Quantum Etching

Kristian Dolghier

Professor Xihong Peng

A Cursory Look at the Nature of Quantum Etching

This project will discuss how the eigenfunction of a Dirac comb interacts with each of the holes and how this knowledge can be applied to dry etching. Dry Etching at beyond extreme ultraviolet lithography (BEUV Lithography), is an upcoming technology which has not been proven commercially successful and this failure is due to several factors. Let us discuss the failings on this new technique and what we can learn from our simulations of a Dirac comb.

Before we move into BEUV lithography, let us discuss the main limitation with current EUV lithography. The main limitation in this lithography is shot noise which is noise in the lithography process which appears as a part of the Poisson distribution of the random arrival and absorption time of photons.[4] This randomness makes the dose (number of photons) that interact with the material variable as the same dose can have wildly different lithography characteristics despite everything being the same. Additionally, a byproduct of this randomness is due to the increased energy of these photons. As the energy increases, there are more secondary electrons which can remove the resist and at lower wavelengths, we see more issues with the resist being used. The conundrum with shot noise is thus, keeping a low dose will produce a smaller etch and have worse critical dimensions(CD's).[4] Additionally, at lower doses, there is a higher variability based on the Poisson distributions of the photons. The other side of the conundrum is that keeping a higher dose will cause more secondary electrons and the increased number of photons will increase the edge blur and thus also put a cap on the limit. Some of this conundrum can be accomplished with novel resists, but these have yet to be found.

For BEUV Lithography, we have the same issues as for EUV lithography, as we have not even reached the extreme of what can be done at EUV. So we have the same issues, there is line edge roughness which is intrinsic. We are currently experimenting with 3 of the highest resolution photoresists including Inpria IB-which is a hafnium based inorganic photoresist-,HSQ-which is an inorganic photoresist with a high resolution and low sensitivity-and CAR(organic chemically amplified resist)-which has an intermediate dose and the highest resolution found.[2] The future of BEUV Lithography depends on these or other novel photos resists with a low enough dose, an extremely high resolution, and something that may limit secondary electrons from interacting. In general, organic photoresists have sensitivity, so CAR's can help by lowering the required dose and compensate in resolution and line edge roughness.[2] However, this is a stopgap at best, as what we need is a novel photoresist that has elements that efficiently absorb photons with a proper sensitivity and line edge roughness. This has not been found yet.

The main purpose of the eigenfunctions and the eigenenergies that I ran in a simulation, is to show how the interaction occurs between several wells and 1 electron. How, based upon the position of the doped well, the entire energy of the system will change. What I am trying to show is that as we etch closer and closer to the quantum world, we will see more and more interactions which we will need to account for. There are already corrective algorithms in some memory controllers that will monitor when a logic gate is inappropriately switched due to an outside particle interacting. This is likely what we will have to do if we continue with our standard transistor and logic gate model of computing. At a dimension lower than 2 nm, the probability of quantum interactions begin to occur with the probability approaching 1 as the dimension approaches 0 nm. [3] These quantum interactions may include quantum tunneling or even just be based on the randomness of the quantum world. There may occur a situation similar to Young's dual experiment where the interaction of observing the calculations will interfere with the calculations and render a system of checking these logic gates unattainable.

There is a possibility that we can limit some of the quantum interference with an insulative molecule such as a class of the motif Bicyclo [2.2.2 ]octane. This class of molecules can suppress electron transmission through alpha-conjugated molecules destructive quantum interference[1]. What is interesting with these molecules is that they have strong anti transmissions properties at certain energies and in fact can have a narrow antiresonance in the minimum transmission value. Additionally, "For 91% of the molecules, the transmission at the Fermi energy is lower than a gap of the same dimensions; for 38% of them, it is lower by more than an order of magnitude."[1] This decrease in transitivity appears to be very useful in the world of lithography as we can have a certain class of molecules that will act as an insulator for a molecule and may stop the electron and possibly the quantum interface that will happen on the dimension of the Dirac comb shown.

In conclusion, as a society we have just started working at etching while using EUV Lithography and it took us many years to achieve this goal. We have beat the issues with shot noise and line edge roughness by using photon resists with an unprecedented resolution. The transition to BEUV Lithography will happen, and these same issues will be overcome, but as we get to etch in the 2nm width, we must be very cognizant of the quantum effects. As shown, class of the motif Bicyclo [2.2.2 ] octane molecules show promise in oscillating certain molecules and stopping the transmissivity of electrons through alpha conjured molecules.[1] These and similar insulators have the possibility of stopping these tiny etches from interacting with one and other as shown in the eigenfunctions I have simulated. If transitivity is lowered, this should be similar to adding walls to the Dirac comb, with the exception of this molecule having the possibility to lower the probability of quantum tunneling.

Works Cited

[1]Garner, Marc H., et al. "The Bicyclo[2.2.2]Octane Motif: A Class of Saturated Group 14 Quantum Interference Based Single-Molecule Insulators." The Journal of Physical Chemistry Letters, vol. 9, no. 24, 2018, pp. 6941-6947., doi:10.1021/acs.jpclett.8b03432.

[2] Mojarad, Nassir, et al. "Beyond EUV Lithography: a Comparative Study of Efficient Photoresists' Performance." Scientific Reports, vol. 5, no. 1, 2015, doi:10.1038/srep09235.

[3]Daniel Steele, and Alex Valavanis. "What Is the Probability of Quantum Tunneling Occurring in This CPU?" Physics Stack Exchange, 10 Apr. 2014, physics.stackexchange.com/questions/107703/what-is-the-probability-of-quantum-tunneling-occurring-in-this-cpu.