Thermal effects in electron beam lithography

Abstract
At the Delft University of Technology, an electron beam (e-beam) writer is being designed, which uses a constant 10 μA beam current at 100 kV and shape sizes of 0.1×0.3 to 1.0×1.0 μm. The brightness of the source is modulated to keep the probe current constant. The maximum current density will be 3.3 104 A/cm2. Therefore, thermal effects are a primary concern. High-energy electrons lose most of their energy at depth in the substrate. The exposure times are, due to the high current density, too short to make thermal diffusion from the bulk significant. Therefore, only the local energy deposition in the resist and the contributions from previously exposed points influence the temperature rise. Presently, the writing speed of lithography systems is restricted by the resist sensitivity. The lower limit to the dose for writing is determined by the statistical noise in the number of electrons, to define the smallest detail. For 0.1 μm lines, the ideal sensitivity of the resist is 0.1 C/m2, thus allowing a writing speed of 1 cm2 /s. Using the ideal resist on silicon, the temperature rise caused by one exposure was calculated to be less than 17 K, at the edge of the exposed point. The heating is higher for low accelerating voltages, since the penetration depth is smaller and the direct energy loss is higher.

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