Device physicsMVP
MOSFET I–V explorer
Long-channel square-law drain-current curves for three gate overdrives, swept over drain voltage.
Inputs
Educational long-channel model
Model: square-law long-channel MOSFET. Operating regions: cutoff / triode / saturation. It ignores channel-length modulation, velocity saturation, and all short-channel effects, so it is a teaching aid, not a device simulator.
µA/V²
V
Interpretation
Each curve rises steeply in the triode region (small Vds) then flattens into saturation once Vds exceeds the overdrive (Vgs − Vth). A larger gate overdrive or W/L gives more current; the saturation current scales with (Vgs − Vth)². This square-law picture is the long-channel ideal — real short devices saturate earlier and the flat region slopes upward.
Formula
Id,sat = ½·μCox·(W/L)·(Vgs−Vth)²
Triode: Id = μCox(W/L)[(Vgs−Vth)Vds − Vds²/2].
Variables
| Symbol | Variable | Unit |
|---|---|---|
| Id | Drain current | A (shown as mA) |
| μCox | Transconductance parameter | A/V² |
| W/L | Width-to-length ratio | dimensionless |
| Vgs, Vth | Gate and threshold voltage | V |
| Vds | Drain voltage | V |
Assumptions & validity
This tool assumes:
- Educational long-channel square-law model.
- Cutoff / triode / saturation regions only.
- Ignores channel-length modulation, velocity saturation, and short-channel effects.
Worked example
kn′ = 200 µA/V², W/L = 10, Vth = 0.5 V, Vgs = 1.5 V (overdrive 1 V).
Id,sat = ½·(200µ·10)·1² = 1 mA