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MOSFET Cutoff vs Linear vs Saturation: Conditions and Equations

A MOSFET operates in one of three regions, set by the gate-source voltage VGS and the drain-source voltage VDS. In the cutoff region, VGS is below the threshold voltage Vth, no channel forms and almost no current flows. In the linear (triode) region, the channel extends from source to drain and the device acts like a resistor whose value is set by the gate voltage. In the saturation region, the channel pinches off at the drain end, so the current is set by VGS and hardly depends on VDS; this is the region for amplifiers and current sources. Note that "saturation" in a bipolar transistor is a different state, the on state of a switch, so the same word means different things.

AspectCutoff regionLinear (triode) regionSaturation region
Condition (nMOS)VGS < VthVGS > Vth and VDS < VGS − VthVGS > Vth and VDS ≥ VGS − Vth
Channel stateNo inversion layer (weak inversion only)Inversion layer extends from source to drainInversion layer vanishes at the drain end (pinch-off)
Drain current (long channel)ID ≈ 0; in reality subthreshold current rises exponentially with VGSID = μCox(W/L)[(VGS − Vth)VDS − VDS²/2]ID = (1/2)μCox(W/L)(VGS − Vth)², multiplied by (1 + λVDS) with channel-length modulation
Current behaviorOff. The theoretical lower limit of subthreshold swing is about 60 mV/decade at room temperatureAt small VDS, ID is nearly proportional to VDS; the slope falls as VDS increasesID hardly depends on VDS and is proportional to (VGS − Vth) squared
Small-signal viewNearly an open circuitAt small VDS, a resistor with on-resistance Ron ≈ 1/[μCox(W/L)(VGS − Vth)]A voltage-controlled current source with transconductance gm = 2ID/(VGS − Vth) and output resistance ro ≈ 1/(λID)
Worked example (μCox(W/L) = 2 mA/V², Vth = 0.5 V)At VGS = 0.3 V the device is cut off (ID = 0 in the equation)At VGS = 1.0 V and VDS = 0.1 V, ID = 90 µA. On-resistance near VDS = 0 is about 1 kΩAt VGS = 1.0 V and VDS ≥ 0.5 V, ID = 250 µA (with λ = 0) and gm = 1 mS
Typical usesA switch in the off state; the off transistor in a digital gateA switch in the on state (the on transistor in a digital gate, analog switches, a conducting power MOSFET), a variable resistorAmplifiers, current sources, current mirrors
Matching BJT regionCutoff region (same name)Saturation region (switch on)Forward-active region (used for amplification)
Short-channel differencesDIBL lowers the threshold voltage and raises off currentMobility degradation and parasitic resistance make the current smaller than the equation predictsVelocity saturation makes the current saturate at a lower VDS, and the dependence on (VGS − Vth) approaches first order

Figures are typical orders of magnitude and vary by process generation and product.

When to use which

Cutoff region
The region for turning the transistor off. The off transistor in a digital gate sits here, and only leakage such as subthreshold current flows. Lowering the threshold voltage makes circuits faster but raises off current exponentially, so it is a trade-off against standby power.
Linear (triode) region
The on state of a transistor used as a switch. The smaller VDS is, the more it behaves like a resistor, and the on-resistance falls as the gate voltage rises. The on transistor of a CMOS output after it settles, analog switches and a conducting power MOSFET in a power supply operate here.
Saturation region
The region for amplifiers and current sources. The current hardly depends on VDS, so the output resistance is high and large voltage gain is possible. In an amplifier, the bias point is chosen so that VDS never falls below VGS − Vth (the overdrive voltage), which sets the lower limit of the output swing.

FAQ

Does saturation mean the same thing in a MOSFET and a BJT?

No. In a MOSFET, the saturation region is where the channel pinches off at the drain end and the drain current saturates (stays nearly constant) with VDS; it is used for amplification. In a bipolar transistor, the saturation region is where both junctions are forward biased and VCE drops to about 0.1 to 0.3 V, the on state of a switch. Matched by function, MOSFET saturation corresponds to the BJT forward-active region, and BJT saturation corresponds to the MOSFET linear region.

Where is the boundary between the linear and saturation regions?

At VDS = VGS − Vth. At that point the gate-to-channel voltage at the drain end equals Vth and the channel pinches off. In the long-channel equations, substituting VDS = VGS − Vth into the linear-region equation gives the saturation equation (1/2)μCox(W/L)(VGS − Vth)², so the current is continuous across the boundary.

Which region do transistors in digital circuits operate in?

In steady state, the on transistor is in the linear region (VDS near 0) and the off transistor is in cutoff. During a transition, the transistor that turns on starts with a large VDS, so it charges or discharges the load capacitance in saturation and then moves into the linear region as the output changes. That is why gate delay is set mainly by the saturation current (drive current).

How do the conditions change for pMOS?

All voltage and current directions are reversed. Using the source-referred gate voltage VSG, VSD and the threshold magnitude |Vth|, the conditions take the same form as for nMOS: cutoff for VSG < |Vth|, linear for VSG > |Vth| and VSD < VSG − |Vth|, and saturation for VSD ≥ VSG − |Vth|. The current equations have the same form, using the hole mobility.

Check your understanding

What is the condition for a long-channel nMOSFET to operate in the saturation region? (Assume VGS > Vth.)

  1. AVDS = 0
  2. BVDS < VGS − Vth
  3. CVDS ≥ VGS − Vth
Show answer and explanation

Answer: C. VDS ≥ VGS − Vth

With VGS > Vth and a channel present, once VDS ≥ VGS − Vth the gate-to-channel voltage at the drain end falls below Vth, the channel pinches off, and drain current becomes nearly independent of VDS—the saturation region. Amplifiers operate here, and the minimum VDS (= VGS − Vth) sets the lower limit of output swing. In short-channel devices velocity saturation makes current saturate at a lower VDS.

When a long-channel MOSFET operates in the saturation region, the drain current ID is roughly proportional to what? (VGS: gate-source voltage, Vth: threshold voltage)

  1. AThe square of (VGS − Vth)
  2. BVGS − Vth
  3. CThe reciprocal of VGS
Show answer and explanation

Answer: A. The square of (VGS − Vth)

In saturation, a long-channel MOSFET follows ID = (1/2)μCox(W/L)(VGS − Vth)², so drain current is proportional to the square of (VGS − Vth) (the square law). VGS − Vth, the overdrive voltage, is a basic analog design parameter. In short-channel devices velocity saturation pushes the dependence toward linear, and mobility degradation and parasitic resistance add further deviations, so real designs use detailed models such as BSIM.

How does a MOSFET behave in the linear region, where the drain-source voltage VDS is sufficiently small?

  1. ALike a variable resistor whose resistance changes with gate voltage
  2. BLike a constant-current source independent of VDS
  3. CLike a diode that conducts in only one direction
Show answer and explanation

Answer: A. Like a variable resistor whose resistance changes with gate voltage

In the linear region drain current is nearly proportional to VDS, and the slope—conductance μCox(W/L)(VGS − Vth)—changes with gate voltage, so the device acts as a gate-controlled variable resistor. A switch's on state lies in this region, and on-resistance falls as gate voltage rises. The property is also used in analog switches and variable-gain circuits. When VDS exceeds VGS − Vth, the device enters saturation.

  1. In a MOSFET in saturation, what is the phenomenon in which raising the drain voltage shortens the effective channel length and slightly increases the drain current?
  2. What is the definition of the transconductance gm of a MOSFET?
  3. When a bipolar transistor is used as a switch, which operating region corresponds to the on state?

Practice MOSFET questions

Key terms explained

Threshold voltage
The gate voltage at which a channel (inversion layer) forms in a MOSFET and current starts to flow. Written as Vth.
Saturation region
The state of a bipolar transistor in which both the base-emitter and base-collector junctions are forward-biased. The collector-emitter voltage falls to about 0.1-0.3 V, corresponding to a switch in the on state.
Cutoff region
The state of a bipolar transistor in which both junctions are reverse-biased and almost no collector current flows. It corresponds to a switch in the off state.
Forward-active region
The state with the base-emitter junction forward-biased and the base-collector junction reverse-biased. A collector current proportional to the base current flows, and it is used for amplification.
Channel-length modulation
In a saturated MOSFET, raising the drain voltage moves the pinch-off point toward the source, shortening the effective channel and slightly increasing drain current. It makes the output resistance finite.
Velocity saturation
Under strong electric fields, carrier drift velocity stops increasing in proportion to the field and levels off at about 1×10⁷ cm/s. In short-channel MOSFETs it makes drain current smaller than the square law predicts.
Transconductance
The ratio of the change in drain current to the change in gate voltage, written gm. It expresses a transistor's amplifying ability; amplifier gain is roughly gm times the load resistance.
Subthreshold swing
The gate voltage needed to change drain current tenfold below threshold. Its theoretical lower limit at room temperature is about 60 mV per decade; the smaller it is, the sharper the on/off switching.

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