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From: bales@athena.mit.edu (James W Bales)
Newsgroups: sci.energy,sci.electronics,sci.physics
Subject: Re: solar cells
Summary: Si cell efficiency up at high fluxes
Keywords: silicon, solar cell, bandgap, indirect, efficiency
Message-ID: <1991Jan7.233136.24484@athena.mit.edu>
Date: 7 Jan 91 23:31:36 GMT
References: <1991Jan5.225316.12934@cs.rochester.edu>
Sender: James W. Bales
Followup-To: bales@athena.mit.edu
Organization: Massachusetts Institute of Technology
Lines: 62

In article <1991Jan5.225316.12934@cs.rochester.edu> dietz@cs.rochester.edu (Paul Dietz) writes:
>>>                           -- silicon solar cells (at least) become
>>>more efficient at high concentration ratios (at constant temperature).
>>>I'm not sure why this is. 
>	Paul F. Dietz
>	dietz@cs.rochester.edu

If I may hazard a guess it is because Si is an "indirect-gap"
semiconductor.

All semiconductors have bandgaps, and to first order photons
whose energies are less than the bandgap don't get absorbed (remember
that a photon's energy is proportional to it's frequency, equivalently
the energy is inversely proportional to it's wavelength. Blue is high
energy, red is low, and infrared even lower). This is because of
conservation of energy. However, momentum must also be conserved.
Photons have very little momentum. For our purposes we can assume
photons have NO momentum. This is the basis for distinguishing
between direct-bandgap and indirect-bandgap semiconductors.

In a direct-bandgap semiconductor an electon changes only its energy,
not momentum, when it absorbs a photon. In an indirect-bandgap
semiconductor an electron MUST change BOTH energy and momentum
when it absorbs a photon (solid-state physicists may flame me
for glossing over a lot of things here). But, since a photon has
no momentum, this means the electron has to get momentum from
somewhere else. Usually this momentum comes from vibrations
of the atoms composing the crystal. The more the atoms are vibrating,
the higher the probability of a given photon being absorbed.

As you increase the photon flux, you increase the current,
which means there are more electrons moving through the active
region of the device (the junction). But, as the electrons flow they
bang into the atoms of the crystal (both the Si atoms and more so
the As and P dopant atoms). This increases the number of lattice
vibrations (aka phonons) available, which means a given photon
is more likely to be absorbed. Viola! Increased efficiency.

Caveat. The temperature of the cell is a measure of the number
of phonons present. So, this process will tend to increase the
temperature of the cell in the active region. When you stated that
this was observed at constant temperature, I assume you mean the
ambient tmperature was kept constant, not the temperature at the
junction.

Incidently, if the temperature of the junction does go up, the bandgap
decreases, which means that a larger fraction of the spectrum can be
absorbed. I don't know enough about Si to say how important this is,
but it could be more important than what I described above, given
a big enough delta T.

Another possibility involves "two-photon absorption" which
would allow the absorption of two photons whose energy,
when summed, is greater than the bandgap energy. We won't go into
that, this is already long enough :-)

Hope this was more than you wanted to hear! I should point out
that my experience is with GaAs, a direct-bandgap material. Has anyone
out there done much with indirect materials who can shed some light
on this?

Jim Bales bales@athena.mit.edu