When the HD model is used velocity overshoot effects could become important
when the carrier temperatures and the electric field are not in equilibrium.
This is the case whenever the electric field changes rapidly, both in space or
in time. An example is shown in Fig. 3.7a where a step like
field profile is assumed. The carrier temperature will respond in the HD
model with retardation. As the mobility is a function of the carrier
temperature the same retardation is seen. As the carrier velocity is defined
as
*v*_{} = *s*_{}^{ . }^{ . }*E* there is a small transition
region where the velocity exceeds its stationary value considerably as shown
in Fig. 3.7b. Also shown is the velocity resulting from
Monte-Carlo (MC) simulations. Due to backscattering the distribution function
in front of the field discontinuity is altered, an effect which cannot be
modeled using a HD model. Overshoot effects are important to model for small
devices as they may alter the performance.

1999-05-31