Spectral mismatch in solar cells

Spectral mismatch in solar cells


In previous few weeks, you have learned semiconductor
physics, basic operating principles of solar cells, optical phenomena, and light management
techniques involved in solar cell as well. The purpose of a solar cell is to convert
energy of electromagnetic radiation directly into electricity. The energy conversion in a solar cell is based
on the photovoltaic effect. Now it’s time, to discuss how to achieve
a maximum conversion efficiency in a solar cell. Is it possible to utilize 100% of incident
solar energy? Is there an upper limit of the conversion
efficiency of a solar cell? What are the loss mechanisms that occur in
a solar cell? To answer all these questions, this week we
will focus on the loss mechanisms in a solar cell and explain some strategies how to tackle
them. Let’s first review the basic operating principles
of a solar cell. As already mentioned the energy conversion
in a solar cell is based on the photovoltaic effect. The photovoltaic effect is described as the
generation of a voltage difference at the junction of two different materials in response
to visible or other radiation. The first step in the energy conversion process
is the absorption of light in the absorber layer of solar cell. The result of the absorption is the generation
of electron-hole pairs. In the second step, the photo-generated electrons
and holes must be separated to prevent their recombination. When the separation occurs the oppositely
charged carriers have to be collected and saved at different parts of the solar cell. Sometimes we call these parts membranes. In this way the photo-generated charge carriers
become a source of electricity and via electrodes, that are attached to the membranes, they can
do a useful work in an external circuit. Before we go deeper into all the loss mechanisms
in a solar cell, first we will take a look at an overview of all of them. We can divide loss mechanisms into two big
categories: optical losses and electrical losses. Optical losses are related to the absorption,
transmission and reflection losses of the incident light, which can be further divided
into spectral mismatch losses and additional optical losses. Under spectral mismatch losses, we mean thermalization
and non-absorption losses of energy of photons that propagate through the absorber of a solar
cell. Additional optical losses include reflection
and transmission losses, parasitic absorption in supporting layers of a solar cell and shading
losses caused by front electrodes. Electrical losses arise mainly from the recombination
of charge carriers in solar cells and other electrical losses. The recombination losses are due to the loss
of charge carriers by bulk and surface recombination, and by fundamental recombination that we relate
to the utilization of the bandgap energy. The other electrical losses represent voltage
drops at series and shunt resistances. In this video, we will first review and quantify
the spectral-mismatch losses in a solar cell. AM1.5 solar spectrum is used to determine
the conversion efficiency of a solar cell. In this figure you see the the spectral-power
density of AM1.5 solar spectrum as function of the wavelength. The unit of spectral-power density is watt
per square meter and per nanometer, the wavelength is presented in nanometers. We usually use two parameters to describe
the spectral properties of incident light. The first one is already mentioned spectral
power density, often also referred to as the spectral irradiance. The second parameter is the photon-flux density. Another important parameter to describe the
incident power of light is irradiance. Irradiance is the total power density of incident
light and we can calculate it by integrating the spectral power density over the wavelength. As the spectral power density and the photon
flux density are related via photon energy, irradiance can also be found by integrating
the product of photon energy and the photon-flux density over the wavelength. When measuring the conversion efficiency of
solar cells we use the AM 1.5 spectrum irradiance of 1000 watts per square meter. As you may recall, depending on the bandgap
energy of the absorber layer and the energy of incident photon, three situations can occur:
The energy of the incident photon is less-than, equal-to, or larger than the bandgap energy. A photon with energy exactly equal to the
bandgap energy, can be absorbed and will generate an electron-hole pair. Electron and hole will occupy an energy state
at the edge of the conduction and valence band, respectively Photons with energy smaller
than the bandgap cannot excite valence electrons to the states in the conduction band, and
will simply pass through the semiconductor material. This is the case to which we refer as non-absorption
losses. On the other hand, photons with energy higher
than the bandgap will be absorbed and will generate electron-hole pairs. However, electrons and holes tend to occupy
most stable states, which are at the edges of the bands, therefore the photon energy
that is in excess of the bandgap energy will be released as heat. This process of releasing the excess energy
of electrons and holes to the lattice is known as thermal relaxation, or thermalization. So, how to quantify the non-absorption losses? Let’s take crystalline-silicon solar cells
as an example. The green area shown in the plot of the AM1.5
spectral-power density represents the region of the spectrum that can be absorbed by a
crystalline silicon solar cell. Lambda-G denotes the wavelength of photons
whose energy corresponds to the bandgap energy of crystalline silicon. Lambda-G is approximately 1110 nm. On the other hand, the spectrum highlighted
in yellow represents photons that do not have enough energy to be absorbed. It is the energy of these photons that represent
the non-absorption loss. First we need to calculate the fraction of
the incident power that the solar cell can absorb. We find this fraction by dividing the irradiance
of photons that have enough energy to be absorbed, these are photons with wavelengths equal and
smaller than Lambda_G, by the total irradiance of the AM 1.5 spectrum. After determining this fraction, the non-absorption
fraction of the total irradiance is calculated by subtracting this fraction from one. In thermalization process, the excess photon
energy with respect to the bandgap is released by the excited electrons and holes as heat
to the lattice. The excess energy of photons lost in thermalization
in a c-Si solar cell is indicated by the red arrow. It is the yellow area of the spectrum above
the brown one. Since the electrons and holes tend to occupy
energy levels at the bottom of the conduction band and the top of the valence band, respectively,
the fraction of the absorbed energy that a solar can deliver as useful energy is equal
to the bandgap of the absorber layer. To calculate the fraction of solar irradiance
that can be delivered as useful energy, we first calculate the power of all photons that
can be absorbed related to the bandgap of crystalline silicon absorber and divide it
with the total irradiance of these photons. It is the brown area in the plot that represents
the fraction of AM1.5 spectrum that can be delivered as useful energy by crystalline
silicon solar cells. From this equation we can conclude that only
the energy of photons corresponding to the bandgap of the absorber is fully utilized. By combining the fraction of incident power
absorbed by a solar cell with the fraction of the power that a solar cell can deliver
as useful energy, we determine the so-called ultimate conversion efficiency for a solar
cell with single absorber. The figure on the left shows the ultimate
conversion efficiency as a function of the bandgap energy for different spectra: the
green line is for the AM1.5 spectrum; the blue line is for the AM0 spectrum and the
red line is for the radiation spectrum of blackbody at 6000 Kelvin. We see from the green line that the maximum
ultimate efficiency is around 48% for a solar cell with the absorber that has a bandgap
of 1.2 eV. In this video, we have reviewed how the bandgap
of a solar cell absorber limits the utilization of radiation with broad spectrum of energies. The mismatch between the bandgap energy of
the solar cell absorber and a broad spectrum of photon energies is the most fundamental
loss limiting the conversion efficiency a solar cell. In the following lectures, we will go through
other loss mechanisms that further decrease the theoretical maximal conversion efficiency.

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