PHD
  1. Inorganic chemistry  1.1. Coordination chemistry  1.1.1. Ligand field theory  1.1.2. Crystal field theory  1.1.3. Molecular Orbital Theory for Coordination Compounds  1.1.4. Stability of Coordination Compounds  1.1.5. Electronic spectra of coordination compounds  1.1.6. Isomerism in Coordination Compounds  1.1.7. Kinetics and mechanism of coordination reactions  1.2. Organometallic Chemistry  1.2.1. Metal Carbonyls  1.2.2. Metal alkyl and aryl  1.2.3. Fischer and Schrock carbonaceans  1.2.4. Oxidative Addition and Reductive Elimination  1.2.5. Metal Hydrides  1.2.6. Catalysis by organometallic compounds  1.2.7. Metallocenes and Sandwich Complexes  1.2.8. CH activation  1.3. Solid state chemistry  1.3.1. Crystal structures and lattices  1.3.2. Band theory and electrical properties  1.3.3. Defects in the crystal  1.3.4. Synthesis of solid state materials  1.3.5. Magnetic and optical properties of solids  1.3.6. Superconductivity  1.3.7. Solid state ionics  1.4. Bio-inorganic chemistry  1.4.1. Metalloproteins and enzymes  1.4.2. Metal ion transport and storage  1.4.3. The role of metals in medicine  1.4.4. Bioinspired catalysis  1.4.5. Metal–DNA interactions  1.4.6. Metal Complexes in Medical Science  1.5. Lanthanides and Actinides  1.5.1. Electronic configuration and oxidation states in lanthanides and actinides  1.5.2. Spectral and Magnetic Properties in Lanthanides and Actinides  1.5.3. Separation and Extraction of Lanthanides and Actinides  1.5.4. Coordination chemistry of f-block elements  1.6. Main Group Chemistry  1.6.1. Chemistry of boron compounds  1.6.2. Chemistry of Silicon and Germanium Compounds  1.6.3. Chemistry of Phosphorus and Sulfur Compounds  1.6.4. Organosilicon chemistry  1.6.5. Noble Gas Chemistry
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition and substitution reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic Reactions  2.1.7. Photochemical reactions  2.2. Stereoscopic  2.2.1. Chirality and optical activity  2.2.2. Structural analysis  2.2.3. Stereoelectronic effects  2.2.4. Asymmetric synthesis  2.2.5. Dynamic Stereochemistry  2.3. Organometallic Chemistry in Organic Synthesis  2.3.1. Organolithium and organomagnesium reagents  2.3.2. Transition metal catalyzed coupling reactions  2.3.3. Palladium-catalyzed reactions  2.3.4. Olefin Metathesis  2.3.5. Gold and silver catalysis  2.4. Natural products chemistry  2.4.1. Alkaloids and terpenoids  2.4.2. Steroids and Flavonoids  2.4.3. Total synthesis of natural products  2.4.4. Biosynthesis of natural products  2.5. Supramolecular Chemistry  2.5.1. Host-Guest Chemistry  2.5.2. Self-assembly and molecular recognition  2.5.3. Supramolecular Catalysis  2.5.4. Molecular Machines
  3. Physical Chemistry  3.1. Thermodynamics  3.1.1. Laws of Thermodynamics  3.1.2. Chemical Potential and Equilibrium  3.1.3. Statistical thermodynamics  3.1.4. Non-equilibrium thermodynamics  3.2. Quantum Chemistry  3.2.1. Schrödinger equation and its applications  3.2.2. Molecular orbital theory  3.2.3. Density functional theory  3.2.4. Post-Hartree–Fock methods  3.3. Chemical kinetics  3.3.1. Reaction rate theory  3.3.2. Mechanism and rate laws  3.3.3. Catalysis and enzyme kinetics  3.3.4. Reaction dynamics  3.4. Spectroscopy and molecular structure  3.4.1. Infrared Spectroscopy  3.4.2. UV-visible spectroscopy  3.4.3. Nuclear Magnetic Resonance Spectroscopy  3.4.4. Mass Spectrometry  3.4.5. Raman Spectroscopy  3.5. Surface and Colloid Chemistry  3.5.1. Absorption and Catalysis  3.5.2. Surfactants and micelles  3.5.3. Colloidal Stability  3.5.4. Nanomaterials and Interfaces
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.1.4. Ion Chromatography  4.2. Electroanalytical techniques  4.2.1. Voltammetry and Polarography  4.2.2. Conductometry and potentiometry  4.2.3. Colometry  4.3. Spectroscopic Methods  4.3.1. Atomic absorption spectroscopy  4.3.2. Fluorescence Spectroscopy  4.3.3. X-ray diffraction  4.3.4. Electron paramagnetic resonance spectroscopy  4.4. Chemometrics  4.4.1. Data processing and statistical methods  4.4.2. Multidisciplinary analysis  4.4.3. Machine Learning in Analytical Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.2. Quantum chemistry methods  5.3. Computational drug design  5.4. Machine Learning in Chemistry  5.5. Ab initio molecular dynamics
  6. Biophysics and Medicinal Chemistry  6.1. Drug discovery and design  6.2. Enzyme kinetics and inhibition  6.3. Chemical biology approach  6.4. Protein-ligand interactions  6.5. Bioorthogonal chemistry
  7. Materials chemistry  7.1. Polymer chemistry  7.1.1. Polymerization mechanism  7.1.2. Functional Polymers  7.1.3. Biodegradable Polymer  7.1.4. Conducting and semiconducting polymers  7.2. Nano Chemistry  7.2.1. Nanoparticles and nanostructures  7.2.2. Carbon-based nanomaterials  7.2.3. Quantum dots  7.3. Energy and Environmental Chemistry  7.3.1. Battery and Fuel Cell Chemistry  7.3.2. Green chemistry and sustainable materials  7.3.3. Photocatalysis

PHD → Inorganic chemistry → Solid state chemistry ↓


Band theory and electrical properties


Band theory is an important concept in solid state chemistry and physics, which helps to understand the behavior of electrons in solid materials, particularly metals, semiconductors, and insulators. This theory provides a framework for explaining the electrical properties of these materials based on the energy levels available to electrons and the way these energy levels are populated.

Fundamental concepts

Atomic orbitals and molecular orbitals

At the atomic level, electrons orbit around the nucleus in defined regions known as atomic orbitals, which are marked by discrete energy levels. When atoms combine to form a solid, their atomic orbitals overlap, forming molecular orbitals that extend over a large number of atoms.

As the number of atoms increases, the number of molecular orbitals that are very close in energy also increases. In solids with very large numbers of atoms (usually on the order of Avogadro's number), these molecular orbitals form continuous energy bands. These bands are the focus of band theory.

Energy bands

In a solid, energy bands are formed due to the numerous molecular orbitals. These bands can accommodate electrons, and the most important bands related to electrical properties are the valence band and the conduction band.

Valence band: It is the energy band that contains valence electrons. These electrons are responsible for the chemical properties of the substance.

Conduction band: This is the energy band where electrons can move freely across the material, which contributes to electrical conductivity.

Classification of solids

Based on the band theory, solids can be classified into conductors, semiconductors, and insulators depending on the relative position of the valence and conduction bands.

Conductor

In conductors such as metals, the valence band and conduction band overlap, or the conduction band is partially filled even at absolute zero temperature (0 K). This means that electrons can easily move from the valence band to the conduction band, giving high electrical conductivity.

Energy ^ Conduction Band Valence Band Overlap

Insulator

Insulators have a large energy gap between the valence band and the conduction band. This energy gap, which is typically greater than 3 eV, means that electrons cannot easily move from the valence band to the conduction band, resulting in low electrical conductivity.

Energy ^ Conduction Band Large Band Gap Valence Band

Semiconductors

Semiconductors have a smaller energy gap than insulators, typically less than 3 eV. Thermal energy at room temperature can excite electrons from the valence band to the conduction band, yielding moderate conductivity that can be easily controlled by external factors such as temperature, light, or doping.

Energy ^ Conduction Band Small Band Gap Valence Band

Band gap and electrical conductivity

The nature of the band gap plays a fundamental role in determining the electrical properties of the material. Let us discuss this in more detail with examples:

Temperature dependence

The electrical conductivity of semiconductors and insulators is highly dependent on temperature. As the temperature increases, more electrons are excited from the valence band to the conduction band, increasing the conductivity. However, metals show a decrease in conductivity with increase in temperature due to increased electron-phonon scattering.

Doping of semiconductors

Doping is the process of adding impurities to a semiconductor to change its electrical properties. There are two main types of doping:

  • N-type doping: This involves adding elements having more valence electrons than the host material, allowing more electrons to enter the conduction band. For example elements like phosphorus in silicon.
  • P-type doping: This involves adding elements with fewer valence electrons, creating holes in the valence band where electrons can move, thereby contributing to conduction. Example of elements like boron in silicon.

Effective mass and maneuverability

The effective mass of an electron in a solid material affects how easily the electron can be accelerated by an electric field. The electron mobility, which defines the drift velocity per unit electric field, is directly affected by the effective mass and scattering processes within the material.

Applications of band theory

Design of semiconductor devices

Understanding band theory is integral to designing and optimizing semiconductor devices such as diodes, transistors, and integrated circuits. By controlling the band gap through material selection and doping, specific electrical properties can be engineered.

Photovoltaic cell

Solar cells convert light energy into electrical energy using the photovoltaic effect. When photons with energy greater than the band gap strike a semiconductor material, electron-hole pairs are produced, which contribute to current flow when connected to an external circuit.

Light emitting diodes (LEDs)

LEDs work on the principle of band gap recombination. When electrons in the conduction band recombine with holes in the valence band, energy is released in the form of light. The colour of the light emitted depends on the band gap of the material used.

Conclusion

Band theory provides a unifying framework for understanding the electrical properties of materials ranging from conductors to insulators. By analyzing energy bands and band gaps, chemists and physicists can predict and tune the behavior of electrons in solids, leading to diverse applications in technology and materials science. As research continues, the limits of what can be achieved with band engineering and materials design are constantly being pushed.


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Band theory and electrical properties

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