Proper unit for gamma. It is computed as the square root of something.

[HansOlsson]

Closes #4369 To confirm I just binged "gamma spice Bulk threshold parameter" and found: https://www.seas.upenn.edu/~jan/spice/spice.MOSparamlist.html which contains the same unit for gamma. And the copilot said: "Its units are Volts^(1/2)."

[HansOlsson]

• What about MosModelLineVariableqs.m_gamma where it is of type Real?

Should also be updated.

• Did you notice that there are two different calculations in the lib? In Modelica.Electrical.Spice3.Internal.Mos1.mos1ModelLineParamsInitEquations it is a sqrt, in Modelica.Electrical.Spice3.Internal.Mos2.mos2ModelLineParamsInitEquationsRevised it is a quotient. I am not sure if this is intentional.

I have mostly skipped units in functions.

out_v.m_gamma := sqrt(2 * SpiceConstants.EPSSIL * SpiceConstants.CHARGE *
			   in_p.m_substrateDoping * 1e6 / out_v.m_oxideCapFactor);         // (cm**3/m**3)

vs.

out_p.m_gamma := sqrt(2.0*Spice3.Internal.SpiceConstants.EPSSIL*
	Spice3.Internal.SpiceConstants.CHARGE*out_p.m_substrateDoping*1.0e6)
	/out_p.m_oxideCapFactor;

An additional problem here is that m_substrateDoping and m_oxideCapFactor both lack units.

Deleted

Additionally spice is weird in that it has prefixed SI-units, and even not really SI-units (like eV).

[HansOlsson]

Oh, I realized that the units are even weirder - and the previous was incorrect.

EPSSIL shouldn't be unit-less, but as far as I understand has unit "F/m", specifically it is computed based on the relative di-electric constant of Silicon being 11.7 and 8.85...e-12 F/m being Modelica.Constants.epsilon_0.

Added: The name EPSSIL means epsilion (di-electric constant) for Silicon.

The m_oxideCapFactor is computed as di-electric-constant divided by thickness and should thus have unit "F/m2" (ignoring unit-conversions - I think thickness is measured in "um").

That would make the first equation unit-correct if doping was measured in "1/m2" instead of "1/m3"; and I don't know how the second equation would be unit-correct.

But: for doping we have: out_p.m_substrateDoping*1.0e6 > Modelica.Electrical.Spice3.Internal.MaterialParameters.IntCondCarrDensity - where IntCondCarrDensity clearly is per volume, and 1.0e6 is cm3 to m3 conversion (for mos1 the IntCondCarrDensity is inlined, but they are the same formulas); so it should have unit "1/m3".

Or basically: There seems to be some remaining unit-issues, but I don't know which ones; and I don't know if it is just a matter of missing/incorrect units or whether some formulas should be updated.