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Questions and Answers
What is the significance of the conduction band in the conduction process?
What is the significance of the conduction band in the conduction process?
The conduction band is crucial because it is where electrons can move freely, allowing conductivity.
What happens to electrons in the conduction band?
What happens to electrons in the conduction band?
Electrons in the conduction band can move freely, contributing to electrical conduction.
How are electrons able to transition from the valence band to the conduction band?
How are electrons able to transition from the valence band to the conduction band?
Electrons transition to the conduction band when they are energized.
What role do energized electrons play in conduction?
What role do energized electrons play in conduction?
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Why is it vital for a material to have electrons in the conduction band?
Why is it vital for a material to have electrons in the conduction band?
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What are the main types of electrical conductors?
What are the main types of electrical conductors?
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What is the drift velocity of electrons?
What is the drift velocity of electrons?
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What does the Drude model describe in classical theory?
What does the Drude model describe in classical theory?
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How do imperfections in a crystal affect electron drift?
How do imperfections in a crystal affect electron drift?
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What happens to electrons in a conductor without the application of an electric field?
What happens to electrons in a conductor without the application of an electric field?
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What is drift velocity in the context of electrical conductors?
What is drift velocity in the context of electrical conductors?
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How does the current density relate to drift velocity in an electrical conductor?
How does the current density relate to drift velocity in an electrical conductor?
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What effect does a changing applied electric field have on the drift velocity of electrons?
What effect does a changing applied electric field have on the drift velocity of electrons?
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In the Drude model, what assumption is made about electron motion between collisions?
In the Drude model, what assumption is made about electron motion between collisions?
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Why might the average velocity of electrons not be consistent over time in a conductor?
Why might the average velocity of electrons not be consistent over time in a conductor?
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Study Notes
Electrical Properties of Material
- The electrical conductivity of a material depends on the number of electrons available for conduction.
- Not all electrons in each atom accelerate when an electric field is applied.
- The number of available electrons for conduction is related to the arrangement of electron states with respect to energy.
- A solid material is composed of a large number of atoms initially separated, then bonded together to form a crystalline structure.
- At large distances, each atom is independent, behaving as if isolated.
- The closer atoms get, electron and nucleus interactions cause perturbations.
Energy Band Structures in Solids
- Distinct atomic states split into closely spaced electron states, creating energy bands.
- Within each band, energy states are discrete but differences between adjacent states are small.
- The arrangement and filling of outermost electron bands determine a material's electrical properties.
- At 0K, electrons occupy the highest filled states, known as the Fermi energy.
- Electrons with energies above the Fermi energy can be accelerated by electric fields and participate in conduction.
- A "hole," a positively charged particle, exists when an electron is absent in a semiconductor or insulator.
- These contribute to electrical conductivity.
- The distinction between conductors, insulators, and semiconductors rests in the number of free electrons and holes.
Conduction in Terms of Band and Atomic Bonding Models
- Conductors (Metals): Electrons must be promoted to empty energy states above the Fermi level to become free carrying electrical charge. Large quantities can be excited by electric fields.
- Insulators and Semiconductors: Empty states adjacent to the filled valence band are not available. Electrons need energy to cross the band gap to reach conducting states. This energy is usually provided through heat or light.
Energy Band Theory of Solids
- Visualizing conductors, insulators, and semiconductors involves plotting available electron energies and forming bands.
- The conduction band is where electrons are free to move when energized via valence band.
- The energy difference between the highest occupied valence band state and lowest unoccupied conduction band state forms the band gap, determining conductivity.
Insulators
- Electrons in the valence band are separated from the conduction band by a large band gap, preventing electron flow.
- The valence band is tightly packed, meaning electrons cannot move even with an applied electric field.
Electrical Conductors
- Electrical conduction is the movement of charges under an applied electric field
- Conductors contain many free or mobile charge carriers.
- In metals, valence electrons form a sea that are free to move, termed conduction electrons.
- Examples of conductors include copper, aluminum, silver, gold.
Drift of Electrons
- Electrons flow between material atoms with drift velocity in the conduction band.
- A conductor consists of atoms with loosely bound valence electrons, easily excited by electric or thermal effects.
- When an electron moves to conduction band, it leaves a positive hole. Both can carry charge.
Classical Theory: The Drude Model
- Electric current density (J) is defined as the net charge flowing across a unit area per unit time (Aq/A∆t).
- Conduction electrons move randomly in a metal.
- Application of an electric field creates a net velocity in the direction of the field.
- This movement contributes to a net flow of charge in the conductor.
Drift Velocity
- Average velocity of electrons in the x-direction at time t is the drift velocity (vdx(t)).
- Electrons acquire a net velocity in the x-direction due to an applied electric field (Ex).
- Collisions of electrons with vibrating atoms cause changes in direction, but these atoms are not stationary. Impurities, defects and random collisions may alter trajectory.
- The average free time between collisions determines the drift velocity.
Calculation of Drift Velocity
- The drift velocity of an electron under the influence of an applied electric field (Ex) is calculated using the acceleration of the charge and the time between collisions.
- The average free time (τ), and mean scattering / relaxation time, are used to calculate the drift velocity.
- The drift velocity increases linearly with the applied electric field (vdx = etEx/me). The constant of proportionality is called the drift mobility. (µd).
- The drift mobility is a measure of how quickly electrons respond to the electric field.
Ohm's Law
- The current density of a material is directly proportional to the applied electric field (Jx = σEx).
- Conductivity (σ) is the proportionality constant.
Electrical Resistivity of Metals
- The total resistivity of a metal is determined by thermal vibrations, impurities, and deformations.
- Resistivity values vary based on the metal.
- Resistivity of metals increases more dramatically with increasing temperature or impurities.
Factors Affecting Resistivity
- Temperature
- Impurities
- Plastic deformation
- Pressure
Effect of Temperature on Resistivity
- Thermal vibrations of atoms increase with increasing temperature.
- This increases scattering events for electrons and reduces conductivity.
- Resistivity increases nearly linearly with temperature for many pure metals.
Temperature Coefficient of Resistivity
- Temperature coefficient (α) is the rate of change in resistivity per degree temperature increase.
- The temperature coefficient of resistance is the rate of change in resistance at a particular temperature.
- Values of the temperature coefficient differ by material type
Influence of Impurities
- Impurities increase resistivity by reducing the mean free path of electrons.
- The increase in resistivity (ρi) is proportional to the concentration of impurities (Ci).
Influence of Plastic Deformation
- Plastic deformation increases the number of electron scattering events, leading to an increase in resistivity.
Electrical c/ct of alloys used for commercial purposes
- Copper is frequently used for electrical applications because of its high electrical conductivity.
- Copper is often improved by adding oxygen (OFHC) for stability.
- Aluminum, with a lower conductivity than copper, is preferred where cost is a concern, or due to its lighter weight.
- Silver has the highest conductivity but its cost makes its use limited to specific cases
Conduction Materials
- Conductors, insulators, semiconductors, electrolytes, superconductors fall under this category.
- Copper is the standard against which other conductors are compared.
- Practical electrical circuits use aluminum more than silver, due to cost and weight.
Report: (Properties of conducting materials)
- Electrical properties (Conductivity, strength, Modulus of elasticity, Thermal coefficient of expansion, Costs, Tensile strength, etc) are discussed in a comparison context for Copper, Aluminum, and Silver.
Charge Carriers in Semiconductors
- Charge carriers (electrons and holes) are responsible for electrical current in semiconductors.
- Electrons are negatively charged and occupy the conduction band.
- Holes are positively charged, vacancies in the valence band, equivalent to the absence of electrons.
Carrier Concentrations
- Carrier concentration (the number of free electrons and holes per unit volume) is critical to a semiconductor's conductivity.
- Intrinsic carrier concentration (ni) increases with temperature as more electrons are excited into the conduction band, and holes in valence band, thus more current is carried.
- Doping, introducing impurities, can significantly affect the concentration of carriers.
Drift of Carriers in Electric and Magnetic Fields
- Drift is the movement of charge carriers in response to applied electric/magnetic fields.
- In an electric field charges accelerate, then collide with impurities.
- In a magnetic field, charges also encounter the Lorentz force which affects direction.
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Description
This quiz delves into the electrical properties of materials, focusing on conductivity and electron states. It explores how atomic structures and energy band formation influence the behavior of electrons in solids, particularly under an electric field. Test your understanding of these key concepts in material science.
