{"id":"pn-junction","level":"matter","name":"P–n junction and depletion region","shortName":"P–n junction","role":"Creates an internal electric field between differently doped regions.","description":"When p-type and n-type regions meet, carrier concentration differences drive diffusion. Mobile charge redistributes near the interface, leaving a region whose fixed ionized dopants produce an electric field. At thermal equilibrium, drift and diffusion balance, so the internal field does not provide a perpetual power source. The depletion approximation models this region as mostly depleted of mobile carriers and makes its electrostatics easier to understand. Applied voltage changes the barrier and charge distribution. Junctions appear in transistor bodies and isolation structures as well as diodes. They help explain why a transistor is more than three metal terminals attached to an otherwise featureless silicon block.","specs":[{"label":"Equilibrium","value":"Drift balances diffusion","context":"No net equilibrium current."},{"label":"Depletion region","value":"Bias-dependent width","context":"Also depends on doping and material properties."},{"label":"Built-in potential","value":"Internal electrostatic barrier","context":"Not a free external voltage source."}],"interfaces":[{"name":"P and N regions","direction":"in","signal":"Carrier concentration difference"},{"name":"Internal field","direction":"out","signal":"Electrostatic barrier and junction capacitance"}],"tradeoff":"Junctions provide useful isolation. Their capacitance and leakage add delay and power costs.","whyAI":"Electrical isolation keeps nearby circuit functions independent. Its nonideal behavior contributes to chip power and timing limits.","related":["doping","mosfet","source-drain"],"sources":[{"title":"MIT 6.012 — PN Junction Electrostatics","url":"https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/188f6340d4d10b0e923d1c0166c8fba1_lec5.pdf"}],"scale":"Device-scale junction; width is illustrative and bias-dependent","kind":"junction","mechanism":["Bring differently doped p-type and n-type regions into contact.","Let carriers redistribute until fixed dopant charge creates an opposing electric field.","At equilibrium, balance carrier diffusion with field-driven drift; applied bias shifts that balance."],"misconception":"The built-in junction field is not a battery that can supply unlimited power to an external circuit.","check":{"question":"What happens to net current at thermal equilibrium?","options":["It grows without external energy","Drift and diffusion contributions balance","The depletion region becomes a metallic short"],"answer":1,"explanation":"Internal carrier motion and opposing contributions can exist while the equilibrium net current is zero."},"branch":"Device physics","subbranch":"Junction electrostatics","science":[{"title":"Built-in junction potential","equation":"V_bi = (k_B T / q) ln(N_A N_D / nᵢ²)","explanation":"The internal potential follows from the different equilibrium carrier populations. N_A and N_D are acceptor and donor densities, while k_B T / q is the thermal voltage.","assumptions":"Ideal equilibrium junction with nondegenerate regions and effective ionized doping densities; this is not an externally available battery voltage."}],"history":[],"learningObjective":"Explain how junction concentration sets a built-in potential.","engineeringExample":"Increasing the product N_A N_D increases the logarithm in V_bi at fixed T; series resistance and breakdown are separate design constraints.","evidenceNotes":"The equation assumes an abrupt equilibrium junction and ideal statistics.","visualFamily":"device-crosssection","prerequisites":["doping"],"labId":"library","scope":"Use the switching investigation to connect physical charge, circuit load and arithmetic; the numerical library has no standalone model of this lesson’s full mechanism.","investigationId":"switching","labScope":"Use the switching investigation to connect physical charge, circuit load and arithmetic; the numerical library has no standalone model of this lesson’s full mechanism."}