  Nuclear recoils in germanium and silicon are shown to have much larger
variance in electron-hole production than their electron-recoil counterparts
for recoil energies between 10 and 200\,keV. This effect--owing primarily to
deviations in the amount of energy given to the crystal lattice in response to
a nuclear recoil of a given energy--has been predicted by the Lindhard model.
We parameterize the variance in terms of an intrinsic nuclear recoil Fano
factor which is 24.3$\pm$0.2 and 26$\pm$8 at around 25\,keV for silicon and
germanium respectively. The variance has important effects on the expected
signal shapes for experiments utilizing low-energy nuclear recoils such as
direct dark matter searches and coherent neutrino-nucleus scattering
measurements.
