Resonant Raman-active localized vibrational modes inAlyGa1−yNxAs1−xalloys: Experiment and first-principles calculations

Abstract

The localized vibrational modes associated with substitutional aluminium and nitrogen atoms in ${\mathrm{Al}}_{y}{\mathrm{Ga}}_{1\ensuremath{-}y}{\mathrm{N}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}$ have been studied within first-principles density functional theory using a supercell approach. Localized vibrational modes related to $\mathrm{N}\text{\ensuremath{-}}{\mathrm{Al}}_{m}{\mathrm{Ga}}_{4\ensuremath{-}m}$ $(1\ensuremath{\leqslant}m\ensuremath{\leqslant}4)$ complexes have been identified, which reveal the formation of $\mathrm{N}\text{\ensuremath{-}}{\mathrm{Al}}_{4}$ units well above random abundance, in qualitative agreement with a large calculated value $(391\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$ of the Al-N bond formation energy. We determine the resonant Raman-active modes from the selection rule obtained by calculating the electron-phonon coupling strength and optical transition matrix elements and compare them with resonant Raman spectroscopy measurements. The localized modes from Raman scattering measurements with frequencies around 325, 385, 400, 450, 500, and $540\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ are found to be in good agreement with the calculated modes (326, 364, 384, 410, 456, 507, and $556\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$). The modes are classified as follows: the two modes at 326 and $556\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ belong to the $\mathrm{N}\text{\ensuremath{-}}\mathrm{Al}{\mathrm{Ga}}_{3}$ configuration; there are three modes which belong to $\mathrm{N}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{Ga}}_{2}$ with frequencies at 326, 364, and $507\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$; the $\mathrm{N}\text{\ensuremath{-}}{\mathrm{Al}}_{3}\mathrm{Ga}$ configuration gives rise to modes whose frequencies are 384 and $456\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$; and the mode at a frequency of $410\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ belongs to the $\mathrm{N}\text{\ensuremath{-}}{\mathrm{Al}}_{4}$ complex. The comparison of line intensities from samples before and after rapid thermal annealing allows us to experimentally distinguish vibrational modes associated with different clusters, in agreement with the theoretical assignments.