In a $p-n$ junction diode, the current $I$ can be expressed as $I=I_{0} \left[\exp \left(\frac{e V}{k_{B} T}\right)-1\right]$, where $I_{0}$ is the reverse saturation current, $V$ is the voltage across the diode (positive for forward bias, negative for reverse bias), $I$ is the current through the diode, $k_{B}$ is the Boltzmann constant $(8.6 \times 10^{-5} \; eV/K)$, and $T$ is the absolute temperature. If for a given diode $I_{0}=5 \times 10^{-12} \; A$ and $T=300 \; K$, then:
$(a)$ What will be the forward current at a forward voltage of $0.6 \; V$?
$(b)$ What will be the increase in the current if the voltage across the diode is increased to $0.7 \; V$?
$(c)$ What is the dynamic resistance?
$(d)$ What will be the current if reverse bias voltage changes from $1 \; V$ to $2 \; V$?

(N/A) The current in a $p-n$ junction diode is given by $I = I_{0} [\exp(eV / k_{B}T) - 1]$.
Given: $I_{0} = 5 \times 10^{-12} \; A$, $T = 300 \; K$, $k_{B} = 8.6 \times 10^{-5} \; eV/K$.
$(a)$ For $V = 0.6 \; V$, the exponent is $eV / k_{B}T = 0.6 / (8.6 \times 10^{-5} \times 300) \approx 23.256$.
$I = 5 \times 10^{-12} \times \exp(23.256) \approx 5 \times 10^{-12} \times 1.259 \times 10^{10} \approx 0.063 \; A$.
$(b)$ For $V = 0.7 \; V$, the exponent is $0.7 / (8.6 \times 10^{-5} \times 300) \approx 27.132$.
$I' = 5 \times 10^{-12} \times \exp(27.132) \approx 5 \times 10^{-12} \times 6.07 \times 10^{11} \approx 3.035 \; A$.
Increase in current $\Delta I = I' - I = 3.035 - 0.063 = 2.972 \; A$.
$(c)$ Dynamic resistance $r_{d} = \Delta V / \Delta I = (0.7 - 0.6) / 2.972 \approx 0.0336 \; \Omega$.
$(d)$ In reverse bias, $V$ is negative. For $V = -1 \; V$ and $V = -2 \; V$, $\exp(eV/k_{B}T) \approx 0$. Thus, $I \approx -I_{0} = -5 \times 10^{-12} \; A$. The current remains effectively constant at $-5 \times 10^{-12} \; A$.