Consider a p-n junction diode having the characteristic i-i_0 (e^… - Vidyadip

Question

Consider a p-n junction diode having the characteristic $\text{i}-\text{i}_0\Big(\text{e}^{\frac{\text{eV}}{\text{kT}}}-1\Big)$ where $\text{i}_0=20\mu\text{A}.$ The diode is operated at T = 300K.

Find the current through the diode when a voltage of 300mV is applied across it in forward bias.
At what voltage does the current double?

✓

Answer

$\text{i}_0=20\times10^{-6}\text{A},\ \text{T}=300\text{K, V}=300\text{mV}$

$\text{i}=\text{i}_0\text{e}^{\frac{\text{eV}}{\text{KT}}-1}$ $=20\times10^{-6}\Big(\text{e}^{\frac{100}{8.62}}-1\Big)=2.18\text{A}=2\text{A}.$

$4=20\times10^{-6}\Big(\text{e}^{\frac{\text{V}}{8.62\times3\times10^{-2}}}-1\Big)$

$\Rightarrow\text{e}^{\frac{\text{V}\times10^3}{8.62\times3}}-1=\frac{4\times10^6}{20}$

$\Rightarrow\text{e}^{\frac{\text{V}\times10^3}{8.62\times3}}=200001\Rightarrow\frac{\text{V}\times10^{3}}{8.62\times3}=12.2060$

$\Rightarrow\text{V}=315\text{mV}=318\text{mV}.$

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