  We provide a theoretical framework for the development of a solid-state
thermal rectifier through a confinement in the available population of phonons
on one side of an asymmetrically graded film stack. Using a modification of the
phonon gas model to account for phonon filtering and population confinement, we
demonstrate that for an ideal material, with low phonon anharmonicity,
significant thermal rectification can be achieved even in the absence of
ballistic phonon transport. This formalism is used to illustrate thermal
rectification in a thin-film of diamond (1-5 nm) graded to dimensions > 1
{\mu}m exhibiting theoretical values of thermal rectification ratios between
0.75 and 6. Our theoretical formulation for thermal rectification is therefore
expected to produce opportunities to design advanced solid-state devices that
enable a variety of critical technologies.
