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  "title": "P–n junction and depletion region",
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  "description": "Creates an internal electric field between differently doped regions.",
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  "revisionDate": "2026-10-07",
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  "topic": "Device physics",
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      "title": "P–n junction and depletion region",
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      "title": "Explore in Atlas",
      "url": "https://semiaifoundry.com/ai-atlas/#pn-junction"
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    {
      "title": "MIT 6.012 — PN Junction Electrostatics",
      "url": "https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/188f6340d4d10b0e923d1c0166c8fba1_lec5.pdf"
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      "title": "Donor and acceptor doping",
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    {
      "title": "Metal–oxide–semiconductor field-effect transistor",
      "url": "https://semiaifoundry.com/learn/atlas/mosfet/"
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  "content": "Device physics · Atlas v1.3.0\n\n# P–n junction and depletion region\n\nCreates an internal electric field between differently doped regions.\n\n[Explore in Atlas](https://semiaifoundry.com/ai-atlas/#pn-junction)Device-scale junction; width is illustrative and bias-dependent\n\nLearning objectiveExplain how junction concentration sets a built-in potential.\n\n## The mechanism\n\nWhen 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.\n\n1.  Bring differently doped p-type and n-type regions into contact.\n2.  Let carriers redistribute until fixed dopant charge creates an opposing electric field.\n3.  At equilibrium, balance carrier diffusion with field-driven drift; applied bias shifts that balance.\n\n## Science and assumptions\n\n### Built-in junction potential\n\n$$\nV_{\\mathrm{bi}}=\\frac{k_B T}{q}\\ln\\!\\left(\\frac{N_A N_D}{n_i^2}\\right)\n$$\n\nBuilt-in potential equals thermal voltage times the natural logarithm of the acceptor–donor density product divided by intrinsic carrier density squared.\n\nSymbols and units\n\nV\\_bi\n\nBuilt-in potential\n\nV\n\nk\\_B\n\nBoltzmann constant\n\nJ/K\n\nT\n\nAbsolute temperature\n\nK\n\nq\n\nPositive elementary charge\n\nC\n\nN\\_A\n\nEffective ionized acceptor density\n\ncm⁻³\n\nN\\_D\n\nEffective ionized donor density\n\ncm⁻³\n\nnᵢ\n\nIntrinsic carrier density\n\ncm⁻³\n\nThe 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.\n\nAssumptions Ideal equilibrium junction with nondegenerate regions and effective ionized doping densities; this is not an externally available battery voltage.\n\n## Engineering example\n\nIncreasing the product $N_{A}$ $N_{D}$ increases the logarithm in $V_{bi}$ at fixed T; series resistance and breakdown are separate design constraints.\n\n## Distinctions and tradeoffs\n\nThe built-in junction field is not a battery that can supply unlimited power to an external circuit.\n\nJunctions provide useful isolation. Their capacitance and leakage add delay and power costs.\n\nElectrical isolation keeps nearby circuit functions independent. Its nonideal behavior contributes to chip power and timing limits.\n\n## Specifications and interfaces\n\nEquilibrium\n\nDrift balances diffusion\n\nNo net equilibrium current.\n\nDepletion region\n\nBias-dependent width\n\nAlso depends on doping and material properties.\n\nBuilt-in potential\n\nInternal electrostatic barrier\n\nNot a free external voltage source.\n\n### Interfaces\n\nP and N regions Input\n\nCarrier concentration difference\n\nInternal field Output\n\nElectrostatic barrier and junction capacitance\n\n## Check your understanding\n\n### What happens to net current at thermal equilibrium?\n\n1.  It grows without external energy\n2.  Drift and diffusion contributions balance\n3.  The depletion region becomes a metallic short\n\nAnswer and reasoning\n\nDrift and diffusion contributions balance\n\nInternal carrier motion and opposing contributions can exist while the equilibrium net current is zero.\n\n## Evidence and scope\n\nThe equation assumes an abrupt equilibrium junction and ideal statistics.\n\nUse the switching investigation to connect physical charge, circuit load and arithmetic; the numerical library has no standalone model of this lesson’s full mechanism.\n\n## Sources\n\n-   [MIT 6.012 — PN Junction Electrostatics](https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/188f6340d4d10b0e923d1c0166c8fba1_lec5.pdf)\n\n[Published lesson data](https://semiaifoundry.com/ai-atlas/lesson-data/pn-junction-6a1fb41fe7e4475e.json) · [Atlas releases and licensing](https://semiaifoundry.com/ai-atlas/licenses.html)\n\n## Continue exploring\n\n### Foundations\n\n-   [Donor and acceptor doping](https://semiaifoundry.com/learn/atlas/doping/)\n\n### Related lessons\n\n-   [Metal–oxide–semiconductor field-effect transistor](https://semiaifoundry.com/learn/atlas/mosfet/)\n-   [Source and drain regions](https://semiaifoundry.com/learn/atlas/source-drain/)"
}