We present a rigorous analysis of the thermal conductivity of bulk silicon (Si) and Si nanowires (Si NWs) which takes into account the exact physical nature of the various acoustic and optical phonon mechanisms. Following the Callaway solution for the Boltzmann equation, where resistive and nonresistive phonon mechanisms are discriminated, we derived formalism for the lattice thermal conductivity that takes into account the phonon incidence angles. The phonon scattering processes are represented by frequency-dependent relaxation time. In addition to the commonly considered acoustic three-phonon processes, a detailed analysis of the role of the optical phonon decay into acoustic phonons is performed. This optical phonon decay mechanism is considered to act as acoustic phonon generation rate partially counteracting the acoustic phonon scattering rates. We have derived the analytical expression describing this physical mechanism which should be included in the general formalism as a correction to the resistive phonon-point-defects and phonon-boundary scattering expressions. The phonon-boundary scattering mechanism is taken as a function of the phonon frequency, incidence angles, and surface roughness. The importance of all the mechanisms we have involved in the model is demonstrated clearly with reference to reported data regarding the isotopic composition effect in bulk Si and Si NW samples. Namely, our model accounts for previously unexplained experimental results regarding (i) the isotope composition effect on the thermal conductivity of bulk silicon reported by Ruf et al. [Solid State Commun. 115, 243 (2000)], (ii) the size effect on κ(T) of individual Si NWs reported by Li et al. [Appl. Phys. Lett. 83, 2934 (2003)], and (iii) the dramatic decrease in the thermal conductivity for rough Si NWs reported by Hochbaum et al. [Nature (London) 451, 163 (2008)].

We report on the application of Brillouin spectroscopy as an approach to non-destructive optical characterization of the elastic constants of semiconductors with the wurtzite symmetry. Three different configurations were used to achieve a complete determination of the elastic stiffness constants of bulk AlN substrates grown by the Physical Vapor Transport (PVT) method. The scattering diagrams of these three configurations are presented showing the geometrical arrangements necessary to observe all the elastic stiffness constants for the partially nontransparent wurtzite type of the crystal structure. Because aluminum nitride (AlN) is a suitable material for the fabrication of light emitting devices, the characterization of its elastic constants was carried out very precisely to provide a reliable data which can be used for the determination of residual stress arising during the growth of AlN thin films or wide band gap semiconductor thin films on substrates of AlN. . Successful preparation of these materials as heterostructures or multiquantum wells has proven the possibility of growth techniques. However, conventionally used methods require the deposition of layers of the nitride on oriented substrates of sapphire, silicon, or gallium arsenic. As a result, the quality of the obtained crystal is strongly influenced by the strains at the interface with the substrate because of the lattice parameters mismatch. III-nitride single crystals with the wurtzite symmetry are considered ideal substrates for wide band gap semiconductors epitaxy [2,3] due to the compatibility of the lattice parameters and the thermal expansion coefficients. However, it is still essential to have knowledge of the effects of residual stress resulting from crystal growth and device processing on the behavior and reliability of semiconductor devices. Precise computation of stresses requires knowledge of the elastic stiffness constants of the grown material as precisely as possible.Our objective in this work is to illustrate a series of Brillouin scattering diagrams showing the geometrical arrangements necessary to observe all the elastic constants of semiconductors with the wurtzite symmetry. Because previous reports of the elastic constants of wurtzite bulk AlN in the literature have tended to disagree with one another, we include a precise and detailed explanation of the derivation of these vibrational parameters from the Brillouin spectra of Bulk AlN single crystals.

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