Band Gap of Nanomaterials Explained | Physics Lecture

The band gap of nanomaterials can be calculated using UV-visible spectroscopy by applying the Tauc equation (αhν)² = A(hν - E_g)ⁿ, where α is the absorption coefficient, hν is photon energy, E_g is the band gap, and n depends on the transition type (n=1/2 for direct allowed transitions). The absorption coefficient α can be calculated using three methods: α = 2.303 × ρ × (M/L) × C (using theoretical density), α = 4πK/λ (using absorption index), or α = 2.303 × A/λ (using absorbance). By plotting (αhν)² against hν and extrapolating the linear portion to the x-axis, the band gap value is obtained. The size-dependent behavior shows red shift (decreased band gap) for larger particles and blue shift (increased band gap) for smaller particles below approximately 10-20 nm due to quantum confinement effects.

This lecture covers key characterization techniques for nanomaterials: UV-visible spectroscopy detects surface plasmon resonance to determine nanoparticle size and shape; zeta potential measurement (ideally above ±30 mV) assesses colloidal stability based on particle charge; dynamic light scattering (DLS) measures hydrodynamic diameter in solution (0.6 nm-6 μm) by analyzing Brownian motion-induced light fluctuations; transmission electron microscopy (TEM) provides high-resolution (0.1 nm) images of thin samples for morphology and crystallography; scanning electron microscopy (SEM) offers 3D surface topography imaging with secondary electron detection; and atomic force microscopy (AFM) monitors tip-sample interactions in contact, tapping, or non-contact modes to image surfaces at atomic resolution without requiring conductive coating.

Various techniques characterize nanomaterials: (1) SEM (Scanning Electron Microscopy) - shows surface morphology, (2) TEM (Transmission Electron Microscopy) - reveals internal structure, (3) AFM (Atomic Force Microscopy) - measures surface topology and roughness, (4) XRD (X-ray Diffraction) - determines crystallographic structure, (5) FTIR - identifies chemical bonds and molecular structure, (6) Raman Spectroscopy - reveals vibrational modes and composition, (7) UV-Vis Spectroscopy - studies optical properties and band gap, (8) TGA (Thermogravimetric Analysis) - measures thermal stability, (9) Zeta Potential - determines surface charge and colloidal stability, (10) XPS (X-ray Photoelectron Spectroscopy) - analyzes surface chemical composition.

Nanomaterials are materials with structural components at least one dimension in the nanoscale (1-100 nm). Key characterization techniques include: UV-Vis Spectroscopy for nanoparticle formation confirmation, X-ray Diffraction for crystal structure and geometry, Scanning Electron Microscopy for surface morphology, Transmission Electron Microscopy for particle size, and FTIR for functional group absorption and binding nature. These techniques enable scientists to understand and manipulate nanomaterials for various applications.

Quantum dots are microscopic crystalline semiconducting particles with unique properties arising from quantum confinement. Due to their extreme smallness (2-10 nanometers), electrons become locked at specific band gaps, producing specific wavelengths of light. This enables quantum dots to theoretically achieve 66% solar conversion efficiency, far exceeding conventional single-junction cells (30%) and even multi-junction cells (51.4%). The Shockley-Queisser limit of 33.7% represents the maximum efficiency for single-junction cells, originally calculated in 1961. Quantum dots offer a promising path to surpass this limit through their tunable band gaps and potential for multiple exciton generation.

Quantum dots enable diverse optoelectronic applications: displays and LEDs use size-tunable band gaps for precise color control; solar cells benefit from broader light absorption; sensors detect molecules through fluorescence changes. Quantum cascade lasers use intraband transitions in quantum wells for wavelength-tunable infrared light. Quantum dot lasers use quantum dots as active medium, achieving population inversion more easily and enabling room-temperature operation with lower threshold currents.

Quantum dot solar cells use nanostructures like indium phosphide quantum dots (~40Å) deposited on TiO2 substrates. The key advantage is tunable band gaps achieved by changing quantum dot size. Two mechanisms enable superior performance: (1) Direct hot electron transfer to TiO2 conduction band before thermalization, and (2) Impact ionization where hot electrons create multiple electron-hole pairs. In bulk semiconductors, energy separations are smaller than phonon energy, causing thermalization. In quantum dots, engineered energy separations exceed phonon energy, favoring impact ionization. This enables quantum yields of 200-400%, far exceeding conventional solar cells' 100% limit.

Quantum dots are semiconductor nanoparticles measuring 2-10 nanometers that exhibit extraordinary optical and electronic properties due to quantum mechanical effects; as their size decreases, their band gap increases, causing them to emit light at shorter wavelengths (blue/green) rather than longer wavelengths (orange/red), enabling tunable color generation and applications in solar cells, LEDs, lasers, photodetectors, photocatalysts, and next-generation quantum dot displays.

Bandgap engineering in optoelectronic materials involves three primary techniques: (1) changing composition in III-V semiconductors (such as GaAs, GaP, GaN, InP, AlGaAs, InGaAsP) to tune bandgap energy from 1.5 eV (red/infrared) to 3.4 eV (blue/violet), (2) applying strain or lattice mismatching during epitaxial growth to modify the crystal structure and thereby alter electronic properties, and (3) creating quantum well structures that confine carriers in one dimension to create discrete energy levels and modify emission characteristics; these techniques allow precise control over light emission and absorption properties for devices like LEDs, solar cells, and photodetectors, though optimization is needed to balance improved optical properties against potential degradation of electrical properties.

Graphene, discovered by Geim and Novoselov (Nobel Prize 2010), is a single layer of carbon atoms arranged in a hexagonal lattice. Unlike bulk materials where atomic orbitals interact extensively, graphene's surface orbitals (pi orbitals) protrude outward, creating unique electronic properties. In graphene, electrons behave as if they have zero effective mass, moving at extremely high velocities. Transition metal dichalcogenides (TMDCs) like tungsten diselenide are two-dimensional materials with different electronic properties. When two layers of TMDC are stacked, Moiré patterns create spatially localized excitons with unique optical properties. A single layer of graphene exhibits optical activity comparable to bulk semiconductor lasers, despite being only one atom thick.

Two-dimensional materials like graphene and transition metal dichalcogenides (TMDs) exhibit unique electronic properties due to their atomic-scale thickness; graphene displays linear energy dispersion at the Dirac points, making electrons behave as massless Dirac fermions, while TMDs like MoS2 and WS2 show direct bandgaps in monolayers that become indirect in bulk, with DFT calculations revealing that LDA overbinds and GGA overestimates lattice parameters, and Raman spectroscopy provides a non-destructive method to characterize layer number and defects through phonon dispersion analysis.

Two-dimensional materials are ultra-thin substances consisting of only a few atomic layers, with graphene being just one atom thick. While graphene is the most famous 2D material, researchers have discovered over 1,800 potential 2D materials, including transition metal dichalcogenides (TMDs) like MoS2, which offer direct bandgaps making them superior to graphene for optoelectronics and photovoltaic applications. Other promising 2D materials include black phosphorus (fabricated in 2013), arsenene, antimonene, borophene, and silicene, each with unique electronic and optical properties. These materials can be combined to create heterostructures with novel properties not found in nature, enabling applications in flexible electronics, solar cells, supercapacitors, and even skin-mounted circuits.

Two-dimensional materials are categorized into three main families: graphene family (graphene and h-BN), transition metal dichalcogenide (TMD) family, and phosphorus family. Graphene exhibits semi-metallic properties while h-BN is insulating. TMD materials show semiconductor, metallic, and superconducting properties depending on the compound. The band gap determines applications: graphene (0-0.45 eV) for high-frequency devices, h-BN (large band gap) as insulator, and TMD materials (intermediate band gaps) for fiber optics, displays, and light-emitting devices. The research focuses on heterostructures combining these materials for advanced electronic and photonic applications.

Two-dimensional transition metal dichalcogenides possess unique electronic structures with two valleys (K and K') at the valence band top. Complex wavefunctions ψ_K ∝ x² - y² + ixy and ψ_K' ∝ x² - y² - ixy carry intrinsic orbital angular momentum. Four-band models show orbital moments exist even without spin-orbit coupling, demonstrating topological origins. Calculations reveal orbital Hall conductivity dominates over spin Hall contributions (ratio ~λ/(πΔ) ≈ 1/30 for typical values). This dominance makes TMDCs ideal candidates for observing orbital Hall effects, with strain offering tunability for device applications.