Physics 240B
M. L. Cohen
Spring 2008
Problem Set #3
Due: 03/18/08
(
20)
1.
"Ultimate efficiency" of a singlegap solar cell. The goal of this problem is to derive
an upper bound on the power conversion efficiency—defined here as the ratio of
output electrical power to input radiative power—of a photovoltaic (PV) device with
a single band gap, E
g
. Consider an idealized solar cell, a pn junction with surface
area 1 m
2
, held at T = 0K. Assume the sun is a blackbody with T = 6000K.
(a)
Compute the incident power (energy/sec) due to the blackbody radiation,
assuming for simplicity, all the black body radiation is focused on the 1m
2
area.
(b)
On an average sunny day around lunchtime, incident sunlight has an intensity of
about 1000 W/m
2
. Why does the number in (a) differ?
(c)
Assuming each incident photon with energy greater than E
g
produces a single
electronhole pair ("detailed balance"), each charge producing a voltage of
magnitude h
ν
g
/e, derive an expression for the output electrical power in terms of
the band gap E
g
. (Hint: If each of the number of absorbable photons resulted in
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 Spring '08
 Cohen
 Energy, Power, Solar cell, EG, output electrical power

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