Talk:X-ray lithography

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Contents 1 Photoelectrons, Secondary electrons and Auger electrons 2 Lithographic Electron Range 3 Charging 4 References

[edit] Photoelectrons, Secondary electrons and Auger electrons

Secondary electrons have energies of 25 eV or less, and can be generated by any ionizing radiation (VUV, EUV, X-ray, ions and other electrons). Auger electrons have energies of hundreds of eV's. The secondaries (generated by and outnumbering the Auger and primary photoelectrons) are the main agents for resist exposure.

The relative ranges of photoelectron primaries and Auger electrons depend on their respective energies. These energies depend on the energy of incident radiation and on the composition of the resist. There is considerable room for optimum selection (reference 3 of the article). When Auger electrons have lower energies than primary photoelectrons, they have shorter ranges. Both decay to secondaries which interact with chemical bonds. When secondary energies are too low, they fail to break the chemical bonds and cease to affect print resolution. Experiments prove that the combined range is less than 20 nm. On the other hand, the secondaries follow a different trend below ~30 eV: the lower the energy, the longer the mean free path though they are not then able to affect resist development.

As they decay, primary photo-electrons and Auger electrons eventually become physically indistinguishable (as in Fermi statistics) from secondary electrons. The range of low-energy secondary electrons is sometimes larger than the range of primary photo-electrons or of Auger electrons. What matters for X-ray lithography is the effective range of electrons that have sufficent energy to make or break chemical bonds in negative or positive resists.

[edit] Lithographic Electron Range

It is supposed by some lithographers that due to a mean free path of ~20 nm for secondary electrons, resolution control begins to become tricky around this dimension. In particular, electron beam lithography suffers negative charging by incident electrons and consequent beam spread which limits resolution. It is difficult therefore to isolate the effective range of secondaries which may be less than 1 nm.

The combined electron mean free path results in an image blur, which is usually modeled as a Gaussian function (sigma=blur) that is convolved with the expected image. As the desired resolution approaches the blur, the dose image becomes broader than the aerial image of the incident X-rays. The blur that matters is the latent image that describes the making or breaking of bonds during the exposure of resist. The developed image is the final relief image produced by the selected high contrast development process on the latent image.

The range of primary, Auger, secondary and ultralow energy higher-order generation electrons which print (as STM studies proved) can be large (tens of nm) or small (nm), according to various cited publications. Since this range is not a fixed number, it is hard to quantify. Line edge roughness is aggravated by the associated uncertainty. Line edge roughness is supposedly statistical in origin and only indirectly dependent on mean range. Under commonly practiced lithography conditions, the various electron ranges can be controlled and utilized.

[edit] Charging

At the energies involved, Auger decay of ionized species is more probable than radiative decay. High-energy radiation exceeding the ionization potential also generates free electrons. Charging of the sample following ionization is a possibility when it cannot be guaranteed the ionized electrons leaving the surface or remaining in the sample are adequately balanced from other sources in time. The energy transfer to electrons as a result of ionizing radiation results in separated positive and negative charges. Insulating films like gate oxides and resists have been observed to charge to a positive or negative potential under X-ray and electron-beam irradiation. Insulating films are eventually neutralized locally by space charge (electrons entering and exiting the surface) at the resist-vacuum interface and Fowler-Nordheim injection from the substrate[1]. The range of the electrons in the film can be affected by the local electric field. The situation is complicated by the presence of holes (positively charged electron vacancies) which are generated along with the secondary electrons, and which may be expected to follow them around[1]. As neutralization proceeds, any initial charge concentration effectively starts to spread out. The final chemical state of the film is reached after neutralization is completed, after all the electrons have eventually slowed down. Usually, excepting X-ray steppers, charging can be further controlled by flood gun or resist thickness or charge dissipation layer.

[edit] References

1. I. A. Glavatskikh, V. S. Kortov, and H-J. Fitting, J. Appl. Phys. vol. 89, pp. 440-448 (2001).