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  "title": "Metal–oxide–semiconductor field-effect transistor",
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  "description": "Uses a gate voltage to control current between source and drain.",
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  "revisionDate": "2026-10-07",
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  "topic": "Device physics",
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      "title": "Metal–oxide–semiconductor field-effect transistor",
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      "title": "What primarily controls a MOSFET channel?",
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    {
      "title": "Explore in Atlas",
      "url": "https://semiaifoundry.com/ai-atlas/#mosfet"
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    {
      "title": "Kahng — US3102230A",
      "url": "https://patents.google.com/patent/US3102230A/en"
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    {
      "title": "MIT 6.012 — MOSFET Cross Section and Operation",
      "url": "https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/5c5960f14ae37d0a65478c4f3f628d98_lec9.pdf"
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    {
      "title": "Purdue ECE 255 — MOSFET Models",
      "url": "https://engineering.purdue.edu/wcchew/ece255s18/ece%20255%20s18%20latex%20pdf%20files/ece255Lecture_9_Feb6_MOSFETs.pdf"
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    {
      "title": "P–n junction and depletion region",
      "url": "https://semiaifoundry.com/learn/atlas/pn-junction/"
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    {
      "title": "Insulators and low-k films",
      "url": "https://semiaifoundry.com/learn/atlas/dielectric/"
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    {
      "title": "Metal gate and high-k dielectric",
      "url": "https://semiaifoundry.com/learn/atlas/gate-stack/"
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    {
      "title": "Controllable semiconductor channel",
      "url": "https://semiaifoundry.com/learn/atlas/channel/"
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    {
      "title": "Source and drain regions",
      "url": "https://semiaifoundry.com/learn/atlas/source-drain/"
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    {
      "title": "Fin field-effect transistor",
      "url": "https://semiaifoundry.com/learn/atlas/finfet/"
    },
    {
      "title": "Gate-all-around nanosheet transistor",
      "url": "https://semiaifoundry.com/learn/atlas/gaa/"
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    {
      "title": "Complementary CMOS inverter",
      "url": "https://semiaifoundry.com/learn/atlas/inverter/"
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    {
      "title": "Diamond-cubic silicon lattice",
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  "content": "Device physics · Atlas v1.3.0\n\n# Metal–oxide–semiconductor field-effect transistor\n\nUses a gate voltage to control current between source and drain.\n\n[Explore in Atlas](https://semiaifoundry.com/ai-atlas/#mosfet)Nanometer-scale active features; schematic cross section\n\nLearning objectiveConnect gate voltage, channel charge and current to a switch.\n\n## The mechanism\n\nThe MOSFET is the central controllable device of CMOS logic. An insulated gate changes the electric potential in the semiconductor channel, regulating current between source and drain. A body or substrate is also part of the device, even when a simplified circuit symbol emphasizes only three terminals. Real operation is continuous and analog: digital circuits choose voltage ranges that stand for zero and one. The atlas cross section separates gate, dielectric, channel, terminals, and body so each function can be inspected. Its dimensions are explanatory rather than a vendor cross section. Moving outward reveals how complementary devices form gates, then memory and arithmetic, through their wiring relationships.\n\n1.  Apply a gate voltage relative to the other transistor terminals.\n2.  Use the gate field to change the mobile charge and potential in the channel.\n3.  Allow the resulting controlled source–drain current to charge or discharge a circuit node.\n\n## Science and assumptions\n\n### Long-channel linear-region current\n\n$$\nI_D\\approx\\mu_n C^{\\prime}_{\\mathrm{ox}}\\frac{W}{L}\\left[(V_{GS}-V_T)V_{DS}-\\frac{V_{DS}^2}{2}\\right]\n$$\n\nLong-channel triode current is mobility times oxide capacitance per area times width-to-length ratio, multiplied by gate overdrive times drain voltage minus half the squared drain voltage.\n\nApplicable here for strong inversion and $0 ≤ V_{DS} < V_{GS} − V_{T}$; it is not a modern short-channel device predictor.\n\nSymbols and units\n\nI\\_D\n\nDrain current\n\nA\n\nμₙ\n\nElectron mobility\n\nm²/(V·s)\n\nC′\\_ox\n\nGate oxide capacitance per area\n\nF/m²\n\nW\n\nChannel width\n\nm\n\nL\n\nChannel length\n\nm\n\nV\\_GS\n\nGate-to-source voltage\n\nV\n\nV\\_T\n\nThreshold voltage\n\nV\n\nV\\_DS\n\nDrain-to-source voltage\n\nV\n\nGate overdrive creates channel charge; drain bias drives it along the channel. Mobility, gate capacitance per area, and width-to-length ratio set the ideal current scale.\n\nAssumptions Long-channel nMOS, strong inversion, $0 ≤ V_{DS} < V_{GS} − V_{T}$, constant mobility, gradual-channel approximation; not a predictive compact model for modern short-channel FinFETs or GAA devices.\n\n## Engineering example\n\nIn the long-channel expression, raising $V_{GS}$ above $V_{T}$ increases the overdrive term; velocity saturation and short-channel effects limit the extrapolation.\n\n## Distinctions and tradeoffs\n\nA MOSFET is an analog physical device; zero and one are voltage-range conventions established by the surrounding digital circuit.\n\nStronger drive can reduce delay. Capacitance and leakage constrain the associated power benefit.\n\nCMOS circuits combine these devices into digital machinery. No isolated transistor implements a neural-network concept by itself.\n\n## Specifications and interfaces\n\nElectrical terminals\n\nGate, source, drain, body\n\nBody may be implicit in simplified diagrams.\n\nControl variable\n\nGate-to-source voltage\n\nOperating behavior also depends on other terminal voltages.\n\nDevice behavior\n\nContinuous current–voltage relation\n\nBinary logic is a circuit-level abstraction.\n\n### Interfaces\n\nGate Input\n\nControl voltage and charging current\n\nSource/drain path Output\n\nControlled conduction current\n\n## Check your understanding\n\n### What primarily controls a MOSFET channel?\n\n1.  The gate electric field\n2.  A mechanical gate that swings open\n3.  A software token stored in the silicon atom\n\nAnswer and reasoning\n\nThe gate electric field\n\nThe insulated gate changes the channel’s electrostatics. Real current varies continuously with terminal voltages.\n\n## Historical context\n\n### 1960 · Kahng files the insulated field-effect device patent\n\nThe patent records a controllable semiconductor device with an insulated electrode, an early foundational step toward MOS integrated circuits. The date is the filing year, not the 1963 grant year.\n\n[Kahng — US3102230A](https://patents.google.com/patent/US3102230A/en)\n\n## Evidence and scope\n\nThe equation is a first-order regime model, not a modern node compact model.\n\nVary gate and drain bias in the long-channel current model; geometry, doping and short-channel behavior are not adjustable here.\n\n## Sources\n\n-   [MIT 6.012 — MOSFET Cross Section and Operation](https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/5c5960f14ae37d0a65478c4f3f628d98_lec9.pdf)\n-   [Purdue ECE 255 — MOSFET Models](https://engineering.purdue.edu/wcchew/ece255s18/ece%20255%20s18%20latex%20pdf%20files/ece255Lecture_9_Feb6_MOSFETs.pdf)\n\n[Published lesson data](https://semiaifoundry.com/ai-atlas/lesson-data/mosfet-5478fa9fd1586d83.json) · [Atlas releases and licensing](https://semiaifoundry.com/ai-atlas/licenses.html)\n\n## Continue exploring\n\n### Foundations\n\n-   [P–n junction and depletion region](https://semiaifoundry.com/learn/atlas/pn-junction/)\n-   [Insulators and low-k films](https://semiaifoundry.com/learn/atlas/dielectric/)\n\n### Related lessons\n\n-   [Metal gate and high-k dielectric](https://semiaifoundry.com/learn/atlas/gate-stack/)\n-   [Controllable semiconductor channel](https://semiaifoundry.com/learn/atlas/channel/)\n-   [Source and drain regions](https://semiaifoundry.com/learn/atlas/source-drain/)\n-   [Fin field-effect transistor](https://semiaifoundry.com/learn/atlas/finfet/)\n-   [Gate-all-around nanosheet transistor](https://semiaifoundry.com/learn/atlas/gaa/)\n-   [Complementary CMOS inverter](https://semiaifoundry.com/learn/atlas/inverter/)\n-   [Diamond-cubic silicon lattice](https://semiaifoundry.com/learn/atlas/crystal-lattice/)"
}