Design an ideal silicon n-channel MOSFET with a polysilicon gate to have a threshold voltage of $V_{T}=0.65 \mathrm{~V}$. Assume an oxide thickness of $t_{\mathrm{ox}}=300 \AA \mathrm{A}$, channel length of $L=1.25 \mu \mathrm{m}$, and a nominal value of $Q_{x}^{\prime}=1.5 \times 10^{11} \mathrm{~cm}^{-2}$. It is desired to have a drain current of $I_{D}=50 \mu \mathrm{A}$ at $V_{G S}=2.5 \mathrm{~V}$ and $V_{D S}=0.1 \mathrm{~V}$. Determine the substrate doping concentration, channel width, and type of gate required.