Thirty nanometers is the distance over which a phonon sprinter hasn't yet had time to accelerate. In thin aluminum nitride films, thermal resistance remains almost unchanged up to this thickness: heat transport proceeds in the ballistic regime, where phonons (quanta of crystal lattice vibrations) fly without collisions. Beyond that, diffusion kicks in, with frequent collisions and resistance growing with thickness. An experiment on a series of films from 1.6 to 2440 nm grown on sapphire has shown this transition with unprecedented clarity.
The average group velocity of phonons in the ballistic regime is 1818 m/s, compared with ~7000 m/s in bulk material. The lifetime of optical phonons increases by an order of magnitude upon transitioning to diffusion and then remains nearly constant from 119 to 2440 nm. Calculations of thermal conductivity accumulation versus mean free path show that the contribution of phonons with paths shorter than 30 nm is negligible. This explains why resistance does not grow at small thicknesses.
Before this work, it was unclear at what film thickness heat transport in AlN switches from ballistic to diffusive, and what role defects and boundaries play. Now it is established: up to 30 nm, resistance is constant, and beyond that it grows with thickness. In the ballistic regime, phonons have low velocities and short lifetimes, while optical phonons "come alive" by an order of magnitude upon transitioning to diffusion. This was achieved by systematically comparing a series of films of different thicknesses, measured with the same thermoreflectance method, against calculations and microstructure.
The practical benefit is direct: you can choose the AlN thickness in heat-spreading layers to stay in the ballistic regime with minimal thermal resistance. This matters for gallium nitride transistors, ultraviolet LEDs, and high-power radio-frequency devices, where AlN serves as a buffer or substrate. The next step is to measure AlN thermal conductivity on other substrates and with different defect densities, and to directly compare with first-principles calculations for specific microstructures. The question of the ultimate ballistic resistance and the exact role of interface defects remains open.
The 30 nm thickness at which the transition occurs is about 100 times smaller than the phonon mean free path in bulk AlN (about 3 μm). That is like a sprinter running a distance a hundred times shorter than his usual acceleration phase.