Enhancement MOSFET I–V curves: reading the threshold voltage and K

Reading the 2N7000's I_D–V_DS and I_D–V_GS curves from PSpice results, and the usual slips when measuring them on a breadboard.

An enhancement N-channel MOSFET only forms a channel and passes drain current once the gate-source voltage V_GS exceeds the threshold V_th. The gate is insulated by oxide, so the DC gate current is practically zero: it is the gate voltage that sets the current. The numbers in sections 1 to 6 are PSpice results for the 2N7000 model and values calculated from them; what a real part did on the breadboard is collected in section 7.

1. The three regions

K is a device constant set by the process and the channel size (some textbooks write it as K_n/2).

In the triode region the current rises with V_DS and the device behaves like a resistor (a closed switch); in saturation the current depends on V_GS alone and hardly on V_DS (an amplifier). The name clashes with the BJT: a MOSFET's saturation region corresponds to a BJT's active region.

2. The test circuit

Put V_GG on the gate, adjust V_DD until V_DS is where you want it, and take I_D = V_RD/R_D from the voltage across R_D. With the flat face of the TO-92 towards you, the 2N7000's legs are source, gate, drain from the left. That looks a lot like a BJT (2N3904: E, B, C), so check the datasheet before plugging it in.

3. I_D–V_DS curves

• The knee sits at V_GS − V_th: the V_DS where the current reaches 99% of its final value is close to V_GS − V_th (to within the 0.1 V spacing of the sweep).
• Saturation current grows with the square of V_GS: each 0.1 V step took it from 1.92 to 6.96, 14.84 and 25.29 mA. Near threshold, 0.1 V multiplies the current several times.
• The triode formula holds too: at V_GS = 2.5 V and V_DS = 0.1 V it gives 10.8 mA, close to PSpice's 10.97 mA.
• 2.1 V is not zero: about 8 µA flows. Below threshold a small current still rises exponentially: the subthreshold region.

4. I_D–V_GS and finding the threshold

In saturation the square root of the current is proportional to V_GS. Plot √I_D against V_GS and you get a straight line: where it meets the horizontal axis is V_th, and its slope squared is K.

Fitting the four points from 2.2 V to 2.5 V (V_DD = 4 V) gives V_th ≈ 2.084 V and K ≈ 147 mA/V², and all four points agree within a few percent. That is 9 mV from the V_th = 2.093 V the lab handout uses. Reading the threshold as 'the first V_GS with nonzero I_D' gets muddled by subthreshold current (as at 2.1 V), so the straight-line fit is more repeatable. The next lab (MOSFET biasing) uses these two values to work out the operating point.

5. Common mistakes with a real part

• The real V_th may differ from the model: the 2N7000 datasheet gives V_GS(th) from 0.8 V minimum, 2.1 V typical, to 3.0 V maximum. The current at a given V_GS can differ hugely between parts, so raise V_GG from a low value and look at the current first. Examples with the K above:

  Vth	ID at VGS 2.5 V	Power at VDS 4 V
  2.3 V	5.9 mA	23.6 mW
  2.084 V (model)	25.5 mA	102 mW
  1.9 V	53.1 mA	212 mW
  1.7 V	94.4 mA	378 mW

  Set a current limit on the supply and back off quickly if the dissipation approaches the datasheet's 400 mW.
• R_D is only 10 Ω, so the voltage is tiny: 1.9 mA at 2.2 V is about 19 mV across R_D, and the 8 µA at 2.1 V is 0.08 mV. Use the meter's mV range, and record anything below its resolution as 'below the measurement limit', not as 0.
• Measure V_DS directly: V_DD = V_DS + I_D·R_D, a 0.25 V difference at 25 mA. Set each V_DS in the table by watching the meter across drain and source while you adjust V_DD.
• Heat makes the current drift: tens of mA times a few volts warms the package, the threshold drops as it warms, and the current creeps up. Read the high-current cells as soon as they settle and turn the supply down.
• Don't leave the gate floating: a floating gate charges from static or your hand and turns the device on at random, and static can damage the oxide. Tie the gate to ground until V_GG is connected.

6. Seeing the whole curve in XY mode

Drive the drain with a 0 to 5 V triangle wave (about 100 Hz), put R_S = 100 Ω between source and ground, and connect CH1 to the drain and CH2 to the source. Since V_S = I_D·R_S, the screen draws the current-voltage curve directly. Two things to keep in mind:

• R_S eats into V_GS: as current flows the source rises, so the real V_GS is less than V_GG. With V_GG = 3 V the model above would pass about 124 mA without R_S, but with R_S = 100 Ω it settles at V_GS ≈ 2.30 V and I_D ≈ 6.98 mA. The flat part of the XY trace is therefore not the 'V_GS = V_GG' curve.
• The X axis is V_D, not V_DS: drain-source voltage is V_D − V_S, so the curve looks shifted right by V_S.
• Keep the triangle above 0 V: if the drain goes negative the MOSFET's body diode conducts, current flows backwards and the left end of the curve bends. Use the generator's offset to get 0 to 5 V and check it on screen.

7. Measuring it on a breadboard

The same circuit (R_D = 10 Ω) was built on a breadboard, the voltage across R_D read with a multimeter, and I_D taken as V_RD/R_D. The table shows the values exactly as recorded (mA).

• The threshold was about 0.55 V lower: the same straight-line fit as in section 4, on the six bench points from 2.0 to 2.5 V, gives V_th ≈ 1.535 V and K ≈ 123 mA/V². K is close to the PSpice fit (147 mA/V²); only V_th is far off. It is inside the datasheet range (0.8 to 3.0 V), so this is part-to-part spread, not a bad part.
• So 2.1 V already passes tens of mA: in PSpice, 2.1 V sat just above threshold and gave about 8 µA; the bench gave 46.99 mA at V_DS 4 V, roughly 5,801 times as much. Under the square law a small voltage difference near threshold turns into a huge ratio.
• The ends bend away from the fitted line: the fit runs 20% above the bench at 2.0 V and 9% above at 2.5 V. Near 100 mA the part warms and mobility drops, so the curve flattens. Say which range you fitted so someone else can reproduce your numbers.
• Saturation is not flat: from V_DS 2 V to 4 V the current still rose 5% to 19% depending on V_GS. That is channel-length modulation and self-heating, both almost absent from the PSpice model.
• It reached the power rating: the V_GS 2.5 V, V_DS 4 V cell is 102.74 mA × 4 V ≈ 411 mW, over the 2N7000's 400 mW (25 °C). With a low-threshold part, read the bottom-right cells quickly and turn the supply down.
• The V_DS 0.1 V row hardly changes: V_DS/I_D is 17.6 Ω at V_GS 2.1 V and 14.8 Ω at 2.5 V. The bench fit says 2.5 V and 0.1 V should give 22.6 mA, so resistance outside the channel (wiring, breadboard contacts, where V_DS was measured) has very likely crept in. For the triode region, put the probes straight on the drain and source legs.

With this measured V_th and K the next lab's bias circuits come out very close to the bench. The bench section of the MOSFET biasing guide makes the comparison.

8. In your lab report

• Draw the boundary V_DS = V_GS − V_th on the I_D–V_DS plot so the triode and saturation regions separate at a glance.
• Plot √I_D from your I_D–V_GS readings to get your own part's V_th and K; the bias lab can then use them instead of the model's.
• Most of the gap between simulation and bench comes from V_th. Saying how far the two curves are shifted sideways (the threshold difference) explains more than a percent error alone.

Plot a pasted table with the lab data analyzer (free form), get currents from resistor voltages with the Ohm's law calculator, and check meter error on small voltages with the multimeter accuracy calculator.