GATE 2018 EC – Question 55

Electronic Devices · Energy Bands and Carrier Concentration · 2 marks · Numerical answer

A junction is made between $p^-$ Si with doping density $N_{A1}=10^{15}\ \text{cm}^{-3}$ and $p$ Si with doping density $N_{A2}=10^{17}\ \text{cm}^{-3}$.

Given: Boltzmann constant $k=1.38\times10^{-23}\ \text{J}\cdot\text{K}^{-1}$, electronic charge $q=1.6\times10^{-19}$ C. Assume 100% acceptor ionization.

At room temperature ($T=300$ K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be ________.

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Correct answer: 0.11 to 0.13

Explanation

For a $p^-$/$p$ junction the built-in potential is set by the ratio of hole densities: $V_{bi}=\frac{kT}{q}\ln\frac{N_{A2}}{N_{A1}}=0.0259\times\ln100=0.0259\times4.605=0.12$ V.