Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 204
relative intensity
1.0
0.8
0.6
0.4
0.2
33% heat
12% recomb.
32% kept
5800 K blackbody
captured energy
available to PV
23% IR transparency
0.0
0.0 0.5 1.0 1.5 2.0
wavelength (¹m)
Figure 13.5: <strong>Energy</strong> budget in silicon PV
cell. The areas of the four regions represent
the fraction of the total incident energy
going to each domain. All light at wavelengths
longer than 1.1 μm (infrared; 23%)
passes through the silicon without being
absorbed. The photons that are absorbed
give excess kinetic energy to electrons, losing
33% of the incident energy as heat. This
effect is progressively more pronounced the
shorter the wavelength. Of the remaining
44%, about a quarter disappear as electrons
“recombine” with vacancies (holes) inthe
silicon before getting a chance to contribute
to a useful current by crossing the junction,
leaving 32% as the maximum theoretical
efficiency.
But as the wavelength gets shorter <strong>and</strong> the energy gets higher, a greater
fraction is lost to heat. Overall, 33% of the incident photon energy is lost
to heat as the boosted electrons rattle the crystal before being tamed.
Now we’re down to 44% of the original incident energy in the form
of conduction-promoted electrons that have shaken off their excess
kinetic energy. But then here’s the rub: electrons are dumb. They don’t
know which way to go to find the junction, so aimlessly bounce around
the lattice, in a motion called a r<strong>and</strong>om walk. 32 Some get lucky <strong>and</strong>
w<strong>and</strong>er into the junction, where they are swept across 33 <strong>and</strong> contribute
33: . . . red arrow in Figure 13.4
to external current. Others fall into an electron vacancy (a hole) ina
32: . . . sometimes called drunken walk, depicted
as me<strong>and</strong>ering paths in Figure 13.4
process called recombination: game over. 34 Roughly speaking, about 34: . . . red “poof” in Figure 13.4
three-quarters 35 of the electrons get lucky by w<strong>and</strong>ering into the junction
before being swallowed by a hole. So of the 44% available, we keep 32%
(called the Shockley-Queisser limit [86]).
Another significant loss arises because some photons are absorbed in
the very top layer above the junction, so that the resulting electrons do
not have the opportunity to be swept across the junction to contribute to
useful energy. The shorter the wavelength, the shallower the photon is
likely to penetrate into the cell. 36 Meanwhile, photons around 1 μm are
likely to penetrate deep—well past the junction—making it less likely
that the liberated electrons will find the junction before settling into
a new home (lattice site) via recombination. Figure 13.4 reflects this
color-dependence, <strong>and</strong> also depicts one electron from the blue photon
being generated above the junction, which will not have an opportunity
to do useful work by crossing the junction.
In total, the basic physics of a PV cell is such that 20% efficiency
is a reasonable expectation for practical implementations. 37 Indeed,
commercial silicon-based PV panels tend to be 15–20% efficient, not
far from the theoretical maximum. This may seem like a low number,
but don’t be disappointed! Biology has only managed to achieve 6%
35: Naïvely, 50% are lucky <strong>and</strong> w<strong>and</strong>er up
to the junction, <strong>and</strong> 50% make the wrong
choice <strong>and</strong> go down. But even those initially
going down still have a chance to w<strong>and</strong>er
back up to the junction before time expires
<strong>and</strong> they recombine, so that effectively 75%
make it.
36: Any given photon has a probability
distribution of being absorbed as a function
of depth. Blue photons can penetrate deep,
but are more likely to be absorbed near
the front surface. A 1 μm photon can be
absorbed near the front surface, but it is
more likely to penetrate deeper into the
silicon.
37: Fancy, very expensive multi-junction
PV cells may be used for special applications
like in space, where size <strong>and</strong> weight
are extremely important <strong>and</strong> cost is less of a
limitation. These devices can reach efficiencies
approaching 50% by stacking multiple
junctions at different b<strong>and</strong> gaps, better utilizing
light across the spectrum.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.