Home › Previous year questions › GATE 2016 EC (EC3) › Question 48GATE 2016 EC (EC3) – Question 48 Electronic Devices · P-N Junction and Semiconductor Devices · 2 marks · Numerical answer
Two unit-area MOS capacitors are shown. Figure I uses dielectric X of thickness $t_1=1$ nm and relative permittivity 4, and Y of thickness $t_2=3$ nm and relative permittivity 20. Figure II uses only X of thickness $t_{eq}$. Equal capacitances require $t_{eq}$ in nm to be ________.
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Show answer and explanation Correct answer: 1.55 to 1.65
Explanation Dielectric layers stacked along the field act as series capacitors. Their reciprocal capacitance per area is $(t_1/4+t_2/20)/\epsilon_0$.
For a single X layer it is $t_{eq}/(4\epsilon_0)$. Equate them to get $t_{eq}=t_1+(4/20)t_2=1+0.6=$ **1.6 nm**.
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