Mobility And Temperature Dependence Of Resistivity- Current And Electricity - Variation Of Resistivity With Temperature

Slide 1: Introduction

Resistivity is a fundamental property of materials related to their ability to conduct electricity.
It determines how easily electric current flows through a material.
Resistivity is denoted by the symbol ρ (rho).
In this lecture, we will discuss the mobility and temperature dependence of resistivity.

Slide 2: Definition of Resistivity

Resistivity is a measure of the resistance of a material to the flow of electric current.
It is defined as the ratio of the electric field (E) applied to a material to the current density (J) it produces.
Mathematically, resistivity (ρ) is given by ρ = E/J.
The SI unit of resistivity is ohm-meter (Ω·m).

Slide 3: Mobility

Mobility refers to the ability of charge carriers (electrons or holes) to move through a material in the presence of an electric field.
It is denoted by the symbol μ (mu) and is measured in square meters per volt-second (m2/V·s).
Mobility is a characteristic property of charge carriers in a material.

Slide 4: Drift Velocity

In the presence of an electric field, charge carriers experience a force that causes them to move.
The average velocity with which charge carriers drift in a particular direction is called drift velocity (v).
Drift velocity is directly proportional to the electric field strength and mobility.
Mathematically, v = μE, where E is the electric field strength.

Slide 5: Conductivity

Conductivity (σ) is the reciprocal of resistivity and is a measure of how well a material conducts electricity.
It indicates the ease with which charge carriers can move through a material.
Mathematically, conductivity is given by σ = 1/ρ.
The SI unit of conductivity is Siemens per meter (S/m).

Slide 6: Relation between Resistivity and Conductivity

Resistivity (ρ) and conductivity (σ) are related by the equation σ = 1/ρ.
In other words, conductivity is the inverse of resistivity, and vice versa.
Materials with high conductivity have low resistivity, and vice versa.

Slide 7: Temperature Dependence of Resistivity

The resistivity of most materials changes with temperature.
For most metals, the resistivity increases with increasing temperature.
This is because as temperature rises, the atoms in the material vibrate more and impede the motion of charge carriers.
On the other hand, the resistivity of some semiconductors decreases with increasing temperature.

Slide 8: Temperature Coefficient of Resistivity

The rate of change of resistivity with temperature is quantified by the temperature coefficient of resistivity (α).
It is defined as α = (1/ρ) * (dρ/dT), where ρ is the resistivity and T is the temperature.
The unit of temperature coefficient of resistivity is per degree Celsius (Ω·m/°C) or per Kelvin (Ω·m/K).

Slide 9: Positive Temperature Coefficient of Resistivity

Materials with a positive temperature coefficient of resistivity (PTC) have their resistivity increase with temperature.
Most metals exhibit a positive temperature coefficient.
Examples: Copper, aluminum, silver.

Slide 10: Negative Temperature Coefficient of Resistivity

Materials with a negative temperature coefficient of resistivity (NTC) have their resistivity decrease with temperature.
Some semiconductors exhibit a negative temperature coefficient.
Example: Silicon, germanium.

Slide 11: Mobility and Temperature Dependence of Resistivity

In materials, the mobility of charge carriers plays a crucial role in determining resistivity.
The mobility of electrons (μe) and the mobility of holes (μh) may have different values.
The total current density (J) in a material depends on the mobility of both electrons and holes.
The average drift velocity (v) of charge carriers also depends on their respective mobilities.

Slide 12: Drift Velocity and Mobility

The drift velocity (v) of charge carriers is related to their mobility (μ) by the equation v = μE.
A higher mobility implies that charge carriers can move more efficiently under the influence of an electric field.
Materials with higher mobilities tend to have lower resistivities and higher conductivities.

Slide 13: Factors Affecting Mobility

The mobility of charge carriers in a material depends on various factors, including:
- Crystal structure and lattice defects.
- Temperature.
- Presence of impurities or doping.
- Electric field strength.

Slide 14: Temperature Dependence of Mobility

The mobility of charge carriers in a material typically decreases with increasing temperature.
As temperature rises, lattice vibrations increase, causing more collisions between charge carriers and lattice atoms.
These collisions impede the motion of charge carriers, resulting in a decrease in mobility.

Slide 15: Example of Temperature Dependence of Mobility

In a pure semiconductor such as silicon, the mobility of electrons decreases with increasing temperature.
At low temperatures, the mobility is relatively high, leading to efficient charge transport.
However, as temperature increases, lattice vibrations impede the motion of electrons, reducing their mobility.

Slide 16: Variation of Resistivity with Temperature

For most metals, resistivity increases with increasing temperature.
This is due to the increased lattice vibrations, which impede the flow of electrons.
The temperature coefficient of resistivity (α) quantifies this increase in resistivity with temperature.

Slide 17: Temperature Coefficient of Resistivity (α)

The temperature coefficient of resistivity (α) is given by α = (1/ρ) * (dρ/dT).
It measures the rate of change of resistivity (ρ) with respect to temperature (T).
The sign of the temperature coefficient indicates whether the resistivity increases or decreases with temperature.

Slide 18: Example of Positive Temperature Coefficient

Copper, a common metal, exhibits a positive temperature coefficient of resistivity.
As temperature increases, the resistivity of copper increases.
This is due to the increased lattice vibrations that impede the motion of electrons, resulting in higher resistance.

Slide 19: Example of Negative Temperature Coefficient

Germanium, a semiconductor, exhibits a negative temperature coefficient of resistivity.
As temperature increases, the resistivity of germanium decreases.
This is because higher temperatures create more charge carriers, increasing conductivity and decreasing resistance.

Slide 20: Applications of Mobility and Temperature Dependence of Resistivity

Understanding the mobility and temperature dependence of resistivity is crucial in many practical applications, including:
- Designing electronic devices and circuits.
- Thermal management of electrical components.
- Materials selection for specific temperature ranges and operating conditions.
- Optimizing energy efficiency in electrical systems.

Slide 21: Mobility and Temperature Dependence of Resistivity

The mobility of charge carriers plays a crucial role in determining the resistivity of a material.
The mobility of electrons (μe) and holes (μh) can have different values.
The resistivity of a material depends on the mobility of both electrons and holes.
The drift velocity of charge carriers also depends on their respective mobilities.
Temperature affects the mobility of charge carriers and thus, the resistivity of a material.

Slide 22: Drift Velocity and Mobility

The drift velocity (v) of charge carriers is related to their mobility (μ) by the equation v = μE.
Higher mobility allows charge carriers to move more efficiently under an electric field.
Materials with higher mobilities tend to have lower resistivities and higher conductivities.
The mobility of charge carriers can be influenced by factors such as crystal structure, temperature, doping, and electric field strength.
In general, higher temperatures reduce the mobility of charge carriers.

Slide 23: Factors Affecting Mobility

Crystal structure and lattice defects can affect charge carrier mobility.
Temperature influences lattice vibrations, affecting the mobility of charge carriers.
The presence of impurities or doping can alter the mobility of charge carriers.
Electric field strength can impact the mobility of charge carriers in a material.
Optimizing these factors is essential for improving the electrical conductivity of materials.

Slide 24: Temperature Dependence of Mobility

The mobility of charge carriers typically decreases with increasing temperature.
As temperature rises, lattice vibrations increase, leading to more collisions between charge carriers and lattice atoms.
These collisions impede the motion of charge carriers and reduce their mobility.
For metals and most semiconductors, higher temperatures result in decreased mobility.
Temperature control is important in maintaining the desired electrical properties of materials.

Slide 25: Example of Temperature Dependence of Mobility

Silicon, a commonly used semiconductor, exhibits a decrease in mobility with increasing temperature.
At low temperatures, the mobility of electrons in silicon is relatively high, facilitating efficient charge transport.
However, as temperature increases, lattice vibrations hinder the motion of electrons, causing a decrease in mobility.

Slide 26: Variation of Resistivity with Temperature

The resistivity of most metals increases with increasing temperature.
This is due to the increased lattice vibrations, which impede the flow of charge carriers.
The temperature coefficient of resistivity (α) quantifies this increase in resistivity.
The temperature coefficient is defined as α = (1/ρ) * (dρ/dT), where ρ is the resistivity and T is the temperature.
A positive α indicates an increase in resistivity with temperature.

Slide 27: Temperature Coefficient of Resistivity (α)

The temperature coefficient of resistivity (α) measures the rate of change of resistivity with respect to temperature.
It is expressed in units of ohm-meter per degree Celsius (Ω·m/°C) or ohm-meter per Kelvin (Ω·m/K).
A positive α indicates that resistivity increases with increasing temperature.
A negative α indicates that resistivity decreases with increasing temperature.
The temperature coefficient provides valuable information for materials selection and designing electrical systems.

Slide 28: Example of Positive Temperature Coefficient

Copper, a commonly used metal, exhibits a positive temperature coefficient of resistivity.
As temperature increases, the resistivity of copper also increases.
This is because higher temperatures result in increased lattice vibrations, hindering the motion of electrons and increasing resistance.

Slide 29: Example of Negative Temperature Coefficient

Germanium, a semiconductor material, exhibits a negative temperature coefficient of resistivity.
As temperature increases, the resistivity of germanium decreases.
This is due to the generation of more charge carriers at higher temperatures, resulting in increased conductivity and decreased resistance.

Slide 30: Applications of Mobility and Temperature Dependence of Resistivity

Understanding mobility and the temperature dependence of resistivity is important in various practical applications, including:
- Designing electronic devices and circuits with desired electrical properties.
- Thermal management of electrical components to prevent temperature-induced changes in resistivity.
- Selecting appropriate materials for specific temperature ranges and operating conditions.
- Optimizing energy efficiency in electrical systems by controlling resistivity and conductivity.
- Developing advanced materials for electronic applications based on their resistivity characteristics.