Dear Hisham,

As you know the electrons have a velocity distribution and their average velocity depends on the applied field. At low electric fields, the proportionality constant is the drift mobility: vn = mun.E, where the electric field E =-grad (phi). This is a translation of Ohm's law in semiconductors. Some authors consider other driving forces , such as the gradient of electron concentration or temperature. However, the average electron velocity saturates at high electric fields. The saturation velocity depends on temperature. Nevertheless, when the electric field is rapidly changing in time or space across small distances (e.g., across junctions), the velocity may overshoot to higher velocities (higher than the saturation velocity). Also, the average velocity may reach to the group (microscopic) velocity, in ballistic or near ballistic transport, when collisions are negligible. This is likely happening in nanoscale devices. Of course, we are talking about electron velocity in crystalline (single crystal), solids, where collisions with lattice defects (including lattice vibrations or phonons and impurities) limit the motion of electrons.

Dear Hicham Helal,

I think by annealing, because the recrystallization of semiconductor allows the grain sizes to be increased and the impurities to decrease.

You can review this article:

Article Transparent and conducting ZnO films grown by spray pyrolysis

Greetings

Dear Hisham,

As you know the electrons have a velocity distribution and their average velocity depends on the applied field. At low electric fields, the proportionality constant is the drift mobility: vn = mun.E, where the electric field E =-grad (phi). This is a translation of Ohm's law in semiconductors. Some authors consider other driving forces , such as the gradient of electron concentration or temperature. However, the average electron velocity saturates at high electric fields. The saturation velocity depends on temperature. Nevertheless, when the electric field is rapidly changing in time or space across small distances (e.g., across junctions), the velocity may overshoot to higher velocities (higher than the saturation velocity). Also, the average velocity may reach to the group (microscopic) velocity, in ballistic or near ballistic transport, when collisions are negligible. This is likely happening in nanoscale devices. Of course, we are talking about electron velocity in crystalline (single crystal), solids, where collisions with lattice defects (including lattice vibrations or phonons and impurities) limit the motion of electrons.

I agree with Labidi Herissi

I agree with Pr Muhammad Hamza El-Saba, and consider electrons lifetime

You may be interested to look at the following investigations about velocity overshoot and how it can be produced and exploited in bulk and layered semiconductor devices:

1- Accurate estimation of electron velocity overshoot in sub-quarter micron silicon structures and MOSFET devices

2-Modeling of velocity «overshoot» in the multivalley semiconductors

3- Velocity overshoot in zincblende and wurtzite GaN

4- Extended velocity overshoot in GaAs HBT