Temperature dependence of the photothermal conductivity of high-purity germanium containing very low concentrations of Al, B, and P

The temperature dependence of the photothermal conductivity in the far-infrared region (10 to 200 ${\mathrm{cm}}^{-1\mathrm{}}$) is studied in pure germanium containing ∼${10}^{10}$ atoms/${\mathrm{cm}}^3$ of Al, B, and P. A theoretical expression for the temperature dependence of the intensities is given which is in excellent agreement with the experimental results. From these very detailed spectra, reliable values for the ground-state energies of the impurities are obtained and a quantitative chemical analysis of the impurity concentration as a function of the position in a Czochralski-grown single crystal is achieved.