13.1.8
Band Theory
Band Theory
Band Theory
Band theory was formulated by considering the quantum effects of the periodic arrangement of the nuclei of atoms in crystalline solids. Band theory explains the various properties of solids.


Band theory
Band theory
- Band theory supposes that there are energy bands occupied by the electrons in solids, as opposed to the sea of freely moving electrons used to model metals.
- Bands can be thought of as electron energy levels for the whole solid rather than an individual atom.
- The existence of these bands can explain the differences in conductivity, insulation and semiconductivity of solids.


Band gaps
Band gaps
- Between each band, there is a range of energies that are forbidden for an electron bound within the solid to have.
- These ranges are called band gaps or forbidden bands.


Types of band
Types of band
- There are two specific bands that are of interest in determining the properties of a solid, the valence band and the conduction band.
- The valence band of a solid is the highest energy band that is completely filled.
- A completely filled energy band is one that has each available state occupied by an electron.
- The next available energy band is called the conduction band.


Conductors and insulators
Conductors and insulators
- Conductors have conduction bands and valence bands that overlap.
- Electrons in the partially filled conduction band gain kinetic energy from the electric field by filling higher energy states in the conduction band.
- This is the process of conduction of electricity.


Conductors and insulators
Conductors and insulators
- Insulators have empty conduction bands due to their large band gaps.
- This means no electrons have enough energy to excite and occupy the conduction band.
Applications of Band Theory
Applications of Band Theory
Band theory can be used to explain the thermal and conductive properties of solids.


Metals
Metals
- Metals are conductors, which means they have an overlap between the valence and conduction bands.
- This means an increase in temperature does not decrease the resistance of the metal.


Metals
Metals
- However, the resistance of metals actually increases with an increase in temperature.
- As the temperature increases, the ions in the metallic lattice vibrate with increasing frequency, causing collisions with the electrons.
- These collisions absorb some of the kinetic energy of the electrons, and so the resistance of the metal is increased.


Intrinsic semiconductors
Intrinsic semiconductors
- An intrinsic semiconductor is a pure material with a band structure similar to that of insulators, except their band gaps are much smaller.
- This means electrons at room temperature have enough energy to excite into the conduction band.


Intrinsic semiconductors
Intrinsic semiconductors
- An increase in temperature increases the number of electrons with enough energy to excite, which decreases the resistance of the semiconductor.


Light-dependent resistors
Light-dependent resistors
- The absorption of light can cause electrons to excite into higher energy levels in atoms.
- The same is true for electrons in semiconductors, which can be excited into the conduction band by absorbing a photon.


Light-dependent resistors
Light-dependent resistors
- The higher the intensity of light shone upon the material, the more photons are absorbed, resulting in more electrons that are excited into the conduction band.
- This means the resistance of the material decreases as the light intensity increases.
- This is a light-dependent resistor or LDR.
1Physical Quantities & Units
2Measurement Techniques
3Kinematics
4Dynamics
4.1Momentum & Newton's Laws of Motion
4.2Non-Uniform Motion
4.3Linear Momentum & Conservation
4.4Force, Density & Pressure
4.4.1Fields
4.4.2Force in Uniform Fields
4.4.3Friction
4.4.4Buoyancy
4.4.5Terminal Speed
4.4.6End of Topic Test - Acceleration Due to Gravity
4.4.7Centre of Mass
4.4.8Forces & Equilibrium
4.4.9End of Topic Test - Scalars & Vectors
4.4.10Moments
4.4.11End of Topic Test - Moments & Centre of Mass
4.4.12Density
4.4.13Pressure
4.5Work, Energy & Power
5Gravitational Fields
5.1Gravitational Fields (A2 only)
6Deformation of Solids
7Thermal Physics
7.1Thermal Physics
7.1.1Temperature
7.1.2Measuring Temperature
7.1.3Ideal Gas Law
7.1.4Ideal Gases
7.1.5Boyle's Law & Charles' Law
7.1.6Molecular Kinetic Theory Model
7.1.7Molecular Kinetic Theory Model 2
7.1.8Thermal Energy Transfer
7.1.9Thermal Energy Transfer Experiments
7.1.10End of Topic Test - Thermal Energy & Ideal Gases
7.1.11First Law of Thermodynamics
8Oscillations
8.1Simple Harmonic Motion
8.2Waves
8.2.1Progressive Waves
8.2.2Intensity of Waves
8.2.3Wave Speed & Phase Difference
8.2.4Longitudinal & Transverse Waves
8.2.5End of Topic Test - Progressive Waves
8.2.6Electromagnetic Waves
8.2.7Doppler Effect
8.2.8Sound Waves
8.2.9Measuring Sound Waves
8.2.10End of Topic Test - Waves
8.2.11Ultrasound Imaging
8.2.12Ultrasound Imaging 2
9Communication
9.1Communication Channels
9.2Digital Communication
10Electric Fields
10.1Electric Fields
11Current Electricity
11.1Current Electricity
11.1.1Basics of Electricity
11.1.2Mean Drift Velocity
11.1.3Current-Voltage Characteristics
11.1.4End of Topic Test - Basics of Electricity
11.1.5Resistivity
11.1.6End of Topic Test - Resistivity & Superconductors
11.1.7Power and Conservation
11.1.8Microphones
11.1.9Components
11.1.10Relays
11.1.11Strain Gauges
12Magnetic Fields
12.1Magnetic Fields
13Modern Physics
13.1Quantum Physics
13.1.1The Photoelectric Effect
13.1.2The Photoelectric Effect Explanation
13.1.3End of Topic Test - The Photoelectric Effect
13.1.4Collisions of Electrons with Atoms
13.1.5Energy Levels & Photon Emission
13.1.6Wave-Particle Duality
13.1.7End of Topic Test - Absorption & Emission
13.1.8Band Theory
13.1.9Diagnostic X-Rays
13.1.10X-Ray Image Processing
13.1.11Absorption of X-Rays
13.1.12CT Scanners
13.2Nuclear Physics
13.2.1Rutherford Scattering
13.2.2Atomic Model
13.2.3Isotopes
13.2.4Stable & Unstable Nuclei
13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei
13.2.6Alpha & Beta Radiation
13.2.7Gamma Radiation
13.2.8Particles, Antiparticles & Photons
13.2.9Quarks & Antiquarks
13.2.10Particle Interactions
13.2.11Radioactive Decay
13.2.12Half Life
13.2.13End of Topic Test - Radioactivity
13.2.14Nuclear Instability
13.2.15Mass & Energy
13.2.16Binding Energy
13.2.17A-A* (AO3/4) - Nuclear Fusion
Jump to other topics
1Physical Quantities & Units
2Measurement Techniques
3Kinematics
4Dynamics
4.1Momentum & Newton's Laws of Motion
4.2Non-Uniform Motion
4.3Linear Momentum & Conservation
4.4Force, Density & Pressure
4.4.1Fields
4.4.2Force in Uniform Fields
4.4.3Friction
4.4.4Buoyancy
4.4.5Terminal Speed
4.4.6End of Topic Test - Acceleration Due to Gravity
4.4.7Centre of Mass
4.4.8Forces & Equilibrium
4.4.9End of Topic Test - Scalars & Vectors
4.4.10Moments
4.4.11End of Topic Test - Moments & Centre of Mass
4.4.12Density
4.4.13Pressure
4.5Work, Energy & Power
5Gravitational Fields
5.1Gravitational Fields (A2 only)
6Deformation of Solids
7Thermal Physics
7.1Thermal Physics
7.1.1Temperature
7.1.2Measuring Temperature
7.1.3Ideal Gas Law
7.1.4Ideal Gases
7.1.5Boyle's Law & Charles' Law
7.1.6Molecular Kinetic Theory Model
7.1.7Molecular Kinetic Theory Model 2
7.1.8Thermal Energy Transfer
7.1.9Thermal Energy Transfer Experiments
7.1.10End of Topic Test - Thermal Energy & Ideal Gases
7.1.11First Law of Thermodynamics
8Oscillations
8.1Simple Harmonic Motion
8.2Waves
8.2.1Progressive Waves
8.2.2Intensity of Waves
8.2.3Wave Speed & Phase Difference
8.2.4Longitudinal & Transverse Waves
8.2.5End of Topic Test - Progressive Waves
8.2.6Electromagnetic Waves
8.2.7Doppler Effect
8.2.8Sound Waves
8.2.9Measuring Sound Waves
8.2.10End of Topic Test - Waves
8.2.11Ultrasound Imaging
8.2.12Ultrasound Imaging 2
9Communication
9.1Communication Channels
9.2Digital Communication
10Electric Fields
10.1Electric Fields
11Current Electricity
11.1Current Electricity
11.1.1Basics of Electricity
11.1.2Mean Drift Velocity
11.1.3Current-Voltage Characteristics
11.1.4End of Topic Test - Basics of Electricity
11.1.5Resistivity
11.1.6End of Topic Test - Resistivity & Superconductors
11.1.7Power and Conservation
11.1.8Microphones
11.1.9Components
11.1.10Relays
11.1.11Strain Gauges
12Magnetic Fields
12.1Magnetic Fields
13Modern Physics
13.1Quantum Physics
13.1.1The Photoelectric Effect
13.1.2The Photoelectric Effect Explanation
13.1.3End of Topic Test - The Photoelectric Effect
13.1.4Collisions of Electrons with Atoms
13.1.5Energy Levels & Photon Emission
13.1.6Wave-Particle Duality
13.1.7End of Topic Test - Absorption & Emission
13.1.8Band Theory
13.1.9Diagnostic X-Rays
13.1.10X-Ray Image Processing
13.1.11Absorption of X-Rays
13.1.12CT Scanners
13.2Nuclear Physics
13.2.1Rutherford Scattering
13.2.2Atomic Model
13.2.3Isotopes
13.2.4Stable & Unstable Nuclei
13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei
13.2.6Alpha & Beta Radiation
13.2.7Gamma Radiation
13.2.8Particles, Antiparticles & Photons
13.2.9Quarks & Antiquarks
13.2.10Particle Interactions
13.2.11Radioactive Decay
13.2.12Half Life
13.2.13End of Topic Test - Radioactivity
13.2.14Nuclear Instability
13.2.15Mass & Energy
13.2.16Binding Energy
13.2.17A-A* (AO3/4) - Nuclear Fusion
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