Home › Previous year questions › GATE 2016 EC (EC2) › Question 48GATE 2016 EC (EC2) – Question 48 Electronic Devices · P-N Junction and Semiconductor Devices · 2 marks · Numerical answer
A long-channel NMOS has source and body tied together; electron mobility is independent of $V_{GS}$ and $V_{DS}$. At $V_{GS}=2$ V, $g_m=0.5\ \mu$A/V for $V_{DS}=50$ mV, and $g_d=8\ \mu$A/V for $V_{DS}=0$. Here $g_m=\partial I_D/\partial V_{GS}$ and $g_d=\partial I_D/\partial V_{DS}$. The threshold voltage in volts is ________.
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Show answer and explanation Correct answer: 1.18 to 1.22
Explanation For the linear-region model, write $K=\mu_nC_{ox}W/L$. Then $g_m=KV_{DS}$, so K=0.5/0.05=10 μA/V².
At zero drain voltage, $g_d=K(V_{GS}-V_T)$. Therefore $8=10(2-V_T)$, in μA/V units.
Solving gives **$V_T=1.2$ V**. Using the two measurements avoids needing the device geometry or mobility separately.
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