Unusual Transconductance Equation

Question

I am a math-heavy electronics noob, and I was reading a paper when I came across this equation:

$$g_m=\frac{2 I_D}{\left(V_{G S}-V_{T H}\right)}\left[1-\frac{1}{2} \frac{\theta_1\left(V_{G S}-V_{T H}\right)}{1+\theta_1\left(V_{G S}-V_{T H}\right)}\right]$$

The paper references Tsividis' Operation and Modeling of The MOS Transistor [2 ed.], but it's not exactly clear where in the 600-page book on MOSFETs one could find this equation especially when its defining term \$\theta_1\$ isn't defined in the symbol key.

Is anyone familiar with this equation? What is it used for... how do I compute \$\theta_1\$ for a given process?

Answer 1

They might be referring to the SPICE level-3 parameter.

Shockingly, the equations can be found in the direct online source:
The Simulation of MOS Integrated Circuits Using SPICE2, Vladimirescu and Liu, EECS Department University of California, Berkeley, Technical Report No. UCB/ERL M80/7, February 1980

On page 28 (34):

and page 32 (38):

It's not clear to me if this explains what you were looking at (was it in regards to MOSFET threshold or mobility, or modeling, perhaps in SPICE?). In any case, this reference is worth including for posterity, and may answer many questions around physical interpretation and modeling of these components.