Shot noise models for sequential processes and the role of lateral mixing

Abstract

Shot-noise in electron-beam and EUV exposure fundamentally limits the useful sensitivity of resists. Here the exposure, amplification and deprotection of chemically amplified resists are treated as a sequence of statistical events to determine the effect of shot noise. Noise among processes is additive and a sequential Poisson process is used to illustrate the 'acid bottleneck' that occurs when less than one acid electron is generated per input electron. Lateral mixing, due to effects such as electron scattering and acid diffusion, are accounted for in a Binomial sorting model that shows the effect is simply a function of the total number of quanta reaching the voxel irrespective of their path.Electron exposure is estimated to generate on average one acid every 3.8, 21 and 36 nm along the trajectories of 5, 50 and 100 KeV electrons. Acid generation appears well correlated with energy deposition, at about 22 eV/acid required for EUV and electron exposure, or three times the DUV level. The model was validated by observing the fraction of small (24 nm and 32 nm across) contacts that cleared as a function of exposure dose at 100 KeV. Approximately 4,500 electrons were EIPBN 05 revised June 6, 2006 2 required to clear, independent of contact size. However, the slope was indicative of a process with only 50 effective events possibly owing to resist surface effects. Circular dissolution smoothing and mechanical fracture are suggested as speculative sources for the near feature size correlation length of the line-edge roughness.

Fundamental limits to EUV photoresist

“…3 If we directly assume Poisson statistics and that Q is also statistical then the dependence on dose and Q has a different form. 5,19 The next question is the effect that increased Q has on resist resolution. Here we define resolution to be the reciprocal of the resist blur which is nominally R P EB .…”

“…The mechanism for spreading the absorbed photon energy and releasing multiple acids is predominantly via secondary electrons and the effect this has on blur has been studied by various authors [19][20][21][22][23] The results of those studies indicate that the deposition of energy by free electrons moving through a material is extremely detailed and complex and hence difficult to analyze. But in general terms it is clear there is one requirement for increasing quantum yield via energy deposition by secondary electrons which is that the IMFP for electrons in the required energy range of few eV must be on the order of the PAG-to-PAG spacing d. If it is significantly larger then there will be excessive added blur whereas if it is significantly smaller the electrons simply cannot travel far enough to get from one PAG molecule to the next.…”

Research Update: Electron beam-based metrology after CMOS

“…130 This relationship illustrates that the process with the lowest occurrence probability dominates the SNR (the same considerations apply in lithography). 131 The beam current determines the number of incident electrons, and the availability of high-brightness monochromated sources enables the formation of high-current, sub-nanometer diameter probes. In addition, the high degree of coherence in modern field-emission sources is leading to novel imaging approaches, such as the use of vortex beams, in conjunction with electron energy-loss spectroscopy to map magnetic and plasmonic behavior at the nanoscale.…”

The tri-lateral challenge of resolution, photospeed, and LER: scaling below 50nm?

“…Since LER is just any deviation from an ideal straight line, it is not surprising that many phenomena have been identified which can cause such deviations. However, there is a growing body of evidence across many different lithographic platforms (optical, ebeam, EUV/soft Xray, ion beam) which suggests that much, if not most, of LER can be explained by the stochastic fluctuations in the number of activated acids from one point to another within the resist [1][2][3][4][5][6][7][8][9] . These fluctuations are in turn leveraged by the steepness of the aerial image, but are smoothed by the effective acid blur of the resist.…”