GATE 2014 EC (EC3) – Question 46
An ideal MOS capacitor has boron substrate doping $10^{15}$ cm⁻³. Applied gate voltage forms a 0.5 µm depletion region with surface potential 0.2 V. Given $\epsilon_0=8.854\times10^{-14}$ F/cm, and relative permittivities 12 for silicon and 4 for SiO₂, find peak oxide electric field (V/µm).
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Correct answer: 2.3 to 2.5
Explanation
Using the stated surface potential and depletion width, the triangular silicon field has interface peak Esi,max=2ψs/W=2×0.2/0.5=0.8V/µm. Normal displacement continuity gives εsiEsi=εoxEox, so Eox=(12/4)×0.8=**2.4V/µm**. The oxide field is uniform in the ideal charge-free oxide. Computing from the separately rounded doping and width gives about2.26V/µm, exposing a small inconsistency in the supplied rounded data.