An n-channel silicon MOSFET is built on a p-type substrate with

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Solid State Physics, Ch Junctions and devices, finished

Problem

An n-channel silicon MOSFET is built on a p-type substrate with NA=5.0×1016 cm−3N_A=5.0\times10^{16}\,\mathrm{cm^{-3}}, under tox=5.0 nmt_{ox}=5.0\,\mathrm{nm} of SiO2\mathrm{SiO_2} (relative permittivity 3.93.9). Its gate and fixed oxide charge give a flat-band voltage VFB=−0.90 VV_{FB}=-0.90\,\mathrm{V}. The channel has Wch=10 μmW_{\rm ch}=10\,\mu\mathrm{m}, Lch=1.0 μmL_{\rm ch}=1.0\,\mu\mathrm{m} and electron mobility μn=400 cm2 V−1s−1\mu_n=400\,\mathrm{cm^2\,V^{-1}s^{-1}}. Take ni=1.0×1010 cm−3n_i=1.0\times10^{10}\,\mathrm{cm^{-3}}, εs=11.7\varepsilon_s=11.7 and kBT/e=25.85 mVk_BT/e=25.85\,\mathrm{mV}. ((a)) Find the threshold voltage VthV_{th}, and say how large an error setting VFB=0V_{FB}=0 would make. ((b)) Find the drain current at VG=2.0 VV_G=2.0\,\mathrm{V} and VD=0.10 VV_D=0.10\,\mathrm{V}. ((c)) Find the saturation drain current at VG=2.0 VV_G=2.0\,\mathrm{V}, and the drain voltage at which saturation begins.

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