Temperature dependence of intrinsic infrared absorption in natural and chemical-vapor deposited diamond

Abstract

Empirical rules are derived that describe the temperature dependence of the infrared absorption spectra of pure diamond for photons of energy hnu=500-4000 cm(-1). We show that with increasing temperature in the range 14<T<850 K, all the features in the infrared spectrum shift to lower frequency at very similar fractional rates. The rate for all the features is, to +/-13%, Deltanu/nu=cn(E-e) where c=-0.027 and n(E-e) is the Bose-Einstein population factor with E-e=860 cm(-1). The intensities of the optical absorption involving the creation of two phonons of energies E-1 and E-2 are expected to increase with T in proportion to [1+n(E-1)][1+n(E-2)]. This expression, combined with the fractional shift rule for the energies of each mode, allows high temperature two-phonon spectra to be simulated accurately from a low temperature spectrum. The temperature dependence of the three-phonon band between 2665 and 3900 cm(-1) is precisely fitted without adjustable parameters by using the shift rule in conjunction with a modified density of three-phonon states. Absorption at 10.6 mum is shown to involve the simultaneous destruction and creation of phonons. Its strong temperature dependence in the range 300<T<800 K is accurately described, without any adjustable parameters, in terms of three main components: the destruction of one phonon of 335 cm(-1) and the creation of a second of 1275 cm(-1); the shift to lower energy of the phonons; and a three-phonon process involving the destruction of one and the creation of two phonons. The analysis demonstrates why diamond has to be effectively cooled when used for the windows of a high-power CO2 laser. (C) 2002 American Institute of Physics.