Podcast
Questions and Answers
Why do electrons in completely filled bands not contribute to electrical conduction?
Why do electrons in completely filled bands not contribute to electrical conduction?
- The Pauli exclusion principle prevents them from changing their energy states.
- Their net momentum is zero due to symmetrical population of states. (correct)
- They are tightly bound to the atomic nuclei and cannot move freely.
- They possess insufficient energy to overcome the band gap.
According to band theory, what primarily dictates whether a solid is classified as an insulator?
According to band theory, what primarily dictates whether a solid is classified as an insulator?
- The presence of impurities within its crystal structure.
- The material's density and atomic weight.
- The magnitude of its band gap ($E_g$). (correct)
- The temperature at which the material is used.
How does the band theory of solids improve upon the free electron theory?
How does the band theory of solids improve upon the free electron theory?
- By considering electron-electron interactions, which are ignored in the free electron model.
- By explaining the existence of insulators, semiconductors, and metals based on their electronic band structures. (correct)
- By accurately predicting the specific heat of metals at low temperatures.
- By incorporating relativistic effects into the calculation of electron energy levels.
What causes the discontinuities or energy gaps in the energy spectrum of electrons in a solid?
What causes the discontinuities or energy gaps in the energy spectrum of electrons in a solid?
What is the significance of effective mass ($m^*$) in the context of electron dynamics within a band?
What is the significance of effective mass ($m^*$) in the context of electron dynamics within a band?
How does temperature affect the conductivity of a semiconductor?
How does temperature affect the conductivity of a semiconductor?
Under what condition does a solid conduct electricity with great ease, classifying it as a metal?
Under what condition does a solid conduct electricity with great ease, classifying it as a metal?
If an electron in a band is subjected to an electric field $F$, how does its acceleration differ from that of a free electron under the same field?
If an electron in a band is subjected to an electric field $F$, how does its acceleration differ from that of a free electron under the same field?
Flashcards
Valence Band
Valence Band
The highest filled electron band in a solid.
Conduction Band
Conduction Band
The electron band above the valence band; may be empty or partially filled, enabling conduction.
Band Gap (Eg)
Band Gap (Eg)
Energy difference between the top of the valence band and the bottom of the conduction band.
Insulators
Insulators
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Semiconductors
Semiconductors
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Metals
Metals
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Effective Mass (m*)
Effective Mass (m*)
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Energy Gaps Origin
Energy Gaps Origin
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Study Notes
- Electrons in a full band do not contribute to electrical conduction.
- Conduction relies on electrons in the uppermost two bands.
- The valence band is the highest filled band.
- The conduction band is above the valence band and can be empty or partially filled.
- The band gap (Eg) is the energy difference between the bottom of the conduction band and the top of the valence band.
- Band gap significantly influences the behavior of solids.
- Free electron theory could not explain insulators and conductors.
Band Theory
- Large band gap (Eg) materials are insulators.
- Small band gap (Eg) materials are semiconductors, they do not conduct at 0K.
- At temperatures above 0K, electrons jump to the conduction band, enabling conduction.
- Metals have partially filled or overlapping valence and conduction bands, allowing easy conduction.
Energy Spectrum Discontinuities
- Discontinuities occur near Brillouin zone boundaries, determined by specific propagation vector values which leads to energy gaps.
- At Brillouin zone boundaries, electron waves undergo Bragg diffraction and are deflected, causing energy gaps.
Electron Dynamics
- Electron motion in a band is k-dependent.
- Acceleration of a free electron in an electric field F is –eF/m.
- Acceleration of an electron in a band under the same field is
- Effective mass (m*) is given by h2(d2E/dk2) and is k-dependent.
- m* is negative in the upper half and positive in the lower half of a band.
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Description
Explanation of electron behavior in bands related to electrical conduction. It covers valence and conduction bands, band gaps, and how these factors differentiate insulators, semiconductors, and metals. Includes how it explains what free electron theory couldn't.
