problem4-69 - PROBLEM 4.69 KNOWN Hot-plate tool for...

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PROBLEM 4.69 KNOWN: Hot-plate tool for micro-lithography processing of 300-mm silicon wafer consisting of an aluminum alloy equalizing block (EB) heated by ring-shaped main and trim electrical heaters (MH and H) providing two-zone control. T FIND: The assignment is to size the heaters, MH and TH, by specifying their applied heat fluxes, and their radial extents, mh th q and q ′′ ′′ , mh th r and r Δ Δ , to maintain an operating temperature of 140 ° C with a uniformity of 0.1 ° C. Consider these steps in the analysis: (a) Perform an energy balance on the EB to obtain an initial estimate for the heater fluxes with mh th q q ′′ = ′′ extending over the full radial limits; using FEHT , determine the upper surface temperature distribution and comment on whether the desired uniformity has been achieved; (b) Re-run your FEHT code with different values of the heater fluxes to obtain the best uniformity possible and plot the surface temperature distribution; (c) Re-run your FEHT code for the best arrangement found in part (b) using the representative distribution of the convection coefficient (see schematic for h(r) for downward flowing
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