Usually researchers measure contrast curves as dependencies of normalized thickness on exposure dose. This means that we assume the solubility rate during development of resists as linear one. At nano-images the edge of developed relief image of resists must be vertical. Computer simulation of development process, executed for its optimization, need to know details of solubility rate, at developing electron sensitive resists at electron lithography.
Chapter Computer Simulation of Processes at Electron and Ion Beam Li...
It is well-known that the development rate depends not only on the development process itself but also on the exposed features. For instance, very small features exposed in a thick positive tone resist material, e.g. PMMA, will show a different development rate than large exposed areas exposed under the same conditions. Furthermore, it is also known for quite a while that the development velocity for small features in such resist material decreases during the development process, the top part of the resist is dissolved faster than the resist material deep down in a small line or hole. One explanation is the following: During the development dissolved resist material has to be transported from the development front to the volume of the developer solution and fresh developer has to be supplied to the development front. The deeper the development front has moved into the resist layer the more limited will be the supply of fresh developer and the longer it will take to remove dissolved resist fragments into the volume of the developer solution, leading to a significant reduction of the development velocity.
As a starting point you might want to take a look at two publications from our group discussion those effects:
Megasonic-assisted development of nanostructures: Investigations on high aspect ratio nanoholes
David Kupper, Daniel Kupper, Yordan M. Georgiev, Thorsten Wahlbrink, Wolfgang Henschel, Guido Bell, and Heinrich Kurz, Appl. Phys. Lett. 85, 5055 (2004), DOI:10.1063/1.1819986
Megasonic-assisted development of nanostructures
David Küpper, Daniel Küpper, Thorsten Wahlbrink, Jens Bolten, Max C. Lemme, Yordan M. Georgiev, and Heinrich Kurz, J. Vac. Sci. Technol. B 24, 1827 (2006), DOI:10.1116/1.2214709
Thank you Jens! I know these paper and accept your argument.
But I could add that this time(depth) dependant development rate is observable also in the case of measure solubility rate at creation of sensitivity and contrast curves d(D) at utilization of various time of development, as well as at study wery thin resists and use of different electron energy.
(please see A simulation model for chemically amplified resists, Microel.eng. 86,2009,pp714-717
or Electrotechnika and Electronika(Publ.CEEC,Sofia) Resists for EBL,No5-6, 2009, pp.13-21
as well as some papers and chapters in my profile
Sure, you are absolutely right. The effect of a non-constant development velocity also exists for large features and/or thin resist films. But under those conditions the effect is significantly less pronounced and can, at least for “normal” applications, be neglected. One field of application where one might have to consider such effects even for very large features might be 3D-Lithography.
I wish to add that generally, at minituarization of lithographic images the problem with optimization of edges of developed profiles increases. At submicron and in nano-dimensional profiles to fabricate near to wertical developed resist profile-edges become absolutely needed. This can be achieved by optimization of lithography results based on experimental investigations or computer simulations. As Jens appointed the knowledge of time-dependent developing rate can be important for 3D-litography, and absolutely needed at fabrication of nano-dimensional structures by electron lithography!!!
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