Mass Action Law — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Mass Action Law Applicable to both intrinsic and extrinsic (doped) semiconductors under thermal equilibrium. Derive electron density n e using Fermi-Dirac statistics and Density of States in conduction band. Derive hole density n h using Fermi-Dirac statistics and Density of States in valence band. Assume the Boltzmann approximation (E c - E F >> kT and E F - E v >> kT). Calculate the product n e n h. Observe that the Fermi level term cancels out, leaving the product dependent only on Temperature and Bandgap energy (equal to n i 2). Must be in thermal equilibrium. Semiconductor must be non-degenerate (doping concentration not excessively high). Temperature must remain constant. Believing that n e = n h is always true (only true for intrinsic/pure semiconductors). Thinking that doping increases n i (n i is a property of the material and temperature, doping changes n e and n h inversely). Confusing majority carrier concentration with impurity concentration (they are approximately equal, but conceptually distinct).