Models In previous sections, we have mentioned device modeling and in some cases shown device simulation results, but SO far we have been deliberately vague about the actual techniques used for device modeling. In the present section we will remedy this situation and go into some detail into the actual device models used, what they tell us, and some interesting new developments in the field. Certainly the most commonly used formalism for device simulation is that of drift-diffusion models. In a drift-diffusion model, the semiconductor device equations are derived from the Boltzmann Transport Equation using numerous approximations. The equations to be solved are the Poisson equation and the current continuity equations [17], eE=p, together with the constitutive relationships for current density (the actual drift-diffusion equations): II-48 j,=qpu,E-qD,Vp. In these equations, E and J are the electric field and current density vectors, p is the net charge density, R and G are carrier recombination and generation rates, and n and p are the electron and hole densities. In addition, q is the electronic charge, and and D are carrier mobility and diffusivity, respectively. These equations are discretized and solved on the mesh using finite-difference or finite-element techniques [242,243]. Drift-diffusion models are highly evolved, and relatively speaking, not terribly computationally intensive, except in the case of 3D models. Because of the assumptions they are based on, however, they are ill-suited to treat many effects becoming important in small-geometry devices, such as velocity overshoot, carrier heating, and quasi-ballistic transport [244]. Nevertheless, because of their computational efficiency, they remain the workhorse simulation tool, even for deep submicron devices. The next step up the device-simulation hierarchy is hydrodynamic and energy balance codes. Based on fewer assumptions, these codes begin to treat non-local effects, but are correspondingly more computer-intensive, based on five equations of state