This chapter examines the physical basis of AlN single crystal growth, focusing on thermodynamic principles, surface energy effects, and kinetic mechanisms. The phase diagram of AlN reveals that near-equilibrium growth (e.g., via Physical Vapor Transport, PVT) is thermodynamically feasible but requires extreme temperatures due to its high bond energy. Despite practical challenges, gas-to-solid phase transitions enable AlN growth at lower temperatures by leveraging supersaturation and supercooling. Surface energy plays a critical role in crystal morphology, driving anisotropic growth patterns and influencing nucleation kinetics. The Gibbs free energy analysis shows that crystal nucleation requires overcoming an energy barrier, dependent on supersaturation and surface area. Surface diffusion models explain atom movement on substrates, where terrace steps and miscut angles dictate growth modes (e.g., 2D nucleation or 3D island formation). The kinetics of AlN vapor-phase epitaxy are governed by adsorption-desorption dynamics, with the Al-adatom/step-edge interaction controlling growth rates. Finally, the chapter establishes relationships between supersaturation, substrate miscut, and growth mode transitions, providing a framework for optimizing epitaxial film quality and device performance.