The physics of electron devices is investigated within the framework of Semiclassical Monte Carlo and Path-Sum Monte Carlo analysis. Analyses of shortchannel III-V trigate nanowire and planar graphene FETs using a Semiclassical Monte Carlo algorithm are provided. In the case of the nanowire FETs, the bandstructure and scattering effects of a survey of materials on the drain current and carrier concentration are investigated in comparison with Si FETs of the same geometry. It is shown that for short channels, the drain current is predominantly determined by associated change in carrier velocity, as opposed to changes in the carrier concentration within the channel. For the graphene FETs, we demonstrate the effects of Zener tunneling and remote charged impurities on the device performance. It is shown that, commensurate with experimental evidence, the devices have great difficulty turning off as a result of the Zener tunneling, and have a conductivity minimum which is affected by remote impurities inducing charge puddling. Each material modeled is matched with experimental data by calibrating the scattering rates with velocity-field curves. Material and geometry specific parameters, models, and methods are described, while discussion of the basic semiclassical Monte Carlo method is left to the extensive volume of publications on the subject. Finally, a novel quantum Path-Sum Monte Carlo algorithm is described and applied to a test case of two layered 6 atom rings (to mimic graphene), to demonstrate the effectiveness of the algorithm in reproducing phase transitions in collective phenomena critical to possible beyond-CMOS devices. First, the method and its implementation are detailed showing its advantages over conventional Path Integral Monte Carlo and other Quantum Monte Carlo approaches. An exact solution of the system within the framework of the algorithm is provided. A Fixed Node derivative of the Path Sum Monte Carlo method is described as a work-around of the infamous Fermion sign problem. Finally, the Fixed Node Path-Sum Monte Carlo algorithm is implemented to a set of points showing the accuracy of the method and the ability to give upper and lower bounds to the phase transition points. / text