  We study the carrier concentration bistabilities that occur to a highly
photo-excited electron gas. The kinetics of this non-equilibrium electron gas
is given by a set of nonlinear rate equations. For low temperatures and cw
photo-excitation we show that they have three steady state solutions when the
photo-excitation energy is in a certain interval which depends on the
electron-electron interaction. Two of them are stable and the other is
unstable. We also find the hysteresis region in terms of which these
bistabilities are expressed. A diffusion model is constructed which allows the
coexistence of two homogeneous spatially separated phases in the
non-equilibrium electron gas. The order parameter is the difference of the
electron population in the bottom of the conduction band of these two steady
stable states. By defining a generalized free potential we obtain the Maxwell
construction that determines the order parameter. This order parameter goes to
zero when we approach to the critical curve. Hence, this phase transition is a
non-equilibrium first order phase transition.
