Home › Previous year questions › GATE 2016 EC (EC2) › Question 47GATE 2016 EC (EC2) – Question 47 Electronic Devices · Carrier Transport · 2 marks · Numerical answer
A silicon region contains no electrons or holes and has ionized donor density $N_D^+=10^{17}\ \mathrm{cm^{-3}}$. The electric field is zero at x=0 and +50 kV/cm at x=L; y and z field components are zero everywhere. Given $q=1.6\times10^{-19}$ C, $\epsilon_0=8.85\times10^{-14}$ F/cm and $\epsilon_r=11.7$, L in nm is ________.
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Show answer and explanation Correct answer: 30 to 34
Explanation Poisson's equation is $dE_x/dx=\rho/\epsilon=qN_D^+/(\epsilon_0\epsilon_r)$. The density is uniform, so the field rises linearly.
Use the two boundary fields: $L=\epsilon_0\epsilon_r(50000)/(qN_D^+)$. This is $3.23578\times10^{-6}$ cm.
Since 1 cm=$10^7$ nm, **L=32.358 nm**, within 30–34 nm.
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