The scattering of holes in ^-type germanium by acoustical and optical phonons, and by ionized impurities has been studied over a wide range of temperature from 7 to 300°K, and for impurity concentrations from 10 13 to 10 17 cm" 3 . The mobility was analyzed on the basis of the following approximations: (1) The light-and heavy-hole valence bands are parabolic with spherical constantenergy surfaces and effective-mass ratios of 0.043 and 0.35;(2) the relaxation time for lattice scattering is the same for the heavy and light holes; and (3) the ionized impurity scattering is describable by the Brooks-Herring formula with the scattering limited to intraband transitions. The following results were obtained: (1) The expectation was substantiated that the lattice scattering at JP<70°K can be attributed to acoustical phonon interactions; the mobility ju a c=3.37X10 7 T~3 12 cm 2 /V-sec was obtained by treating it as the sole adjustable parameter in the range 10 to 70°K; (2) the stronger T~2-3 dependence of mobility in the range 120 to 300°K can be attributed to the advent of optical mode scattering if the ratio of optical to acoustical mode coupling constants (8 op /Sac) 2 is chosen to be 3.8; (3) the Brooks-Herring formula describes the ionized impurity scattering very well from 30 to 300°K for impurity concentrations Ni< 10 16 cm -3 , but overestimates the mobility for higher Ni or lower T. The eventual failure of the analysis may be attributed to the neglect of carrier-carrier and interband ionized impurity scattering.
UJ o UJ o o LL. Q FIG. 2. Arrhenius plot for self-diffusion in Zr. Open circles are data of Federer and Lundy (Ref. 16); solid line represnets the fitted equation (5).have the expected magnitudes, and the fit to available data is as close as can be. Although the present model applies strictly to Ti, Zr, and Hf, where the metastable oo phase has been reported, the authors believe that a similar mechanism should apply to the other anomalous bcc metals, the only requirement being the tendency to form trigonal bonds on a (111) plane, as in the co structure. Further work, both theoretical and experimental, is needed to elucidate this point. A cluster-variation study of the temperature dependence of the concentration of co embryos above T 0 is in progress.Highly resolved satellite peaks due to acoustoelectrically amplified phonons are observed on the wings of double-crystal x-ray diffraction peaks in InSb single crystals. The frequencies of the observed phonon peaks range between 0.9 and 6.3 GHz, depending on carrier concentration. Second-and third-order satellites are also visible in all profiles, showing the generation of second and third harmonics of the fundamental frequencies of the amplified phonons and, possibly, the existence of multiphonon scattering.
This paper contains a description of an experimental determination of the energy distribution functions of hot holes in germanium, and the application of the results to the analysis of the dominant scattering and energy-loss mechanisms. The distribution functions are obtained from the study of the modulation of the free-hole, intervalence-band absorption of infrared radiation by application of pulses of high electric field. Details of the distribution function can be obtained because a correlation exists between the absorption at a given wavelength and the hole concentration at a given energy. An auxiliary investigation of the temperature dependence of the equilibrium absorption spectrum empirically supplies the necessary calibrating relations for the above correlation and an approximate valence-band structure with equivalent spherical energy surfaces. The hot-carrier studies were made at field strengths up to 2800 V/cm/at 77°K, on germanium samples with hole concentrations in the range of 10 15 /cm 3 . The infrared modulation effects are themselves of interest and the techniques are described in detail. Positive and negative modulation of transmitted intensity as high as 50% could be obtained. The dependence of the modulation (and distribution functions) onxrystallographic direction, carrier concentration, and polarization of the light was investigated. Three features of the experimental distributions stand out: (a) the non-Maxwellian character, typified by the relatively small number of high-energy carriers, (b) the slow rise in average energy from 0.01 to 0.028 eV as the field strength is raised to 2000 V/cm, and (c) the large ratios of drift to root-mean-square velocity, z>dArms^0.4 for E>400 V/cm, corresponding to strong displacement of the hole distributions in momentum space. These features, together with energy-loss rate calculations, substantiate the importance of inelastic scattering and the dominant role of optical-phonon interactions. A picture of the steady-state hot-carrier effect emerges, emphasizing a cyclic streaming motion of holes in k space, in contrast to the usual diffusion formulation. Briefly indicated are some consequences of this picture regarding the relative population of light and heavy holes, the anisotropy of infrared absorption and hot-carrier mobility, and the efficiency of impact ionization of deeplying acceptors. 6 For review articles and early references on hot carriers, see
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