# Mobility

## What Do You Mean By Mobility?

We define Mobility in Physics (solid-state Physics) as the measurement of the ease with which charged particles move through a solid material under the influence of an applied electric field.

If we observe the working of an electric circuit when a potential difference is applied across the circuit, electrons get a push and they start mobilizing from one end to the other, and electricity generates, which is how we define mobility of charge carriers like electrons.

On this page, we will understand what is mobility, the unit of mobility, what the relation between mobility and drift velocity is, and mobility definition in Physics in detail.

### Define Mobility In Physics

Under the definition of mobility of charge carriers, we will understand what is electron mobility followed by what is ionic mobility.

Electron Mobility

Now, we will define mobility of a charge carrier in detail:

In solid-state physics, electron mobility describes how fast an electron can move through a metal or a semiconductor (for mobility in semiconductor) when charges are pulled by an electric field.

There is an analogous term for the mobility of holes, called hole mobility. The term carrier mobility is common to both electron mobility and hole mobility.

Electron and hole mobility is out-of-the-box cases of electrical mobility of charged particles in a fluid under the effect of the external electric field.

When an external electric field E is applied across a material, the electrons respond by making a motion with an average velocity called the drift velocity, which is denoted by vd. The mobility is denoted by μ.

The relation between mobility and drift velocity is given by the following equation:

vd =  μE…..(1)

Equation (1) is the relation between mobility and drift velocity.

→  μ =  vd/E  ….(2)

Equation (2) is electron mobility in terms of Mathematics.

From equation (2), we define mobility of a charge carrier as the value of the drift velocity per unit of electric field strength.

Now, let’s determine the unit of mobility:

### Unit of Mobility

Electron mobility is always specified in units of cm2/(V⋅s). This unit is different from the SI unit of mobility, where the unit of mobility is m2/(V⋅s).

Electron mobility and mobility are related to each other by;

1 m2/(V⋅s) = 104 cm2/(V⋅s)

### Mobility in Semiconductor

Mobility in a semiconductor is defined as how speedily charge carriers like electrons move in a semiconductor.

Semiconductor mobility relies on the impurity concentrations in a doped semiconductor that includes the concentrations of both donor and acceptor, defect concentration, temperature, and electron-hole concentrations.

### Semiconductor Mobility

The logic behind the conductivity in a semiconductor can be understood in terms of electron-hole pairs.

In the presence of an applied electric field, the electrons and holes move in opposite directions to each other to produce a current. The electric current across a semiconductor is proportional to the voltage applied at its ends.

So, V = μE.  μ is called the mobility in semiconductor.

Point To Note:

Electron mobility is always greater than hole mobility.

From this graph, we can see that the faster the particle moves at a given electric field strength, the larger the mobility, and vice-versa.

Also, the mobility of a particular type of particle in a given solid varies with temperature as shown in the above graph.

### What is Ionic Mobility?

The average velocity or the drift velocity with which an ion drifts through a specified gas under the influence of an electric field is called ionic mobility.

In simple terms, Ionic Mobility is characterized as the speed achieved by an ion moving through a gas under an applied unit electric field. It is denoted by a symbol  μ.

### SI Unit of Ionic Mobility

The unit of ionic mobility is m2s-1volt-1.

### Ionic Mobility Calculator

Ionic Mobility calculated by using the following formula:

Ionic Mobility = Speed of Ions/Potential Gradient

### Factors Affecting Ionic Mobility

Factors that affect ionic mobility are as follows:

• Temperature,

• Nature of electrolyte, and

• Size of an ion

• The relation between ionic mobility and transportation number is given as;

λa or λc is equal to ta or tc × λ

Where,

λa and λc, both are ionic mobilities, and

ta or tc  = transportation number

• The ionic mobility gets strongly affected by the solvent viscosity and the degree of solvation. The dissociation constants of ions rely on the dielectric constant of the solvent. Therefore, the use of a nonaqueous solvent or the mixed solvent affects the mobility and may improve the separation, viz: the solvent effect.

### What is Mobility in Physics?

We know that mobility in Physics is the motion of electrons or ions under the influence of an applied external electric field.

When an electric field is passed, a particular type of charged particle moves through a solid material under the effect of an electric field.

Such particles are both carried along with the electric field and simultaneously collide with atoms of the solid.

The combination of electric field and collisions/hitting causes these charge carriers to move with an average velocity, called the drift velocity. The charge carrier in most metals is the negatively charged electron, which is also known as electron scattering. So, now we understand what mobility is.

1. Why is Mobility Important in Metal Physics?

Ans: In metallic Physics, the concept of mobility has less relevance. On the other hand, for mobility in semiconductors, the behaviour of transistors and other electronic devices can vary depending on whether there are many electrons with low mobility (low-speed) or some electrons with high mobility. Therefore, in terms of semiconductors, mobility plays a very important parameter for semiconductor materials.

2. What Affects Mobility in Semiconductors?

Ans: We know that carrier mobility in a semiconductor is one of the most important parameters for the functioning of electronic devices.

The mobility measures the ability of how freely the charge carriers, viz: electrons or holes move in the material as and when subjected to an applied external electric field.

The magnitude of the mobility directly affects the performance of the device because it determines the operation speed via the transit time across the electronic device, the operating frequency of the circuit, and the sensitivity in the magnetic sensor.

3. What is the Drift Velocity of a Charge Carrier?

Ans: Drift velocity of charge carriers in a conductor depends upon two factors, one is the intensity of the electric field applied across the conductor and the other is the Mobility of the charge carrier.