Fundamental aspects of electron beam lithography. I. Depth-dose response of polymeric electron beam resists

Abstract

The application of a phenomenological depth-dose theory to the exposure of negative electron resists is described in detail. The model predicts a cross-linking rate dnc/dt=(Gc/100) × (J0/e)(Va/RG)Λ(f) cm−3 sec−1, where Gc is the number of crosslinks produced per 100 eV lost in the polymer. Jo is the incident current density, Va the initial kinetic energy, RG the electron Grun range, and Λ(f) the depth-dose function in terms of the normalized penetration f=z/RG. Since the G value of a negative resist decreases with exposure, it is suggested that a more meaningful parameter characterizing a negative resist is the absorbed energy required to gel the polymer at the resist-substrate interface. This interface or threshold gel energy density, Eg(i), is independent of the beam parameters and varies from about 1022 eV cm−3 for polyvinyl ferrocene to 3.8×1018 eV cm−3 for epoxidized polybutadienes. The model predicts that the threshold sensitivity should vary as Va0.75 which agrees reasonably well with published experimental values. It also predicts that at a given accelerating voltage, there is a unique initial resist thickness at which the top surface and interface receive identical doses. This unique thickness turns out to be roughly the electron diffusion range RD. The transverse resolution or linewidth for negative resists has been investigated as a function of accelerating voltage and found to be given by twice the diffusion range. Since RD decreases with decreasing Va, the linewidth likewise decreases as the accelerating voltage is lowered. The optimum operating conditions for a 500-nm resist film for electron lithography are predicted to be Va≈5 kV exposed to yield about a 400-nm film after development. It should be noted that these conditions result in a maximum crosslink density per incident electron and a minimum linewidth. However, there may be specific applications where other sets of operating conditions are useful. A geometric model is suggested which appears to account for the observed behavior of sensitivity of negative resists.

Review of metal-containing resists in electron beam lithography: perspectives for extreme ultraviolet patterning

“…Several metallopolymers have been utilized for electron beam patterning. Earliest of the reports out of the Bell Labs utilized ferrocene containing polymers such as poly(vinyl ferrocene) for negative-tone electron beam resists 166 , 167 . One such platform utilized polyferrocenylsilane (PFS) backbone synthesized by ring opening polymerization of silaferrocenophanes 168 .…”

Nanotube fountain pen: Towards 3D manufacturing of metallic nanostructures

“…At the nanometer scale, unlike conventional nanolithographic technologies [16][17][18], additive nanolithography http://dx.doi.org/10.1016/j.carbon.2015.01.043 0008-6223/Ó 2015 Elsevier Ltd. All rights reserved.…”

The Physics and Chemistry of the Lithographic Process

“…One can then determine the totaI energy absorption from the integral over all space of the product of electron flux and the rate of energy loss. Figure 20 Heidenreich et al (33,38) developed an empirical or phenomenological model for determining gel energies and profiles in negative resists. For the case of a uniform large area exposure such as one encounters in the determination of the contrast curve, the incident electron energy dissipation density depends only on the depth z into the resist.…”

“…The area input dose at the line center y = 0 is thus (1 + ~)Do. D (0) = C/cm~ [38] It should be noted that Eq. [32] is a quasi-monoenergetic approximation applying only for penetration z such that the loss in electron energy is about 0.1 Va.…”