3.2.4 Velocity Overshoot

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_$\nu$ = s_$\nu$ ^. $\mu_{\nu}^{}$ ^. 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.

Figure 3.7: a) Carrier temperature response for a step in electric field when using the HD model. b) Carrier mobility and velocity response for a step in electric field when using the HD model.