  The parameter-free computation of charge transport properties of
semiconductors is now routine owing to advances in the ab-initio description of
the electron-phonon interaction. Many studies focus on the low-field regime in
which the carrier temperature equals the lattice temperature and the current
power spectral density (PSD) is proportional to the mobility. The calculation
of high-field transport and noise properties offers a stricter test of the
theory as these relations no longer hold, yet few such calculations have been
reported. Here, we compute the high-field mobility and PSD of hot holes in
silicon from first principles at temperatures of 77 and 300 K and electric
fields up to 20 kV cm$^{-1}$ along various crystallographic axes. We find that
the calculations quantitatively reproduce experimental trends including the
anisotropy and electric-field dependence of hole mobility and PSD. The
experimentally observed rapid variation of energy relaxation time with electric
field at cryogenic temperatures is also correctly predicted. However, as in
low-field studies, absolute quantitative agreement is in general lacking, a
discrepancy that has been attributed to inaccuracies in the calculated valence
band structure. Our work highlights the use of high-field transport and noise
properties as a rigorous test of the theory of electron-phonon interactions in
semiconductors.
