GATE 2016 EC – Question 48
The figure below shows the doping distribution in a $p$-type semiconductor in log scale.
[Figure: A log-scale plot of $N_A$ against position. $N_A$ rises as a straight line on the log scale from $10^{14}$ cm$^{-3}$ at 1 μm to $10^{16}$ cm$^{-3}$ at 2 μm.]
The magnitude of the electric field (in kV/cm) in the semiconductor due to non uniform doping is ________
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Correct answer: 1.10 to 1.25
Explanation
In equilibrium a nonuniform doping creates a field $E = \frac{kT}{q}\frac{d(\ln N_A)}{dx}$ (taking $kT/q = 26$ mV at 300 K). The doping increases by a factor of 100 over 1 μm, so $\frac{d(\ln N_A)}{dx} = \frac{\ln 100}{10^{-4}\text{ cm}} = 4.605 \times 10^4$ cm$^{-1}$. The field is $0.026 \times 4.605 \times 10^4 = 1197$ V/cm, which is about 1.2 kV/cm.