# Smallest minimum feature size possible for transistors printed by photolithography

I'm doing a project about Moore's Law, one of the subtopics I've come to is photolithography. The way I understand it is that the MOSFET transistors are currently printed on a silicon wafer by projection printing (mostly with 193nm UV light).

With this technique your minimum feature size (CD) will be:

$CD = k_1 \cdot \frac{\lambda}{NA}$

but you're limited by your depth of focus ($D_f$)

$D_f = k_2 \cdot \frac{\lambda}{NA^2}$

From what I've read immersion lithography (increasing the NA) is the most advanced form of photolithography, but it's reaching its limit. Other lithography techniques are being researched; smaller wavelengths (EUV, X-ray lithography, electron beam lithography), each with their own issues and too expensive as of yet for large scale production.

My question is, since I'm looking into the physical bariers Moore's law is going to face, is there a calculable limit to the minimum feature size possible with photolithography and/or next-generation lithography.

• Moore's Law: an expression of hubris by a certain species of chimpanzee wherein the idea of physical, repeatably observable physical laws is confused with the grotesquely overswollen estimation by that chimpanzee species of its own ability to control the World. Simply put, there is no such law, and the crashing of CPU speed development into fundamental heat dissipation limits as well as the lithographic problems you cite are a falsification of the law, as though it weren't bleeding obvious that hubris begets psychosis in the first place! – Selene Routley Oct 15 '13 at 1:37
• Having said this, it is a good question, but I'm not quite sure it's a fundamental physics question but rather a technological one and what tradeoffs can be made for what costs. As your equations show, there is no hard lithography limit if we can go down in wavelength, however, the question becomes what lenses and other imaging technology are there and are they practicable for this application. Moreover, you need to have the doping process efficient at this wavelength, so this will be one physical consideration: what are the doping processes and how do they depend on wavelength. Furthermore, – Selene Routley Oct 15 '13 at 2:51
• ...you may get all kinds of side effects such as Compton scattering, even pair production if you're looking really far into the future with really short wavelengths (about 1.1MeV per photon)! In that case there may be electron writing techniques. – Selene Routley Oct 15 '13 at 2:53