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Questions and Answers
What does the mean free path (λ) represent in the context of electron dynamics?
What does the mean free path (λ) represent in the context of electron dynamics?
How is the mean collision time (τc) related to the mean free path (λ) and drift velocity (Vd)?
How is the mean collision time (τc) related to the mean free path (λ) and drift velocity (Vd)?
What is the typical order of relaxation time (τ) in the presence of an electric field?
What is the typical order of relaxation time (τ) in the presence of an electric field?
Current density (J) is defined as which of the following?
Current density (J) is defined as which of the following?
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What distinguishes electrical conductivity in semiconductors from conductors?
What distinguishes electrical conductivity in semiconductors from conductors?
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What does the negative sign in the equation indicate about heat flow?
What does the negative sign in the equation indicate about heat flow?
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What is the formula for thermal conductivity, K?
What is the formula for thermal conductivity, K?
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How is the excess energy during electron travel from point A to point B derived?
How is the excess energy during electron travel from point A to point B derived?
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In terms of particle movement, how is the deficiency of energy from B to A expressed?
In terms of particle movement, how is the deficiency of energy from B to A expressed?
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What is the significance of 'dx' in the context of thermal conductivity?
What is the significance of 'dx' in the context of thermal conductivity?
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According to the Wiedemann-Franz law, what is the relationship between thermal and electrical conductivity?
According to the Wiedemann-Franz law, what is the relationship between thermal and electrical conductivity?
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Which variable in the formula for excess energy depends on the temperature difference?
Which variable in the formula for excess energy depends on the temperature difference?
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What does 'nvKBdT' represent in the context of heat transfer?
What does 'nvKBdT' represent in the context of heat transfer?
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What is the primary responsibility of free electrons in a metal according to Quantum free electron theory?
What is the primary responsibility of free electrons in a metal according to Quantum free electron theory?
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What does the potential energy of electrons inside a metal equal according to Quantum free electron theory?
What does the potential energy of electrons inside a metal equal according to Quantum free electron theory?
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Which principle regulates the distribution of electrons among different energy levels in a metal?
Which principle regulates the distribution of electrons among different energy levels in a metal?
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What is one of the assumptions regarding electrons in the Quantum free electron theory?
What is one of the assumptions regarding electrons in the Quantum free electron theory?
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Which scientist is credited with the introduction of Quantum free electron theory?
Which scientist is credited with the introduction of Quantum free electron theory?
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What happens to the energy of electrons due to interactions with other electrons according to Quantum free electron theory?
What happens to the energy of electrons due to interactions with other electrons according to Quantum free electron theory?
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What describes the motion of electrons within the metal as per the Quantum free electron theory?
What describes the motion of electrons within the metal as per the Quantum free electron theory?
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What is the result of the velocity and energy distribution of electrons inside a metal?
What is the result of the velocity and energy distribution of electrons inside a metal?
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What happens to the motion of free electrons in a semiconductor in the absence of an electric field?
What happens to the motion of free electrons in a semiconductor in the absence of an electric field?
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What is the relationship between drift velocity and acceleration when an electric field is applied to electrons?
What is the relationship between drift velocity and acceleration when an electric field is applied to electrons?
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Which formula correctly represents the current density in terms of charge carrier density and drift velocity?
Which formula correctly represents the current density in terms of charge carrier density and drift velocity?
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What is the theoretical value of the Lorentz number (L)?
What is the theoretical value of the Lorentz number (L)?
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Which of the following properties can classical free electron theory NOT explain?
Which of the following properties can classical free electron theory NOT explain?
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What does the equation σ = ne²λ / (3kBT) indicate about electrical conductivity with respect to temperature?
What does the equation σ = ne²λ / (3kBT) indicate about electrical conductivity with respect to temperature?
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Which of the following quantities is the relaxation time (τ) expressed in terms of?
Which of the following quantities is the relaxation time (τ) expressed in terms of?
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What assumption in classical free electron theory about electrical conductivity has proven to be incorrect at low temperatures?
What assumption in classical free electron theory about electrical conductivity has proven to be incorrect at low temperatures?
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How does the classical free electron theory explain thermal conductivity?
How does the classical free electron theory explain thermal conductivity?
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When an electric field is applied, what force do electrons experience?
When an electric field is applied, what force do electrons experience?
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What does the equation a = (eE)/m represent in the context of electrons in a semiconductor?
What does the equation a = (eE)/m represent in the context of electrons in a semiconductor?
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Which of the following phenomena cannot be explained by classical free electron theory?
Which of the following phenomena cannot be explained by classical free electron theory?
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Given a current of 5 A and charge carrier density of 5×10²⁶/m³, how does one find the drift speed?
Given a current of 5 A and charge carrier density of 5×10²⁶/m³, how does one find the drift speed?
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What was the experimental value of the Lorentz number (L) reported?
What was the experimental value of the Lorentz number (L) reported?
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According to classical free electron theory, which factor is assumed to directly affect electrical conductivity?
According to classical free electron theory, which factor is assumed to directly affect electrical conductivity?
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Which of the following statements about charge carriers in a semiconductor is true?
Which of the following statements about charge carriers in a semiconductor is true?
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What happens to the electrical conductivity of a semiconductor as temperature increases?
What happens to the electrical conductivity of a semiconductor as temperature increases?
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What does the deviation between the theoretical and experimental values of L indicate?
What does the deviation between the theoretical and experimental values of L indicate?
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What describes the Fermi level in a system of electrons?
What describes the Fermi level in a system of electrons?
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What condition allows for recombination to occur in a system?
What condition allows for recombination to occur in a system?
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How is the probability of finding an electron in a particular energy state affected as temperature increases?
How is the probability of finding an electron in a particular energy state affected as temperature increases?
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What happens to the function f(E) at absolute zero (0 K) for energy levels below the Fermi energy (Ef)?
What happens to the function f(E) at absolute zero (0 K) for energy levels below the Fermi energy (Ef)?
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What is indicated by a filled energy level in the context of the Fermi function?
What is indicated by a filled energy level in the context of the Fermi function?
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What does the term 'Fermi function' refer to?
What does the term 'Fermi function' refer to?
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What is an implication of Pauli’s exclusion principle at absolute zero?
What is an implication of Pauli’s exclusion principle at absolute zero?
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What is the relationship between radiative recombination and its probability?
What is the relationship between radiative recombination and its probability?
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Study Notes
Electronic Materials
- Conducting materials have low resistivity, conducting heat and electricity. Electrical conduction is due to free electrons, while normal conduction involves free electrons and phonons.
Basic Terminology
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Conductors: Materials with high electrical and thermal conductivity. Measurements show metal and alloy conductivity is around 108 Ω-1 m-1.
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Bound electrons: Valence electrons in an isolated atom, bound to their parent nucleus.
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Free electrons: Valence electrons in a solid, not bound to individual atoms due to overlapping neighboring atom boundaries. They can move easily throughout the solid.
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Difference between ordinary gas and free electron gas: Ordinary gas molecules are neutral, while a free electron gas is charged. Gas molecule density is lower than free electron density.
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Electric field (E): Potential drop (V) per unit length (l) of a conductor with uniform cross-section. E = V/l Vm-1.
Current Density (j)
- Current per unit area of cross-section of a conductor, normal to current flow. J = I/A Am-2 where I is current and A the area.
Conducting Materials Classification
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Zero resistive materials: Superconductors like alloys of aluminum, zinc, gallium, niobium, which exhibit zero resistance below a transition temperature. These are used in power systems, superconducting magnets, and memory storage.
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Low resistive materials: Metals like silver, aluminum, and their alloys. These have high electrical conductivity used in electrical components and power transmission.
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High resistive materials: Tungsten, platinum, and nichrome. These have high resistivity and low temperature coefficients, used in resistors and heating elements.
Electron Theory of Solids
- The outermost electrons in an atom determine electrical properties in a solid.
- The free electron theory of solids details solid structure and properties through their electron structure. The theory is applicable to all solids (metals and non-metals), explaining conductor, semiconductor and insulator behavior. It can also discuss thermal and magnetic properties.
- Classical free electron theory, developed by Drude and Lorentz, posits that electrons in metals can be considered a free electron gas. Mutual repulsion is disregarded. Total energy is the kinetic energy.
- Quantum free electron theory (Somerfield) incorporates quantum mechanical concepts into the model and utilizes Fermi-Dirac statistics.
- Zone/band theory: This theory looks at electron behavior in a periodic field and the lattice. It accounts for the mechanism of superconductivity.
Classical Free Electron Theory Postulates
- Metal structure consists of a positive ion core with valence electrons freely moving among the ion cores.
- In the absence of electric field, electrons move randomly and collide elastically.
- When an electric field is applied, electrons accelerate in the opposite direction to the field.
- Free electrons follow Maxwell-Boltzmann statistics.
Drift Velocity (Vd)
- The average velocity acquired by a free electron in a particular direction due to an applied electric field. Vd = a/t; where 'a' is acceleration and t is time.
Mobility (µ)
- Drift velocity per unit electric field. µ = Vd/E m2V-1 s-1.
Mean Free Path (λ)
- The average distance a free electron travels between successive collisions.
Relaxation Time (τ)
- Time taken by an electron to reach equilibrium position from a disturbed position in the presence of an electric field.
Band Gap (Eg)
- Energy difference between the maximum energy of the valence band and the minimum energy of the conduction band.
Thermal Conductivity (K)
- Measure of a material’s ability to conduct heat. K = (rate of heat flow)/(temp. gradient)
Wiedemann-Franz Law
- The ratio of thermal conductivity to electrical conductivity is directly proportional to the absolute temperature (K/σ α T).
Drawbacks of Classical Free Electron Theory
- Discrepancy between theoretical and experimental values of specific heat.
- Cannot explain the conductivity of insulators or semiconductors.
- Failure to explain superconductivity and other related phenomena.
Quantum Free Electron Theory
- Assumes electrons are fully responsible for electrical conduction and have constant potential inside the metal and wave nature.
- Electrons follow Fermi-Dirac statistics and energy distributions, with interactions disregarded.
Energy Bands in Solids
- Grouping of energy levels of valence electrons forms the valence band.
- Conduction band represents levels for free electrons with higher energy.
- Forbidden band represents an energy gap separating the valence and conduction bands; it contains no energy levels.
Types of Electronic Materials
- Conductor: Materials with overlapping valence and conduction bands and low resistivity.
- Insulator: Possess a large forbidden energy gap, high resistivity and completely filled valence band.
- Semiconductors: Have a small forbidden energy gap, intermediate resistivity.
Direct and Indirect Band Gap Semiconductors
- Direct: A minimum energy of the conduction band lies directly above a maximum energy in the valence band; electrons change state directly, releasing emitted light.
- Indirect: The minimum energy of the conduction band does not lie directly above the maximum energy of the valence band, momentum changes must occur; releasing the emitted light differently (usually heat).
Fermi Levels and Fermi Functions
- The highest energy level an electron can occupy at absolute zero temperature.
- Fermi energy: the energy of electrons in the Fermi level at absolute zero.
- Fermi function (Fermi-Dirac distribution): describes the probability of an electron occupying a given energy level at a particular temperature; the highest occupied energy level.
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Description
Explore the principles of electronic materials, focusing on conductors and their properties. This quiz covers basic terminology such as free and bound electrons, electrical conduction, and the differences between gases and free electron gases. Test your understanding of key concepts in electrical conduction and material behavior.
