A p - n junction diode has the characteristic i = i_0\! (e^ eV/kT -...

Given:
Reverse saturation current, $i_0 = 20 \mu\text{A} = 20 \times 10^{-6} \text{ A}$
Forward bias voltage, $V = 300 \text{ mV} = 0.3 \text{ V}$
Temperature, $T = 300 \text{ K}$
Boltzmann constant, $k = 1.38 \times 10^{-23} \text{ J/K}$
Elementary charge, $e = 1.6 \times 10^{-19} \text{ C}$

First, calculate the exponent $\dfrac{eV}{kT}$:
$\dfrac{eV}{kT} = \dfrac{1.6 \times 10^{-19} \times 0.3}{1.38 \times 10^{-23} \times 300}$

$\dfrac{eV}{kT} = \dfrac{0.48 \times 10^{-19}}{4.14 \times 10^{-21}} = \dfrac{48}{4.14} \approx 11.6$

The current through the diode is given by:
$i = i_0 \lleft(e^{\dfrac{eV}{kT}}$ - 1 )$<br><br>Since$e^{11.6} \gg 1$, we can neglect the$-1$term:<br>$i \approxi_0 e^{\dfrac{eV}{kT}}

Using $e^{11.6} \approx1.09 \times10^5$:
$i \approx20 \times10^{-6} \times1.09 \times10^5$

$i \approx2.18$\text{ A}

The closest value among the given options is $2 \text{ A}.$