Collective impact ionization has been used to explain lock-on in semi-insulating GaAs under high-voltage bias. We have used this theory to study some of the steady-state properties of lock-on current filaments. In steady state, the heat gained from the field is exactly compensated by the cooling due to phonon scattering. In the simplest approximation, the carrier distribution approaches a quasi-equilibrium Maxwell-Boltzmann distribution. In this report, we examine the validity of this approximation. We find that this approximation leads to a filament carrier density that is much lower than the high density needed to achieve a quasi-equilibrium distribution. Further work on this subject is in progress.