The general dynamic features of the velocity and energy balance equati
ons are investigated. For the small-signal response an analytical theo
ry based on the linear response correlation functions is developed. Fo
r the nonlinear and large-signal response the direct numerical solving
of the balance equations has been used. For both responses good agree
ment with the Monte Carlo simulation of the small- and large-signal ch
aracteristics of hot electrons in n-InP are obtained. The eigenvalue s
pectrum for hot electrons in n-InP is analyzed using the analytical co
nsideration of the balance equations. The minimum frequency of the int
rinsic relaxation processes of the hot carrier system is shown to be a
bout 5-10 THz at high electric fields E greater-than-or-equal-to 30 kV
/cm. Possibilities of using of this high frequency in the high-speed d
evices are discussed.