Thermomodulation Spectra of Al, Au, and Cu

Thermotransmission and thermoreflection measurements were made on semitransparent films of Al, Au, and Cu at about 370 and 120 K in the range 0.5-5 eV. The data yield the thermomodulation spectrum $\Delta {\epsilon }_2$ of the imaginary part of the dielectric constant directly, without Kramers-Kronig analysis. A comparison of the interband region of $\Delta {\epsilon }_2$ for Cu with the piezo-modulation spectrum of a single crystal shows that broadening of the Fermi distribution and volume strain caused by thermal expansion are the principal causes of the $\Delta {\epsilon }_2$ spectrum. The $\Delta {\epsilon }_2$ spectrum for Al is particularly simple and can be discussed using closed-form expressions for the optical conductivity. It appears that the temperature dependence of the interband relaxation time for transitions across gaps produced by $\left|V_{111}\right|$ is smaller than that for transitions across gaps caused by $\left|V_{200}\right|$, which in turn is smaller than that for the infrared intraband transitions.