Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 202
physics is outside the scope of this course, but it is worth painting a
general picture—enough to appreciate how much we can expect to get
out of a PV panel.
current (e – flow)
e -
external
circuit
e -
+ + + + + + + +
e -
+ + +
– – – – – – – – – – –
e -
e -
light rays from the sun (photons)
top grid contacts
n-doped silicon (phosphorous)
p-n junction
p-doped silicon (boron)
bottom contact
Figure 13.4: PV cell structure <strong>and</strong> function.
A junction between n–doped <strong>and</strong> p–doped
semiconductors sets up an electric field
across the junction. If an electron promoted
to the conduction b<strong>and</strong> by an incoming photon
w<strong>and</strong>ers into the junction, it is swept
across (red arrow) <strong>and</strong> successfully contributes
to current. Electrons do not contribute
if created above the junction—as is
more probable for blue photons that are not
likely to penetrate as far. Electrons do not
contribute to the external (useful) current if
they recombine (fill a hole) before finding
the junction (red “poof”).
Figure 13.4 illustrates the basic scheme. The underlying idea is that
adjoining two slabs of silicon into which small amounts of two kinds
of impurities have been deliberately introduced 17 that either contribute
extra electrons (n-type, for negative charge donors) or create vacancies
for electrons (p-type, for effective positive charge donors). Putting p-
doped <strong>and</strong> n-doped materials together creates a junction 18 exhibiting
a contact potential. The result is that “donated” electrons right at the
junction in the n-doped material decide to relocate across the junction to
vacancies in the p-doped material, creating a wall of negative charge on
the p-side of the junction <strong>and</strong> leaving behind “holes” (missing electrons)
effectively creating positive charges 19 on the n-side of the junction. In the
region right around the junction 20 an electric field is set up between the
separated charges. Any electron w<strong>and</strong>ering into this depletion region will be
swept across the junction, across the contact potential, <strong>and</strong> will contribute
to a current that is then driven around the external circuit to return to
its p-side home. 21 Figure 13.4 shows additional salient features that will
be pointed out as the story develops below.
17: . . . either during or after the semiconductor
crystal growth; a process called “doping”
18: So-called p–n junctions form the basis
of diodes <strong>and</strong> transistors.
19: When a (negatively-charged) electron
leaves an otherwise neutral medium, the
medium becomes more positively charged.
20: . . . called the “depletion region,” as electrons
have been depleted from the portion
of the n-side adjacent to the junction
21: Once it is “home,” the electron will fill a
vacancy created by a sun-liberated electron
to end the journey.
13.3.1 Theoretical Efficiency of Photovoltaics
We will now follow the fate of one photon as it encounters the photovoltaic
material. Doing so will expose the physical process of photovoltaics
<strong>and</strong> simultaneously track losses to elucidate efficiency expectations.
The basic scheme is that a photon knocks an electron away from an atom
in the PV cell, <strong>and</strong> this electron has some chance of being swept across
the junction upon which it contributes to a useful current. 22 The goal
is to get an electron across the line. It is not unlike some sports where
crossing a line is the goal, but many factors are lined up defending
against successful attainment of this goal. Efficiency is related to the
chance that a photon will produce a “win.”
22: Current is just flow of charge, <strong>and</strong> in this
case is just movement of electrons through
the external circuit.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.