TABLE OF CONTENTS Aiming at steady-state device simulation, the position-dependent and time-invariant BE is to be considered. The force field and all material properties are independent of time.
This equation, which is posed in the simulation domain D, is supplemented by boundary conditions modeling the interaction of the device with the environment. The distribution function is normalized as (see also Section 3)
In the scattering operator Q = Q g ? Q l the scattering rate S is independent of time:
To describe a time-invariant system an absolute time scale is not needed. Only the time difference between two consecutive events is significant. A phase space trajectory with the initial condition K( t 0) = k 0 and R( t 0) = r 0 is obtained by formal integration of the equations of motion.
In addition to the time argument of the functions K and R, the parameters t 0, k 0, r 0 describing the initial condition of the phase space trajectory are stated explicitly. Expressions (61) can be read as the phase space position of a particle at time t that passes through k 0 and r 0 at time to. In this regard, the order of t 0 and t is irrelevant. For t ? t 0 the meaning of k 0 and r 0 would be that of a final...
