First-principles investigation of microscopic mechanisms underlying hole mobilities in diamond, silicon, and germanium

Silicon (Si) dominates the semiconductor industry but currently suffers from significant hole mobility degradation in advanced transistors due to its abnormally low hole mobility ($505\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$), compared to its group IV neighbors, diamond and germanium (Ge) (both $\ensuremath{\sim}2000\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$). While Ge's high mobility is understandable by its lighter effective hole mass due to its narrower direct bandgap at $\mathrm{\ensuremath{\Gamma}}$ point, diamond's superior hole mobility remains difficult to understand since its bandgap is ultrawide. Conventional wisdom attributes diamond's high mobility to reduced phonon scattering due to high acoustic phonon group velocity and optical phonon frequency, overcoming its heaviest effective mass. However, our study reveals that this mechanism alone is insufficient to explain the observed mobility. We demonstrate that the diamond's abnormally light effective hole mass is a primary factor contributing to its high mobility; otherwise, its hole mobility would be approximately nine times lower than Si's. The unexpectedly light mass in diamond stems from larger transition matrix elements, resulting from substantial electronic wave-function overlap between valence and conduction bands, remarkably overcoming the effect of diamond's large bandgap. Furthermore, our investigation uncovers a unique feature in diamond's valence band structure: an inherent strain-enhanced mobility characteristic, where the top valence band manifests as a light-hole (lh) state along certain crystallographic directions (e.g., [100]), instead of the typical heavy-hole (hh) state. Contrary to prevailing assumptions, we observe a strong coupling between holes and transverse acoustic (TA) phonons, and even TA scattering dominates over longitudinal acoustic (LA) scattering in both diamond and Si, challenging the long-held belief that TA scattering is negligible. Our calculations yield a dilation deformation potential of 3.45 eV for diamond, significantly diverging from previously reported values, e.g., 7 or $\ensuremath{-}35$ eV. This discrepancy further highlights limitations in understanding individual scattering mechanisms in diamond using classical phenomenological models. These findings shed new light on the hole mobility in semiconductors and provide new clues to enhance further the hole mobility in group IV semiconductors towards advanced semiconductor technology nodes.