Press one crystal doped n-type against the same crystal doped p-type and the seam becomes a one-way valve for current — the diode at the root of all electronics. Electrons and holes diffuse across, leave bare charged dopants behind, and raise a built-in barrier; forward bias lowers it exponentially, reverse bias only widens it. Rendered, not quoted.
sourceShockley, W. The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors. Bell Syst. Tech. J. 28 (1949) 435–489 · DOI 10.1002/j.1538-7305.1949.tb03645.x · archive.org/bstj28-3-435
Two regions of one crystal: n-type (donors, spare electrons) meets p-type (acceptors, holes). Carriers diffuse across the seam and recombine, leaving a charge-stripped depletion region of fixed ionized dopants.
That exposed charge raises a built-in potential Vbi = (kT/q)·ln(Na·Nd/ni²) — a barrier the majority carriers must climb.
Bias tilts the barrier. The current that survives is the Shockley law I = I₀(e^{qV/kT} − 1): exponential forward, a flat leak −I₀ reverse. Ideal, abrupt, low-injection.
Upstream lives the-semiconductor-doping: it makes the n-type and p-type materials separately, each obeying mass-action n·p = ni².
THE PN JUNCTION is what happens when you join them into one lattice. Doping gives the two carrier reservoirs; the junction turns the gradient between them into rectification. The valve is the doping made directional — Shockley 1949.
Re-runs the full selfcheck() live and reports. It confirms the diode rectifies and stays flat under reverse bias. If the RED TEAM tampers the engine symmetric, this badge flips.
Deterministic: fixed constants, no randomness. Green = the law holds; red = the seam was broken.
Constants: q=1.602176634e-19 C · k=1.380649e-23 J/K · T=300 K
Device: I₀=1e-12 A · ni=1.0e16 m⁻³ · dopings Na,Nd swept.
Applied bias V is the free knob; everything else is fixed law.
Live I–V curve (log-current). The knee sits near Vbi; reverse bias flatlines at −I₀. Depletion barrier drawn faint behind.
computing…
Proven at boot: rectification ratio, zero at V=0, built-in-potential monotonic in doping, ≈60 mV/decade forward slope.
"An ideal diode is a perfect switch." No. The Shockley law is exponential, not a step: there is real current below the knee and a real (if tiny) reverse leak −I₀ that doubles roughly every 10 K.
"Forward drop is fixed at 0.7 V." Only by convention — V=(kT/q)ln(I/I₀) slides ~60 mV per decade of current and shifts with temperature.
The junction conducts equally both ways.
↳ It rectifies: forward grows as e^{qV/kT}; reverse saturates at −I₀. I(+0.5V) ≫ |I(−0.5V)| by many orders.
Vbi is a fixed material constant.
↳ Vbi=(kT/q)ln(Na·Nd/ni²) grows with doping and falls with temperature.
Reverse bias is harmless forever.
↳ amber Real diodes suffer avalanche / Zener breakdown past a reverse limit — outside the ideal Shockley law modelled here.
The disclosed planted void. Force the engine symmetric — I = I₀·sinh(qV/kT) — so reverse current equals forward and the valve stops rectifying.
Press it and watch WINDOW 7 catch the broken asymmetry live. selfcheck() also plants & removes this internally at boot to prove the detector fires.