From the graphs we see that gate leakage currents of all transistors decrease with increasing \$T_{OX}\$. This means that the increase in total leakage current must be attributed to subthreshold conduction.
Why would subthreshold current increase? The following equation for subthreshold curent appears in BSIMv4.7 User's Manual:
While there are many parameters involved, the main suspect is the treshold voltage, \$V_{th}\$, which is known to be sensitive to gate oxide thickness (as well as almost any other transistor's parameter).
In order to verify this I built the following circuit:
Sweeping \$T_{OX}\$ and measuring \$V_{th}\$ resulted in:
This linear decrease in threshold voltage explains an exponential increase in subthreshold leakage (based on the above equation).
The natural continuation of the answer would be to explain why \$V_{th}\$ decreases with \$T_{OX}\$. The equation used to calculate the threshold voltage for BSIMv4.7 model in Spice is:
\$T_{OX}\$ dependence appears in the above equation both explicitly (TOXE) and implicitly (through other parameters which depend on \$T_{OX}\$). It is beyond my expertise and knowledge to perform this task and map various numerical parameters into physical effects taking place in the actual transistor.
In summary:
The reduction in threshold voltage due to thicker oxide leads to higher subtreshold leakage current. The exact effects which cause the reduction are very complex.
Your model of the solenoid is very simple- perhaps there is a lot of distributed capacitance across the coil. Try simulating that with some dozens of pF across the coil. Also, perhaps there is a cable between the circuit and the solenoid with even more parallel capacitance.
Breadboards are not really great for this sort of thing, possibly you're getting some EMFs across the connections that are mucking things up (or stabilizing them!)- in particular I would suggest getting the high current paths off the breadboard (which probably means everything for such a simple circuit).
It's possible the op-amp model is not perfect (typically they're macromodels and don't attempt to model the behavior exactly- in return for which you get an answer faster, even if it's not quite right). But I would expect this kind of application would be right in their wheelhouse.
Best Answer
You can use Qucs.
There are some tutorials here: http://qucs.sourceforge.net/docs.html
For logics circuits, you can use this great online simulator called Logicly.