Threshold and the regions

Output curves and three regions

Fix the gate voltage, sweep the drain, and record the drain current: that is one output curve. The figure draws four, for V_GS = 0.9, 1.2, 1.5 and 1.8 V on a W/L = 2/1 µm NMOS.

Below a certain gate voltage, the threshold voltage V_th, the device is in cutoff: almost no current flows. In triode the channel reaches from source to drain and the device behaves like a resistor. In saturation the channel pinches off near the drain once V_DS passes V_Dsat, and the current is set mainly by the gate.

The textbook square law puts the knee at V_Dsat = V_GS − V_th, the overdrive. With V_th = 0.556 V for this device (the lab below), that predicts knees at 0.34, 0.64, 0.94 and 1.24 V. The model puts them at 0.26, 0.44, 0.60 and 0.74 V. Even a 1 µm channel saturates early. The charge in the depletion layer under the channel pulls the knee in to about V_ov/1.3 at low drive, and velocity saturation (E2.3) pulls it in further at high drive.

Two ways to extract a threshold

The channel does not switch on at a sharp voltage: the current grows smoothly over a few hundred millivolts. So V_th has to be defined by a method, and two are common. Both use a small V_DS of 50 mV.

The two methods differ by 47 mV on the same device. Neither is wrong, since they answer different questions, so a quoted threshold must name its method, its V_DS, and the W and L it was measured on.

What moves the threshold

The lab extracts constant-current thresholds for a set of devices, then repeats with the drain raised and with the body lowered.

Length. The 0.15 µm NMOS has the highest threshold, 0.152 V above the 4 µm one, while many textbooks teach that short channels lose threshold. SKY130 adds extra doping at the ends of the channel, called halo implants, to limit leakage. In a short channel the halos fill more of the channel and raise V_th: the reverse short-channel effect.

Drain voltage. At V_DS = 1.8 V the short device's threshold drops by 93 mV, the long one's by only 21 mV. The drain's field reaches the source end of a short channel and lowers the barrier electrons must cross: drain-induced barrier lowering (DIBL).

Body. Lowering the body 0.5 V below the source raises V_th by 104 mV; 1 V raises it by 189 mV. A source above its body needs more gate voltage to form the channel: the body effect. In a stack of NMOS devices, every one above the bottom pays it.

PMOS. The same rules hold with every sign flipped, but the SKY130 PMOS threshold is large: 0.79 V at L = 0.15 µm and 0.99 V at L = 1 µm. On a 1.8 V supply that leaves little overdrive, a budget every later circuit must respect.

Try it

Each WHEN i(VA)=1.333333u finds the gate voltage at which one device reaches 100 nA × W/L. alter changes a source between runs, so the same netlist measures the drain and body effects. Open Plots to see the four sweeps.

Try it: add an NMOS with W = 2 and L = 20 (the longest bin) and predict its threshold from the trend. Then set VDS to 0.9 V in the first run and see every short-channel threshold fall.

Check yourself

* the L = 1 um device: source lifted to 0.5 V, body tied to the source
.lib sky130 tt
VS s 0 0.5
VGS g s 0
VDS d s 0.05
VC d d3 0
XN3 d3 g s s sky130_fd_pr__nfet_01v8 W=2 L=1
.control
dc VGS 0 1.8 0.002
meas dc vt WHEN i(VC)=200n
.endc
.end