Effective Phonon Mean Free Paths for Thermal Modeling of Modern Semiconductors

Accurate knowledge of phonon transport lengths is essential for predicting size-dependent thermal conductivity in modern semiconductor devices, yet existing “average” phonon mean free path (MFP) definitions are often crude and inconsistent. This work provides the first-principles calculation of the effective MFP,$\Lambda _{\text {eff}}$, obtained directly from thickness-dependent thermal conductivity of 17 modern semiconductors including Si, Ge, diamond, silicon carbide (SiC), GaN, AlN,$\beta $-Ga2O3, and others. We compare$\Lambda _{\text {eff}}$with three commonly used MFP metrics, conventional$\Lambda _{\text {conv}}$, midpoint$\Lambda _{\text {mid}}$, and weighted-average$\Lambda _{\text {ave}}$. Our results show that$\Lambda _{\text {conv}}$severely underestimates phonon transport lengths,$\Lambda _{\text {mid}}$provides only a partial approximation, and$\Lambda _{\text {ave}}$is strongly biased toward long-MFP phonons. In contrast,$\Lambda _{\text {eff}}$reliably predicts when a material transitions from bulk-like to ballistic or quasiballistic conduction, making it the most physically meaningful descriptor for device-scale modeling. We also introduce a “normalized effective MFP” that quantifies transport length per unit heat carried, and a two-MFP model that captures both short- and long-MFP phonon channels while closely matching first-principles results. The tabulated$\Lambda _{\text {eff}}$values and the proposed models provide compact, experimentally accessible tools for thermal design in transistors, RF and power electronics, optoelectronics, quantum devices, and other nanoscale semiconductor technologies.