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EMOSFET principle, characteristics, ac model

Short answer

An n-channel EMOSFET creates an inversion layer when VGS exceeds threshold Vt. ID is zero below Vt, follows k(VGS−Vt)² in saturation and k[2(VGS−Vt)VDS−VDS²] in triode. AC model: open gate, current source gm·vgs from drain to source, gm=2k(VGSQ−Vt).

Describe the principle of operation of EMOSFET with the help of IV characteristic curves and algebraic expressions. Also show its ac equivalent circuit model.

An enhancement MOSFET (E-MOSFET) has no physical channel when VGS = 0. A channel is created (induced) by the gate voltage, and the drain current flows through that channel.

Structure and principle (n-channel)

   S      G       D
   |      |       |
 [n+]--[oxide]--[n+]
 \_____ p-substrate _____/
  • Two n+ regions (source, drain) are diffused into a p-type substrate. A thin SiO2 layer insulates the metal gate from the substrate.
  • With VGS = 0 there are two back-to-back p-n junctions, so ID ≈ 0 (cut-off).
  • When VGS is made positive, holes are repelled from beneath the gate and electrons are attracted. At VGS = Vt (threshold voltage) an n-type inversion layer forms and joins source to drain.
  • A larger VGS gives more electrons, a deeper channel and so more current.
  • With VGS > Vt and a small VDS, the channel acts as a resistor. As VDS increases, the channel near the drain narrows. At VDS = VGS − Vt the channel pinches off at the drain end and ID stops increasing.

Regions and algebraic expressions

RegionConditionDrain current
Cut-offVGS < VtID = 0
Triode (ohmic)VGS > Vt, VDS < VGS − VtID = k [2(VGS − Vt) VDS − VDS²]
SaturationVGS > Vt, VDS ≥ VGS − VtID = k (VGS − Vt)²

Here k = μn Cox W / (2L) is the device constant, found from data as k = ID(on)/(VGS(on) − Vt)².

IV characteristics

 ID ^                          transfer curve
    |   VGS4 ------------      ID
    |   VGS3 ------------       |        /
    |  / VGS2 -----------       |      _/
    | /   VGS1 ----------       |   __/
    +----------------> VDS      +--+-----------> VGS
   (saturation to the right of       Vt
    the VDS = VGS - Vt boundary)
  • Output curves: ID against VDS for several VGS values. They rise in the triode region and become almost flat (saturation) beyond VDS = VGS − Vt.
  • Transfer curve: parabolic ID against VGS, starting at Vt.

AC equivalent circuit model

Small-signal parameters at the Q point:

  • gm = ∂ID/∂VGS = 2k (VGSQ − Vt)
  • ro = 1/(λ ID) (drain resistance, large)
 G o---                     +----------+-----o D
        +                   |          |
       vgs  (open)    gm·vgs (↓)      [ro]
        -                   |          |
 S o------------------------+----------+-----o S

The gate-source path is an open circuit (infinite input resistance), and the drain-source path is a voltage-controlled current source gm·vgs (flowing from drain to source) in parallel with ro.

✓ Answer checked by Claude Opus 5.5 (high effort)

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