ECE 3040 Homework 3
The goal of this homework is to design a photocell (also known as a photoelectric cell or photoelectric resistor)
that will respond to light and change it’s resistance. This device may be used in a later homework problem.
The photocell is basically nothing more than a resistor made out of semiconductor material and is typically
arranged in a package as a long skinny slither of very thin semiconductor, most often CdS due to it’s near
optimal bandgap for adsorbing the solar spectrum and relative inexpensive materials. While a real device is has
a long serpentine shape (see below) we will simply use a rectangular block as was done in class.
The working specifications of your design are for a resistance of 1 Giga-ohm in dark and 3Mega-ohms in bright
light (Intensity, Io=50 mW/cm2 light intensity).
Given:
The mobilities of un=100 cm2/V-sec and up=500 cm2/V-sec
The CdS material is p-type with Na=1e14 cm-3 and ni=2e6 cm-3.
Note: For this problem it is okay to assume low level injection and thus it is okay to use the formula:
BUT if this were a real world problem, the type of variations we want to achieve in resistance are so large that
High level Injection conditions apply and strictly speaking we should use (do not do this in this homework) the
formula:
1) It is determined that the resistor “trace” (width viewed from the light’s perspective as shown in figures above)
will have a width of 0.2 mm and a thickness (same as depth “L” in our light absorption lecture 9) of 4 um.
What is the needed length to achieve 1 Giga-ohm resistance in the dark?
2) Assuming that the bandgap energy is 1.4 eV and that the light has the same photon energy (1.4 eV) and is
completely absorbed uniformly in the semiconductor, what is the generation rate, GL in the semiconductor?
Hint: calculate the flux of photons in 1 cm2 from the power density (intensity) and the amount of energy needed
to generate each electron-hole pair, then find how much of this flux is incident on the photocell given your
results from part 1, then convert this to a generation rate using the assumption of uniform absorption/generation
throughout the thickness of the semiconductor film.
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