30 Jul 2025

FETs and JFET Characteristics

Field-effect control, n- and p-channel JFET operation, output regions, transfer law, and device parameters.

bsc semester-iv mj-7 semiconductor-devices fet jfet

A field-effect transistor controls current in a semiconductor channel by an electric field. Conduction uses majority carriers, and the control terminal draws very little dc current. A JFET forms its gate from a reverse-biased p-n junction.

n-channel JFET operation

An n-type channel joins source to drain and p-type gate regions contact its sides. Use

\[V_{DS}=V_D-V_S\ge0, \qquad V_{GS}=V_G-V_S\le0.\]

The reverse-biased gate depletion regions narrow the channel. For small $V_{DS}$ the channel behaves approximately as a voltage-controlled resistor. Because

\[V_{GD}=V_{GS}-V_{DS},\]

the gate-drain junction is most reverse biased near the drain, so depletion grows asymmetrically.

Let $V_P=V_{GS(off)}<0$. Pinch-off first occurs at the drain end when

\[V_{GD}=V_P,\]

or

\[\boxed{V_{DS,sat}=V_{GS}-V_P}.\]

Beyond this boundary the pinch-off point moves slightly toward the source and the added drain voltage falls mainly across the depleted region. Current therefore saturates; pinch-off does not mean zero drain current.

An ideal gradual-channel model gives, for $V_P\le V_{GS}\le0$,

\[I_D=\frac{2I_{DSS}}{V_P^2} \left[(V_{GS}-V_P)V_{DS}-\frac{V_{DS}^2}{2}\right], \quad 0\le V_{DS}\le V_{GS}-V_P,\]

and in saturation,

\[\boxed{I_D=I_{DSS}\left(1-\frac{V_{GS}}{V_P}\right)^2}, \quad V_{DS}\ge V_{GS}-V_P.\]

At $V_{GS}=0$, $I_D=I_{DSS}$ in saturation. At $V_{GS}\le V_P$, the channel is cut off apart from leakage. At sufficiently large $V_{DS}$, gate-junction breakdown ends the normal saturation region.

Normalized saturation transfer laws. The JFET current falls to zero at the negative cutoff voltage; the ideal enhancement nMOS current begins at positive threshold.

The editable source is fet-transfer.tex.

JFET parameters

At a bias point, the transconductance, drain resistance, and amplification factor are

\[g_m=\left.\frac{\partial I_D}{\partial V_{GS}}\right|_{V_{DS}}, \qquad r_d=\left.\frac{\partial V_{DS}}{\partial I_D}\right|_{V_{GS}},\] \[\mu_F=-\left.\frac{\partial V_{DS}}{\partial V_{GS}}\right|_{I_D} =g_mr_d.\]

$g_m$ is in siemens, $r_d$ in ohms, and $\mu_F$ is dimensionless. From Shockley’s transfer law,

\[\boxed{g_m=-\frac{2I_{DSS}}{V_P} \left(1-\frac{V_{GS}}{V_P}\right) =g_{m0}\sqrt{\frac{I_D}{I_{DSS}}}}, \qquad g_{m0}=-\frac{2I_{DSS}}{V_P}>0.\]

The $g_m$ residual is verified as zero in transistor-check.mac.

For a p-channel JFET, holes carry the channel current and all voltage and current polarities reverse. The magnitude characteristics have the same form after consistent sign reversal.