An ideal MOS capacitor (p-type semiconductor) is under strong inversion with $V_G = 2$ V. The inversion charge density is $Q_{IN} = 2.2\ \mu ext{C/cm}^2$. Assume oxide capacitance per unit area $C_{ox} = 1.7\ \mu ext{F/cm}^2$. For $V_G = 4$ V, the value of $Q_{IN}$ is ____________ $\mu$C/cm$^2$ (rounded to one decimal place).

Question

An ideal MOS capacitor (p-type semiconductor) is under strong inversion with $V_G = 2$ V. The inversion charge density is $Q_{IN} = 2.2\ \mu	ext{C/cm}^2$. Assume oxide capacitance per unit area $C_{ox} = 1.7\ \mu	ext{F/cm}^2$. For $V_G = 4$ V, the value of $Q_{IN}$ is ____________ $\mu$C/cm$^2$ (rounded to one decimal place).

cdquestions Admin · Accepted Answer

In strong inversion, inversion charge density varies approximately linearly with gate overdrive: $$ Q_{IN} \approx C_{ox}(V_G - V_{th}) $$ Given: at $V_G = 2$ V, $$ Q_{IN} = 2.2\ \mu\text{C/cm}^2 = C_{ox}(2 - V_{th}) $$ $$ 2.2 = 1.7(2 - V_{th}) $$ $$ 2 - V_{th} = \frac{2.2}{1.7} = 1.294 $$ $$ V_{th} \approx 0.706\ \text{V} $$ Now compute inversion charge at $V_G = 4$ V: $$ Q_{IN} = 1.7 (4 - 0.706) $$ $$ Q_{IN} = 1.7 \times 3.294 \approx 5.60\ \mu\text{C/cm}^2 $$ Rounded to one decimal place: $$ \boxed{5.6\ \mu\text{C/cm}^2} \quad (\text{acceptable range: } 5.5\text{–}5.7) $$

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Correct Answer: 5.5

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