Simulation of the spatial distribution and molecular weight of polymethylmethacrylate fragments in electron beam lithography exposures

Abstract

We report a three-dimensional (3D) simulation model based on the kinetic transport theory for calculating the distribution of PMMA fragments after an exposure to electron impact. The conditions employed for the modeling were chosen to resemble a typical electron beam lithography exposure. The model accounts for inelastic collisions of electrons in PMMA and resulting random main-chain scissions. We have considered gratings composed of parallel lines distanced by 10–50nm and exposed to electrons with energies of 10–60keV. By the model simulations, we have generated and analyzed the detailed 3D distributions of small PMMA fragments (one to ten monomers) that are soluble at the development stage and thus are responsible for the clearance in the gratings. In terms of the spatial distributions of soluble fragments, we have formulated the criteria that define the total clearance as well as the local grating development and investigated their dependence on the grating period, electron dose, and energy.

The Interdependence of Exposure and Development Conditions when Optimizing Low-Energy EBL for Nano-Scale Resolution

“…Use of such empirical Gfactors involves a significant level of uncertainty, since the experimental conditions differ dramatically from those employed in EBL. We have also shown that the G-factor is not necessarily a constant, but may depend on the energies of electrons involved in collisions (Aktary et al, 2006), which should be accounted for. Furthermore, using the distributions of deposited energy as a starting point for the computations of the number of scissions is not an unequivocal choice, since a part of deposited energy is thermalized without scissions involved, whereas the actual yield of scissions is related intimately with the details of individual collisions of electrons with atoms of PMMA.…”

“…Outline of our model for resist exposure in EBL. In the model, the probability of main-chain scissions is computed directly through the differential cross-section for inelastic collisions resulting in the scissions (Aktary et al, 2006). The model avoids uncertainties related with the conversion of the distributions of deposited energy into the number of main-chain scissions through the empirical radiation chemical yield.…”

“…Clearly, this systematic understanding should rely on a solid knowledge of the physico-chemical molecular-level processes behind the resist exposure to electrons as well as the subsequent post-exposure development stages. Over the last several years we have been investigating thoroughly, both experimentally and by numeric modeling, the impact of the major EBL process factors on the quality of dense nanoscale patterns in the popular positive-tone resist, PMMA (Aktary et al, 2006;Mohammad et al, 2007;Mohammad et al, 2009. In this chapter, we outline the methodologies that we have developed for fabrication and visualization of nanopatterns in PMMA, as well as our model for the exposure, fragmentation, and dissolution of positive resists.…”

Gold-implanted shallow conducting layers in polymethylmethacrylate

“…PMMA ͑polymethylmethacrylate͒ is an important polymer because of its wide use as an electron resist for high resolution lithography [14][15][16][17][18][19] for forming patterns for microand nanodevices. Gold has been used as a dopant metal species for PMMA doping but not by using ion implantation as the doping mechanism.…”

Conducting polymer formed by low energy gold ion implantation

“…In the work described here we have used very low energy gold ion implantation into thin films of polymethylmethacrylate ͑PMMA͒. PMMA is an important polymer used widely as a resist for high resolution lithography by electron beam, [15][16][17][18][19][20][21][22] ion beam, deep-UV, and x-ray irradiation. 21,22 For the extremely low ion energy used here, the buried conducting layer is only a few nanometers deep and of width about 1 nm.…”