In this dissertation, we use finite element method together with other numerical techniques to study advanced electron devices. We study the radiation properties in electron waveguide structure with multi-step discontinuities and soft wall lateral confinement. Radiation mechanism and conditions are examined by numerical simulation of dispersion relations and transport properties. The study of geometry variations shows its significant impact on the radiation intensity and direction. In particular, the periodic corrugation structure exhibits strong directional radiation. This interesting feature may be useful to design a nano-scale transmitter, a communication device for future nano-scale system. Non-quasi-static effects in AC characteristics of carbon nanotube field-effect transistors are examined by solving a full time-dependent, open-boundary Schrödinger equation. The non-quasi-static characteristics, such as the finite channel charging time, and the dependence of small signal transconductance and gate capacitance on the frequency, are explored. The validity of the widely used quasi-static approximation is examined. The results show that the quasi-static approximation overestimates the transconductance and gate capacitance at high frequencies, but gives a more accurate value for the intrinsic cut-off frequency over a wide range of bias conditions. The influence of metal interconnect resistance on the performance of vertical and lateral power MOSFETs is studied. Vertical MOSFETs in a D2PAK and DirectFET package, and lateral MOSFETs in power IC and flip chip are investigated as the case studies. The impact of various layout patterns and material properties on RDS(on) will provide useful guidelines for practical vertical and lateral power MOSFETs design.