ECE/OPTI 414a/514a
Practice Problem Set #4
1. Assume a silicon PV cell with an ideality factor of 1.5 that has an Isc = 2.25A
at 25oC and a reverse saturation current of 1.30X10-9A.
a. Compute the corresponding open circuit voltage at 25oC.
b. Compute the short circuit current and open circuit voltage at 15oC and 60oC
using the temperature sensitivity factors discussed in class (use Voc and Isc
at 25oC for the normalization values.
2. The PV cell from Problem 1with T = 25oC now has a series resistance of
0.11Ω, and a shunt resistance of 450kΩ. Assume that Isc for the cell without
parasitic resistance is 2.25A.
a. Determine the FF without parasitic resistance.
b. Compute the FF as a result of series and shunt resistance (i.e. two FF’s one
with series resistance and one with shunt resistance.)
c. Now assume that the cell is operating with both types of parasitic
resistance. Find the new Vmpp, Impp, and Pmpp. (Hint: start with a value for
V~0.5Vmpp without parasitic resistance and iterate until the current is
consistent on both sides of the equation for I. Then increase the voltage
value until an approximate MPP value is found. It will require 4 or 5
iterations.)
3. The absorption of silicon (indirect bandgap) for a photon with energy of 2.5eV
is 4.5X103/cm. Compute the absorption coefficient at a wavelength of 700 nm.
Assume that the phonon energy involved in the transition at both wavelengths
is 0.05Eg. Assume that the material is at room temperature (300K).
4. Assume a p-n step junction in silicon with the p-type material doped at a
concentration of 1016/cm3 and the n-type material doped at 1018/cm3. The
intrinsic carrier density is 1.5X1010/cm3 and all dopants are fully ionized.
Assume that the effective density of states for silicon is
19
3.22 10
/cm3 for the
conduction band and
19
1.83 10
/cm3 for the valence band. Assume that the
temperature is 300K and silicon relative permittivity of 11.7.
a. Compute the hole concentration on the n-side and electron concentration
on the p- side of the junction;
b. Compute the built in potential across the junction;
c. Compute the width of the depletion region;
d. Compute is position of the Fermi level in the quasi-neutral n- and p-
regions relative to the conduction band edge.
e. Compute the maximum value for the electric field.
