Shortcut methods and tricks to solve numericals on current through a P-N junction:

1. For germanium diodes, the dynamic resistance is typically 10 times the forward bias voltage. So, you can directly calculate the current by dividing the forward bias voltage by 10.

In this case, the current through the diode is 0.3 V / 10 Ω = 0.03 A.

2. For silicon solar cells, the reverse saturation current is typically 1/1000th of the short-circuit current. So, you can estimate the reverse saturation current by dividing the short-circuit current by 1000.

In this case, the reverse saturation current is 150 mA / 1000 = 0.15 mA.

3. For Zener diodes, the dynamic resistance is typically 1/10th of the breakdown voltage. So, you can directly calculate the current by dividing the breakdown voltage by 10 times the dynamic resistance.

In this case, the current through the diode is 5 V / (10 Ω x 10) = 0.5 A.

4. For calculating the depletion width, you can use the formula: $$W = \sqrt{\frac{2\epsilon(V_{bi} + V_{a})}{qN_A N_D}}$$ where:

• W is the depletion width
• ε is the permittivity of the semiconductor
• V_bi is the built-in potential
• V_a is the applied voltage
• q is the electronic charge
• N_A and N_D are the doping concentrations on the P-side and N-side, respectively

For silicon, the permittivity is 1.04 x 10^-12 F/m, and the electronic charge is 1.6 x 10^-19 C.

Using these values, you can calculate the depletion width for the given doping concentrations.

5. For calculating the built-in potential, you can use the formula: $$V_{bi} = \frac{kT}{q}\ln\left(\frac{N_AN_D}{n_i^2}\right)$$ where:

• V_bi is the built-in potential
• k is the Boltzmann constant (1.38 x 10^-23 J/K)
• T is the temperature (in Kelvin)
• q is the electronic charge
• N_A and N_D are the doping concentrations on the P-side and N-side, respectively
• n_i is the intrinsic carrier concentration of the semiconductor

For silicon at room temperature (300 K), the intrinsic carrier concentration is approximately 1.5 x 10^10 cm^-3.

Using these values, you can calculate the built-in potential for the given doping concentrations.