We present a novel method to explicity solve the Boltzman equation for highly energetic electrons interacting with polar optical phonons and scattering mainly in forward direction. Our approach reduces the collision integral of the Boltzmann equation into a differential operator which is much easier to manipulate than the integral form and does not require a relaxation time approximation. The spatial diffusion of highly energetic electrons is calculated and discussed in context with high speed velocity transients ("ballistic transport"). Explicit results compare favorably with sophisticated Monte Carlo simulations and are well suited to treat complex transport problems in submicron III-V devices. As an example we calculate the current voltage characteristic of a "camel-back diode".
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