Question

An ideal p-n junction germanium diode has a reverse saturation current of 10 \(\mu A\) at 300 K. The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of 100 mA at 300 K is _________. (Consider the Boltzmann constant \( k_B = 1.38 \times 10^{-23} { J/K} \) and the charge of an electron \( e = 1.6 \times 10^{-19} { C} \).

Hint:

For p-n junction diodes, use the Shockley diode equation to calculate the forward voltage. The reverse saturation current \( I_s \) is an essential parameter, and the thermal voltage \( V_T \) depends on temperature. For high forward currents, the voltage can be found by solving the Shockley equation, which involves the natural logarithm of the ratio of current to reverse saturation current.

Answer 1

Correct Answer: 0.23

We use the diode current equation: \[ I = I_s \left( e^{\frac{V}{nV_T}} - 1 \right), \] where:
- \( I_s = 10 \, \mu A \) is the reverse saturation current,
- \( V \) is the forward voltage,
- \( n \) is the ideality factor (for an ideal diode, \( n = 1 \)),
- \( V_T = \frac{k_B T}{q} \) is the thermal voltage.
For a temperature of 300 K, the thermal voltage is: \[ V_T = \frac{1.38 \times 10^{-23} \times 300}{1.6 \times 10^{-19}} = 0.02585 \, {V}. \] Now, we solve for \( V \) when the forward current \( I = 100 \, {mA} \): \[ 100 \times 10^{-3} = 10 \times 10^{-6} \left( e^{\frac{V}{0.02585}} - 1 \right). \] Simplifying: \[ 10^{-4} = 10^{-5} \left( e^{\frac{V}{0.02585}} - 1 \right), \] \[ 10 = e^{\frac{V}{0.02585}} - 1, \] \[ e^{\frac{V}{0.02585}} = 11, \] \[ \frac{V}{0.02585} = \ln(11), \] \[ V = 0.02585 \times \ln(11) \approx 0.23 \, {V}. \] Thus, the voltage required is 0.23 V.