A PN junction is formed using P-type and N-type semiconductors with doping concentrations:

N_A= 10¹²/cm³, N_D =10¹⁰/cm³

Given: Thermal voltage: V_T = 25 mV

Intrinsic carrier concentration: n_i = 10⁶ /cm³

What is the built-in voltage V0 across the PN junction?

Question

Question

This question was previously asked in

RRB JE CBT 2 (Electronics Engineering) ReExam Official Paper (Held On: 04 Jun, 2025)

Answer 1

Explanation:

The built-in voltage V₀ of a PN junction is given by the equation:

V₀ = V_T × ln((N_A × N_D) / n_i²)

Where:

Calculation:

Substitute the given values into the formula:

V₀ = 25 × ln((10¹² × 10¹⁰) / (10⁶)²)

Simplify the terms:

V₀ = 25 × ln((10²²) / (10¹²))

V₀ = 25 × ln(10¹⁰)

Using the property of logarithms, ln(10^x) = x × ln(10):

V₀ = 25 × 10 × ln(10)

V₀ = 250 × ln(10) mV

Conclusion:

The correct built-in voltage across the PN junction is 250 × ln(10) mV, which corresponds to Option 1.