The present work focuses on the growth and characterizations of GaN and InN layers and nanostructures on p-Si(100) and p-Si(111) substrates by plasma-assisted molecular beam epitaxy and the studies of GaN/p-Si and InN/p-Si heterojunctions properties. The thesis is divided in to seven different chapters. Chapter 1 gives a brief introduction on III-nitride materials, growth systems, substrates, possible device applications and technical background. Chapter 2 deals with experimental techniques including the details of PAMBE system used in the present work and characterization tools for III-nitride epitaxial layers as well as nanostructures. Chapter 3 involves the growth of GaN films on p-Si(100) and p-Si(111) substrates. Phase pure wurtzite GaN films are grown on Si (100) substrates by introducing a silicon nitride layer followed by low temperature GaN growth as buffer layers. GaN films grown directly on Si (100) are found to be phase mixtured, containing both cubic and hexagonal modifications. The x-ray diffraction (XRD), scanning electron microscopy (SEM), photoluminescence (PL) spectroscopy studies reveal that the significant enhancement in the structural and optical properties of GaN films grown with silicon nitride buffer layer grown at 800 oC, when compared to the samples grown in the absence of silicon nitride buffer layer and with silicon nitride buffer layer grown at 600 oC. Core-level photoelectron spectroscopy of SixNy layers reveals the sources for superior qualities of GaN epilayers grown with the high temperature substrate nitridation process. The discussion has been carried out on the typical inverted rectification behavior exhibited by n-GaN/p-Si heterojunctions. Considerable modulation in the transport mechanism is observed with the nitridation conditions. The heterojunction fabricated with the sample of substrate nitridation at high temperature exhibites superior rectifying nature with reduced trap concentrations. Lowest ideality factors (~1.5) are observed in the heterojunctions grown with high temperature substrate nitridation which is attributed to the recombination tunneling at the space charge region transport mechanism at lower voltages and at higher voltages space charge limited current conduction is the dominating transport mechanism. Whereas, thermally generated carrier tunneling and recombination tunneling are the dominating transport mechanisms in the heterojunctions grown without substrate nitridation and low temperature substrate nitridation, respectively. A brief comparison of the structural, optical and heterojunction properties of GaN grown on Si(100) and Si(111) has been carried out. Chapter 4 involves the growth and characterizations of InN nanostructures and thinfilms on p-Si(100) and p-Si(111) substrates. InN QDs are grown on Si(100) at different densities. The PL characteristics of InN QDs are studied. A deterioration process of InN QDs, caused by the oxygen incorporation into the InN lattice and formation of In2O3/InN composite structures was established from the results of TEM, XPS and PL studies. The results confirm the partial oxidation of the outer shell of the InN QDs, while the inner core of the QDs remains unoxidized. InN nanorods are grown on p-Si(100), structural characterizations are carried out by SEM, and TEM. InN nanodots are grown on p-Si(100), structural characterizations are performed. InN films were grown on Si(100) and Si(111) substrates and structural characterizations are carried out. Chapter 5 deals with the the heterojunction properties of InN/p-Si(100) and InN/p-Si(111).The transport behavior of the InN NDs/p-Si(100) diodes is studied at various bias voltages and temperatures. The temperature dependent ZB BH and ideality factors of the forward I-V data are observed, while it is governed through the modified Richardson’s plot. The difference in FB BH and C-V BH and the deviation of ideality factor from unity indicate the presence of inhomogeneities at the interface. The band offsets derived from C-V measurements are found to be Δ EC=1.8 eV and Δ EV =1.3 eV, which are in close agreement with Anderson’s model. The band offsets of InN/p-Si heterojunctions are estimated using XPS data. A type-III band alignment with a valence band offset of Δ EV =1.39 eV and conduction band offset of ΔEC=1.81 eV is identified. The charge neutrality level model provides a reasonable description of the band alignment of the InN/p-Si interface. The interface dipole deduced by comparison with the electron affinity model is 0.06 eV. The transport studies of InN NR/p-Si(100) heterojunctions have been carried out by conductive atomic force microscopy (CAFM) as well as conventional large area contacts. Discussion of the electrical properties has been carried out based on local current-voltage (I-V) curves, as well as on the 2D conductance maps. The comparative studies on transport properties of diodes fabricated with InN NRs and NDs grown on p-Si(100) substrates and InN thin films grown on p-Si(111) substrates have also been carried out. Chapter 6 deals with the growth and characterizations of InN/GaN heterostructures on p-Si(100) and p-Si(111) substarets and also on the InN/GaN/p-Si heterojunction properties. The X-ray diffraction (XRD), scanning electron microscopy (SEM) studies reveal a considerable variation in crystalline quality of InN with grown parameters. Deterioration in the rectifying nature is observed in the case of InN/GaN/p-Si(100) heterojunction substrate when compared to InN/GaN/p-Si (111) due to the defect mediated tunneling effect, caused by the high defect concentration in the GaN and InN films grown on Si(100) and also due to the trap centers exist in the interfaces. Reduction in ideality factor is also observed in the case of n-InN/n-GaN/p–Si(111) when compared to n-InN/n-GaN/p–Si(100) heterojunction. The sum of the ideality factors of individual diodes is consistent with experimentally observed high ideality factors of n-InN/n-GaN/p–Si double heterojunctions due to double rectifying heterojunctions and metal semiconductor junctions. Variation of effective barrier heights and ideality factors with temperature are confirmed, which indicate the inhomogeneity in barrier height, might be due to various types of defects present at the GaN/Si and InN/GaN interfaces. The dependence of forward currents on both the voltage and temperatures are explained by multi step tunneling model and the activation energis were estimated to be 25meV and 100meV for n-InN/n-GaN/p–Si(100) and n-InN/n-GaN/p–Si(111) heterojunctions, respectively. Chapter 7 gives the summary of the present study and also discusses about future research directions in this area.