In an abrupt p-n junction, the doping concentrations on the p-side an...
Given information:
- Doping concentration on p-side (NA) = 9 x 10^16 /cm^3
- Doping concentration on n-side (ND) = 1 x 10^16 /cm^3
- Depletion width on n-side (xn) = 3 μm
- The p-n junction is reverse biased
To find:
- Depletion width on the p-side
Explanation:
Reverse biased p-n junction:
- In a reverse biased p-n junction, the positive terminal of the battery is connected to the n-side and the negative terminal is connected to the p-side.
- This creates a potential barrier which opposes the flow of majority carriers (electrons in n-side and holes in p-side) from one side to the other.
- The potential barrier width increases, leading to an increase in the depletion width on both sides.
Depletion width calculation:
- The depletion width (x) can be calculated using the following equation:
x = sqrt((2*ε*Vbi)/(q*(1/NA+1/ND))) - sqrt((2*ε*Vbi)/(q*NA*ND))
where ε is the permittivity of the semiconductor, Vbi is the built-in potential, q is the charge of an electron, NA and ND are the doping concentrations on the p-side and n-side respectively.
- The first term inside the square root represents the depletion width on the n-side and the second term represents the depletion width on the p-side.
Built-in potential calculation:
- The built-in potential (Vbi) can be calculated using the following equation:
Vbi = (kT/q) * ln(NA*ND/ni^2)
where k is the Boltzmann constant, T is the temperature in Kelvin, q is the charge of an electron, ni is the intrinsic carrier concentration (ni^2 = (Nc*Nv)*exp(-Eg/kT)), Nc and Nv are the effective densities of states in the conduction and valence bands respectively, and Eg is the bandgap energy.
Substituting the given values in the above equations, we get:
Vbi = 0.742 V
x = sqrt((2*ε*Vbi)/(q*(1/NA+1/ND))) - sqrt((2*ε*Vbi)/(q*NA*ND))
where ε = 11.8 * ε0 (ε0 is the permittivity of free space)
q = 1.602 x 10^-19 C
k = 1.381 x 10^-23 J/K
T = 300 K
ni = 1.5 x 10^10 /cm^3
Nc = 2.8 x 10^19 /cm^3
Nv = 1.04 x 10^19 /cm^3
Eg = 1.12 eV
x = 0.3 μm (approx)
Therefore, the depletion width on the p-side is 0.3 μm (option B).