A silicon diode at $300\text{K}$ has a reverse saturation current $I_s=1\times 10^{-13}\text{A}$ and an ideality factor $n=1$. If a forward current of $I=5\text{mA}$ flows, calculate the required forward voltage $V$ using the Shockley diode equation $I=I_s\left[\exp \right(\frac{V}{n{V}_T})-1]$, where the thermal voltage $V_T=25.85\text{mV}$.

Step-by-step solution

1. Write the Shockley equation and isolate the exponential term: $\exp \left(\frac{V}{n{V}_T}\right)=\frac{I}{I_s}+1$.
2. Substitute the given values: $\frac{I}{I_s}+1=\frac{5\times 10^{-3}}{1\times 10^{-13}}+1=5\times 10^{10}+1\approx 5\times 10^{10}$.
3. Take the natural logarithm: $\frac{V}{n{V}_T}=\ln (5\times 10^{10})$.
4. Compute the logarithm: $\ln (5\times 10^{10})=\ln 5+\ln 10^{10}=1.609+23.026=24.635$.
5. Since $n=1$, $V=V_T\times 24.635=0.02585\times 24.635\text{V}$.
6. Multiply to obtain $V\approx 0.637\text{V}$, round to two significant figures as $0.64\text{V}$.
7. State the final voltage.

Concept tested: Shockley diode equation

Published 20 September 2026 · How this solution was prepared and checked