Home › Previous year questions › GATE 2016 EC (EC2) › Question 46GATE 2016 EC (EC2) – Question 46 Electronic Devices · P-N Junction and Semiconductor Devices · 2 marks · Multiple choice
For avalanche breakdown in a silicon $p^+n$ junction, the n region has uniform donor density $N_D$. Breakdown occurs when the maximum field reaches $E_{crit}$, assumed independent of $N_D$. The built-in voltage is negligible compared with $V_{BR}$. Which relationship holds?
$V_{BR}\sqrt{N_D}=\mathrm{constant}$ $N_D\sqrt{V_{BR}}=\mathrm{constant}$ $N_DV_{BR}=\mathrm{constant}$ $N_D/V_{BR}=\mathrm{constant}$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (C) $N_DV_{BR}=\mathrm{constant}$
Explanation For a one-sided abrupt junction, the field is triangular: $E_{max}=qN_DW/\epsilon$ and $V_{BR}=E_{max}W/2$ when built-in voltage is neglected.
At breakdown set $E_{max}=E_{crit}$, so $W=\epsilon E_{crit}/(qN_D)$. Substitution gives $V_{BR}=\epsilon E_{crit}^2/(2qN_D)$.
All other quantities are fixed, so **$N_DV_{BR}$ is constant, C**.
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