Energy Band Diagram
Valence and conduction bands split by E_g — tune T to see thermal excitation follow exp(−E_g/2kT).
Key Notes
In a solid, atomic energy levels broaden into BANDS due to overlap of electron wavefunctions.
Valence band: highest filled (or partially filled) band at T = 0. Conduction band: next higher (mostly empty).
Energy gap E_g = bottom of conduction band − top of valence band.
Conductors: bands overlap or valence band partially filled ⇒ free electrons readily move. Eg ≈ 0.
Insulators: large gap (E_g > ~3 eV). Few electrons can be thermally excited to the CB.
Semiconductors: small gap (E_g ~ 0.5-2 eV). Some thermal excitation at room temperature.
Conduction in semiconductors involves BOTH electrons in CB and HOLES (missing electrons in VB) — holes act like positive charge carriers.
Doping creates extra states INSIDE the gap close to CB (donor → n-type) or VB (acceptor → p-type), dramatically changing conductivity.
Formulas
Carrier density (intrinsic)
Strongly temperature-dependent — small E_g ⇒ more carriers.
Conductivity
n = electron density, p = hole density, μ = mobility.
Band gaps (room T)
Determines wavelength of LED light (E_g = hc/λ).
Important Points
BAND structure is the language of semiconductor physics. Memorise: conductor (overlap), semiconductor (small gap), insulator (big gap).
Carrier density in intrinsic Si at room T: n_i ≈ 10¹⁶/m³ — extremely small compared to metals (~10²⁸).
Increasing T excites more carriers into CB ⇒ conductivity INCREASES (opposite of metals).
Doping with one part per million can change resistivity by 6+ orders of magnitude — that's why semiconductor industry exists.
Direct vs indirect bandgap: direct (GaAs) ⇒ efficient light emission/absorption. Indirect (Si) ⇒ inefficient ⇒ Si LEDs are uncommon.
Fermi level: at the middle of E_g for intrinsic semiconductors; shifts toward CB for n-type, toward VB for p-type.
Energy Band Diagram notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.