ^III В ^V semiconductor crystals. The structure constants, electron and vibrational spectra, and probabilities of scattering are calculated for the crystals from unified positions within the electronic density functional method. The theory does not involve any phenomenological assumptions on positions of minima in the conduction band, effective carrier masses, interatomic forces, or scattering probabilities. The electron-phonon coupling constants (the deformation potentials) for actual Γ−X, Γ−L, and X−L transitions for scattering between the nonequivalent X−X and L−L valleys in the conduction bands of AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb crystals with sphalerite structure are calculated. Results obtained are compared with theoretical calculations within the phenomenological rigid ion model and with those performed by the selfconsistent frozen phonon method.     

Measurements of line intensities and determination of transition moment parameters from experimental data for the ν1 and ν3 bands of D2S

First measurements of line intensities for ν₁ and ν₃ bands of D₂³²S are reported. About 300 intensities of D₂³²S vibration–rotation lines were obtained from experimental high-resolution spectra recorded in the 1810–2051 cm⁻¹ region with the Fourier Transform Spectrometer built in Reims. Empirical values of transition moment parameters for ν₁ and ν₃ bands of D₂³²S were determined for the first time using a least-square fit to the observed intensities. Experimental D₂³²S intensities were compared with recent global variational predictions [Vl.G. Tyuterev, L. Régalia-Jarlot, D.W. Schwenke, S.A. Tashkun, Y.G. Borkov, C. R. Phys. 5 (2004) 189–199] computed from isotopically invariant potential and dipole moment functions of the hydrogen sulphide molecule. Average discrepancy between these calculations and our observed data was 0.03 cm⁻¹ for line positions of this spectral range. The discrepancy between these calculations and our measurements for the sum of line intensities was 5.5% and 3.5% for the ν₁ and ν₃ bands, correspondingly.     

Dynamics of the chalcopyrite lattice

The symmetry properties of the normal modes of the chalcopyrite lattice are analyzed. The phonon spectra of chalcopyrite and sphalerite are compared. There is a discussion of the intensity of the IR absorption lines due to single-phonon processes. Selection rules are found for direct and indirect transitions. Carrier scattering by phonons is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 42–48, October, 1970.     

Phonons in Si3Ge1 and Si1Ge3 short-period superlattices

Oscillatory spectra and single-phonon state densities are calculated in the Keating atomic interaction model for the ultrathin superlattices Si₃Ge₁ and Si₁Ge₃. Fundamental features of the superlattice phonon spectra and their relationship to the spectra of Si and Ge crystals are analyzed. Conditions required for oscillation localization in the interface region are studied and the role of the Si-Ge bond in formation of interlayer oscillations is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii. Fizika, No. 8, pp. 40–44, August, 1993.     

Line Positions and Intensities of the ν1+ ν2+ 3ν3, ν2+ 4ν3, and 3ν1+ 2ν2Bands of Ozone

Using a Fourier transform spectrometer, we have recorded the spectra of ozone in the region of 4600 cm⁻¹, with a resolution of 0.008 cm⁻¹. The strongest absorption in this region is due to the ν₁+ ν₂+ 3ν₃band which is in Coriolis interaction with the ν₂+ 4ν₃band. We have been able to assign more than 1700 transitions for these two bands. To correctly reproduce the calculation of energy levels, it has been necessary to introduce the (320) state which strongly perturbs the (113) and (014) states through Coriolis- and Fermi-type resonances. Seventy transitions of the 3ν₁+ 2ν₂band have also been observed. The final fit on 926 energy levels withJ_max= 50 andK_max= 16 gives RMS = 3.1 × 10⁻³cm⁻¹and provides a satisfactory agreement of calculated and observed upper levels for most of the transitions. The following values for band centers are derived: ν₀(ν₁+ ν₂+ 3ν₃) = 4658.950 cm⁻¹, ν₀(3ν₁+ 2ν₂) = 4643.821 cm⁻¹, and ν₀(ν₂+ 4ν₃) = 4632.888 cm⁻¹. Line intensities have been measured and fitted, leading to the determination of transition moment parameters for the two bands ν₁+ ν₂+ 3ν₃and ν₂+ 4ν₃. Using these parameters we have obtained the following estimations for the integrated band intensities,S_V(ν₁+ ν₂+ 3ν₃) = 8.84 × 10⁻²²,S_V(ν₂+ 4ν₃) = 1.70 × 10⁻²², andS_V(3ν₁+ 2ν₂) = 0.49 × 10⁻²²cm⁻¹/molecule cm⁻²at 296 K, which correspond to a cutoff of 10⁻²⁶cm⁻¹/molecule cm⁻².     

Asymptotic behavior of rotational energies of rigid X2Y-type molecules

In this study the asymptotic behavior of rotational energies of simple rigid molecules of X₂Y-type is considered. This behavior is obtained using various forms of an effective rotational Hamiltonian. The results of calculations for highly excited rotational energies of the molecules H₂O and CH₂ are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 9–12, January, 1990.     

Model with uniquely deducible parameters for the combined analysis of two resonating vibrational states. Anharmonic resonances in molecules of asymmetric-gyroscope type

A model of an effective Hamiltonian with parameters that are uniquely deducible from the spectrum for the combined analysis of the rotational structure of two resonating vibrational states is proposed and validated. Anharmonic resonances in molecules of asymmetric-gyroscope type are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 108–112, February, 1982.     

Investigation of the stability of the inverse spectroscopic problem of diatomic molecules

The stability and convergence of the inverse spectroscopic problem is investigated for diatomic molecules in the¹ electron state for a potential representation by series in the Dunham variable z_d=(r-r_e)/r_e, the Ogilvie-Tipping z_ot=(r-r_e)/(r + r_e), the Simmond-Parr-Finlan z_S= (r-r_e)/r and the Tucker z_t=sign (p)[1 -(r_e/r)^P]. None among the representations under investigation was that which would give a significant systematic improvement in stability as compared with others. The convergence is related to the selection of the initial approximation in the method of least squares, and is practically independent of the functional form of the potential. For the Dunham representation the solutions of the inverse problem yield quantities close to the true values of the expansion coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–101, May, 1984.     

Update of the anharmonic force field parameters of the ozone molecule

A new set of spectroscopic constants of the ¹⁶O₃ molecule (ω_i, x_ij, y_ijk, γ^DD, _i^X, β_ij^X,…), which determine vibrational dependence of band centres and rotational parameters, is derived from recent accurate analysis of high-resolution experimental ro-vibrational spectra through the theoretical approach based on second-order perturbation expansions in normal coordinates accounting for Darling–Dennison resonance interactions. These values are used to update empirical values of anharmonic coefficients (k_ijl, k_ijlm) of the potential function expansion in normal coordinates. Quadratic f_rr, f_r, f_rr′, f as well as cubic f_rst and quartic f_rstl force constants in internal (bond lengths, bond angle) coordinates are also derived. A detailed discussion is devoted to the accuracy of parameter determination for each of four steps of calculations. It is emphasised that the conventional method based on the inversion of formulae of the perturbation theory gives the largest uncertainties at the last step of calculations: the determination of the anharmonic force field in internal coordinates.