Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 203
A photon leaves the hot solar surface aimed right at a PV panel on Earth.
The photon can be any “color,” distributed according to the Planck
spectrum 23 in Figure 13.1. The most probable wavelength for a 5,800 K
blackbody—according to Eq. 13.5—is ∼0.5 μm, but it could reasonably
be anywhere from 0.2–3 μm. The atmosphere will knock out (absorb
or scatter) most of the ultraviolet light before it reaches the panel, <strong>and</strong>
some of the infrared light is absorbed in the atmosphere as well. But
almost 75% of the energy 24 makes it to the panel. What happens next
depends on the wavelength.
First, we must underst<strong>and</strong> something about the silicon material. The
atoms in a typical silicon PV cell are arranged in an orderly lattice, grown
as a single crystal. Expensive panels have mono-crystalline silicon,
meaning that each 15 cm square cell comprising the panel is a thin slice
of one giant crystal. Less expensive poly-crystalline (or multi-crystalline)
panels have cells that are a patchwork 25 of r<strong>and</strong>omly-oriented crystals
at the millimeter to centimeter scale. But microscopically, both types are
orderly crystals. Silicon has four electrons in its valance shell (outermost
shell), so that a “happy” silicon atom is home to a four-outer-electron
family. These electrons are said to exist in the valance b<strong>and</strong>. 26 But
provided a sufficient energy kick, an electron can leave home <strong>and</strong> enter
the conduction b<strong>and</strong>, 27 where it can freely move through the crystal <strong>and</strong>
can potentially contribute to an electric current, if it finds the junction.
The threshold energy level to promote an electron from the valence to
the conduction b<strong>and</strong> is called the b<strong>and</strong> gap, 28 which for silicon is 1.1 eV
(1.8 × 10 −19 J).
Infrared photons at a wavelength of λ> 1.1 μm have an energy of
E < 1.1 eV, 29 according to Eq. 13.1. The energy falls below the b<strong>and</strong>
gap of silicon, <strong>and</strong> as such is not capable of promoting an electron
within the silicon from the valance b<strong>and</strong> to the conduction b<strong>and</strong>. These
longer-wavelength photons sail right through the silicon crystal as if it
were transparent glass. Since these photons are not absorbed, the part of
the incident energy in the infrared beyond 1.1 μm is lost. For the solar
spectrum, this amounts to 23%, <strong>and</strong> is portrayed in Figure 13.5.
23: The spectrum can be thought of as a
probability distribution for photon wavelength,
if picking out one photon.
24: This is roughly 1,000 W/m 2 out of the
1,360 W/m 2 incident at the top of the atmosphere
(the solar constant, which will be
derived in Section 13.4).
25: See banner image for this chapter on
page 197.
26: The term “b<strong>and</strong>” is used to describe
energy levels. The valance b<strong>and</strong> is a lower
energy level.
27: . . . higher energy level
28: . . . difference between conduction <strong>and</strong>
valance b<strong>and</strong> energy levels
29: That λ 1.1 μm happens to correspond
to 1.1 eV is a numerical coincidence,
but perhaps convenient, in that remembering
1.1 for silicon covers it from both directions.
For the 77% of sunlight whose photons are energetic enough to bump
an electron into the conduction b<strong>and</strong>, 30 it’s game-on, right? Well, not 30: . . . denoted as e − in Figure 13.4
so fast—literally. Photons whose energy is higher than 1.1 eV have more
energy than is needed to lift the electron into the conduction b<strong>and</strong>. It
only takes 1.1 eV to promote the electron, so a blue-green photon at
0.5 μm (∼ 2.5 eV) has an excess of about 1.4 eV. The lucky electron is not
just lifted out, but is given a huge boost in the process, rocketing out
of the atom. It’s going too fast! It knocks into atoms in the crystal <strong>and</strong>
generally shakes things up a bit before settling down. We call this heat,
or thermal energy: 31 its excess kinetic energy is transferred to vibrations
(r<strong>and</strong>omized kinetic energy of atoms) in the crystal lattice. The blue
curve in Figure 13.5 reflects this loss: we get to keep all the energy at
1.1 μm (1.1 eV), thus the blue curve joins the overall black curve here.
31: Solar panels in the sun get pretty hot.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.