Thermal Conductivity of Electron-Irradiated Germanium

Abstract

Measurements of the change In low-temperature thermal conductivity of high-purity single-crystal Ge were made upon 2-MeV electron irradiation and annealing. Strong scattering of phonons by small concentrations of radiation-induced defects is observed. The additive thermal resistivity increases as the 0.58 power of the time integrated flux 3> rather than the first power observed for GaAs. Irradiation to 3.4X10 18 2-MeV e/cm 2 below 50°K gave 1/K-1/JTo-1.7XlO" 11^5 * cm-deg/W at 20°K. For <S> between 10* and 10" 2-MeV e/cm 2 , the magnitude of the increase in thermal resistivity of Ge is comparable to that observed for GaAs even though the lattice strain is much smaller. Strain and mass-difference scattering theories cannot explain the Ge data as they can the GaAs data. The Keyes or Pyle phonon-electron scattering theories, however, can explain the Ge results. A small amount of annealing of the additive thermal resistivity was observed to begin at 35°K in the high-purity Ge studied here. This is in agreement with the first annealing stage seen by electrical measurements in degenerate n-type Ge by MacKay and Klontz and in degenerate _^-type Ge by Gobeli. Large recovery states are seen at 125 and 200°K. In the annealing-temperature interval between 140 and 200 °K, the thermal conductivity is strongly dependent on electron trapping and can be significantly decreased by a short illumination which changes the charge states of the defects. This demonstrates the phonon-electron scattering nature of the thermal resistivity. Measurements of the temperature dependence of the thermal conductivity indicate that the defects anneal as point defects. The large precipitation of point defects seen in GaAs is not seen in Ge, and almost complete recovery of the radiation-induced defects occurs by 405°K. Minima are observed in the temperature dependence of the thermal conductivity, suggesting localized mode scattering.

Bombardment-Produced Defects inp-Type Germanium at Low Temperatures

“…14 For a given generation rate the electric field of the calculated generation rate seems to be roughly 15% below the experimental field although the slopes of the curves are in excellent agreement. The difference in the fields could be accounted for by saying that the effective electron velocity is not v but really v cos0, since this would require a slight increase in the field to obtain the same theoretical generation rate.…”

Bound-Electron-Lattice Coupling and Vibronic Spectra

“…IIIC we analyze the special case of the intraconfiguration transition 5 D 0 -^7FQ of Sm 2+ for which the even coupling vanishes, and show that for it the vibronic structure approximates a part of the density of states of the vibrations of the undisturbed lattice. Within the Born-Oppenheimer approximation, 9 we write the total wave function for the coupled electronlattice system as *(',e) = *(r,G)*(0), (la) where \[/, the electronic wave function, is a function of the electron coordinates (r) and nuclear normal mode (Q) coordinates, and <j> is the nuclear wave function. Further, under the Franck-Condon principle, that the positions of the nucleii remain fixed during an electronic transition, we may write the probability of a dipole transition between electron-lattice states as 1 (%>n'\P<\*Jn)=(f j \P*\4'i)…”

“…For the case of inversion symmetry (case II), the electric-dipole transition probability becomes, to terms of first order in U K Q K , (9) where the subscripts u and g refer to odd and even vibrational modes. The displacement a K in (9) is finite only for the even modes, since for case II the charge distribution |#/Vy| is on a time average still even, and can interact only with the even vibrations to give a displacement of the even normal coordinates, Q Kg .…”

“…It is not clear at this time how this complication affects the perturbation treatment used to obtain Eq. (9) or how it affects the assumption, inherent in the electrostatic-coupling small. The vibronic structure recently reported by Kiss 26 for the transitions 77Y 2 > -> 8£< 2 > and 1T^ -* 8T 2 (2) of Dy 2+ in CaF 2 and SrF 2 may be an indication, however, that a K need not always be small.…”

Effects of Electron Irradiation on the Thermal Conductivity ofn- andp-Type Germanium

“…This observation was compared to the phenomenon already noticed by Goff and Pearlman 11 and related, on the basis of the Keyes model, 8 to the scattering of phonons by electrons bound to donors. The effects of electron 12 and fast-neutron 10 ' 13 irradiations on the thermal conductivity of initially ^-type germanium were also studied: A pronounced decrease of K on the lowtemperature side of the peak was obtained. In both studies, however, the electron and fast-neutron doses used were such that the crystals measured after irradiations were all converted to ^>-type.…”