Raman spectra of isotopic GaN

First-order Raman spectra of wurtzite GaN made from natural Ga and isotopically pure ¹⁵N and natural N (99.63% ¹⁴N) were measured at low temperature. The Raman frequencies of the polar optical phonons [A₁(TO,LO), E₁(TO,LO)] shift according to the inverse square root of the reduced masses, as expected. The isotope shifts of the two nonpolar E₂ modes deviate significantly from the reduced-mass behavior as well as from the dependence expected for pure N or Ga vibrations which might be expected in view of their large frequency difference. This indicates that the E₂ modes involve mixed Ga and N vibrations. From fits to the experimental data with a coupled two-mode model we determine the mode eigenvectors. They confirm the results of an ab initio calculation which we have done for the zone-center vibrations of wurtzite GaN. Our calculations also predict a vanishing coupling between the two B₁ silent modes. We also measured a ⁿᵃᵗGa¹⁴N0.5¹⁵N0.5 alloy sample. Additional negative frequency shifts due to isotope disorder are observed for the A₁(TO,LO), E₁(TO,LO), and the high-frequency E₂ modes as compared to the reduced-mass or coupled-mode behavior. An estimate from second-order perturbation theory provides a quantitative explanation of this result.