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We provide a theoretical framework for the development of a solid-statethermal rectifier through a confinement in the available population of phononson one side of an asymmetrically graded film stack. Using a modification of thephonon gas model to account for phonon filtering and population confinement, wedemonstrate that for an ideal material, with low phonon anharmonicity,significant thermal rectification can be achieved even in the absence ofballistic phonon transport. This formalism is used to illustrate thermalrectification in a thin-film of diamond (1-5 nm) graded to dimensions > 1{\mu}m exhibiting theoretical values of thermal rectification ratios between0.75 and 6. Our theoretical formulation for thermal rectification is thereforeexpected to produce opportunities to design advanced solid-state devices thatenable a variety of critical technologies.

A Theoretical Paradigm for Thermal Rectification via Phonon Filtering and Energy Carrier Confinement