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 Va 0.75 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.