Scaling of MOSFETs below the 65 nm technology node makes the theoretical description and modeling of carrier transport in these devices challenging. Not only the degradation of electrostatic channel control but also the carrier transport in the channel is determined by quantum mechanical effects. The two major quantum effects to be taken into account are size quantization in the channel and quantum mechanical tunneling along the channel. Both effects call into question the use of powerful and well-developed simulation methods based on the semiclassical Boltzmann equation. Continued scaling of MOSFET feature sizes well below 50nm requires the development of new simulation techniques capable of incorporating the quantum effects properly. One of the promising approaches developed at the institute is the Wigner function method. An attractive feature of the Wigner function approach is that it also includes all scattering mechanisms in a natural way via the Boltzmann scattering integrals, allowing a transport model to be developed, which accounts for both quantum interference phenomena and realistic scattering mechanisms. The Wigner equation formalism treats the scattering and quantum mechanical effects equally through the corresponding scattering integrals. The collision-free propagation of the carriers is described by the Liouville operator acting on the Wigner function and is similar to that of the Boltzmann equation. Analogous to the solution of the Boltzmann equation, it prompts for a solution of the Wigner equation with a Monte Carlo algorithm. However, because the kernel of the quantum scattering operator is not positively defined, the numerical weight of a particle trajectory increases rapidly in absolute value, and the numerical stability of a trajectory-based Monte Carlo algorithm becomes a critical issue. A multiple trajectories method has been developed at the institute in order to overcome this difficulty. In this algorithm the problem of the growing statistical weight of a single trajectory is addressed by creating a cascade of trajectories with positive and negative finite weights. The latter algorithm allows the annihilation of trajectories with similar statistical properties, which introduces a possibility to control the number of trajectories and reduce the variance of the stochastic solution for the Wigner equation. An important advantage of this algorithm is that it allows the simultaneous solution of the Wigner and Poisson equations: the carrier concentration can be used to update the potential in the device by solving the Poisson equation. Examples of self-consistent potentials for n-i-n Si structures with an intrinsic region of length ranging from 20 nm to 2.5 nm calculated with Wigner and classical Monte Carlo methods are shown in the figure. The doping profile is assumed to increase gradually from the intrinsic channel to the highly doped contacts. Electron-phonon and Coulomb scattering were included. As expected, for thick structures the classical and quantum calculations yield similar results. For the thinnest structure of 2.5, an extra space charge due to electrons tunneling under the barrier becomes important, which results in the potential barrier increase. Despite the potential barrier increase, the current in self-consistent Wigner simulations was approximately 20% higher compared to its classical value found by a self-consistent solution of the Boltzmann and the Poisson equations.