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I suspect you're probably just seeing it clamp. The models are expected to be run with like 1-3V or whatever. Try reducing your sweep range

I have tried a variety of sweep ranges and saw similar results. I am just confused why the diode behaves essentially like a resistor in forward bias

If something is limiting the current through the diode, then given the exponential characteristic of the diode I-V curve, at only slightly above the threshold voltage, the diode wants to draw more current than is available, so your maximum current is dictated by (presumably) any series resistance modeled in the device. Your curve shows a 1.1kOhm resistance. I'm not sure which device you're measuring above, but the model for

sky130_fd_pr__diode_pw2nd_05v5

has

RS

(series resistance) equal to 981 ohms. Which brings up a major point about simulation---Level 3 diodes are some proprietary thing (Cadence, maybe?) although in principle the only thing that makes a level 3 diode special is the ability to relate various parameters to physical area measurements. But that depends on whether the device defines

area

or not. The parameter

RS

in the sky130 device model says

rs = 981 ; Units: ohm (ohm/meter^2 if area defined)

. For reasons that I have never been entirely clear on,

area

is given in ridiculously small units such the the default area is given as

1.0e+12

. My guess is that the units are chosen so that the value for

RS

matches what it would be for a 1um^2 area if

area

is not given as a parameter but also has the right value for

ohm/m^2

if

area

is given. Also note that while ngspice implements some apparently-correct level 3 model based on physical dimensions, it does not simulate the entire (proprietary) diode level 3 model. To my knowledge, Xyce does not (yet) implement the level 3 diode (I have requested it).