# Mobility of electron in semiconductor formula | electronics

The term mobility in electronics refers to the ability to move. Mobility of electron in semiconductors gives the idea of the movement of the electrons in the semiconductor materials. The mobility of free electrons and holes are not same and it depends on many factors. In this article, we are going to discuss the electrical mobility of electrons and holes in semiconductors and conductors.

• Definition of Electrical Mobility
• Formula of Mobility of electron
• Unit of Mobility
• Mobility of electron in conductor and semiconductor
• Mobility of Holes in semiconductor
• Why the mobility of free electron is greater than the mobility of hole?

## Definition of Electrical Mobility in semiconductor

The charge carriers move by the influence of an external electric field. So, due to the application of an electric field charge carriers will get some drift velocity to move in the conductors or the Semiconductors. Electrical mobility of charge carriers is defined as the drift velocity of the carriers per unit applied electric field.

## Formula of Mobility of charge carriers

Now, what is the electron mobility formula? Let, after applying an external electric field E, the charge carriers get the drift velocity V. Then the formula for the mobility of the charge carriers is,

$\small {\color{Blue} \mu =\frac{V}{E}}$ ………………..(1)

This is the formula of mobility of charge carriers. This is also the the electron mobility formula.

## Unit of Mobility

The SI unit of drift velocity is m/s and the SI unit of the electric field is V/m.

So, the SI unit of Mobility is m2/V.s

## Dimension of mobility of electron

Drift velocity has the dimension of [LT-1] and the dimension of electric field is [MLT-3I-1]. Then the dimensional formula of mobility of charges is [M-1T2I].

## Electron Mobilityin semiconductorand conductor

Free electrons move in the conduction band. The mobility of the electron is the drift velocity of the electron in presence of a unit amount of electric field. One can get the mobility of electrons both in conductors and semiconductors. The value of Electron mobility is different in different materials.

## Mobility of Holes in Semiconductor

We all know that there is no hole in a conductor. So, hole mobility is applicable only for semiconductors. Sometimes it is called semiconductor mobility. Mobility of holes is the ability of movement of holes in the semiconductor in presence of an external electric field. The value of the mobility of holes in crystalline silicon is 450 cm2/V.s.

## Why is the mobility of free electron greater than the mobility of hole?

Holes are not the physical objects. They are the absence of electrons. So, the movement of holes is nothing but the movement of electrons in the opposite direction.

Now, free electrons move in the conduction band and the holes move in the valance band. Now, the binding force of the nucleus on free electrons is smaller than that on the holes (or valence electrons) in the valence band as the valence band is closer to the nucleus. Hence, the free electrons in the conduction band require a smaller electric field to move compared to the holes at the valence band. Therefore, the mobility of free electrons in conduction band is greater than that of holes at valence band.

This is all from this article on electron mobility formula in electronics. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

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