Under which condition the drift velocity stops increasing proportionally with respect to the electric field Our professor asked us a question the other day but i wasn't able to figure it out. If we increasing Electric field then drift velocity will increase, Because of this Equation:
Vd = μ * E
But at which point drift velocity stops increasing proportionally with respect to the electric field ?
 A: The linear relationship between the average carrier velocity and the applied field breaks down when high fields are applied. As the electric field is increased, the average carrier velocity increases as well, but at high fields, the velocity gradually saturates reaching the saturation velocity. 
Relation between carrier velocity and the electric field applied for (a)materials without an accessible higher band and (b) materials with an accessible higher band
This velocity originates from various scattering mechanisms such as optical phonon scattering, phonon dispersion, phonon absorption as well as emission, and the energy band non-parabolicity.
A simple explanation would be that when the carrier energy increases beyond the optical phonon energy, the probability of emitting an optical phonon increases abruptly. This results in an increased scattering rate of highly energetic electrons, primarily due to optical phonon emission. This effect increases the transit time of carriers through the channel. The high-field mobility model is based on the low-field mobility with further extensions to address the high-field phenomenon.
