SOLUTION OF THE MULTIVALLEY BOLTZMANN TRANSPORT-EQUATIONS IN SI AND GAAS BASED ON THE TIME SCALES OF HYDRODYNAMIC EQUATIONS

The previously developed hydrokinetic transport theory is used to arri ve at a multivalley transport model for the electron distribution func tion evolving at the energy relaxation scale. The hydrokinetic distrib ution described by hydrodynamic parameters, including the density, mea n energy, and average velocity, is introduced to approximate the kinet ic distribution. The developed multivalley hydrokinetic model, togethe r with the Monte Carlo method, is applied to study nonequilibrium ener gy and momentum distribution functions of electrons in n-type: Si [100 ] and GaAs. It is shown that the hydrokinetic concept can be used to c haracterize extreme nonequilibrium phenomena of the distribution and t ransport parameters in terms of the relaxation scales of hydrodynamic parameters. The study suggests that evolution of the distribution is s trongly influenced by energy relaxation. It is also found that in ultr afast transient situations the influence of velocity relaxation on the distribution function is more pronounced if the ratio tau(epsilon)/ta u(m) is larger, where tau(epsilon) and tau(m) are energy and momentum relaxation times, respectively. In general, similar influences of ener gy and momentum dependences also show in the relaxation times. hi Si a t room temperature, the ratio is near or below 10 at low or medium fie ld, and the distribution, which is subjected to a rapid change in fiel d, weakly depends on the velocity relaxation. in the Gamma valley of G aAs, although the ratio is not larger than that in Si, effects of velo city relaxation are considerably stronger due to much more pronounced velocity overshoot. The hydrokinetic distribution at the energy relaxa tion scale therefore provides a good description for electrons in Si i n extreme nonequilibrium situations, but not in GaAs during the strong overshoot/undershoot interval. In the L valleys the ratio is much lar ger than 10 at low or medium fields. Consequently, The L-valley distri bution function subjected to a drastically increasing field from a low value is also strongly influenced by velocity relaxation even though no overshoot is observed. (C) 1995 American Institute of Physics.