HighField Energy Distribution, Mobility, and Diffusion of Heavy Holes in pGermanium
Abstract
A novel approximation scheme for hotcarrier distribution functions is introduced and employed in a calculation of the highfield mobility and diffusion coefficients of heavy holes in pGe at 77°K. It is assumed that the heavyhole band has an isotropic and momentumindependent effective mass, and that the holes are scattered elastically by acoustic phonons and inelastically by optical phonons. Interaction with the lighthole and splitoff bands is neglected. The principal results of the calculation are as follows: Over the decade 1 kV/cm<E<10 kV/cm the mobility obeys the powerlaw relation μ~e^{0.8}. The diffusion tensor is moderately anisotropic with D_{II}>D_{⊥}, but neither coefficient departs greatly from the zerofield diffusion constant, 250 cm^{2}/sec, in the field range up to 35 kV/cm. The calculation method makes use of a parametrized model of the distribution function which characterizes the energy dependence of its angular average by two distinct Maxwellians intersecting at the opticalphonon energy, but which makes no a priori assumptions about the angular dependence of the distribution function. Solution for the Maxwellian temperatures is effected by means of a special set of "anisotropy balance equations." These equations involve only the isotropic part of the distribution function and may be used to obtain the parameter values of any parametrized energy distribution, of which the present model is but a special case. Following a procedure originally outlined by Wannier, a derivation of these equations is given first for isotropic scattering and a spherical, constant mass, as required for the pGe calculation. An alternative method is used to derive a more general set of balance equations valid for scattering probabilities of the form P(kk') and spherical bands of arbitrary dispersion law. An errorestimate criterion is formulated. This criterion permits evaluation of the influence on calculated transport quantities of distributionfunction parametrizations with one additional parameter.
 Publication:

Physical Review B
 Pub Date:
 February 1970
 DOI:
 10.1103/PhysRevB.1.1614
 Bibcode:
 1970PhRvB...1.1614P