# I Velocity saturation and mobility in metals and semiconductor

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1. Mar 3, 2016

### radius2

Hi,

Lately, I've been trying to compare and understand conduction properties of metals and semiconductors. However, there are two question on my mind that I'm still trying to figure out. Maybe someone here might be able to provide some clues.

1. It is known that a linear increase of the electric field over a semiconductor results in a corresponding linear increase of the drift velocity of the carriers. However, after a certain field strength, the carrier drift velocity saturates and doesn't increase linearly with the field anymore. My question is, does velocity saturation occur in metals too after a certain limit and if not, why?

2. According to what I have been able to find, the mobility for semiconductors is higher than for metals. For example, electron mobility in intrinsic silicon is μ=0,135m^2/Vs while electron mobility in copper is μ=0,0044m^2/Vs. Of course, copper is still a much better conductor due to the high concentration of free electrons. However I'm trying to figure out: why is mobility larger in semiconductors?

2. Mar 8, 2016

### Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Mar 29, 2016

### Henryk

Hi,
I'm not sure if your statement no 1 is correct, but I can answer your no 2 question.
Mobility is defined as $\mu = \frac V E$ where V is extra velocity due to the applied field. From Newton's law $m_{eff}V = eE\tau$ where $\tau$ is scattering time. Combining the two equation you get $\mu = \frac {e\tau}m_{eff}$.
In a typical metal, such as copper, the effective mass is close to the mass of a free electron, but in, for example, silicon, the effective mass of electrons can be as low as 0.19, hence higher mobility (the effective mass of electrons in silicon is anisotropic, so it is a bit more complicated that that).

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