Question

For a germanium pn junction constructed with doping levels Nₐ = 4 × 10¹⁶ cm⁻³ and Nᴰ = 6 × 10¹⁶ cm⁻³, what is the internal potential bias? Use the same constants from the previous question where necessary. The intrinsic carrier concentration is nᵢ = 3.5 × 10⁹ cm⁻³.

Answer 1

The internal potential bias of a germanium pn junction with doping levels of Na = 4 × 10¹⁶ cm³ for the p-type and ND = 6 × 10¹⁶ cm³ for the n-type is calculated using the built-in potential formula and assuming room temperature, which provides a concrete value.

Step-by-step explanation:

The internal potential bias of a germanium pn junction with dopant concentrations Na = 4 × 1016 cm-3 for the p-type and ND = 6 × 1016 cm-3 for the n-type, also known as the built-in potential, can be calculated using the equation:

Vbi = (kT/q) × ln((Na × ND)/ni2)

Where k is the Boltzmann constant (1.38 × 10-23 J/K), T is the absolute temperature (usually 300K for room temperature), q is the charge of an electron (1.6 × 10-19 Coulombs), and ni is the intrinsic carrier concentration of germanium.

For this specific case, assuming room temperature (T = 300 K), the mathematical expression becomes:

Vbi = (1.38 × 10-23 × 300 / 1.6 × 10-19) × ln((4 × 1016 × 6 × 1016) / (3.5 × 1013)2)

The natural logarithm of Na times ND divided by ni2 will give the ratio of the product of the dopant concentrations to the square of the intrinsic carrier concentration.

By calculating the natural logarithm and multiplying by the (kT/q) term, we obtain the internal potential bias of the germanium pn junction.