VthVds

VthVds is not a standard separate device, but a way to refer to the interplay between threshold voltage (Vth) and drain-source voltage (Vds) in MOSFETs. Understanding how Vth and Vds affect device behavior is essential for predicting current flow and switching performance, especially in short-channel and modern CMOS transistors where Vds can influence the effective threshold.

In a MOSFET, the current depends on the gate-to-source voltage (Vgs) relative to Vth and on the drain-source voltage Vds. When Vgs is below Vth, the device is off. If Vgs exceeds Vth, the device conducts. In the triode (linear) region, where Vds < Vgs − Vth, the drain current Id follows a quadratic-like relation with Vds: Id ≈ μCox(W/L)[(Vgs − Vth)Vds − Vds^2/2]. In the saturation region, where Vds ≥ Vgs − Vth, Id becomes approximately constant with Vds for an ideal long-channel device: Id ≈ (1/2)μCox(W/L)(Vgs − Vth)^2. In practice, Id in saturation still varies with Vds due to channel-length modulation, described by a small-signal parameter λ, giving Id ≈ Id,sat(1 + λVds).

Vth itself can depend on Vds through short-channel effects. DIBL (drain-induced barrier lowering) reduces the effective Vth as Vds increases, while the body effect (Vsb, the source-bulk voltage) shifts Vth via the substrate bias. These effects mean the threshold seen by the gate is not constant as operating voltages change, a key consideration in device models and circuit design.

Overall, the VthVds relationship is central to MOSFET modeling, affecting current, switching speed, and variability, and is addressed in SPICE device models and short-channel design guidelines.