Building an astable multivibrator from MOSFETs for longer time constants and more reliable operation suggests I should know a bit more about their operation with minuscule currents and low voltages. I have a small stock of low-threshold ZVNL110A MOSFETs, but using something less obsolete seems in order.
Dirt-cheap 2N7000 MOSFETs have a maximum IDSS around 1 µA at room temperature, which would be way too high in this situation; there wouldn’t be much difference between their ON and OFF states.
The test setup is simplicity itself:
The initial reading from a 4 V bench supply was 0.00 µA on the Siglent SDM3045, my best low-current meter, so I put a 10 MΩ resistor across the drain and source terminals:
Close enough, particularly given the silver fourth band on that old carbon composition resistor and its no-doubt unclean surface.
The rest of the 2N7000 MOSFETs have IDSS ≤ 10 nA, which you can’t distinguish from zero on that scale.
The 2N7000 datasheet specs give a threshold voltage from 0.8 to 2.5 V for 1 mA drain current, bracketing a 2.1 V typical value, which would be too high for a nearly dead lithium cell.
I calibrated the VGS(thr) current at 11 µA with a 348 kΩ resistor:
Which produced 11.49 µA at 4 V, just as it should, so I plugged in a MOSFET and twiddled the trimpot for a nice round 10 µA:
Most transistors conducted 10 µA with the gate at 1.42 V, with a few outliers spanning 50 mV on either side. Close enough and low enough!.
Now, to conjure an astable.