Dependence of standard deviation of Vth to transistor's length

[electronics20]

Dear scholars
In subthreshold region, why does the standard deviation of Vth decreases when length of transistors increases?
Thanks in advance

 

[erikl]

The Pelgrom equation shows that ΔVth is inversely proportional to the square root of the gate dimensions W*L: ΔVth ~ (WL)^-1/2.

For more explanation, s. these 2 pages from Binkley's book "Tradeoffs and Optimization in Analog CMOS Design": View attachment Vth_standard_deviation_dependency_on_gate_length.pdf .