Experimental Determination of the Energy Distribution Functions and Analysis of the Energy-Loss Mechanisms of Hot Carriers inp-Type Germanium

Abstract

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\ifmmode^\circ\else\textdegree\fi{}K, on germanium samples with hole concentrations in the range of ${10}^{15}$/${\mathrm{cm}}^{3}$. 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) on crystallographic 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, $\frac{{v}_{\mathrm{d}}}{{v}_{\mathrm{rms}}}\ensuremath{\gtrsim}0.4$ for Eg400 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.