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.
(Image will be Uploaded soon)
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 \[t_{c} \times \lambda _{\infty}\]
Where,
\[ \lambda _{a}\] 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.
FAQs on Mobility
1. What is meant by the mobility of a charge carrier in Physics, as per the CBSE 2025-26 syllabus?
Mobility (symbol μ) of a charge carrier is defined as the magnitude of its drift velocity acquired per unit strength of the applied electric field. In simple terms, it measures how quickly and easily a charge carrier, such as an electron or a hole, can move through a metal or a semiconductor when an electric field is applied. A higher mobility indicates that charge carriers can move faster for the same electric field strength.
2. What is the formula for mobility, and what does each term represent?
The formula for the mobility (μ) of a charge carrier is given by:
μ = eτ / m
Where:
- e is the magnitude of the charge on the carrier (e.g., 1.6 x 10⁻¹⁹ C for an electron).
- τ (tau) is the average relaxation time, which is the average time between successive collisions of the charge carrier with the ions or atoms of the conductor.
- m is the effective mass of the charge carrier.
3. How are mobility and drift velocity related to each other?
Mobility (μ) and drift velocity (v_d) are directly proportional. The relationship is expressed by the formula:
v_d = μE
This equation shows that the drift velocity of a charge carrier is the product of its mobility and the strength of the external electric field (E). Mobility acts as the constant of proportionality, linking the cause (electric field) to the effect (the average drift velocity of charges).
4. What are the SI unit and dimensional formula for mobility?
The SI unit and dimensions for mobility are derived from its formula (μ = v_d / E).
- SI Unit: The SI unit is metre squared per volt-second, written as m²/ (V·s) or m²V⁻¹s⁻¹.
- Dimensional Formula: The dimensional formula for mobility is [M⁻¹ T² I].
5. Why is the concept of mobility particularly important for semiconductors compared to metals?
The physical significance of mobility is crucial for semiconductors due to these reasons:
- Device Performance: In semiconductor devices like transistors and diodes, the speed of operation depends on how fast charge carriers can move across junctions. High mobility leads to faster switching times and allows devices to operate at higher frequencies.
- Dual Charge Carriers: Semiconductors have two types of charge carriers: electrons and holes, each with its own distinct mobility. The overall conductivity depends on the mobility and concentration of both.
- Doping and Purity: Mobility is highly sensitive to impurities and temperature, which are key factors in controlling the properties of semiconductors through a process called doping.
In metals, the charge carrier concentration is extremely high and constant, so conductivity is the more commonly used parameter. In contrast, for semiconductors, mobility is a critical performance metric.
6. How does an increase in temperature affect the mobility of charge carriers in conductors and semiconductors?
The effect of temperature on mobility differs significantly between conductors and semiconductors.
- In Conductors (Metals): As temperature increases, the thermal vibrations of the metal lattice ions become more intense. This leads to more frequent collisions for the free electrons, which decreases the average relaxation time (τ). Since mobility (μ) is directly proportional to τ, the mobility of electrons in conductors decreases with rising temperature.
- In Semiconductors: As temperature increases, the lattice vibrations also increase, which tends to decrease mobility just like in conductors. However, a temperature rise in semiconductors also breaks more covalent bonds, creating a significantly larger number of charge carriers (electrons and holes). While the mobility of individual carriers decreases due to scattering, the overall conductivity of the semiconductor still increases because of the massive increase in carrier concentration.
7. Why is the mobility of electrons generally higher than that of holes in a semiconductor?
The mobility of electrons is typically higher than that of holes because electrons and holes have different effective masses (m*) and move through different energy bands.
- Electrons: They move in the nearly empty conduction band. They have a smaller effective mass, meaning they behave like 'lighter' particles and can be accelerated more easily by an electric field.
- Holes: A hole is the absence of an electron in the densely packed valence band. For a hole to move, a valence electron must jump into its position, which is a more complex, multi-step process. This makes the hole behave like a 'heavier' particle with a larger effective mass, resulting in lower mobility.
