Phonon density of states of bulk gallium nitride

Abstract

We report the measured phonon density of states of a bulk GaN powder by time-of-flight neutron spectroscopy. The observed one-phonon excitation spectrum consists of two broad bands centered at about 23 and 39 meV corresponding to the acoustic and the first group of optical phonons; two sharp bands of upper optic modes at about 75 and 86 meV; and a gap of 45-65 meV. The phonon dispersion curves, lattice specific heat, and Debye temperature are calculated from fitting the data with a rigid-ion model.

Structural and vibrational analysis of nanocrystalline Ga1−xMnxN films deposited by reactive magnetron sputtering

“…Consistently, the shape of the spectrum of the nanocrystalline undoped sample resembles a broadened version of the vibrational mode density of states of the corresponding crystal 26 and with the density of states ͑DOS͒ extracted from neutron diffraction experiments. 27 The influence of Mn in the vibrational properties of the Ga 1−x Mn x N films was noticed through general aspects of the changes produced in the spectrum, but no apparent specific band was found. The presence of Mn affects more intensively the band related to the LO modes due the anisotropic changes in the lattice parameters of the GaN structure caused by Mn insertion in the Ga site, which is consistent with the strong increase in the ␤11 parameter for small x values ͑Table I͒.…”

Unprecedented Integral-Free Debye Temperature Formulas: Sample Applications to Heat Capacities of ZnSe and ZnTe

“…Consequently, all the approximation formulas derived in Appendix B, for low-and high-capacity branches of the ( ) function (cf. Figure 9), can be readily used for calculations of the ℎ ( ℎ ) dependence implied by (29). This means, in particular, that (27) and (28) can be simultaneously used (as already indicated by the inclusion of the subscript "h") for high-precision calculations of the dependencies of the "true" Debye temperatures,…”

“…In view of the analogy of the analytical connections (1) and (29), between the ( ) = Θ ( )/ ratios with ( ) values, on the one hand, and the ℎ ( ) = Θ ℎ ( )/ ratios with ℎ ( ) values, on the other hand, it is obvious that the physical causes of the general differences, Θ ℎ ( ) > Θ ( ) (see Figures 4 and 5), between "true" and effective Debye temperatures, must be sought in the mechanisms which are responsible for the inherent differences, ( ) − ℎ ( ) > 0 (Section 2), between measured (isobaric) and theoretical (isochoric/harmonic) lattice heat capacities. For nonmagnetic materials these differences are well known to be due to (i) possible electronic contributions, ( ) ( ) = 1 (in (5)), which are responsible for qualitatively different asymptotic behaviours, that is, ( ) → 1 versus ℎ ( ) → 3 3 , in the → 0 limit,…”

“…Of considerable interest, particularly from theoretical points of view [3,14,21,28,29,32,36,56,72], is the determination of the "true" ( ℎ ( )-related) Debye temperature curves, Θ ℎ ( ). The latter are defined with respect to the harmonic (isochoric) lattice heat capacities, ℎ ( ) (see (4)), by [14,21] …”

“…Furthermore, towards higher temperatures, many Θ ( ) curves show a more or less pronounced increase up to certain material-specific maxima, Θ max , the actual magnitudes of which are in many cases significantly higher than the respective Θ min levels. Such typical nonmonotonic behaviours of Θ ( ) curves in the cryogenic region have been found in particular for Si and Ge [18][19][20][21] as well as for a large variety of III-V [11,12,15,[22][23][24][25][26][27][28][29][30], II-VI [14,[31][32][33][34][35][36][37][38], and I-VII [16,39,40] materials.…”