Solar Cells Based on Single PN Junctions - Nanophysics of Solar and Renewable Energy - page 142

uppermost dashed curve in Figure 6.8 describes this result, using the vacuum given
by Plancks law of solar spectrum.
Changing to the concentrating situation, where both f factors are 1.0 (input and
output radiation both use a full hemispherical range of angles), the new equation is

Ae N 0 ð Ae N 0 ð Þ 1 I ¼ E G ; E 2 ¼1; T s Þ E G ; E 2 ¼1; T c Þ½ ð eV = kT :

exp Amperes

ð 6 : 10a Þ

It is now seen that a larger open-circuit voltage V is needed to balance the larger solar
input from the concentrating optics. This means a larger efficiency, since the open-
circuit voltage times the current is the power. In this case, Shockley andQuiesser thus
find efficiency 40.8% at 1.1 eV for a fully concentrated single-junction solar cell; see
Figure 5.1 for an example of such optics, where the imagined cell of area A is at the
bottom of the field.

This analysis is based on the direct sunlight and does not include correction for the
diffuse scattered light. This analysis is invalid for a cloudy sky.
In this way, the complex situation was analyzed to provide themaximumef ciency
of the single-junction device as a function of the single bandgap energy, under
assumed illumination conditions. The solid line plots of Figure 6.8 are numerically
obtained from the Shockley - Quiesser analysis using the below-atmosphere spectra,
as illustrated in Figure 5.2.
As we will see later, the most straightforward means of improving the solar cell
ef ciency is to put two or more single-gap cells in tandem (series connection), so
that the highest energy photons are processed with the largest bandgap junction,
and later cells process those photons whose energy was insuf cient to generate
electron - hole pairs in the prior junctions. A cascade of tandem cells can approach
the ef ciency of the Carnot machine, in principle. In practice, tandem cells of at
least 40% ef ciency under concentration have been demonstrated. The materials
science and engineering of these tandem structures make them more expensive,
but this can be counterbalanced by using concentrating light systems. The cells are
more efficient at higher light intensity, because the open-circuit voltage increases
with light intensity.

6.2
Thin-Film Solar Cells versus Crystalline Cells

An important class of solar cells are those made of thin films of semiconductors.

These are cheaper because they use less of the primary material: a few micrometers
rather than a fraction of a millimeter, but are generally of lower ef ciency because
recombination occurs at the grain boundaries. The grain size in polycrystalline lms
varies from millimeters to around a micrometer, but nanocrystalline films are also
used with grains as small as 10 nm. Grain boundaries foster recombination of
photogenerated electrons and holes, which occurs at defects such as dangling bonds
at the surfaces. The dangling bonds can bemitigated by adding hydrogen to ll empty