Question

Define mobility. Give its unit.

Answer 1

Hint: In this circuit, we first define mobility as is a proportionality constant that relates drift velocity of the carriers with the electric field in a conductive material. Mobility is mostly used in semiconductors to describe the behavior of carriers, whereas it is not much used in metals. The SI unit of mobility is $${\displaystyle \frac{m^2}{sV}}$$.

Complete Step-by-Step solution:
Mobility denoted by $\mu$ is a proportionality constant that relates drift velocity of the carriers with the electric field in a conductive material. These Carriers may be electrons or holes.
$v=\mu E$
Here $v$ denotes the drift velocity that is the ensemble average of all the velocity of the carriers.
        $E$ is the electric field applied across the material.

Thus from the equation, we can see that the unit of mobility is the units of drift velocity divided by the units of the electric field that is
$$\Rightarrow \mu ={\displaystyle \frac{{\displaystyle \frac{m}{s}}}{{\displaystyle \frac{V}{m}}}}$$
$$\Rightarrow \mu ={\displaystyle \frac{m^2}{sV}}$$

So the SI units of mobility is $${\displaystyle \frac{m^2}{sV}}$$ .
Mobility is mostly used in semiconductors to describe the behavior of carriers, whereas it is not much used in metals.
When carriers like electrons or holes in a material are accelerated due to an electric field but these carriers undergo periodic collisions or scattering due to which the velocity of each carrier changes and becomes random in nature. Now if we take the ensemble average velocity of the electrons it will be proportional to the electric field.
And this proportionality constant is nothing but mobility.
Mobility depends on many parameters like the temperature, the number of impurities in the crystal, and the quality of a semiconductor crystal. The mobility of electrons is always greater than that of holes for example mobility of electron in silicon is 1000 $c{m}^2$/ (V⋅s), in germanium is 4000 $c{m}^2$/ (V⋅s), and in gallium arsenide is 10000 $c{m}^2$/ (V⋅s). On the other hand, the mobility of the hole in gallium arsenide is 100 $c{m}^2$/ (V⋅s), in silicon is 450, and in germanium is 2000.

Note: For these types of questions we need to know about basic semiconductor physics like what is a P-type and N-type semiconductor, Diffusion and drift mechanism, Mobility and conductivity, etc. We also need to know their expression and how to find them.