Recently, high-κ materials have become the focus of research and been extensively utilized as the gate dielectric layer in aggressive scaled complementary metal-oxide-semiconductor (CMOS) technology. Hafnium dioxide (HfO2) is the most promising high-κ material because of its excellent chemical, thermal, mechanical and dielectric properties and also possesses good thermodynamic stability and better band offsets with silicon. Hence, HfO2 has already been used as gate dielectric in modern CMOS devices. For future technologies, it is very difficult to scale the silicon transistor gate length, so it is a necessary requirement of replacing the channel material from silicon to some high mobility material. Two-dimensional layered materials such as graphene and molybdenum disulfide (MoS2) are potential candidates to replace silicon. Due to its planar structure and atomically thin nature, they suit well with the conventional MOSFET technology and are very stable mechanically as well as chemically. HfO2 plays a vital role as a gate dielectric, not only in silicon CMOS technology but also in future nano-electronic devices such as graphene/MoS2 based devices, since high-κ media is expected to screen the charged impurities located in the vicinity of channel material, which results in enhancement of carrier mobility. So, for sustenance and enhancement of new technology, extensive study of the functional materials and its processing is required. In the present work, optimization of HfO2 thin films for gate dielectric applications in Nano-electronic devices using electron beam evaporation is discussed. HfO2 thin films have been optimized in two different thickness regimes, (i) about 35 nm physical thicknesses for back gate oxide graphene/MoS2 transistors and (ii) about 5 nm physical thickness to get Equivalent Oxide Thickness (EOT) less than 1 nm for top gate applications. Optical, chemical, compositional, structural and electrical characterizations of these films have been done using Ellipsometry, X-ray Photoelectron Spectroscopy (XPS), Rutherford Back Scattering (RBS), X-ray Diffraction (XRD), Capacitance-Voltage and Current-Voltage characterization techniques. The amount of O2 flow rate, during evaporation is optimized for 35 nm thick HfO2 films, to achieve the best optical, chemical and electrical properties. It has been observed that with increasing oxygen flow rate, thickness of the films increased and refractive index decreased due to increase in porosity resulting from the scattering of the evaporant. The films deposited at low O2 flow rates (1 and 3 SCCM) show better optical and compositional properties. The effects of post deposition annealing (PDA) and post metallization annealing (PMA) in forming gas ambient (FGA) on the optical and electrical properties of the films have been analyzed. The film deposited at 3 SCCM O2 flow rate shows the best properties as measured on MOS capacitors. A high density film (ρ=8.2 gram/cm3, 85% of bulk density) with high dielectric constant of κ=19 and leakage current density of J=2.0×10-6 A/cm2 at -1 MV/cm has been achieved at optimized deposition conditions. Bilayer graphene on HfO2/Si substrate has been successfully identified and also transistor has been fabricated with HfO2 (35 nm) as a back gate. High transconductance compared to other back gated devices such as SiO2/Si and Al2O3/Si and high mobility have been achieved. The performance of back gated bilayer graphene transistors on HfO2 films deposited at two O2 flow rates of 3 SCCM and 20 SCCM has been evaluated. It is found that the device on the film deposited at 3 SCCM O2 flow rate shows better properties. This suggests that an optimum oxygen pressure is necessary to get good quality films for high performance devices. MoS2 layers on the optimized HfO2/Si substrate have been successfully identified and transistor has been fabricated with HfO2 (32 nm) as a back gate. The device is switching at lower voltages compared to SiO2 back gated devices with high ION/IOFF ratio (>106). The effect of film thickness on optical, structural, compositional and electrical properties for top gate applications has been studied. Also the effect of gate electrode material and its processing on electrical properties of MOS capacitors have been studied. EOT of 1.2 nm with leakage current density of 1×10-4 A/cm2 at -1V has been achieved.