Explaining the weak inversion slope

could somebody explain to me about the weak inversion slope?

Thanks

calculate slope + inversion

When you trace an Id-Vg @ Vd=contant courve of a MOSTand you draw it on a logarithmic vertical scale, you will notice that, for Vg < Vth, the Id current (in the log scale) increases linearly with Vg. The slope of this section of the couve is called the WI slope or, more exactly, the inverse slope.

It tells you how ideal your transistor is. That is a, if this slope were infinite, that woud mean that your MOST behaves as a perfect switch. As in WI the diffusion meachanisms dominate, the relation between Id and Vg is exponential (see for instance the EKV model or the Tsividis book). Non ideal bulk transistors have an "n" factor of about 1.4-1.7, whereas SOI MOST have "n" factors from 1.05 (deeply fully depleted) to 1.5 (partially depleted).

Most likely, the slope factor is expressed in mV/decades. That means the mV needed to make Id increase one decade. The relationship between "n" and S is

S=n.Ut.ln(10). Ut is the thermal potential.

So, a MOST with n=1 has an S of about 60mV/dec. The smallest S, the steepest the Id-Vg transfer. That is why this is called the inverse slope factor.