Given data:
Donor doping concentration (Na) = 1.5 * 10^16 cm^−3
Temperature (T) = 270K
Intrinsic concentration (ni) = 2 * 10^9 cm^−3
Applied forward bias voltage (V) = 0.93V

Calculation:

1. Calculate the majority carrier electron density (n0) using the donor doping concentration (Na) and intrinsic concentration (ni) as follows:

n0 = Na = 1.5 * 10^16 cm^−3

2. Calculate the minority carrier hole density (p) using the law of mass action:

p = ni^2 / n0

Substituting the given values:

p = (2 * 10^9 cm^−3)^2 / (1.5 * 10^16 cm^−3)

Simplifying:

p = (4 * 10^18 cm^−6) / (1.5 * 10^16 cm^−3)

p ≈ 2.67 * 10^2 cm^−3

Therefore, the value of minority carrier hole density is approximately 2.67 * 10^2 cm^−3.

Explanation:

In a PN junction, doping is done to create regions with excess electrons (N-type) or excess holes (P-type). The majority carriers are the dominant carriers in each region, while the minority carriers are the less abundant carriers.

In this case, the donor doping concentration (Na) represents the concentration of N-type dopants, which are donors of excess electrons. The majority carrier electron density (n0) is equal to the donor doping concentration (Na) since the N-type region is majority carrier dominated.

The intrinsic concentration (ni) represents the concentration of thermally generated electron-hole pairs in the absence of doping. It is a function of temperature and is typically much lower than the doping concentration.

Applying a forward bias voltage to the PN junction allows current to flow through the junction. The minority carriers, in this case, the holes, are injected into the N-type region and contribute to the overall current. The minority carrier hole density (p) is calculated using the law of mass action, which relates the minority carrier concentration to the majority carrier concentration.

In this calculation, the given values of donor doping concentration (Na), intrinsic concentration (ni), and temperature (T) are used to determine the minority carrier hole density (p). The result provides insight into the behavior of the PN junction under forward bias conditions.