Raman selection rules in C⁴_6v hexagonal crystals: allowed combinations and overtones of vibrational modes in wurtzite GaN

Abstract

A discrete set of oscillators belongs to the critical points in the lattice vibration spectrum. The vibrational states of crystals are classified according to appropriate irreducible representations of the relevant wave vector space groups. Suitable space-group selection rules are used to determine the active one and two phonon combinations and overtone processes in hexagonal structures. Experimental Raman spectra of the hexagonal C 4 6v GaN are discussed in terms of the derived selection rules.

Characterization of bulk GaN crystals grown from solution at near atmospheric pressure

“…In the future, we plan to carry out these measurements using a single mode laser. We note that for GaN, eight optical phonon modes are predicted, 1A 1 (TO), 1A 1 (LO), 2B 1 , 1E 1 (TO), 1E 1 (LO), and 2E 2 , all of which have been observed with RS, with the exception of the 2B 1 modes which are optically inactive [7][8][9]. The peak positions and intense sharp lines indicate good local crystalline quality and stress-free crystals, and the 1A 1 (LO) phonon lineshape is consistent with a low free carrier concentration.…”

Multi‐phonon processes in C 6V 4 (P6 3 mc) hexagonal semiconductors: GaN, ZnO, ZnS, BeO, CdS, and Al 2 O 3 – sapphire: D 3d 6 (R3c)

“…If the KP of two different modes contains an allowed mode in Table 1, the combination is permitted. For example, the combination of Γ 5 and M 3 modes results in Γ 5 ⊗ M 3 = M 3 ⊕ M 4 . It means, that we may measure the resulting frequency; w(M 3 ) + w(M 4 ).…”

“…The number and symmetries of vibrational modes in any compound with a well established space group is determined by so -called reducible representation of lattice modes (LMRR) [2,3], ( also called as displacement representation DR [4]). The explicit form of the LMRR for hexagonal GaN has been recently derived [5].…”