The molecular beam epitaxy of In-face InN (0001) epilayers with optimized surface morphology, structural quality, and electrical properties was investigated. Namely, compact InN epilayers with atomically flat surfaces, grown in a step-flow mode, were obtained using stoichiometric fluxes of In and N and substrate temperatures in the range from 400°C to 435°C. Typical values for the electron concentration and the Hall mobility at 300 K were 4.3 × 1018 cm−3 and 1210 cm2/Vs, respectively. The growth mode of InN during the very first stage of the nucleation was investigated analytically, and it was found that the growth proceeds through nucleation and fast coalescence of two-dimensional (2-D)–like InN islands. The preceding conditions were used to grow an InN/GaN quantum well (QW) heterostructure, which exhibited well-defined interfaces. Schottky contacts were successfully fabricated using a 15-nm GaN barrier enhancement cap layer. Capacitance-voltage measurements revealed the confinement of electrons within the InN QW and demonstrated the capability to modulate the electron density within an InN channel. The sheet concentration of the confined electrons (1.5 × 1013 cm−2) is similar to the calculated sheet polarization charge concentration (1.3 × 1013 cm−2) at the InN/GaN interface. However, electrons may also originate from ionized donors with a density of 8 × 1018 cm−3 within the InN layer.