The fast development and growth of portable electronic devices for wireless communications demand radio frequency (RF) devices that can amplify signal power in the range of microwave frequencies and beyond. The transistor is the core of power amplifier circuits. This requires transistors to be capable of amplifying the current or the power so that larger power will be delivered to the load than the power received from the input signal at high frequency. This work focuses on exploring new materials and new device structures to develop novel devices that can operate at very high speed. In chapter 2, the high frequency performance limitations of graphene transistor with channel length less than 100 nm are explored. A nano-scale transistor simulation approach is presented based on the non-equilibrium Greens' function (NEGF) formalism self-consistently solved with the two-dimensional Poisson equation under the ballistic limit. The simulated results predict that intrinsic cutoff frequency fT of graphene transistor can be close to 2 THz at 15 nm channel length. The parasitic resistances and capacitances are included in the simulation, which degrade the on current Ion, the transconductance gm, and the peak fT. In spite of zero gap, graphene based electronics are promising for specific application. For instance, since graphene and other two dimensional materials are bendable, they show promise for the emerging field of flexible electronics. In chapter 3, we explored the possibility of developing a 2D materials based vertical tunneling device. An analytical model to calculate the channel potentials and current-voltage characteristics in a Symmetric tunneling Field-Effect-Transistor (SymFET) is presented. The current in a SymFET flows by tunneling from a n-type graphene layer to a p-type graphene layer. A large current peak occurs when the Dirac points are aligned at a particular drain-to-source bias VDS. The model shows that the current of the SymFET is weakly dependent on temperature. The resonant current peak is controlled by chemical doping and applied gate bias. The on/off ratio increases with graphene coherence length and doping concentration. The symmetric resonant peak in SymFET is a good candidate for high-speed analog applications. Rest of the work focuses on Gallium Nitride (GaN), a compound semiconductor with high electron mobility, high saturation velocity and large band gap. Several novel device concepts based on GaN heterostructure have been proposed for high frequency and high power applications. In chapter 4, we compared the performance of GaN Schottky diodes on bulk GaN substrates and GaN-on-sapphire substrates. The forward bias IV characteristics of GaN Schottky diodes on bulk GaN substrate and GaN-on-sapphire substrate are well explained by the thermionic emission model. Due to the high quality of the GaN bulk substrate with low dislocation density, GaN Schottky diodes on bulk GaN substrate show > 4 orders of magnitude less reverse leakage current density than those on GaN-on-sapphire substrate. The dislocation induced Schottky barrier lowering is added into the thermionic emission model, which explains the temperature dependent IV characteristics. In additional, we also discussed the lateral GaN Schottky diode between metal/2DEGs. The advantages of lateral GaN Schottky diodes are a), the intrinsic cutoff frequency is in the THz range, and b),lateral GaN schottky diodes can be directly integrated with GaN HEMTs, which offers the feasibility to design GaN MMIC. In chapter 5, a GaN Heterostructure barrier diode (HBD) is designed using the polarization charge and band offset at the AlGaN/GaN heterojunction. GaN HBD is similar to GaAs planar doped barrier (PDB) diode. The polarization charge at AlGaN/GaN interface behaves as a delta-doping which induces a barrier without any chemical doping. The IV characteristics can be explained by the barrier controlled thermionic emission current. One advantage of GaN HBD is the constant capacitance, which reduces the nonlinearity of the device. GaN HBDs can be directly integrated with GaN HEMTs, and serve as frequency multipliers or mixers for RF applications. In chapter 6, a GaN based negative effective mass oscillator (NEMO) is proposed. In the designed structure, a graded AlGaN emitter is used to inject hot electrons into the GaN collector. The current in NEMO is estimated under the ballistic limits. Negative differential resistances (NDRs) can be observed with more than 50% of the injected electrons occupied the negative effective mass (NEM) region. The negative effective mass oscillator with hot electron injection has been simulated by solving the Boltzmann transport equation in 1D real-space and k-space. A stable self-sustaining current oscillation is observed. The designed NEMO structures are grown by MBE on bulk GaN substrates. NDRs are observed in four NEMO samples under DC and pulsed measurements. The influence of traps and defects on NDRs is also discussed.