(a) The same NiSi silicide is maintained on the gate and source-drain contact regions as MOSFETs are scaled according to the constant field scaling rules from the 65 \mathrm{~nm} node to the 45 \mathrm{~nm} node. What happens to the sheet resistance of the gate poly? Does it increase, decrease, or remain constant?
(b) Derive the constant field scaling rules for the peak f_{T} value and for the optimum noise resistance R_{S O P T} of a MOSFET, knowing that the g_{m} / W at peak f_{T} increases with the scaling factor S. Ignore the contribution of the source and drain resistances to f_{T} and R_{S O P T}.