  High harmonic generation (HHG) in solid and gaseous targets has been proven
to be a powerful avenue for the generation of attosecond pulses, whereas the
influence of electron-phonon scattering on HHG is a critical outstanding
problem. Here we first introduce a temperature dependent lattice vibration
model by characterizing the spacing fluctuation. Our results reveal that (i)
structural disorder induced by lattice vibration does not lead to generation of
even-order harmonics; (ii) dephasing of HHG occurs as the lattice temperature
is growing; (iii) an open-trajectory picture predicts the maximal photon energy
in the temperature-dependent HHG spectra. Moreover, a formula assessing
dephasing time with lattice temperature is proposed to identify the timescale
of electron-phonon scattering. This work paves a way to study
non-Born-Oppenheimer effect in solids driven by strong field.
