A new Monte Carlo simulation technique considering the uncertainty relation and the Pauli principle is proposed for analyzing a quasi-ballistic metal oxide semiconductor field-effect transistor (MOSFET). Instead of the conventional phase space that consists of continuous position and momentum, a discrete phase space represented by a complete basis set of the state vector is employed. The carrier dynamics in the device are analyzed using the Monte Carlo simulation framework, in which a possible transition among numerous probabilistic transitions between these discrete states is selected using random numbers. The technique is applied to a 90nm MOSFET. Analysis shows how the phonon scattering disturbs the ballistic transport, and yields a result that the backscattered flux due to phonon scattering amounts to 27% of the original carrier flux injected from the source for the device.