Dhristi JEE 2022-24

What Do You Mean By Mobility?

Mobility can be defined defined in different ways but in physics when we talk about a solid state the measurement of the ease with which any particular type of charged particle moves through a solid material when that material is under the influence of an electric charge then we can state that mobility has taken place between the charge particle and the electric field. When these particles are pulled along by the electric field they are bound to collide with atoms of the solid. Now with this occurring phenomena we can derive the definition of drift velocity which occurs when a combination of electric field and collision causes the particles to move with an average velocity. We also see that the charge carrier in most metals contains negatively charged electrons.

Now with the drift velocity we can define mobility as the value of the drift velocity per unit of electric field strength so the faster the particle moves at a given electric field strength the larger its mobility will be, mobility may vary with temperature depending on any particular type in any particular solid. The dependence of mobility on the type of solid can be explained by the examples of semiconductors where the electric current is also carried by the motion of positively charged particles namely holes and each of which corresponds to the absence of an electron now with this the condition arises complications of their separate mobilities because there are several electronic devices which require him abilities for officiant operation, we will not look into this at the moment because we will have to enter quantum electro dynamics for that so we will just keep it till mobility and how it depends on the type of solid and other basic characteristics.

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 the mobility definition in Physics in detail.


Electron Scattering

Electron scattering occurs when there is a deflection of the path of electrons when the password is solid, a metal, semi conductor or an insulator. When these electrostatic forces operate between the negatively charged electrons and atoms within the solid, then deflections or collisions are caused. These forces in turn reduce the speed of the electrons by limiting their performance on the electronic devices that we use, based on transistors and integrated circuits. Electron scattering can also be explained by the deflection of a beam of electrons by target, which is also used to prove the size and charge distribution of atomic nuclei. When we talk about electrons and how they scatter we go way back to the 1970s and because of the foundation of electron scattering during that time, it has been proved and has helped us to confirm that protons and neutrons are made up of elementary subatomic particles known as quarks.


Electron Paramagnetic Resonance

Electron pair a magnetic resonance under bracket EPR which can also be called as electron spin resonance or a set of selective absorption of weak radio frequency electromagnetic radiation, this phenomena and can be sighted in the microwave region so what basically happens is that the unpaired electrons in the atomic structure of any given material which is simultaneously subjected to a constant strong magnetic field, now with the unpaid electrons and the way they Spain they tend to behave like tiny magnets so when materials that contain such electrons are subjected to a strong stationary magnetic field, the magnetic axis of the unpaid electrons or as we mentioned earlier the elementary magnets, they partially align themselves with the strong external field and deep recess in the field as much as they access of spinning tops often trace concept surfaces similarly as the process in the gravitational field of earth.

When we observe the absorption of energy from the weak alternating magnetic field of the microwave when it's given frequency corresponds to the natural frequency of the process of the elementary magnets then we define resonance. The measurement of the radiation absorbed works as a function of the changing variable which gives us an electronic paramagnetic resonance spectrum, such a typically graph of microwave energy absorption when compared with applied stationary magnetic field can be used to identify paramagnetic substances with which we can investigate the nature of chemical bonds present within the molecules by identifying the unpaid electrons present and their interaction with the immediate surroundings.


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 the 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 a 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 are 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 \[V_{d}\]. The mobility is denoted by \[\mu\].

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

              \[V_{d} =  \mu E\]…..(1)

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

\[\rightarrow \mu = \frac{V_{d}}{E} \]….(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 \[\frac{cm^{2}}{(V⋅s)}\]. This unit is different from the SI unit of mobility, where the unit of mobility is \[\frac{m^{2}}{(V⋅s)}\]. 

Electron mobility and mobility are related to each other by;

\[\frac{1 m^{2}}{(V.s)} = \frac{10^{4} cm^{2}}{(V⋅s)} \]


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, \[V = \mu E \].  \[\mu\] is called the mobility in semiconductors.


Point To Note:

Electron mobility is always greater than hole mobility.


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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  \[\mu\].


SI Unit of Ionic Mobility

The unit of ionic mobility is \[m^{2}s^{-1} volt^{-1}\].


Ionic Mobility Calculator

Ionic Mobility calculated by using the following formula:

\[\text{Ionic Mobility} = \frac{\text{Speed of Ions}}{\text{Potential Gradient}}\]


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;

       \[\lambda _{a}\] or \[\lambda _{c}\] is equal to  \[t_{a}\] or \[t_{c} \times \lambda _{\infty}\] 


\[ \lambda _{a}\] and \[ \lambda _{c}\], both are ionic mobilities, and

 \[t_{a}\] or \[t_{c}\]  = transportation number

  • The ionic mobility is 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.

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FAQs (Frequently Asked Questions)

1. Why is Mobility Important in Metal Physics?

In metallic Physics, the concept of mobility has less relevance. On the other hand, for mobility in semiconductors, the behavior 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?

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?

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.

4.  Importance of quantum electrodynamics?

Quantum electrodynamics also known as quantum electrodynamics (QED), all quantum field theory which talks about the interactions of charged particles with the electromagnetic field. It can be used to describe mathematical notions but not confined to it along with those it also describes all interactions of light with matter but also there are charge particles with one another. QED  can be sought as a related mystic theory in which Albert Einstein's theory of special relativity is built into each equation.

5. What can be understood by the concept of electron diffraction?

Electron diffraction, interference effects owing to the wavelike nature of a beam of electrons when passing near matter. According to the proposal (1924) of the French physicist Louis de Broglie, electrons and other particles consist of different wavelengths which are inversely proportional to the momentum so consequently, high-speed electrons with short wavelength, a range which is usually comparable to the spacing is between atomic layers and crystals can be seen in contrast with other particles which have longer where plants. With high-speed electrons having short wavelengths, a beam of such high speed electrons should undergo diffraction, a characteristic wave effect, when directed through thin sheets of material or when reflected from the faces of crystals. Electron diffraction was observed by C.J.Davisson and L.H.Germer in New York and by G.P.Thompson in Aberdeen. This  fraction is used to identify a substance chemically or can be used to locate the position of atoms in a given substance.