Vibrational modes in epitaxialTi1−xScxN(001)layers: Anab initiocalculation and Raman spectroscopy study

Abstract

${\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$ alloys were used to investigate the effects of carrier density and the density of states (DOS) at the Fermi level ${E}_{f}$ on vibrational modes, phonon anomalies, and superconducting transition temperatures ${T}_{c}.$ Single-crystal ${\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$ layers, 2000 \AA{} thick, with compositions spanning the entire alloy range $(0<~x<~1),$ were grown on MgO(001) by ultrahigh vacuum reactive magnetron sputter deposition at 750 \ifmmode^\circ\else\textdegree\fi{}C. The Raman spectrum of pure TiN is dominated by two-phonon features while ${\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$ spectra with $0.12<~x<~0.81$ exhibit primarily one-phonon peaks. The acoustic peak softens from 310 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with $x=0.12$ to $\ensuremath{\simeq}200{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with $x=0.81,$ due to the corresponding increase in the lattice constant. All alloy layers exhibit an optical double-peak feature related to local vibrational modes at Ti and Sc sites. The two optical peaks shift from 560 and 640 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{Ti}}_{0.88}{\mathrm{Sc}}_{0.12}\mathrm{N}$ to \ensuremath{\simeq} 480 and 570 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{Ti}}_{0.19}{\mathrm{Sc}}_{0.81}\mathrm{N}$ with an intensity ratio which is proportional to $(1\ensuremath{-}x)/x.$ ${T}_{c}$ for TiN is 5.4 K and decreases steeply with increasing x to ${T}_{c}=4.5,$ 3.4, and 1.9 K with $x=0.06,$ 0.12, and 0.18, respectively. The decrease is due to a reduced DOS at ${E}_{f}$ in combination with a weaker effective coupling at higher x. The strong coupling for TiN is related to an anomaly in the longitudinal acoustic branch, which is absent for ScN, in the calculated phonon dispersion curves. Experimental evidence for the vanishing phonon anomaly is supplied by a broadening in the acoustic Raman peak with increasing x.