In Section 2.6 and Section 2.7 purely quantum mechanical effects and quantum transport have been briefly discussed. During the derivation of the BTE, purely quantum mechanical effects such as confinement have been ignored. As stated in Section 2.6, a Schrödinger equation for the confined electron gas has to be solved in order to obtain the correct electron density. Solving the Schrödinger equation (cf. Equation (2.56)) self-consistently with the BTE for electrons and holes as well as Poisson’s equation might be computationally too demanding. Thus, approximations are sought, which at least capture the most important characteristics of confinement and quantum transport. Since having the physically correct electron concentration at the interface of any MOS structure is of highest importance, the effect of carrier confinement should be correctly reproduced by any approximation. One of the first approximations to be used was the improved modified local density approximation (IMLDA) [7] and its predecessor MLDA [80]. Both methods are based on solutions of the Schrödinger equation for an infinitely wide square well potential, where IMLDA also takes the electric field normal to the oxide-semiconductor interface into account. Nevertheless, IMLDA can only be used to obtain a corrected electron or hole density at the interface of MOS structures, where carrier confinement occurs. As will be shown later in this work, the important case of screening of a single fixed point charge in a semiconductor or insulator needs to be correctly and generically described. The model to describe carrier confinement considered in this work is the density gradient approximation.