Two-phonon Absorption Research Articles

Two-phonon resonances and bound-states in molecular crystals. II. Absorption coefficient

For pt.I see ibid., vol.11, p.1283 (1978). Using the Green function obtained in pt.I, the author obtains explicit expression for the two-phonon absorption coefficient of internal modes of molecular crystals. This expression is compared with the IR transmission spectra of CO2, N2O and OCS crystals and excellent agreement is found, in terms of two-phonon bound-states and resonances, for both shape and intensity of the bands under consideration.

Refractive-index measurements and nonlinear moment parameters for polycrystalline ZnSe

We have measured the refractive index and its temperature derivative, of polycrystalline ZnSe at seven wavelengths between 3.5 and 15 \ensuremath{\mu}m (3 to 14 times the reststrahl frequency). We have used these data to determine relations among the effective ionic charge and the coefficients of the second- and third-order terms in an expansion of the crystal electric-dipole moment in powers of the lattice displacements. Comparison of ours with other data suggests that two-phonon absorption in ZnSe arises mainly from this nonlinear behavior of its electric-dipole moment.

Two-phonon absorption in InSb, InAs, and GaAs

Far-infrared absorption in the III–V compound semiconductors InSb, InAs, and GaAs has been measured using a Fourier transform spectrometer. The high-resolution spectra of the three materials were found to be very similar. Features on the spectra were assigned to two-phonon sum and difference processes with the aid of two-phonon density-of-states curves for InSb and GaAs calculated from a shell model fit to phonon dispersion curves. Interpretation of the spectrum of InAs was possible because of its similarity to that of InSb and GaAs. The frequencies of phonons at certain points in the Brillouin zone of InSb and GaAs determined from the mode assignments to the infrared spectra were in good agreement with previous measurements by inelastic neutron scattering and Raman scattering.

Two-phonon absorption in InP and GaP

Far-infrared absorption in crystals of GaP and InP was investigated using a high-resolution Fourier-transform spectrometer. The two-phonon absorption was found to be very similar in these two materials. Van Hove singularities on the GaP spectrum were identified with the aid of calculated two-phonon sum and overtone density-of-states curves. The analysis of the InP spectrum was based on its homology to GaP. Many of the prominent features of the absorption spectra are assigned to pairs of phonons on the hexagonal face of the Brillouin zone while phonon pairs at Γ, X and L generally contribute only minor features to the spectra.

Cooperative excitations and infrared absorption in nitrous oxide crystals

The i.r. spectrum of crystalline nitrous oxide has been reinvestigated. The longitudinal—transverse mode splitting of the three fundamentals has been determined and the factor group splitting of ν 2 has been observed. A large number of internal isotopic and combination bands have been assigned. In the region of combination bands extended two-phonon absorption bands have been observed which are particularly prominent in the region of ν 1 + ν 3 and ν 2 + ν 3. The energy of one- and two-phonon states has been calculated using a resonant dipole—dipole interaction potential. The results of calculation agree well with experiment. The intensity and profile of the two-phonon bands has been calculated using a mechanism of induced dipoles. It is shown that two-phonon bands arise by direct excitation via non-linear terms in the dipole operator.

Two-phonon absorption in the ν 1 + ν 2, 2ν 20 + ν 2 region of carbon dioxide crystal

The absorption spectrum of carbon dioxide crystal in the ν 1 + ν 2, 2ν 2 0 + ν 2 region is calculated in the approximation of dipole-dipole potential and direct excitation of the two quanta by non linear terms in the electric moment. A good agreement with experiments is obtained.

Far-infrared phonon absorption in InSb

Far-infrared absorption due to single-phonon and two-phonon processes was investigated in undoped InSb using a high-resolution Fourier-transform spectrometer. Single-phonon absorption by both transverse- and longitudinal-optical modes at the Brillouin-zone center was observed. Two-phonon absorption spectra correlated well with two-phonon density-of-states curves calculated using parameters derived from inelastic-neutron-scattering experiments. Brillouin-zone locations of critical points that gave rise to prominent features on the two-phonon density-of-states curve were identified by investigating phonon frequency contours on symmetry planes. Critical points at (0.6, 0, 0), $X$, and $L$ for phonon combinations involving transverse modes and on the (111) boundary plane of the Brillouin zone for combinations containing the longitudinal-acoustical phonon gave rise to almost all the prominent features observed on the two-phonon absorption spectra. Derived frequencies for phonon modes at (0.6, 0, 0), $X$, and $L$ agreed well with values determined directly from inelastic-neutron-scattering experiments. Although strong features, arising from 2TA overtones at $X$ and $L$, appear in the calculated spectrum, no absorption corresponding to these features was observed.

Lattice vibrations of CdCl_2, CdBr_2, MnCl_2, and CoCl_2: infrared and Raman spectra*

The fundamental lattice vibrations of the trigonal CdCl2 structure have been analyzed group theoretically. All k=0 optical modes are either infrared or Raman active, so a complete vibrational analysis is possible. Results of far-infrared measurements on crystal and powder samples using a Fourier-transform spectrometer together with single-crystal Raman spectra are presented for CdCl2, CdBr2, MnCl2, and CoCl2. Symmetry assignments of the observed frequencies are made on the basis of polarization behavior. Second-order infrared and Raman spectra are also presented; peaks in the two-phonon axial infrared absorption spectra are assigned to allowed fundamental combinations at k=0. The infrared absorption spectra exhibit additional features in the range 200–4000 cm−1 that are ascribed to impurities.

One- and two-phonon spectra of crystalline silicon tetrafluoride

The infrared and Raman spectra of crystalline SiF4 at —196°C are discussed. Two-phonon absorption bands are observed and the results are discussed

Theory of two-phonon absorption processes in liquid paraffins

Calculated absorption spectra are given for linear C8H18, C10H22, C16H34 and C20H42 chains, based on the assumption of a two-phonon absorption mechanism. In the present work the normal modes of vibration of different finite chains are computed directly, without recourse to the Pitzer sampling approximation and without the assumption of strict k-selection rules. The calculated spectra are found to be much more sensitive to chain length than the experimental spectra. A possible explanation of the relative insensitivity of the observed spectra is suggested in terms of a characteristic chain segment length common to all the chains. Ironically, the apparent importance of chain segmentation in the two-phonon absorption suggests that one-phonon transitions may also play a significant role in the absorption process.

Assignments of the Two-Phonon Infrared Absorption Spectrum of LiF

Measurements of the far-infrared lattice absorption in LiF at several temperatures are reported. An approximate calculation of the relative two-phonon absorption intensity has been made considering the anharmonic mechanism only and using the lattice-dynamical data, resulting from a modified deformation-dipole model, of Karo and Hardy. The wave-vector density used was 64000 points per zone (1685 independent wave-vector positions). Such a density with a simple bin-sampling smoothing procedure gave a fairly good wave-number resolution in the computed two-phonon spectra. The agreement with the two-phonon difference absorption presented here and the summation results reported elsewhere is poor, but the discrepancies may be seen to be in the lattice-dynamical data. By identifying the phonon branches responsible for the features in the computed spectrum and considering various criteria necessary for strongly combining branches, it was possible to take the more accurate frequencies recently measured by inelastic neutron scattering and satisfactorily explain the experimental features. Phonon branches of less symmetry than the three major branches were found to contribute appreciably. No evidence was found for sizeable three-phonon absorption in the far infrared.

Electric field-induced changes in the two-phonon infrared absorption spectrum of diamond

Electric field-induced changes in the two-phonon infrared absorption in diamond have been observed in the region 2400 to 2700 cm-1. The induced spectrum is very similar to the second order raman spectrum for a similar experimental configuration. This similarity is attributed to field-induced changes in the selection rules governing two-phonon absorption.

Two-phonon absorption processes in liquid octane, decane, hexadecane and nujol

Similarities in the measured 100–300 cm-1 absorption spectra of liquid paraffins over a wide range of chain lengths suggest that an identical absorption mechanism is dominant in each case. The intensity and temperature dependence of the 250 cm-1 band in nujol, in particular, are indicative of a multiphonon process. The present paper offers a theoretical explanation for the spectra of octane, decane, hexadecane and nujol, in terms of two-phonon absorptions. Calculations based on the Lax and Burstein approach (suitably modified to take account of finite chain length) reproduce the general features of the spectrum fairly well in each case, and provide an adequate account of the observed temperature dependence of the band in nujol.

LO-Phonon—Assisted Two-Phonon Absorption in KI

The two-photon absorption constant is measured experimentally with high resolution in the exciton region of KI. Fine structure is resolved in which the $2P$ exciton is seen at 6.263 eV. The peak at 6.285 eV is identified as a LO-phonon---assisted transition. The latter assertion is verified theoretically by invoking third-order time-dependent perturbation theory.

Optical and dielectric properties and lattice dynamics of some fluorite structure ionic crystals

Some optical, dielectric and lattice properties of three alkaline earth fluorides (calcium, strontium and barium fluorides) and of two other isomorphous fluorides (cadmium and lead fluoride) are reported. Results obtained from experimental studies on infrared and Raman spectra give the fundamental transverse and longitudinal optical lattice mode frequencies, the two-phonon absorption spectra, and the spectra associated with U centre absorptions. Calculations of phonon dispersion curves, density of states and density of com­bined states functions, have been made for all five crystals and these are compared with the experimental results.

Selection Rules for Anharmonic Interactions of Nearest Neighbors in Crystals with the Zinc Blende or Diamond Structure

Selection rules are derived for multiple-phonon processes which are dominated by anharmonic interactions between nearest-neighbor lattice particles. These nearest-neighbor selection rules (NSR) are different from and supplementary to the usual group-theoretical selection rules. NSR for wave vectors at $X$ or $L$ are expressed in Born's (NSRB) and in Keating's (NSRK) formalism. The NSRB refer to anharmonic two-particle interactions; the NSRK allow interactions between two or more particles. The applicability of the NSR to various multiple-phonon processes---with emphasis on infrared two-phonon absorption---is investigated and the results of some relevant model calculations are given. Practical rules for further applications are proposed.

Infra-red cyclotron resonance in n-type epitaxial InAs with evidence of polaron coupling

We have measured infra-red cyclotron resonance in epitaxial thin films of indium arsenide on semi-insulating gallium arsenide and bulk indium arsenide substrates. A novel feature is that the crystal quality and perfection of thin films is found to be better than the best available bulk specimens as indicated by the observation of clear, narrow cyclotron absorptions. By a study of the magnetic absorption at different temperatures we have separated effects due to cyclotron resonance spin up, spin down and impurity resonance. Theoretical extrapolation of results yields a low field, zero k-vector effective mass for conduction band electrons in InAs of m* = (00230±00003)m0. Information on the impurity binding energy is presented. Our two-phonon absorption measurements also provide accurate values of ωTO = 2155±3 cm−1 ωLO = 2418±3 cm−1. Evidence of resonant electron-phonon (polaron) coupling in InAs, of similar nature to that previously reported for InSb, is shown by comparison with theoretically predicted absorption peak positions, effective masses and half widths and has yielded an estimate of Frohlich coupling constant of α = 005±001. The use of such epitaxial layers for optical measurements has been extended to GaAs. Microwave 2 mm cyclotron resonance has been observed in a thin epitaxial film of GaAs yielding an electron effective mass of m* = (0068±0.002)m0.

Note on the Two-Phonon Absorption in Ultrasonic Spin Resonance in Ge

The theory of two-phonon absorption is given for the ultrasonic donor-spin resonance in Ge. The result of calculations predicts that the dependence of two-phonon absorption on the direction of magnetic fields is different from that of one-phonon absorption. It is shown that the observation of two-phonon absorption can be expected in Sb-doped Ge at low temperatures.

Infra-red absorption of beryllium in cadmium telluride: I

The dispersion curves and normal modes of vibration of CdTe have been calculated using a shell model. The single-phonon and combined two-phonon density of states have been computed and the latter is compared with measured two-phonon infra-red absorption. The infra-red absorption induced in CdTe by Be impurity is also calculated and compared with experiment. A resonance mode of Be is observed at 61 cm-1 and a local mode at 391 cm-1; calculated values of these modes obtained using a defect mass approximation are in good agreement with experiment. The structure of observed side bands arising from a simultaneous excitation of the local Be mode and lattice band modes is discussed.

Two-phonon absorption spectrum of NaNO 3

From the low temperature two-phonon absorption spectrum of single crystals of NaNO 3 some information has been obtained about the wave vector dispersion of the phonon branches for the inner (NO - 3)-vibrations and the lattice vibrations.