Carrier Statistics, Transport & Recombination

Carrier Statistics, Transport & Recombination: Carrier Statistics: Fermi-Dirac, Density of States & Fermi Level, Carrier Transport: Drift, Diffusion, Mobility & Conductivity, Generation, Recombination & Carrier Lifetime, Semiconductor Equations: Poisson, Continuity & Drift-Diffusion.

• Carrier Statistics: Fermi-Dirac, Density of States & Fermi Level — Counting carriers properly. Learn the density of states g(E) near band edges, the Fermi-Dirac distribution and its meaning, the Maxwell-Boltzmann approximation and when it is valid (E − E_F > 3kT), effective densities of states N_c and N_v from effective masses, the equations n = N_c·e^(−(E_c−E_F)/kT) and p = N_v·e^(−(E_F−E_v)/kT), intrinsic level E_i, Fermi-level position vs doping and temperature, and degenerate semiconductors — with Python evaluating the Fermi function, computing N_c, N_v, n_i and checking Boltzmann validity.
• Carrier Transport: Drift, Diffusion, Mobility & Conductivity — How carriers move and make current. Learn drift in an electric field, mobility and its dependence on doping (ionised-impurity scattering) and temperature (lattice scattering), Matthiessen's rule, velocity saturation at high fields, conductivity and resistivity, sheet resistance, diffusion driven by concentration gradients, the diffusion coefficient and the Einstein relation D = µkT/q, drift + diffusion current densities for electrons and holes, and built-in fields in non-uniform doping — with Python computing Caughey-Thomas mobility, resistivity, drift and diffusion currents.
• Generation, Recombination & Carrier Lifetime — How excess carriers appear and disappear. Learn thermal and optical generation, excess carriers and low-level injection, recombination mechanisms — radiative (band-to-band), Shockley-Read-Hall through traps, Auger, and surface recombination — minority-carrier lifetime, diffusion length L = √(Dτ), steady-state and transient behaviour, photoconductivity, and why lifetime matters for diodes, BJTs, solar cells, LEDs and switching speed (lifetime control with Au/Pt or irradiation) — with Python computing SRH lifetimes, diffusion lengths, decay transients and Auger limits.
• Semiconductor Equations: Poisson, Continuity & Drift-Diffusion — The complete mathematical description behind device simulators. Learn, step by step, Poisson's equation (charge → field → potential), the electron and hole continuity equations (conservation with generation and recombination), the drift-diffusion current equations, how they couple, boundary conditions (ohmic contacts, Schottky contacts, depletion edges, surfaces), the minority-carrier diffusion equation and its standard solutions, and how TCAD tools solve them numerically — with Python solving the steady-state diffusion equation by finite differences (matching the analytic sinh solution) and integrating Poisson's equation in a depletion layer.