GATE 2016 EC (EC3) – Question 47
An active npn BJT has the linear excess-electron base profile shown. Emitter–base junction area is $0.001\ \mathrm{cm^2}$, base electron mobility is $800\ \mathrm{cm^2/(V\,s)}$ and depletion widths are negligible. At room temperature $V_T=26$ mV and $q=1.6\times10^{-19}$ C. Collector current in mA is ________.
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Correct answer: 6.55 to 6.75
Explanation
Einstein's relation gives $D_n=\mu_nV_T=800(0.026)=20.8\ \mathrm{cm^2/s}$. The profile falls from $10^{14}\ \mathrm{cm^{-3}}$ to zero over 0.5 μm=$5\times10^{-5}$ cm.
Its gradient magnitude is $2\times10^{18}\ \mathrm{cm^{-4}}$. Electron diffusion current magnitude is $qAD_n|dn/dx|$.
Substitution gives $1.6\times10^{-19}(0.001)(20.8)(2\times10^{18})=0.006656$ A, or **6.656 mA**.