This simulator lets you replace lattice atoms of silicon with donors or acceptors and see what changes: which carrier dominates, how many minority carriers remain, and how conductivity and drift current respond. A Hall-bar-style test bar shows the dopant sites and mobile carriers in 3D.
• A doped silicon test bar with substitutional dopant sites, mobile electrons and holes, bias contacts and a conductivity measurement. • Controls for dopant type (donor, n-type, or acceptor, p-type), dopant concentration exponent (10¹³ to 10¹⁷ cm⁻³), applied electric field (-20 to 20 V/cm) and animated carrier markers. • Readouts for majority and minority concentration, conductivity, resistivity and conventional current density. • Experiments for a donor sample (n ≈ 10¹⁶ cm⁻³, p ≈ 10⁴ cm⁻³, conductivity about 2.16 S/cm) and an acceptor sample at the same level, which conducts less because the fixed hole mobility is smaller.
With complete ionization, charge neutrality gives n - p = ND for donors or p - n = NA for acceptors, and the mass action law np = ni² (ni = 10¹⁰ cm⁻³ here) fixes the minority carrier density. Conductivity is σ = q(nμn + pμp), with μn = 1350 and μp = 480 cm²/(V·s), then J = σE and ρ = 1/σ. Adding ten times more dopant raises the majority carrier density about tenfold and cuts the minority density by the same factor.
The model assumes uniform silicon at 300 K, complete ionization and nondegenerate statistics. Mobilities are fixed, ignoring impurity scattering, high-field saturation and temperature. Drift-marker speeds and the visible dopant fraction are enlarged teaching encodings, not to scale.
N-type silicon is doped with donor atoms that contribute free electrons, making electrons the majority carrier. P-type silicon is doped with acceptors that create holes, making holes the majority carrier.
The mass action law np = ni² holds in equilibrium. Raising the majority carrier density pushes the minority density down by the same factor, so a 10¹⁶ cm⁻³ donor sample has roughly 10⁴ holes per cm³.
In this model holes have a lower fixed mobility (480 cm²/(V·s)) than electrons (1350), so the same carrier density carries less current.
Impurity scattering, velocity saturation, temperature dependence, incomplete ionization and degenerate doping are all left out. It is a room-temperature teaching model.