The p-type region of a silicon p-n junction is doped with 1016 boron atoms per cubic centimeter, and the n-type region is doped with 1018 phosphorus atoms per cubic centimeter. Assume a step p-n junction and that all doping atoms are ionized. The intrinsic carrier concentration in silicon at 300K is 1.5∗1010cm−3
To determine the majority and minority carrier concentrations in the p-type and n-type regions of a silicon p-n junction, we need to understand the concepts of doping, intrinsic carrier concentration, and the behavior of majority and minority carriers in a semiconductor.
Doping: Doping is the process of intentionally adding impurities to a semiconductor material to change its electrical properties. By adding impurities with a different number of valence electrons, it is possible to create either p-type or n-type regions in the semiconductor.
Intrinsic Carrier Concentration: The intrinsic carrier concentration (ni) is a property of the semiconductor material itself, without any impurities. It represents the number of thermally generated electron-hole pairs per unit volume under thermal equilibrium conditions.
Majority and Minority Carriers: Majority carriers are the charge carriers (either electrons or holes) that are present in greater numbers in a semiconductor region, while minority carriers are present in smaller numbers.
Now, let's use the given information to calculate the majority and minority carrier concentrations for the p-type and n-type regions.
1. p-type region (boron-doped):
- Dopant concentration: 10^16 boron atoms per cubic centimeter.
- Boron is a trivalent impurity, meaning it has 3 valence electrons. In silicon, which is a tetravalent material, each boron atom accepts one electron from a neighboring silicon atom, creating a hole.
- Therefore, the majority carriers in the p-type region are holes, and the minority carriers are electrons.
- Majority carrier concentration (p): It equals the dopant concentration since all the boron atoms are ionized and contributing to hole formation.
p = 10^16 cm^-3
- Minority carrier concentration (n): In thermal equilibrium, the product of the majority (p) and minority (n) carrier concentrations should be equal to the square of the intrinsic carrier concentration (ni) at a given temperature (T).
pn = ni^2
Since we know ni = 1.5*10^10 cm^-3, we can solve for n:
n = ni^2/p
= (1.5*10^10)^2 / (10^16)
= 2.25*10^4 cm^-3
2. n-type region (phosphorus-doped):
- Dopant concentration: 10^18 phosphorus atoms per cubic centimeter.
- Phosphorus is a pentavalent impurity, meaning it has 5 valence electrons. In silicon, each phosphorus atom donates one extra electron, creating excess electrons.
- Therefore, the majority carriers in the n-type region are electrons, and the minority carriers are holes.
- Majority carrier concentration (n): It equals the dopant concentration since all the phosphorus atoms are ionized, contributing to electron formation.
n = 10^18 cm^-3
- Minority carrier concentration (p): As before, we can use the equation pn = ni^2 to solve for p:
p = ni^2/n
= (1.5*10^10)^2 / (10^18)
= 2.25*10^-8 cm^-3
To summarize:
In the p-type region:
- Majority carrier concentration (p) = 10^16 cm^-3 (holes)
- Minority carrier concentration (n) = 2.25*10^4 cm^-3 (electrons)
In the n-type region:
- Majority carrier concentration (n) = 10^18 cm^-3 (electrons)
- Minority carrier concentration (p) = 2.25*10^-8 cm^-3 (holes)
These carrier concentrations determine the behavior and electrical properties of the p-n junction, such as the formation of a depletion region and the flow of current under forward and reverse bias conditions.