Slide 1: Mobility and Temperature Dependence of Resistivity
Definition of resistivity
Factors affecting resistivity
Role of temperature in resistivity
Relationship between resistivity and temperature
Concept of mobility
Slide 2: Resistivity
Definition: Resistivity is a measure of a material’s ability to oppose the flow of electric current.
Mathematically represented as ρ (rho)
Unit: Ωm (ohm-meter)
Determined by factors such as nature of the material, impurities, and temperature
High resistivity materials restrict the flow of current, whereas low resistivity materials facilitate current flow more easily
Slide 3: Factors Affecting Resistivity
Nature of the material: Different materials have different inherent resistivities due to variations in atomic structure and electron behavior.
Impurities: Presence of impurities in a material increases resistivity as they disrupt electron flow.
Temperature: Temperature affects resistivity, with most materials showing an increase in resistivity with increasing temperature.
Slide 4: Role of Temperature in Resistivity
As temperature increases, resistivity of most materials also increases.
This is because an increase in temperature causes atoms to vibrate more vigorously, hindering the flow of electrons.
Vibrating atoms create more obstacles for electrons to navigate, resulting in increased resistivity.
Slide 5: Relationship between Resistivity and Temperature
Resistivity (ρ) is related to temperature (T) using the formula: ρ = ρ₀(1 + α(T - T₀))
ρ₀ represents the initial resistivity at a reference temperature T₀
α is the temperature coefficient of resistivity, which varies for different materials
(1 + α(T - T₀)) represents the temperature correction factor
Slide 6: Concept of Mobility
Mobility is a measure of how easily charge carriers move through a material under the influence of an electric field.
Mathematically represented as μ (mu)
Unit: m²/Vs
Mobility is inversely related to resistivity, i.e., materials with high mobility have low resistivity and vice versa.
Slide 7: Relationship between Mobility and Resistivity
Resistivity (ρ) is inversely related to mobility (μ) using the formula: ρ = 1/qnμ
q represents the charge of the carriers (either electrons or holes)
n is the number density of charge carriers
Slide 8: Examples of Mobility and Resistivity
Example 1:
Copper has high mobility (due to its free electrons) and low resistivity.
It is widely used in electrical wiring and conductive materials.
Example 2:
Rubber has low mobility (as it is an insulator) and high resistivity.
It is used as an insulating material to prevent the flow of electric current.
Example 3:
Semiconductors have intermediate mobility and resistivity.
They find applications in electronic devices such as diodes and transistors.
Slide 9: Temperature Dependence of Resistivity in Metals
In metals, resistivity increases with temperature, following a linear relationship.
The temperature coefficient of resistivity (α) is positive for most metals.
Exceptions: Some metals, like nichrome, have a negative temperature coefficient, resulting in decreased resistivity with increasing temperature.
Slide 10: Temperature Dependence of Resistivity in Semiconductors
In intrinsic semiconductors (pure form), resistivity decreases with increasing temperature due to greater availability of charge carriers.
In doped (extrinsic) semiconductors, resistivity generally increases with temperature due to impurities and scattering of charge carriers.
Semiconductors display a non-linear relationship between resistivity and temperature.
Slide 11: Current and Electricity
Definition of electric current
Types of current: direct current (DC) and alternating current (AC)
Relationship between current, voltage, and resistance (Ohm’s Law: I = V/R)
Units of current: ampere (A)
Conservation of charge: charge is neither created nor destroyed; it only flows from one place to another
Slide 12: Electric Current
Definition: Electric current is the flow of electric charge through a conductor.
Electric charges (electrons or ions) move in response to an applied electric field.
In a conductor, electrons flow from the negative terminal to the positive terminal of a voltage source, creating electric current.
Slide 13: Direct Current (DC) and Alternating Current (AC)
Direct Current (DC): Steady flow of electric charge in one direction.
Examples: Batteries, electronic devices
Symbol: ──►
Alternating Current (AC): Periodic reversal of the direction of electric charge flow.
Examples: Mains electricity
Symbol:
~
Slide 14: Ohm’s Law
Ohm’s Law: States that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to the resistance of the conductor.
Mathematically represented as: I = V/R
I: Current in amperes (A)
V: Voltage in volts (V)
R: Resistance in ohms (Ω)
Slide 15: Units of Current
Current is measured in amperes (A), named after the physicist André Marie Ampère.
Submultiples of the ampere include:
Milliampere (mA): 1 mA = 10⁻³ A
Microampere (μA): 1 μA = 10⁻⁶ A
Nanoampere (nA): 1 nA = 10⁻⁹ A
Picoampere (pA): 1 pA = 10⁻¹² A
Slide 16: Conservation of Charge
Charge is a fundamental property of matter, and it cannot be created or destroyed.
According to the law of conservation of charge, the total amount of electric charge in an isolated system remains constant.
In an electric circuit, charge carriers (electrons or ions) redistribute themselves, but the total charge remains the same.
Slide 17: Mobility
Definition: Mobility is the ability of charged particles (electrons or ions) to move through a conductor under the influence of an electric field.
Mobility depends on the nature of the charge carriers and the material they are moving through.
Higher mobility allows for easier flow of charge and lower resistance.
Slide 18: Mobility and Conductivity
Mobility (μ) is inversely related to the resistance (R) of a material.
Conductivity (σ) is the reciprocal of resistivity (ρ): σ = 1/ρ.
Conductivity is directly proportional to mobility: σ = qnμ.
q: Charge of the carriers (e.g., electron charge)
n: Number density of carriers
Slide 19: Examples of Mobility
Example 1:
Copper has high mobility due to the presence of free electrons.
It is commonly used in electrical wiring and conductive materials.
Example 2:
In a semiconductor material like silicon, the mobility of charge carriers is lower than in metals.
This affects the conductivity and makes semiconductors useful for electronic devices.
Example 3:
Insulators, such as rubber or wood, have very low mobility, resulting in high resistance.
They are used to prevent the flow of electric current.
Slide 20: Temperature Dependence of Resistivity
Temperature affects the resistivity (ρ) of most materials.
Resistivity typically increases with increasing temperature, except for certain materials with negative temperature coefficients.
This relationship is due to the increased scattering of charge carriers by vibrating atoms at higher temperatures.
Slide 21: Temperature Dependence of Resistivity in Insulators
Insulators have very high resistivity and low mobility.
Temperature increase in insulators leads to a slight increase in resistivity due to increased thermal vibrations.
Unlike metals, insulators do not exhibit a linear relationship between resistivity and temperature.
Examples of insulators: rubber, plastic, glass.
Slide 22: Superconductivity
Superconductivity is a phenomenon observed in certain materials at very low temperatures.
Superconductors have zero resistivity, meaning they can conduct electric current without any loss of energy.
Critical temperature (Tc): The temperature below which a material becomes superconducting.
Applications of superconductors include magnetic resonance imaging (MRI) machines and particle accelerators.
Slide 23: Semiconductors
Semiconductors have intermediate conductivity between conductors and insulators.
They have a narrow band gap between the valence band and the conduction band.
Examples of semiconductors: silicon, germanium.
Semiconductors are widely used in electronic devices like diodes, transistors, and integrated circuits.
Slide 24: Band Theory of Solids
Band theory describes the behavior of electrons in solids.
Energy levels of electrons are grouped into bands: valence band and conduction band.
The energy gap between these bands determines the behavior of the material (conductor, insulator, or semiconductor).
Semiconductors have a small band gap that allows electron flow under certain conditions.
Slide 25: Intrinsic and Extrinsic Semiconductors
Intrinsic semiconductors are pure semiconducting materials with their own electrons and holes.
Extrinsic semiconductors are doped semiconductors, intentionally introduced with impurities (dopants) to modify their electrical properties.
Dopants can either add extra electrons (n-type) or create electron deficiencies (p-type).
Slide 26: Doping in Semiconductors
n-type semiconductor: Doped with an element that provides extra electrons (such as phosphorus).
p-type semiconductor: Doped with an element that creates electron deficiencies or “holes” (such as boron).
Doping changes the electrical conductivity and behavior of the semiconductor.
Slide 27: P-N Junction
A p-n junction is formed by joining a p-type semiconductor and an n-type semiconductor.
It creates a region with excess electrons (n-side) and a region with excess holes (p-side).
The junction acts as a barrier to electron flow, creating a diode.
Slide 28: Current Flow in a P-N Junction
Under forward bias, the positive terminal of a voltage source is connected to the p-side and the negative terminal to the n-side.
Electrons flow from n to p, and holes flow from p to n, creating current flow across the junction.
Under reverse bias, the direction of the voltage source is reversed, inhibiting current flow.
Slide 29: Solving Problems Involving Resistivity and Mobility
Examples:
Calculate the resistivity of a wire with length 2 m, cross-sectional area 0.5 mm², and resistance 100 Ω.
Determine the mobility of electrons in a conductor with a resistivity of 2.5 × 10⁻⁷ Ωm and number density of 5 × 10²⁸ m⁻³.
A material has a resistivity of 10 Ωm at 25°C. If its temperature coefficient is 0.004 Ωm/°C, calculate the resistivity at 50°C.
Use relevant formulas and constants to solve these problems.
Slide 30: Summary
Resistivity is a measure of a material’s ability to resist the flow of electric current.
Temperature affects resistivity, with most materials exhibiting increased resistivity at higher temperatures.
Mobility is a measure of the ease with which charge carriers move through a material.
Temperature dependence of resistivity differs for metals, semiconductors, and insulators.
Superconductivity allows for zero-resistance current flow.
Semiconductors have a narrow band gap and are widely used for electronic devices.
Doping in semiconductors modifies their electrical properties.
P-N junctions create diodes and control the flow of electric current.