Among the group-III nitride (III-N) semiconductors, InN has been the leaststudied and also the most complex. However, InN is a promising material for sub-THz electronic devices due to the very high values of its electron low-field mobility(14,000 cm2/V.s) and maximum drift velocity (5.2 x 107 cm/s). InN and InN-richalloys are also very interesting for optoelectronic devices in the IR wavelength regionof telecommunications, as well as tandem solar cell applications, due to its 0.65 eVbandgap. This PhD dissertation is based on the study of plasma assisted molecularbeam epitaxy (PAMBE) of InN on Si (111) and r-plane (1102) sapphire substrates.Epitaxial growth on silicon is interesting for low cost production and/or monolithicintegration with Si integrated circuits (ICs). Growth of a-plane InN on r-plane (1102)sapphire substrates can be used for realizing quantum well heterostructures, free frompolarization induced electric fields. Also, it has been theoretically predicted thatnitrogen stabilized non-polar surfaces could be free from electron accumulation.Direct InN growth on Si (111), using the optimum conditions for InN growthon GaN (0001) – substrate temperature 400-450oC and stoichiometric III/V flux ratio– results to 3D growth mode and porous columnar InN epilayers with bad adhesion atthe InN/Si interface. A two-step growth process was developed, consisting ofnucleating a very thin InN layer on Si at low temperature under N-rich growthconditions, and the growth of the main epilayer at the optimum InN (0001) growthconditions. The fast coalescence of the initial 3D islands of InN results to acontinuous 20 nm InN film on the Si (111) surface with low 10 x 10 μm2 AFM rmssurface roughness of 0.4 nm, which allows the main epilayer to be overgrown in stepflowgrowth mode, achieving an atomically smooth surface. The fast coalescence alsoassists defects annihilation near the InN/Si interface and 0.5 μm films exhibitedthreading dislocation (TD) density of 4.0x109 cm-2 for the edge-type and 1.7x109 cm-2for the screw-type TDs. Similar defect densities were determined by TEM for InNfilms grown after initial deposition of an AlN/GaN nucleation layer on Si. However,those films exhibited significantly better electron mobility and lower crystal mosaicityaccording to XRD rocking curves.The experiments of InN growth on r-plane (1102) Al2O3 substrates revealedthat different InN crystallographic orientations could be realized depending on theInN nucleation conditions. Single crystal cubic (001) InN was grown on r-planesapphire by using one-step growth at ~ 400oC, while polar c-plane (0001) orsemipolar s-plane (1011) InN were observed by using a two-step growth process withInN nucleation at low temperature under N-rich or near stoichiometric III/V flux ratioconditions, respectively. Pure a-plane (1120 ) InN films were realized only when aplaneGaN or AlN nucleation-buffer layers were initially grown on r-plane sapphire.The structural quality of the a-plane InN films improved with increasing epilayerthickness, which is attributed to interaction and annihilation of defects. However, thegrowth of a-plane InN proceeds in 3D growth mode resulting to increasing surfaceroughness with increasing film thickness. A comparative study of the thicknessdependent electrical properties of a-plane InN films grown on r-plane Al2O3 and cplanefilms grown on GaN/Al2O3 (0001) templates was carried out by roomtemperature Hall-effect measurements. For both InN orientations, a rather linearincrease of the electron sheet density (NS) with increasing thickness, consistent with aconstant bulk concentration around 1 x 1019 cm-3 was observed. However, the electron mobilities of the c-plane InN films were more than three times those of the a-planefilms, attributed to the presence of higher dislocation density (1.4 x 1011 cm-2) in thea-plane InN films. The analysis of the Hall-effect measurements, by considering thecontribution of two conducting layers, indicates a similar accumulation of lowmobility electrons with NS > 1014 cm-2 at the films’ surface/interfacial region for boththe a- and c-plane InN films. In general, similar electron concentrations weremeasured for all the different orientation InN films (polar c-plane, non-polar a-plane,semi-polar s-plane and cubic (001) InN). This suggests that similar surface/interfacialelectron accumulation occurs independently of the InN crystallographic orientation,and the bulk donors are not related to the threading dislocations, since significantvariations of defect densities occur for the different InN orientations. A SIMSinvestigation of a c-plane InN film exhibiting electron concentration of 1.09 x 1020cm-3 excludes hydrogen as the possible donor since its concentrations was 6.5x1018cm-3. Only oxygen approached a concentration level near 1020 cm-3 and this might bethe unintentionally incorporated donor.Finally, the spontaneous growth of InN nanopillars (NPs) on Si (111) and rplanesapphire substrates was investigated. Optimization of the different growthparameters resulted to well-separated (0001) InN NPs on Si (111) that exhibitedphotoluminescence. Almost in all cases, the growth rate of the InN NPs along the caxisis multiple of the In-limited growth rate. A non-uniform amorphous SixNy layerwas inevitable under unoptimised growth conditions, leading to frequently observedNP misorientation (tilt) on Si substrates. Only c-axis oriented InN NPs were formedon the r-plane sapphire substrates.In conclusion, the thesis has created new scientific knowledge for theheteroepitaxy of InN on Si (111) and (1102) sapphire. Comparison with c-plane InNgrown on GaN (0001) allowed the generic characteristics of InN to be extracted fromthe orientation-dependent ones.