Internal Friction and Defect Interaction in Germanium: Experimental

Abstract

Some aspects of the interrelation of lattice defects and impurities in single crystals of germanium have been studied by means of the internal friction method. The logarithmic decrement of Ge crystals undergoing small-amplitude longitudinal forced vibrations was measured as a function of temperature, frequency, and concentration of impurities and edge dislocations.A peak in the curve of logarithmic decrement vs temperature was found at 380\ifmmode^\circ\else\textdegree\fi{}C, for a frequency of 40 kc/sec. From the peak shape and from the dependence of its position on the applied vibrational frequency, it was inferred that the peak is due to an anelastic relaxation phenomenon with relaxation time $\ensuremath{\tau}={\ensuremath{\tau}}_{0}\mathrm{exp}(\frac{H}{\mathrm{RT}})$, where ${\ensuremath{\tau}}_{0}={10}^{\ensuremath{-}13\ifmmode\pm\else\textpm\fi{}1}$ second and $H=25\ifmmode\pm\else\textpm\fi{}3$ kcal/mole. At high temperatures the logarithmic decrement was found to rise with temperature according to the equation $\ensuremath{\delta}={\ensuremath{\delta}}_{0}\mathrm{exp}(\ensuremath{-}\frac{{H}^{\ensuremath{'}}}{\mathrm{RT}})$, where ${H}^{\ensuremath{'}}=23\ifmmode\pm\else\textpm\fi{}2$ kcal/mole.A phenomenological interpretation of these results is given in terms of a mechanism depending on the interaction of lattice vacancies with the edge components of dislocations present in the specimens. By using this interpretation, the activation energies for the generation of lattice vacancies, for their diffusion, and for self diffusion in germanium are derived. The respective values, which are 48\ifmmode\pm\else\textpm\fi{}4, 25\ifmmode\pm\else\textpm\fi{}3, and 73\ifmmode\pm\else\textpm\fi{}5 kcal/mole, are in agreement with analogous values obtained by other observers. It is also implied that ${10}^{10}$ vacancies/${\mathrm{cm}}^{3}$ are normally forzen into Ge crystals during growth. This concentration corresponds to the equilibrium concentration in the vicinity of 550\ifmmode^\circ\else\textdegree\fi{}C.