Switching speed of ICs vs gate length

[ZeroFunGame]

TL;DR Summary

Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if there are fundamental physical limits here that correlates the switching speed to gate length?

Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if there are fundamental physical limits here that correlates the switching speed to gate length?

 

[Borek]

Whenever I see words "frequency" and "size" together I start to think about capacitance.

Doesn't mean it is a problem at the frequencies you listed (can be, I just don't know), but it definitely starts to be a serious problem when you get to higher frequencies.

 

[phyzguy]

Summary: Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if there are fundamental physical limits here that correlates the switching speed to gate length?

Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if there are fundamental physical limits here that correlates the switching speed to gate length?

To first order, the answer is simple. The capacitance C of a MOSFET gate is proportional to Cox*W*L, where Cox is the gate oxide capacitance, W is the gate width, and L is the gate length. The current I of a MOSFET is proportional to μ*Cox*W/L, where μ is the carrier mobility. In an IC, you basically have a series of MOSFETs, where the output current of one MOSFET drives the input (the gate, with its capacitance C) of the next MOSFET. Now if you have a current I driving a capacitance C, I = C dV/dt. So dV/dt, which is how fast the circuit operates, is proportional to I/C, which equals μ/L^2. So as the gate length gets shorter, the circuit runs faster. For many years, this drove the IC industry, and ICs got smaller, faster, and cheaper as L scaled down. Today, these simple relationships no longer hold, because second order effects dominate. So things are not speeding up nearly as fast as they did in the past.

 

[Baluncore]

Fundamentally, the input to output capacitance of an inverting device forms a "Miller Integrator".
A Miller Integrator is a low pass filter. It limits the speed of amplifiers and logic gates.
http://www.ecircuitcenter.com/Circuits_Audio_Amp/Miller_Integrator/Miller_Integrator.htmhttps://en.wikipedia.org/wiki/Op_amp_integrator