Photovoltaics
solar cells

Photovoltaics

This article outlines the importance of solar cell technology in the context of world’s increasing energy needs, as well as the need to move away from fossil fuels in order to combat climate change. These factors drive the need for better solar cell technology, in terms of efficiency as well as carbon footprint during manufacturing. In order to understand all the challenges facing solar cell development, an understanding of the fundamental design, physics and materials making up solar cells is needed. This article moves from the very basics of semiconductors all the way to multijunction solar cells, making an effort to add historical and industrial context along the way. Ultimately, with the steadily decreasing cost of silicon-based solar cells, researchers need accurate data about their new devices as quickly as possible in order to maximize their opportunities in the market. The right tests, models and tools will allow them to do that.

Table of Contents
Share on facebook
Share on pinterest
Share on twitter
Share on email
Share on linkedin

World's Increasing Energy Needs

We all use energy in our lives, and not just for sustaining our human biology in waking, walking and wondering. To look at this website requires electrical energy. The energy to make the device you’re reading on had to come from somewhere. If you own a vehicle, you probably have to charge it or fill it with gas to get around.

There are many kinds of energy, and humanity has become pretty good at getting and converting energy from a lot of different sources. We’ve also started using more of it over time.

Primary Energy Sources

Data Source: https://www.iea.org/geco/data/

One of the types of energy everyone is most familiar with, electrical energy (or electricity), is actually a secondary energy source. The reason is that we have to produce it through some other means, and some of those means (primary energy sources) are in the pie chart above.

For example, we can turn turbines with flowing water, and the spinning turbine can then generate electricity. This is known as hydroelectric energy.

Nuclear energy takes advantage of Einstein’s famous equation, E=mc2, where mass (m) is converted to energy (E) during the splitting of an atom (nuclear fission). This releases huge amounts of heat that can be used to boil water into steam, which can then turn a turbine to generate electricity.

A much cleaner form of nuclear energy involves putting atoms together (nuclear fusion). Fusion is the reaction that powers our sun, and needs intense heat and pressure to happen, so it’s still under development. However, it’s seen great progress in recent years.

Coal, oil and gas are called fossil fuels, because they are produced from plants and animals that have decayed over hundreds of millions of years. As you can see from the above pie chart, we get a huge portion of our energy from burning fossil fuels. Burning fossil fuels releases energy that can produce steam, turn a turbine, and again give us electricity. It can also just produce motion, as in internal combustion engines.

Wind energy takes advantage of the Earth’s breeze to spin turbines and—you guessed it—generate electricity.

Solar energy is named after the latin word solaris, meaning “of the sun”. There are many ways of using the sun’s energy, ranging from using it to heat homes and industrial processes directly, or to heat molten salts and water for electricity. There are also ways to convert solar energy directly into electricity.

Solar photovoltaic energy takes advantage of the photoelectric effect, where an electrical current flows as a result of the sun shining on specific kinds of materials.

Think photo=light and volt=electricity. If you’ve ever seen a solar panel, that’s an example of solar photovoltaic energy, and we’ll see that it plays an important role in meeting the world’s anticipated energy needs.

There are many other ways to generate energy; this is just a sample of the main ways we get the energy for all the things we do around the world.

Future Energy Demands

Humanity’s need to use energy is not going away. In fact, our energy usage keeps growing. According to the International Energy Agency, the world’s energy consumption in 2018 increased at almost twice the rate of growth since 2010, needing an additional generation of 1000 TWh (a trillion kilowatt-hours, or about how much energy it would take for everyone on Earth to run a hairdryer for four days straight).

The 2018 World Energy Outlook reports that global energy demand is expected to increase by more than 25% by 2040.

These projections are conservative in the sense that they assume humanity doesn’t drastically increase its energy usage, particularly in third-world and developing countries. However, we can and should do better than that, because we need to strive to improve the living conditions of everyone on Earth. An investigation of the data reveals that GDP, life expectancy, and infant mortality statistics all improve with increased energy use per person. Bottom line: everything gets better with more energy.

“A first world lifestyle requires about 10 kW per person. For 10 billion people, humanity needs to generate 100 terawatts. Achieving this is a moral imperative; achieving it sustainably requires civilization scale deployment of solar energy production infrastructure.”

Michael Taschuk, CTO of G2V Optics
Photovoltaics: Testing Solar Cells 10
GDP per capita (in USD/person/year) vs Energy use per capita (W/person) of data from the World bank shows an overall increase of GDP with energy use.
Photovoltaics: Testing Solar Cells 11
Infant mortality rate (per 100k population) vs Energy use per capita of data from the World bank shows an overall decrease in infant mortality with energy use.

To really improve the living conditions of every human on the planet, then, we need to increase energy production by about five times by 2100.

This would require a heroic effort, and amounts to a new 1 GW power plant starting and maintaining operation every day.

This energy has to come from the different sources mentioned above. Some of them are non-renewable, meaning they don’t regenerate faster than we use them. The graph below shows change in how the electricity we used was generated in 2018.

Graph showing the additional energy produced by different energy sources in 2017-2018. Data Source: Global Energy Status Report https://www.iea.org/geco/data/

A many-pronged approach is needed to try and meet the energy demands of tomorrow. As we start to deplete our fossil fuel reserves, we can see that we’ll need much more energy from renewable sources of hydro, wind and solar photovoltaics (solar energy).

There’s another big reason we want to move away from our dependence on fossil fuels, though.

Alternative Energies to Minimize Climate Change

The average temperature of our planet is rising, a phenomenon known as global warming. The Earth’s climate has always undergone cycles, but what we’re seeing is much bigger than the ebb-and-flow throughout history. Scientists have estimated that human activity from industrialization since the late 19th century has caused about 1.0 C of global temperature change. What’s the cause for this change? Our planet has a natural greenhouse effect. The sun heats up the land, oceans, and atmosphere. Some of this energy escapes back into space, but parts of it are also captured in different molecules that keep all this thermal energy cycling in the atmosphere. These molecules are known as greenhouse gases, and include carbon dioxide (CO2), water vapour (H2O), methane (CH4), Chlorofluorocarbons (CFCs) and others. Carbon dioxide is one of the most prevalent, and one that humans have generated a lot of through the burning of fossil fuels. The graph below shows just how much we’ve changed the amount of carbon dioxide in the atmosphere. In 2018, energy-related carbon dioxide emissions rose to a historic high of 33.1 Gt (Gigatons).
Photovoltaics: Testing Solar Cells 12

“… atmospheric CO2 has increased since the Industrial Revolution” Image source: NASA: https://climate.nasa.gov/vital-signs/carbon-dioxide/

The effects of global warming and climate change are widespread. Higher carbon dioxide leads to ocean acidification, which devastates aquatic life. Higher temperatures melt the polar ice caps, raise the sea level, and cause huge changes to global weather patterns. We’ve already seen impacts such as increased drought or heavy precipitation in regions not equipped to deal with it. Temperature extremes cause species loss and extinction, not to mention the risks to health, livelihood, food security, water supply and economic growth.
Photovoltaics: Testing Solar Cells 13

IPCC 2018 report on p.13, showing the impacts and risks of global warming for different systems. Image Source:https://report.ipcc.ch/sr15/pdf/sr15_spm_final.pdf

Many nations have recognized the need to take action to prevent climate change. The Paris Agreement was ratified in 2016 with the goal of ensuring global temperature rise remains below 2℃ as well as strengthening our ability to respond to climate change. Since then, it’s become clear that even more efforts are needed. A 2018 report by the Intergovernmental Panel on Climate Change (IPCC) concluded that we need to keep the global temperature rise to 1.5℃ if we really want to avoid the worst impacts of climate change. Combating climate change is no easy task. According to the World Energy Outlook, the path to keeping our sustainable development goals will require “convergence of cheaper renewable energy technologies, digital applications and the rising role of electricity.”

Solar energy is a central part of the strategies toward a sustainable future.

Solar energy is anticipated to play a crucial role, not only in meeting the world’s energy needs, but also in minimizing climate change. Breakthroughs are making solar photovoltaics more and more efficient. They’re the fastest growing resource for power generation (the worldwide photovoltaic electricity in 2014 was 40x that of 2006) . They also show the highest power density among all the renewable energy options. Add to this the fact that they don’t produce any pollution during their operation, have low maintenance costs, and run off of our warm G2V type star that will shine for billions of years to come, photovoltaics emerge as an essential part of our energy future.

What is Photovoltaics?

The photoelectric effect, where electricity is generated from a material when it absorbs light, was first discovered in 1887 by Heinrich Hertz. He saw that the energy needed to make a spark between two electrodes changed when he shone UV light on them. Digging deeper, scientists found that electrons (tiny negatively charged atomic particles that are the stuff of electricity) were freed from metals with light shining on them. Since then, we’ve come a very long way, with contributions to understanding from intellectual giants like Albert Einstein and Max Planck who helped us understand light as both a particle (called a photon) and a wave. This in turn helped us get a grasp of why and how light could knock out electrons from materials.
Photovoltaics: Testing Solar Cells 15
The photoelectric effect, where light can free electrons from a material.

The photovoltaic effect is closely related to the photoelectric effect, with a key difference. In the photoelectric effect, electrons are emitted into space. But, in the photovoltaic effect, electrons enter what we call the conduction band of the material. Since the photovoltaic effect doesn’t require breaking an electron completely free of a material, it requires less energy, and thus can occur more often.

 

What do we mean by the “conduction band”? Well, there are two main bands of energies that electrons can have. One range of energies, where an electron is bound around a single atom or molecule, is called the valence band. The other, where the electron is free to move from one atom or molecule to another, is called the conduction band. We’ll discuss this a bit more later, but the general idea is that when an electron is in the conduction band, we can conduct electricity, or have electrons move about more freely.

 

There’s a second requirement for the photovoltaic effect, though. Once an electron is in the conduction band, for the photovoltaic effect to occur, the electron has to move under the influence of an electric potential (or voltage). We’ll see later that this potential can be produced in semiconductors by putting two different, specific materials in close contact.

 

Electrons that move away from their parent material create a charge difference between where they are, and where they were. This charge difference generates a voltage, much like that across the terminals of a battery, and the moving electrons make up an electrical current. Current and voltage give us electrical power, or energy over time. The photovoltaic effect is the more practical way we convert solar energy into electrical energy. It’s what solar cells rely on.

 

The first photovoltaic cell was made at Bell labs in 1954, and it could only convert about 4% of sunlight into electricity. Today, we’re doing much better, with commercial conversion efficiencies closer to about 20%, and research efficiencies pushing much higher, as shown in the NREL graph below. They’ve also gotten a lot cheaper, too, with cost decreasing by about 10% every year. There are many growing advantages to using solar cells.

Photovoltaics: Testing Solar Cells 16
A plot of the best research-cell efficiencies, courtesy of the National Renewable Energy Laboratory (NREL), Golden, CO.

For more information on their screening procedures for researchers who make it onto the graph, visit their website: https://www.nrel.gov/pv/cell-efficiency.html

Photovoltaics: Testing Solar Cells 17
'Swanson’s Law' graph showing the steadily decreasing cost of solar module installation.

Image Source: https://www.researchgate.net/publication/311255868_’Swanson’s_Law’_plan_to_mitigate_global_climate_change

We’ve still got a long way to go, though. Solar cells don’t generate emissions during their operation, but to make them we still need to burn fossil fuels. All energy sources have these so-called indirect emission equivalents, measured in grams of CO2 per kilowatt-hour. To compare all the different methods of energy production fairly, a case study of power plant generation calculated a lifecycle greenhouse gas emission of 53 g CO2-eq/kWh for a photovoltaic power plant, compared to 975 g for a coal-fired plant, 742 g for an oil-fired plant, 24 g for nuclear, 11 g for hydro, 15 g for geothermal, and 29 g for wind. It is also worth considering that solar cells are often made using some materials which are hard to handle and recycle. In order to develop solar cells to their maximum potential and mitigate their disadvantages, we need to understand in detail everything that’s happening between materials, electricity, and light.

What are Photovoltaic Solar Cells?

There are different scales of solar cell products and technologies, and it’s important to understand some of the terms used in research and in industry. At the smallest level, we have the photovoltaic cell (or PV cell), which is the basic building block of any photovoltaic system. It is a semiconductor diode where the junction is exposed to light (more about this and semiconductors below). A photovoltaic module consists of many PV cells connected in series. If you connect PV modules together, you make a photovoltaic panel (or solar panel). Join several PV panels together and you get a photovoltaic array (or solar array). Photovoltaic systems (or solar systems) consist of solar arrays along with voltage converters and inverters as well as systems for tracking maximum power. Photovoltaic systems can be mounted on the ground, built into roofs, walls, or patios, or even connected to the electrical grid.
Photovoltaics: Testing Solar Cells 19
Scaling of photovoltaic elements from cells to systems

Photovoltaics are found in systems as small as cell phone battery packs, or as large as fields. They all work on the same basic principles, though.

Theory of Solar Cells

Semiconductors Basics

As we mentioned, a photovoltaic cell is a semiconductor diode. That might not be a very helpful explanation if you don’t know what a semiconductor is, or what a diode is, so we’ll give you a brief overview here. If you already know, you can feel free to skip ahead to Photovoltaic cell basics.

Semiconductors make up microchips, and pretty much anything digital or computerized. To understand what they do differently from other substances, we have to look at the periodic table of elements.

The Right Elements

Photovoltaics: Testing Solar Cells 21
Image Source: https://i.pinimg.com/originals/77/e4/ab/77e4abc1a255dc30b94f13d0f2ce1256.png
Photovoltaics: Testing Solar Cells 22
Some of the group III, IV, and V elements of the periodic table.
Carbon (C), silicon (Si) and germanium (Ge) are all in the same column on the periodic table, which means that they all have four electrons in their outer electron shell (or orbital). Most elements “like” to have eight electrons in their outer shell, which makes them more energetically stable (this is called the octet rule). An electron covalent bond is made up of two shared electrons. In order for carbon, silicon and germanium to get their eight electrons, then, they have to form four bonds. This formation of four bonds makes for a great geometry, because four bonding directions create a lattice, or a frame, that forms nice crystals.
Photovoltaics: Testing Solar Cells 23
TODO A 3D representation of the tetragonal Si crystal lattice.

Once these elements have their four bonds, the electrons are shared equally, and each atom is content to stay as it is. There are no extra electrons that are free to move around, so there’s no electrical conductivity. For these reasons, these elements (carbon, silicon and germanium) are normally really good insulators when they’re pure. Because silicon is the most common element used within solar cells, we’ll use silicon as an example for the rest of this section.

Semiconductor Doping

The process of creating a  semiconductor starts by taking silicon and making it impure, in a process called doping. This is when you mix silicon with a little bit of another substance, distinguished by two types. N-type doping (which stands for negative-type doping) is what you get when you mix in a small amount of phosphorus, arsenic, or antimony. You might recognize that these three elements are all situated to the right of silicon on the periodic table, which means they each have five electrons in their outer orbital. When they get put into the silicon lattice, we’re left with an extra electron that is not bonded to anything. It’s free to float around, which means the material can now conduct electricity. Electrons are negative, and since we’re adding an extra electron for every impurity put in, this gives the doping its n-type name.
Photovoltaics: Testing Solar Cells 24
The bonding in an n-type doped semiconductor that results in an extra electron.

P-type doping (which stands for positive-type doping) is produced when you mix in a small amount of boron or gallium. These elements are to the left of silicon, so they only have three electrons in their outer orbital. When they join into a lattice, there’s one direction that will not have a bond, and will form a “hole” where an electron is missing. This is a place where an electron can jump to, leaving a hole somewhere else. In this way, the hole (or a missing electron) can be thought of as a positive charge that can move around the lattice, which is why this doping is called p-type.

Photovoltaics: Testing Solar Cells 25
The bonding in a p-type doped semiconductor that results in a missing electron (a hole).

Both the n-type and p-type doping produce materials that can conduct a small amount of electricity. They’re not as good as metal conductors, however, which is why they were given the name semiconductor, meaning partially conductive.

Now that we’ve gained a basic understanding of semiconductors, it’s time to apply this understanding to the most basic semiconductor device: the diode.

Diode Construction

The PN Junction

You can make a semiconductor diode by putting an n-type and a p-type semiconductor next to each other. Something pretty interesting happens in the place where the two materials meet, which is called the junction. The side of the p-type semiconductor is called the anode, and the n-type semiconductor is called the cathode.

The Depletion Region

You might have heard the adage that opposites attract, which is true for magnets and electrical charges. This means that the negative electrons in the n-type semiconductor are attracted to the positive charges (vacancies) in the p-type. Some of the electrons move across, and as soon as they leave their parent material, they create a charge difference. This charge difference results in an electric potential (voltage) that prevents any more charge carriers from moving. We now have a region charges have moved out of; in other words, a layer where there are no more free carriers. This is called the depletion region because the carriers have been depleted there. No charge can naturally flow across this region, so this semiconductor construction won’t conduct electricity by itself.
Photovoltaics: Testing Solar Cells 26
The diffusion of charge carriers across a semiconductor junction creates the depletion region and a junction potential.

Overcoming the Junction Potential

If we hook up a battery or other power source to the diode, we can apply an electric potential (voltage) that overcomes the voltage setup by the semiconductor at the junction. Now charges aren’t stopped, and can move freely once again. Electric current will flow if you apply a sufficient voltage – usually for silicon PN junctions the so-called junction potential needed is about 0.6 V to 0.7 V. The current that flows increases quite quickly once you’ve overcome the junction potential. The IV curve that models this behaviour is shown below, and the equation that describes the exponential rise is named after the co-inventor of the transistor, William Shockley.
Photovoltaics: Testing Solar Cells 27
IV Characteristic curve of a diode.

You can now understand why one of the main things diodes are used for is a one-way gate, because they’ll only conduct current in one direction, and only if the junction potential is overcome.

Now that you understand what a semiconductor diode is, we can go back to our main focus, which is the photovoltaic cell, a specific kind of semiconductor diode.

Photovoltaic Cell Basics

Photovoltaics: Testing Solar Cells 28
The Different Layers of a Photovoltaic Cell

A photovoltaic cell is a diode with a large surface area. The top layer material is kept thin because we want light to be able to pass through it to strike the depletion region. If you remember, the photovoltaic effect happens when light energy is absorbed by an electron. 

In the case of a photovoltaic cell, the incident light is absorbed by an electron in the depletion region. It turns out that, for this energy to be captured in a photovoltaic cell, it has to have a certain energy.

The Band Gap

There is a minimum energy that an electron has to obtain before it breaks free of the lattice to move around and conduct electricity. This is the difference between the energy of a bound electron and a free electron.

There’s no one single value, though; there’s actually a range of energies that electrons can have when they’re bound, and this range and state is referred to as the valence band of electrons.

The range of energies and state of electrons that are free to conduct is called the conduction band. The extra energy that electrons have to gain to move from bondage to freedom is the minimum difference between the valence band and the conduction band. We call this difference the band gap.

In silicon, the band gap energy is about 1.11 electron-volts (eV) (an electron volt is the energy that one electron gains when it’s under the influence of one volt of electric potential).

In a semiconductor, the band gap energy is small enough that we can move electrons between being bound and being free, simply by shining light on the material. For comparison, insulators have a band gap energy that is too high (usually greater than 3 eV), meaning that it takes too much energy to free electrons, so under normal conditions, they aren’t conductive. In metals, the valence and conduction bands overlap, so electrons can easily change states between valence and conduction bands, providing a surplus of electrons that can conduct current.

Photovoltaics: Testing Solar Cells 29
The difference in energy bands between metals, semiconductors and insulators.

Electron-Hole Pair Generation

All right, now let’s say we have light shining on our semiconductor diode of the right energy—larger than the band gap. It gets absorbed by an electron. This electron moves from the valence band into the conduction band, going from bondage to freedom. It can move around now.

The gap that it left behind is a hole. By shining light on our semiconductor, we’ve created both a conductive electron and a hole. For this reason, the process is often called electron-hole pair generation.

Capturing the Electric Current

Under normal circumstances, the electron-hole pair would quickly recombine because the charges would attract each other. However, the first thing the electron and hole see is the junction potential we talked about earlier in the depletion region. The junction voltage prevents the electron and the hole from recombining right away. In fact, the junction voltage pushes them away from each other, and this is where the science of a photovoltaic cell really shines.
Photovoltaics: Testing Solar Cells 30
Electron-hole pair generation in a solar cell.

If we connect a wire between the top and bottom of our photovoltaic cell, this electron can now move all the way around through the wire, and reach the hole on the other side of the diode. We’ve just generated a current.

Voilà!

We have our photovoltaic cell: a semiconductor diode that conducts electricity when we shine light on it. We’ve converted energy from the sun into electricity.

Direction of Photocurrent Flow

There are several important details to understand and emphasize here. The first thing is the direction of photocurrent flow. The electric current that flows as a result of light is actually in the opposite direction of the normal diode current. Normally current (defined as the movement of positive charge) moves from the anode to the cathode in a diode. In a photovoltaic cell, however, we see that it’s moving in the opposite direction the long way around: from the cathode to the anode.

Photovoltaics: Testing Solar Cells 31
The junction potential in a semiconductor directs charges to flow in the opposite direction than they would normally flow in a diode.
Photovoltaics: Testing Solar Cells 32
Normal direction of current flow in a diode
Photovoltaics: Testing Solar Cells 33
The direction of current in a solar cell is driven by the junction potential, in the opposite direction of a normal diode.

Basic (One-Diode) Model of a PV Cell

Remembering that a photovoltaic cell is just a special kind of semiconductor diode, if we want to figure out the total current flowing, we can just add (or in this case, subtract), the diode current from the photoelectric current. If we assume the light shining on a photovoltaic cell stays about the same, then the photoelectric current is just a constant, while the diode current is given by Shockley’s equation. Since the current we’re most interested in for a photovoltaic cell is the photoelectric current, we choose that direction to be positive, resulting in the following equation for current:

Photovoltaics: Testing Solar Cells 34
Source: https://www.pveducation.org/pvcdrom/solar-cell-operation/iv-curve

Note that when we don’t have any light shining on the solar cell (IL = 0), the equation is just Shockley equation. Because this is how the solar cell behaves under dark conditions, the second term in the equation is often called the dark current.

The resulting curve is an inverted and shifted Shockley diode curve that is famous in photovoltaics, called the solar cell IV characteristic curve:

Photovoltaics: Testing Solar Cells 35
A typical IV curve for an illuminated solar cell.

Another quick note is that the way this curve is depicted depends on what is defined as the current-carrying particle. Whether you say that it’s the negative electron, or a positive hole, changes the sign and therefore whether the graph is flipped upside down or not. What’s important is that both definitions are correct ways of representing what’s occurring in a solar cell.

Basic Circuit Model

Another equivalent way to think about the current flow in a photovoltaic cell is that the diode’s natural current flow leeches away some of the current that would normally go to the load.

To better understand the behaviour of the photovoltaic cell, it is common to make use of electric circuit analogies in order to understand what’s physically going on. We call this a circuit model, and we can actually draw the electric circuit associated with the model described above. The photocurrent is then represented by a constant current source connected to a regular diode and our intended load.

Photovoltaics: Testing Solar Cells 36
Circuit showing another way of thinking about the photocurrent being split between the diode, and the intended load.

While the model we’ve described doesn’t quite take into account everything that’s happening (as we’ll see later), this is a really good starting point since it benefits from being pretty straightforward to talk about and put measures around. For these reasons, a lot of standards and values have been assigned to describe this IV curve graph and allow solar cell devices to be compared.

What is the Maximum Power We Can Get?

The maximum current in the device will flow when there’s no resistance; that is, when we hook a simple wire between the terminals. Since this is what happens in a short-circuit, the maximum current is called the short-circuit current, or Isc. This current isn’t doing anything useful, though, and is in fact neutralizing the voltage across the photovoltaic cell.

What we have to do to make the current useful, is to make it do work, or transfer some of its energy into a load. The more load we have, the higher the voltage the cell will have, where all of its junction potential will be used to move the electrons. The highest load we can possibly have is when there’s an infinite amount of resistance, or when the wires aren’t connected at all, and the electrons would have to cross an air gap in order to make it to the other terminal. Because this maximum voltage happens when the circuit is open (i.e. disconnected), we call this the open-circuit voltage, or Voc. In this case, we don’t have a current flowing, so again, we aren’t getting much use of the solar cell. We have to use the solar cell, then, somewhere in between the two extremes of Isc and Voc.

The IV Rectangle

Power in an electric circuit is calculated by multiplying the current by the voltage. Ideally we would have Isc multiplied by Voc. What happens as the voltage in the cell increases, is that the number of electrons actually escaping the depletion region starts to drop. So the curve drops quickly beyond a certain point. However, there is a steady rise of power from the photovoltaic cell as we increase voltage, and before we fall off the “cliff” of the curve. There’s a point where we’ll get the maximum power, and this configuration is called the maximum power point, or MPP.

We can see that multiplying current by voltage at the maximum power point (or anywhere else, for that matter) is the same thing as calculating the area of a rectangle on the curve. This rectangle will always be less than the maximum we’d love to achieve if there were a way to get power = Isc x Voc. Because these calculations can be thought of as area calculations, scientists define a term called the Fill Factor (written as FF), that describes how much power we are getting out of the cell compared to the dream of Isc x Voc.

In other words, the Fill Factor represents how close we are to “filling” the rectangle of Isc x Voc.

A quick note worth mentioning is that the current often depends on the area of the solar cell in question. Because researchers build different sizes of solar cells at different stages of development, in order to compare the currents more fairly, the current density is usually used, which is the current divided by the area (usually in units of mA per cm2), symbolized by the letter J. So you’ll often see this symbol in place of the current I that we’ve been talking about so far, as we see in the typical equation for Fill Factor below.

Photovoltaics: Testing Solar Cells 37
Fill Factor Equation
Source: https://books.google.ca/books?id=4Ok7DQAAQBAJ The Physics of Solar Cells, by Jenny Nelson

All of these metrics are shown below.

Photovoltaics: Testing Solar Cells 38

Image modified from: http://www.alternative-energy-tutorials.com/energy-articles/solar-cell-i-v-characteristic.html

Photovoltaics: Testing Solar Cells 39
The IV and power curves for a solar cell, showing the maximum power point and how it can be thought of as “filling” the ideal IV rectangle. Also shown are the maximum power points of the best recorded solar cells of other types.

Calculating Solar Cell Efficiency

An important metric of any photovoltaic cell is its efficiency. This is usually defined as the ratio of energy we get out of the cell to the energy put into it by sunlight. We can calculate it using many of the parameters above, by remarking that the input power is the ideal Isc x Voc multiplied by the fill factor. If we know our input power density (or irradiance) of the sun, Ps, we can then calculate the efficiency, which is the division of the two:
Photovoltaics: Testing Solar Cells 40

This efficiency (eta above) is one of the most important measurements at the end of the day, because it determines how much electricity humanity can get from solar cells. If we can make photovoltaic cells that convert a greater portion of the sun’s energy, that means we’re that much closer to meeting the energy requirements for a bright future.

Band Gap and Junction Potential Trade-Offs

The last detail to emphasize before we go further is the band gap energy. When we design a photovoltaic cell, we want to make it as easy as possible to generate that electric current, which means having a low band gap energy. A low band gap energy allows us to absorb more of the sun’s energy (because any light with energy lower than the band gap won’t be absorbed). However, the band gap energy and the junction potential are closely linked. In other words, the lower the band gap energy, the lower the junction potential. How much energy our freed electron has (i.e. its voltage) is determined by how much it’s accelerated by the junction potential. So if we have a really low band gap energy, we’re going to be generating a really low voltage in our photovoltaic cell. That can be impractical, because for useful electricity, we might then have to chain together a huge number of photovoltaic cells.
- For Advanced Users -
Since these cells are in series, the current through each of the cells is the same. In any set of solar cells, there is a distribution of physical properties that determine solar cell efficiency. As a result, there is a distribution of efficiencies. Under constant illumination, the lowest efficiency will produce the lowest number of charge carriers, limiting current for the entire series of cells.

As you might have already figured out, there’s a balance to be found and some limits to what we can do, which is what scientists and engineers are trying to overcome when they design different types of solar cells.

Types of Photovoltaic Solar Cells

The Limit of Single-Junction

So far, we’ve only talked about single junction diodes, where there is only one pair of n-type and p-type semiconductors. There is an important fundamental limit to the efficiency of this type of solar cell, known as the Shockley-Queisser limit. To understand this limit, we have to go back to the very beginning of the twentieth century, when a scientist named Max Planck produced a law for emitted radiation. Specifically, he produced an equation for the light emitted by what’s known as a black body, that is, something that absorbs all of the light we shine on it. The physics behind this is that every atom in the universe is in motion, and as a result of that motion, some light is emitted, even if it’s a tiny amount. Planck’s equation (now known as Planck’s Law) described the power of light emitted by a black body (per unit area, per frequency). Black body emission varies with temperature.
Photovoltaics: Testing Solar Cells 42
Equation Source: https://physics.info/planck/
It turns out that a black body of 5800 K is a really good way of modelling our sun’s spectral emission, as you can see below when we plot the above equation against wavelength.
Photovoltaics: Testing Solar Cells 43
Spectral distribution of solar radiation compared to that of a 5800 K black body. Source: Incropera and DeWitt (2007)
What Shockley and Queisser did was to make use of this model to calculate how much energy we can hope to squeeze from the sun shining on a photovoltaic cell. We’ll go through a quick description of their calculation in order to understand how realistic and important the limit really is, and the role it plays in guiding modern developments. First of all, they assumed that all photons (particles of light) with energy greater than the band gap will create a free electron. This is an assumption that makes their calculation an upper limit, because they’re starting by absorbing all light that meets the band gap requirement. In most cases any extra energy above the band gap is lost as heat. By adding up all the photons with energy greater than the bandgap, assuming each one creates an electron-hole pair, then comparing that to the total power incident on a solar cell, Shockley and Queisser could come up with the best-case scenario for how efficient a solar cell could be.
- For Advanced Users -

Here are some more in-depth details about Shockley and Queisser’s calculations.

They started by calculating the number of photons of energy greater than the band gap, that are shining on a given area in a second. Because each photon has an energy E = hv, we just divide that out from Planck’s equation, then add up all the contributions of energies higher than the band gap:

Photovoltaics: Testing Solar Cells 44
Equation 2.2 from Shockley paper, Qs

Shockley paper: http://metronu.ulb.ac.be/npauly/art_2014_2015/shockley_1961.pdf

The total power we can get out, assuming all of this absorbed energy is converted into electricity, is this number of photons multiplied by the area we’re interested in, multiplied by how much energy each of those photons is carrying:

Photovoltaics: Testing Solar Cells 45
Equation 2.4 from Shockley paper, output power
The last step we need is to compare our output to what was put in. For the incident power, all we do is take Planck’s law and sum up all the contributions over the spectrum:
Photovoltaics: Testing Solar Cells 46
Equation 2.6 from Shockley paper, Ps is the total energy density falling upon unit area in unit time for blackbody radiation at temperature T8

If we divide output power by input power, we get efficiency:

Photovoltaics: Testing Solar Cells 47
Equation 2.8 from Shockley paper

This equation might look intimidating, but the important thing is its shape, and where the efficiency is maximized.

The graph below gives us both those things.

Photovoltaics: Testing Solar Cells 48
The maximum possible solar cell efficiency for different band gap energies.

Image Source: By Sbyrnes321 – Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=13252694

We can see that the maximum efficiency is around 32-33%, and happens for band gaps between 1.1 and 1.4 eV. This is specific to our sun as a black body of 5800 K. You might remember that the band gap of silicon is 1.11 eV, which falls within this ideal region, holding a maximum theoretical efficiency of about 32%. As the first industrial solar cell material, silicon is, in fact, a really good choice.

Shockley and Queisser did further calculations to improve the realism of their model. They considered radiative recombination, which is when electrons and holes recombine and produce light. They considered black body radiation from the device itself resulting in some losses. They also talked about the importance of incident angle of sunlight, as well as the resistance across the output terminal that results in the most useful electricity compared to heat losses. Finally, they also considered that not all of the light will actually create electron-hole pairs. This is because of the charge recombination we mentioned above, but also because some materials like silicon have to vibrate a certain way in order for light to be absorbed, so only a cross-section of the light with sufficient energy will actually generate hole-pairs. Also, not all of the junction voltage will be gained by the electrons – some of it will be converted to heat as the charge carriers try to make their way out of the depletion region.

To really measure and quantify these effects for different solar cells, sophisticated physical models need to be paired with the right experimental measurements.

Advanced solar simulators, combined with an IV measuring instrument, allow researchers to get the data they need to understand how effects like the above are influencing their solar cell designs.

 Research on modern solar cells focuses on many of the issues that Shockley and Queisser discussed in their seminal paper, as well as trying to find ways to “hack” the limit they calculated.

Some other practical considerations include reflection off the front surface or metal terminals. For example, the calculation they did was for a single-junction photovoltaic cell of a single material (one pair of n-type and p-type semiconductors). One way to improve things is to use multiple materials with multiple junctions, which has resulted in a lot of different so-called multi-junction solar cell designs.

Solar Cell Design

Solar Cell Design Goals

We’ve already talked about a few of the goals engineers and scientists have in mind when designing solar cells, and it’s worth mentioning a few more in order to understand the direction of research and device evolution.

The first main goal of solar cell design is to increase absorption, to get more energy out of each cell. We’ve already mentioned a few of the challenges and limits around this goal. Other things that we want to maximize are charge separation and transport, which means keeping the charges apart until they’ve done what they’re intended to do, as well as maximizing the photovoltage, which, as we’ve discussed already, means that each electron will have a higher energy, and you’ll need less solar cells to do useful work.

The next design goals are closely related to the above, and arise from overcoming unwanted effects that take place in the solar cell. One of these is called surface recombination, where the electric charge carriers reach the surface of the device, and instead of traveling around the circuit where they’re intended, each electron-hole pair comes back together and recombines.

Part of the reason this occurs is that just above the surface of a device, the junction potential doesn’t really exist, so charge carriers are free to take whichever path is easiest to recombine.

A final design goal is to improve solar cell production techniques so that we can mass-produce them more cheaply and offer this source of energy to a wider portion of humanity.

Evolution of Solar Cell Design

After the first solar cell was created in 1954, one of the next big advances in design happened in the 1980s, with the development of so-called black cells. These solar cells increased absorption by lowering the amount of reflected light. They accomplished this by texturing the surface of the solar cell, which is a way of gradually transitioning between air and the solar cell material, minimizing the drastic boundary changes that result in high-amplitude reflections. In the early beginnings of the solar cell industry, the main method for producing silicon crystals was via the Czochralski process, where a single crystal is drawn slowly out of a molten melt. Another method that was much more expensive was the float process, where a single crystal is gradually formed from an existing many-crystal (polycrystalline) rod by moving a molten zone through it and allowing the crystals to join and align.
Photovoltaics: Testing Solar Cells 49
The Czochralski process of silicon crystal growth.
Source: http://www.top-alternative-energy-sources.com/Czochralski-process.html

Also in the 1980s, solar cells were made with silicon dioxide (SiO2) on the front surface, which served as a barrier to prevent carriers from reaching the surface and recombining prematurely.

Because this technique also allowed silicon to have a natural layer of protection from the elements, it became more commercially worthwhile to make solar cells out of the float process, which produced better quality silicon with charge carriers that could travel much farther. With this technique, silicon cells achieved 20% efficiency in 1985.

Another technique to increase absorption was to minimize the area covered by the metal contacts. The metal used to complete the circuit of a solar cell has to attach to the front and back surfaces. The use of point contacts reduces the shadowing of this metal and results in increased absorption. This technique allowed Stanford to achieve 22% efficiency in 1992.

Later, it was realized that point contacts at the rear of the solar cell actually help to prevent recombination at the back of the cell, because the silicon to silicon dioxide interface was easier to produce without defects, compared to the silicon to metal interface. This technique, along with a few other refinements, pushed silicon solar cell efficiency up to 24% in 1994.

A schematic of a solar cell employing many of these techniques is shown below.

Photovoltaics: Testing Solar Cells 50
An example of a solar cell design that features a textured front, an antireflective coating (ARC) and minimal shadowing on the front side (through buried contacts), along with point contacts on the rear and a passivated front SiO2 layer to minimize surface recombination.
Also in the 1980s, solar cells were made with silicon dioxide (SiO2) on the front surface, which served as a barrier to prevent carriers from reaching the surface and recombining prematurely. Because this technique also allowed silicon to have a natural layer of protection from the elements, it became more commercially worthwhile to make solar cells out of the float process, which produced better quality silicon with charge carriers that could travel much farther. With this technique, silicon cells achieved 20% efficiency in 1985. Another technique to increase absorption was to minimize the area covered by the metal contacts. The metal used to complete the circuit of a solar cell has to attach to the front and back surfaces. Use of point contacts reduces the shadowing of this metal, and results in an increased absorption. This technique allowed Stanford to achieve 22% efficiency in 1992. Later, it was realized that point contacts at the rear of the solar cell actually help to prevent recombination at the back of the cell, because the silicon to silicon dioxide interface was easier to produce without defects, compared to the silicon to metal interface. This technique, along with a few other refinements, pushed silicon solar cell efficiency up to 24% in 1994. A schematic of a solar cell employing many of these techniques is shown below. Other techniques abound in the field of photovoltaic design and development. Another such one to reduce shadowing is to bury the metal contacts in the semiconductor material. Another approach to reduce surface recombination at the back surface of a solar cell is to have a heavily doped layer that produces a different kind of junction: a p+-p junction. This is a barrier to electrons that might be produced there, but that we don’t want unless they’re coming around from the other side (and have already flowed through our load). A final technique worth mentioning is called solar concentration (in concentrator photovoltaic cells), where collecting optics focus light onto solar cells. The reasoning behind this approach is that solar cells are more costly to manufacture compared to lenses, so having a smaller footprint of solar cells is worth investigating. However, in practice, it is very difficult to compete with the steady decrease in the price of full-footprint silicon solar cells.
Photovoltaics: Testing Solar Cells 51
Diagram of a solar concentrator, where optics are used to focus onto the solar cell.
Solar concentrators for Concentrated-solar technology systems
Photo of a solar concentrator array.

Multi-Junction Solar Cells

All of the design methods and progress we’ve talked about so far have centered on silicon and a single junction. As you might imagine, there’s no law saying that we have to stick with silicon, nor do we have to stick to a single junction! We’ll talk about alternative materials in the next section (because there’s a lot of ground to cover there), but the multi-junction approach is a general design concept that is pretty easy to understand.

When we were calculating the maximum efficiency of solar cells, we said that a photon with energy greater than the band gap would move a single electron into the conduction band. Any excess energy is mostly converted into heat. That means that all of the sunlight with energy greater than the band gap is not being absorbed very efficiently.

The multi-junction solar cell tries to rectify this inefficiency by presenting multiple band gaps to the incoming sunlight. Basically, it presents a series of materials and junctions to the light, usually starting with the highest energy (shortest wavelength) light at the top of a stack, and working down to the lowest energy (longest wavelength) at the bottom.

Photovoltaics: Testing Solar Cells 52
Light absorption in a single band gap vs a two band gap system. The single gap system won’t absorb photons below a certain energy, and for photons above the band gap energy, the excess is lost as heat. The two band gap system absorbs all three of the photons shown, with minimal heat loss.
Photovoltaics: Testing Solar Cells 53
A comparison of the absorption of a single junction solar cell versus a multi-junction solar cell.
While the greatest power could be extracted from a multi-junction cell if each junction could be optimized independently (and therefore part of its own electrical circuit), this isn’t really practical, and usually the stack has contacts at the top and bottom, and none in the middle. This means that the performance is somewhat constrained because, for example, the currents from each cell have to match one another. However, multi-junction cells allow us to absorb much more of the solar spectrum, with record efficiencies up to 39%. The number of junctions so far has included two-junction, triple-junction, four-junction, five-junction and six-junction solar cells. Multi-junction cells are sometimes called tandem cells, usually when they consist of two materials with very different band gaps. One of the disadvantages and limits of multi-junction devices is that the carriers have to diffuse out to the metal contacts, which limits having a huge stack of junctions. To get around this, some designers have made use of quantum tunneling to create tunnel junctions and allow the carriers to get out to the metal contacts by non-classical means (it’s not quite teleportation, but it’s pretty close).
Photovoltaics: Testing Solar Cells 54
An example of the layer stack in a multi-junction solar cell.
Image Modified from Source: https://pdfs.semanticscholar.org/e528/e2d097e6df1dcfbe5c4ef09c28fd123a12ef.pdf

An Overview of the Materials Used for Solar Cells

We’ve talked a little about some innovative design solutions that researchers have used to try and optimize solar cells, but the other half of the equation is changing the material being used. This opens up quite a wide array of options, each with their own advantages and challenges.

Monocrystalline Silicon Solar Cells

Up to this point, all that we have focused on is monocrystalline silicon; that is, silicon made from a single large crystal, with all the crystal planes and lattice aligned. There’s one thing we haven’t yet mentioned about monocrystalline silicon: it has what is called an indirect band gap. This means that, in order for light to be absorbed and send an electron into the conduction band, there has to be a certain change in vibration in the crystal lattice. This specific vibration is not always going to happen, which makes monocrystalline silicon have a low absorption coefficient.
- For Advanced Users -
The specific vibrations we discuss here are phonons – quantized lattice vibrations. Physicists think of these as particles, and when combined with the photon and the electron, we have a three body interaction which are inherently less likely because they have more moving parts that have to be correct to occur.
What’s more is that temperature affects vibrations, which means that how good or bad silicon is at absorbing light is going to be highly dependent on temperature. To get around the low absorption issue, monocrystalline silicon solar cells have to be fairly thick, to give light as much opportunity as possible to be absorbed. We’ve already talked about the other strategies used, such as light trapping and increasing the optical depth. Silicon, as we can see, is not an ideal material, but we’ve made it work very well. While its band gap energy (1.1 eV) is in the right set of energies for the solar maximum, there’s still some improvement that can be found by choosing a material a higher absorption coefficient and less temperature dependence.
Photovoltaics: Testing Solar Cells 56
Photo of a monocrystalline silicon rod.

Image Source: http://www.tindosolar.com.au/learn-more/poly-vs-mono-crystalline/

III-V Semiconductor Solar Cells

Semiconductors can be made from alloys that contain equal numbers of atoms from groups III and V of the periodic table, and these are called III-V semiconductors.

Group III elements include those in the column of boron, aluminium, gallium, and indium, all of which have three electrons in their outer shell.

Group V elements include those in the column of nitrogen, phosphorous, arsenic, and antimony, all of which have five electrons in their outer shell.

In a III-V semiconductor, atoms arrange into what’s called a zincblende crystal structure, also known as a face-centered cubic structure or cubic closest packing (CCP).

Photovoltaics: Testing Solar Cells 57
The zincblende crystal structure found in III-V semiconductors.

By construction, all the valence electrons in a III-V semiconductor are used up in bonding, so there aren’t any free to conduct. However, by doping in a similar manner to silicon, we introduce impurities that can then make it a semiconductor.

One of the main advantages of III-V semiconductors is that the crystal composition can be varied by replacing some group III atoms with other group III atoms. This changes the bonding and packing distances of the atoms. Why would we want to do this? The reason is that the crystal structure determines the band gap energy. III-V semiconductors, therefore, give us the ability to tune the band gap to our heart’s desire.

The methods by which III-V semiconductors are made include liquid phase epitaxy (LPE), molecular beam epitaxy (MBE), metal organic chemical vapour deposition (MOCVD), and metal organic vapour phase epitaxy (MOVPE), all of which allow for fine control of the make-up and thickness of semiconductor layers. Unfortunately, these methods are also fairly expensive.

Photovoltaics: Testing Solar Cells 58
Diagram illustrating Molecular Beam Epitaxy (MBE), one of the manufacturing methods for III-V semiconductors.
Image Modified from Source: https://www.sciencedirect.com/science/article/pii/B9780124159952000155
You might have guessed that this freedom to tune the band gap means that III-V semiconductors are what researchers use in developing multi-junction solar cells. By far the most widely used III-V solar cell is gallium arsenide (GaAs), which has a band gap of 1.42 eV at room temperature. It’s in the range of the ideal bandgaps for solar absorption, and it has the bonus of having a direct-gap absorption, which means that the lattice vibrations don’t matter in deciding whether or not light will get absorbed. That means its absorption coefficient is about ten times better than silicon, and doesn’t have the same temperature dependence. Other III-V semiconductors include indium phosphide (InP), gallium antimonide (GaSb), aluminium gallium arsenide (AlGaAs), indium gallium phosphide (InGaP), and indium gallium arsenide (InGaAs). In this list we can see how different group III elements are exchanged to make different band gap energies. The exact ratio of one to the other will determine what the final band gap energy will be.
Photovoltaics: Testing Solar Cells 59
III-V semiconductors are the materials that most enable multi-junction solar cells.
Image Modified from Source: https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-20-S2-A319&id=229725
All in all, III-V semiconductors offer a great host of advantages over silicon as a material for photovoltaics. However, the biggest drawback, and one that every new solar technology faces, is cost. The price of silicon is steadily decreasing, and it’s very challenging to compete with that constantly lowering price point, especially when, as in the case of III-V semiconductors, the fabrication methods are so costly. Nevertheless, there are some situations where III-V semiconductors are the best choice for photovoltaics. Many III-V semiconductors exhibit the property of being radiation hard, which means they don’t degrade as quickly under intense radiation. This makes them ideal for space applications, where the ratio of power to mass is more important (because of the cost to launch it), and where any solar cell will have to survive the intense bombardment of the unfiltered sun’s radiation.
Photovoltaics: Testing Solar Cells 60
Image Source: https://www.solarpowerworldonline.com/2016/03/kind-solar-panels-nasa-use/

Thin Film Solar Cells

Monocrystalline silicon and the III-V semiconductor solar cells both have very stringent demands on material quality. To further reduce the cost per watt of energy, researchers sought materials that can be mass-produced relatively easily, and have less stringent demands. The category of thin film solar cells encompasses a variety of techniques with this goal of mass-production in mind (note that it doesn’t necessarily refer to the thickness of the material itself, since some of the other cells we’ve talked about are also very thin).
Photovoltaics: Testing Solar Cells 61
While thin film solar cells refer mostly to mass manufacturability, many are also touted as being thin enough to be flexible.
Image Source: http://globaldaily.com/climasphere/global-challenge-global-solutions-efficient-flexible-thin-film-solar-cells/

In all of these technologies, because of their mass-produced nature, the materials usually have more defects that will prevent the charge carriers from travelling as far as we’d like. To get around or compensate for this issue, materials usually need to be really good light absorbers.

Alternatively, several junctions are used, or the electric potential of the junction is extended to help carriers along, as is done in p-i-n semiconductors which have an intrinsic (undoped) semiconductor layer in the middle.

This solar cell technology produces cells with many defects, making them difficult to dope, and ultimately setting a limit on the junction potential that can be achieved. Defects also make the films more resistive, and overall make the cell’s performance dependent on the density of carriers present. To model this complex behaviour can be very challenging, and is a topic we’ll tackle in the Data Sets & Models section.

Amorphous Silicon (a-Si)

Probably the best-developed thin-film solar cell technology is amorphous silicon, which means silicon that isn’t arranged into a perfect crystal structure. It’s been in commercial production since 1980, and has the immediate advantage of not needing special crystal vibrations in order to absorb light (since the crystal lattices are all mismatched anyway). Therefore it has a direct band gap, and absorbs more strongly than monocrystalline silicon.

Photovoltaics: Testing Solar Cells 62
An illustration of the difference in crystal lattice structure between monocrystalline silicon (left), amorphous silicon (middle) and hydrogen-passivated amorphous silicon (right).
Amorphous silicon does have a problem, because of the mismatched crystal lattices, that some bonds are left dangling. These dangling bonds can interfere with current flow, so often these cells are passivated with hydrogen to latch onto and fill in all the dangling bonds. Although it hasn’t yet achieved the efficiency records of monocrystalline silicon (a-Si currently sits around 10 or 11% efficiency), the less stringent manufacturing methods make amorphous silicon an interesting prospect.

Copper-Indium Gallium Diselenide (CIGS)

It turns out that junctions of CIGS next to CIGS (called homojunctions) don’t have a very high efficiency. A different material is needed for the front, usually cadmium sulfide (CdS), which serves as a window layer to diminish surface recombination.
Of all the materials we know, copper-indium diselenide (CIS) has the highest optical absorption. Its band gap, however, is around 1 eV, so researchers introduced gallium into the lattice to raise the band gap energy closer to the solar ideal. This resulted in the popular copper-indium-gallium diselenide (CuInGaSe2 or CIGS) material for photovoltaic cell construction. CIGS have what’s called a chalcopyrite crystal structure, shown below. They’re made either by vapour deposition, or by “selenising” copper-indium films.
Photovoltaics: Testing Solar Cells 63
The chalcopyrite crystal structure of CIGS.
It turns out that junctions of CIGS next to CIGS (called homojunctions) don’t have a very high efficiency. A different material is needed for the front, usually cadmium sulfide (CdS), which serves as a window layer to diminish surface recombination.
Photovoltaics: Testing Solar Cells 64
CIGS solar cells are some of the best candidates for flexible solar cells.
Having a heterojunction introduces many of CIGS’ main challenges, including lattice differences and diffusion of particles between the materials, both of which distort the energy bands throughout the material. The grains of CIGS crystals also limit how far carriers can move before recombining.

Cadmium Telluride (CdTe)

Cadmium telluride (CdTe) is made from the II-VI group elements, and has a direct band gap of 1.44 eV, making it one of the best-suited materials for photovoltaic applications. It has a wurtzite crystal structure shown below.

Photovoltaics: Testing Solar Cells 65
The wurtzite crystal structure of CdTe.
However, carriers don’t move through the material as well as they do in GaAs cells, partly because of the higher defect density in CdTe. Higher defects also make CdTe harder to dope, although some treatments have been found to deal with their effects (by saturating the defects’ traps). Heating in Cadmium chloride (CdCl2) was discovered to be crucial in improving the material quality of CdTe cells.
Photovoltaics: Testing Solar Cells 66
A photo of CdTe crystals.
Image Source: https://www.5nplus.com/cadmium-telluride.html
Like CIGS, CdTe also performs better with a CdS heterojunction on the front. The heterojunction introduces the same problems here as in CIGS. The higher density of defects in CdTe at the boundaries results in a high dark-current (the unwanted current that flows when no light is shining on a cell) and a low maximum voltage achievable. Nonetheless, the ideal band gap energy of CdTe is excellent for solar cell applications.

Dye-Sensitized Solar Cells

Solar cells that involve liquid dyes are actually quite similar to batteries. There are electrodes at either end, and a substance that is losing an electron while another is gain an electron (oxidation and reduction, also known as redox). The only difference in a solar cell is that the electron loss (into the conduction band) starts with absorption of a photon. In 1991, Gratzel and Regan realized a low-cost solar cell that used liquid dye on a titanium (IV) oxide film. The overall scheme is shown below, and has come to be known as a general approach of dye-sensitized solar cells.
Dye sensitized solar cell - cathode - liquid - anode
The process of light absorption and electrical transfer in a dye-sensitized solar cell.
Image modified from Source: https://www.gamry.com/application-notes/physechem/dssc-dye-sensitized-solar-cells/
The basic process goes like this: a dye molecule (D) absorbs light and becomes (D*). One of its electrons is now in the conduction band, and moves away from D* (leaving D+). It then moves through the wire from the anode to the cathode. On its way there, it travels through a load and does useful work for us. When it gets to the cathode, it’s absorbed by an oxidizer (Ox) (often iodide). The oxidizer, in turn, replaces the electron needed by D+. The presence of a liquid, however, made dye-sensitized solar cells not very attractive to researchers, because they could freeze and generally suffered from more instability than other types of solar cells. They also have short transport properties, meaning they don’t respond rapidly enough to capture as much energy as possible. However, they are still being studied and have made great progress, achieving efficiencies as high as about 12%. Some studies that limit the travel distance of carriers are looking very promising as well. An interesting early application of dye-sensitized solar cells was in sunglasses that could power devices. The lenses were the solar cells.
Photovoltaics: Testing Solar Cells 67
A dye-sensitized solar cell made the lenses of these glasses that could then charge devices.
Image Source: https://www.yankodesign.com/2008/12/17/solar-powered-solar-panel-sun-glasses/
Finally, dye-sensitized solar cells have also acted as an important stepping stone toward one of the most studied types of solar cells today: perovskites.

Perovskite Solar Cells

A Russian mineralogist named Lev A. Perovski discovered a class of materials that were, some time later in 2009, discovered to be useful in solar cells. Originally they were studied for ferroelectricity and superconductivity. These materials bear his name and are known as perovskites.

They follow the general formula ABX3, where A and B are both positive ions (cations) located in different parts of an octahedral configuration (where six atoms surround a central one). Usually A is divalent (with 2 electrons in its outer shell), while B is tetravalent (with 4 electrons in its outer shell). X, meanwhile, is a negative ion (anion) that is usually either oxygen or a halogen. The A atom is usually located in the center of a cube of an octahedral crystal near 12 anions, while the B atom is at one of the actual octahedral sites with 6 anions. The diagram shows this unique 3-dimensional structure.

Photovoltaics: Testing Solar Cells 68
The octahedral ABX3 crystal structure of perovskites.
Perovskites, which being ionic dissolve easily in polar solvents, first started as a type of dye-sensitized solar cell, when a methylammonium lead halide perovskite was adsorbed onto titanium (IV) oxide. Like other dye-based solar cells, it exhibited instability and had a fairly low efficiency of 3-4%. In 2012, however, a long-term stable perovskite solar cell was developed by replacing the liquid electrolyte with a solid hole (p-type) conductor. That led to a marked increase in efficiency and interest in the material which pushed the efficiencies above 20%.
Photovoltaics: Testing Solar Cells 69
Diagram showing light absorption and structure of a solid-hole-conductor perovskite cell.
Image modified from Source: https://cen.acs.org/articles/94/i18/future-low-cost-solar-cells.html
Saule Technologies – Inkjet-Printed Perovskite Solar Cells
Perovskite solar cells are another candidate for thin, flexible solar cells.

Image Source: https://sauletech.com/press/

What makes perovskites particularly interesting is that the band gap depends on how flat or two-dimensional the lattice is, so it gives researchers the ability to find the optimal band gap as is done with III-V semiconductors. In contrast to III-V semiconductors, however, perovskites are substantially cheaper. Because of these two combined factors, perovskite technology was selected as one of the biggest scientific breakthroughs of 2013 by the editors of both Science and Nature.

Photovoltaics: Testing Solar Cells 70
Perovskite solar cells could be the low-cost, easy-to-manufacture solution sought by the industry.
Image Source: http://www.ox.ac.uk/news/2016-10-05-non-toxic-solvent-removes-barrier-commercialisation-perovskite-solar-cells
Currently, organo-lead perovskites are at the center of perovskite research. They’ve benefitted from all the research already done in dye-sensitized solar cells, and offer additional advantages of broad spectral absorption, low recombination losses, and the ability to process them in liquid solutions (which is the reason why they’re inexpensive). An example of a modern perovskite solar cell is shown below.
Photovoltaics: Testing Solar Cells 71
Typical material sandwich in a perovskite solar cell.

Organic Solar Cells

Perovskites already use some organic elements (which include carbon, hydrogen, nitrogen and oxygen), but there are other solar cells in development that fall purely on the organic side of the chemistry spectrum. The driving motivation behind organic solar cell development is that the materials would be cheap, as would the production, because mass-producing carbon chains is technology that is well developed in, for example, plastics.

These solar cells have benefited from advances in the development of LEDs based on similar technology, but they still have substantial development ahead in order to be competitive with silicon.

While there are a wide variety of organic solar cell materials, the majority rely on organic molecules with sp2 hybridization – that is, carbon double bonds. The electrons of these double bonds can move to fill in positive charge gaps, which makes the materials hole conductors. Usually they have a band gap around 2 eV, which isn’t ideal for solar absorption.

Photovoltaics: Testing Solar Cells 72
Photovoltaics: Testing Solar Cells 73
Process of electron and energy transfer in an organic solar cell.
Recently there’s been a lot of focus around organic solar cells using fullerenes, which are a large series of carbon rings attached together in a configuration like a soccer ball (or football).
Photovoltaics: Testing Solar Cells 74
Typical structure and materials in organic solar cells.
Another challenge faced by organic solar cells is that charge carriers generally don’t travel very far, and the mobility of charge carriers in general is not as strong as it is in traditional semiconductors. They do have a relatively high absorption coefficient, but are still limited to efficiencies between 9-11%.

Graphene Solar Cells

A particular type of organic material used in solar cells is worth discussing because of the particularly high research interest in it: graphene. Graphene is a form of carbon with alternating double-bonds that form a two-dimensional honeycomb sheet. It was discovered in 2004 by Andre Geim and Konstantin Novoselov at the University of Manchester, who isolated it by peeling a layer off graphite (pencil lead) using scotch tape. They eventually won the Nobel prize for it in 2010.
Photovoltaics: Testing Solar Cells 75
The atom structure of graphene, forming infinite two-dimensional sheets.

While graphene is stronger than steel and highly conductive (due to the array of double bonds), it has a few other properties that make it particularly useful for solar cells. It is both very flexible and optically transparent (absorbing 2.3% of incident light from UV to IR), making it ideal for application in thin-film solar cells.

 

Remember that, in order to capture the current out of the absorption region of a solar cell, we have to run wires from the top to the bottom of the cell, passing through our load on the way. These wires shadow the front surface and decrease the overall light hitting our active area.

 

Graphene, on the other hand, can be applied as a collector to the front surface, and will serve to transmit much more of the light without shadowing, while still capturing and conducting the charge coming out of the absorption region. Its flexibility allows it to be used in thin-film solar cells, particularly in perovskites, where the main collector used is Indium Titanium Oxide (ITO), a brittle glass that cannot be bent without breaking. Graphene thus unlocks more of the potential benefits of perovskite flexibility.

 

Graphene has also been used to increase photon collection efficiency (PCE) in the perovskite active material itself, with some doped graphene allowing larger perovskite grains to form on the carbon network. In this role, it has been used as a carrier transport material.

 

Finally, it has also been used to protect the unstable perovskite films, because graphene has better physical, chemical, and thermal stability. While graphene by itself doesn’t make a solar cell, in combination with other material properties it unlocks a lot of potential advances.

The Economics of Silicon & the Challenge of Research

As you might have already figured out, photovoltaics is a huge and interesting field of research that, as we’ve said, will play a major role in humanity’s energy future. We also mentioned above that there’s been so much development on monocrystalline silicon solar cells that there’s a steady trend of decreasing price, known as Swanson’s law.

Photovoltaics: Testing Solar Cells 77
Silicon solar cells drive the economics of the photovoltaics industry.

The cost per watt is one of the bottom line metrics in the energy industry. The economies of manufacturing silicon have come very far since the invention of the first solar cell; so far, in fact, that much of the cost is in the installation and accompanying overhead rather than the cost of the devices themselves. The cost per watt for silicon dipped below a US-dollar years ago, and will continue to go down.

Photovoltaics: Testing Solar Cells 78
For researchers of new photovoltaic technologies to be competitive in the market, they need rapid access to accurate data about their devices.
Image Source: http://gunam.metu.edu.tr/

Silicon’s dominance in the market can make it very challenging for new photovoltaic technologies to gain traction. Therefore, it’s crucial that researchers get the most accurate data possible, as quickly as possible.

G2V Optics’ LED Solar Simulators

At G2V Optics, we have the technology and expertise to meet the need for fast, accurate solar cell testing data. With our class-leading, high precision solar simulators, researchers can test their solar cells accurately and under controlled and reproducible conditions.

pico.

Small Area Solar Simulator

sunbrick.

Large Area Solar Simulator

Additionally, our IV cards allow for a simultaneous capture and parametric scan of a solar cell, so researchers can quickly characterize their devices and generate standard curves without the need for multiple tools or pieces of software.

Finally, our devices offer an optional ability to measure spectrally resolved responsivity (SRR) – our low-resolution EQE. The SRR unit is capable of measuring the spectral responsivity or quantum efficiency at the LED wavelengths used in the instrument.

This capability can be used to study the behaviour of different absorber materials within your devices, or to measure the performance of different junctions in a multi-junction solar cell.

This additional information can be crucial for evaluating whether a device meets specifications, and where it might need additional development.

If you’re a researcher in this field, contact us to find out more about how our solar simulation products can help you capture the best data about your photovoltaic devices.

References

Alternative Energy Tutorials. (2019, August). Solar Cell I-V Characteristic and Solar I-V Curves. Retrieved from Alternative Energy Tutorials:
http://www.alternative-energy-tutorials.com/energy-articles/solar-cell-i-v-characteristic.html
American Chemical Society. (n.d.). Energy from the Sun. Retrieved September 4, 2019, from ACS Climate Science Toolkit:
https://www.acs.org/content/acs/en/climatescience/energybalance/energyfromsun.html
Barbarino, M. (2018, September 19). Fusion Energy in the 21st Century: Status and the Way Forward. Retrieved from IAEA News:
https://www.iaea.org/newscenter/news/fusion-energy-in-the-21st-century-status-and-the-way-forward
Born to Engineer. (2017, August). What are the Most Efficienct Forms of Renewable Energy. Retrieved September 4, 2019, from Born to Engineer:
https://www.borntoengineer.com/efficient-form-renewable-energy
Brain, M. (n.d.). How Semiconductors Work. Retrieved September 3, 2019, from HowStuffWorks:
https://electronics.howstuffworks.com/diode.htm
Branson, J. (2013, April 22). Black Body Radiation. Retrieved from Quantum Physics 130 Notes:
https://quantummechanics.ucsd.edu/ph130a/130_notes/node48.html
Burns, C. (2008, December 17). Solar Powered Solar Panel Sun Glasses. Retrieved September 4, 2019, from Yanko Design:
https://www.yankodesign.com/2008/12/17/solar-powered-solar-panel-sun-glasses/
Cao, Y., Liu, Y., Zkeeruddin, S. M., Hagfeldt, A., & Gratzel, M. (2018, June 20). Direct Contact of Selective Charge Extraction Layers Enables High-Efficiency Molecular Photovoltaics. Joule, 2(6), 1108-1117. doi:
https://doi.org/10.1016/j.joule.2018.03.017
Coates, E. (n.d.). Introduction to diodes. Retrieved September 3, 2019, from Learnabout Electronics:
http://www.learnabout-electronics.org/Semiconductors/diodes_20.php
Commonwealth of Australia. (n.d.). Greenhouse Effect. Retrieved September 4, 2019, from Understanding Climate Change:
https://www.environment.gov.au/climate-change/climate-science-data/climate-science/greenhouse-effect
Cotal, H., Fetzer, C., Boisvert, J., Kinsey, G., King, R., Hebert, P., . . . Karam, N. (2009). III-V multijunction solar cells for concentrating photovoltaics. Energy & Environmental Science, 174-192. Retrieved from
https://pdfs.semanticscholar.org/e528/e2d097e6df1dcfbe5c4ef09c28fd123a12ef.pdf
Editors. (2013). Newcomer Juices Up the Race to Harness Sunlight. Science, 342(6165), 1438-1439.
https://doi.org/10.1126/science.342.6165.1438-b
Elert, G. (n.d.). Blackbody Radiation. Retrieved September 4, 2019, from The Physics Hypertextbook:
https://physics.info/planck/
Energy Information Administration. (2009). Annual Energy Outlook 2009 With Projections to 2030. Washington, DC: U.S. Department of Energy. Retrieved from
http://large.stanford.edu/publications/coal/references/docs/0383(2009).pdf
Gamry Instruments. (n.d.). DSSC: Dye Sensitized Solar Cells. Retrieved September 4, 2019, from Gamry Instruments Application Notes:
https://www.gamry.com/application-notes/physechem/dssc-dye-sensitized-solar-cells/
Green Rhino Energy. (n.d.). Concentrating Photovoltaics (CPV). Retrieved September 3, 2019, from Green Rhino Energy:
http://www.greenrhinoenergy.com/solar/technologies/pv_concentration.php
Green, M. A., Dunlop, E. D., Levi, D. H., Hohl-Ebinger, J., Yoshita, M., & Ho-Baillie, A. W. (2019, July). Solar cell efficiency tables (version 54). Progress in Photovoltaics, 27(7), 565-575. doi:
https://doi.org/10.1002/pip.3171
Gunam. (n.d.). GUNAM – Center for Solar Energy Research and Applications. Retrieved September 3, 2019, from Gunam:
http://gunam.metu.edu.tr/
Harper, D. (n.d.). solar (adj.). Retrieved September 4, 2019, from Online Etymology Dictionary:
https://www.etymonline.com/word/solar
Honsberg, C., & Bowden, S. (2019). Retrieved from Photovoltaics Education Website:
http://www.pveducation.org/
Hoppe, H., & Sariciftci, N. S. (2004). Organic solar cells: An overview. Journal of Materials Research, 19(7), 1924-1945. doi:
https://doi.org/10.1557/JMR.2004.0252
IEA. (2018). Global Energy & CO2 Status Report. International Energy Agency. Retrieved September 4, 2019, from
https://www.iea.org/geco/
Intergovernmental Panel on Climate Change. (2018). Global warming of 1.5 degrees C. Switzerland: IPCC. Retrieved September 4, 2019, from
https://report.ipcc.ch/sr15/pdf/sr15_spm_final.pdf
IRENA and IEA-PVPS. (2016). End-of-life management: Solar Photovoltaic Panels. International Rewable Energy Agency (IRENA). Retrieved September 4, 2019, from
https://www.irena.org/publications/2016/Jun/End-of-life-management-Solar-Photovoltaic-Panels
Jacoby, M. (2016, May 2). The future of low-cost solar cells. Retrieved from Chemical & Engineering News:
https://cen.acs.org/articles/94/i18/future-low-cost-solar-cells.html
Jordehi, A. R. (2016q). Parameter estimation of solar photovoltaic (PV) cells: A review. Renewable and Sustainable Energy Reviews, 61, 354-371. doi:
https://doi.org/10.1016/j.rser.2016.03.049
Juno Publishing and Media Solutions Ltd. (2012, December 10). Sharp claims record 37.7% efficiency for non-concentrator solar cell. Retrieved from Semiconductor Today:
http://www.semiconductor-today.com/news_items/2012/DEC/SHARP_101212.html
Kashyap, S. (n.d.). Retrieved September 3, 2019, from Satish Kashyap:
http://www.satishkashyap.com/
Krishnan, A. (2017, January 9). Understanding Current-Voltage Curves of Non-Linear Devices. Retrieved from All About Circuits:
https://www.allaboutcircuits.com/technical-articles/understanding-i-v-curves-of-non-linear-devices/
Kuphaldt, T. R. (n.d.). Lessons in Electric Circuits – Calculating Electric Power. Retrieved September 4, 2019, from All About Circuits:
https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/calculating-electric-power/
Lim, E. L., Yap, C. C., Jumali, M. H., Teridi, M. A., & Teh, C. H. (2018). A Mini Review: Can Graphene Be a Novel Material for Perovskite Solar Cell Applications? Nano-Micro Letters, 10(27), 1-12. doi:
https://doi.org/10.1007/s40820-017-0182-0
Lin, C.-C., Chen, H.-C., Tsai, Y. L., Han, H.-V., Shih, H.-S., Chang, Y.-A., . . . Yu, P. (2012). Highly efficient CdS-quantum-dot-sensitized GaAs solar cells. Optics Express, 20(S2), A319-A326. doi:
https://doi.org/10.1364/OE.20.00A319
Martin-Palma, R. J., & Lakhtakia, A. (2013). Chapter 15 – Vapor-Deposition Techniques. In Engineered Biomicry (pp. 383-398).
Mele, E. (2019, June 5). Structure – Zinc Blende (ZnS). Retrieved from Chemistry LibreTexts:
https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Map%253A_Inorganic_Chemistry_(Housecroft)/06%253A_Structures_and_energetics_of_metallic_and_ionic_solids/6.11%253A_Ionic_Lattices/6.11E%253A_Structure_-_Zinc_Blende_(ZnS)
Meroli, S. (2019, September 3). Czochralski vs Float Zone: growing mono-crystalline silicon. Retrieved from Stefano Meroli: Life of an engineer at CERN:
http://meroli.web.cern.ch/Lecture_silicon_floatzone_czochralski.html
Morris, M. (2003). Electron-hole pair (EHP) generation. Retrieved from Semiconductor theory:
http://www.science-campus.com/engineering/electronics/semiconductor_theory/semiconductor_5.html
NASA. (n.d.). Climate Change: How Do We Know? Retrieved September 3, 2019, from Global Climate Change: Vital Signs of the Planet:
https://climate.nasa.gov/evidence/
National Programme on Technology Enhanced Learning (India). (2019, June 5). The Octet Rule. Retrieved from Chemistry LIbreTexts:
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Electronic_Structure_of_Atoms_and_Molecules/Electronic_Configurations/The_Octet_Rule
Nature, V. E. (2013). 365 days: Nature’s 10 – Ten people who mattered this year. Nature. Retrieved September 4, 2019, from
https://www.nature.com/news/365-days-nature-s-10-1.14367
Nave, R. (n.d.). Doped Semiconductors. Retrieved September 3, 2019, from HyperPhysics:
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/dope.html
Nelson, J. (2003). The Physics of Solar Cells. London, UK: Imperial College Press. Retrieved from
https://www.worldscientific.com/worldscibooks/10.1142/p276
Nicol, W. (2018, November 15). What is graphene? Retrieved September 23, 2019, from Digital Trends: Emerging Tech:
https://www.digitaltrends.com/cool-tech/what-is-graphene/
NREL. (n.d.). Best Research-Cell Efficiency Chart. Retrieved September 4, 2019, from NREL Photovoltaic Research:
https://www.nrel.gov/pv/cell-efficiency.html
NREL. (n.d.). The History of Solar. Retrieved September 4, 2019, from US DOE Energy Efficiency and Renewable Energy:
https://www1.eere.energy.gov/solar/pdfs/solar_timeline.pdf
O’Regan, B., & Gratzel, M. (1991). A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO2 films. Nature, 353, 737-740. Retrieved from
https://www.nature.com/articles/353737a0
Partain, L., Hansen, R., Hansen, S., Bennett, D., Newlands, A., & Fraas, L. (2016). ‘Swanson’s Law’ plan to mitigate global climate change. 2016 IEEE 43rd Photovoltaics Specialists Conference (PVSC).
https://doi.org/10.1109/PVSC.2016.7750284
Paschotta, R. (n.d.). Band Gap. Retrieved September 4, 2019, from RP Photonics Encyclopedia:
https://www.rp-photonics.com/band_gap.html
Service, R. F. (2018, April 23). Solar cells that work in low light could charge devices indoors. Retrieved September 4, 2019, from Science:
https://www.sciencemag.org/news/2018/04/solar-cells-work-low-light-could-charge-devices-indoors
Shockley, W. (1922). The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors. The Bell System Technical Journal, 28, 435-454. Retrieved September 4, 2019, from
https://archive.org/details/bellsystemtechni28amerrich/page/434
Shockley, W., & Queisser, H. (1961). Detailed Balance Limit of Efficiency of p-n Junction Solar Cells. Journal of Applied Physics, 32. doi:
https://doi.org/10.1063/1.1736034
Solar Cell Central. (n.d.). P/N Junctions and Band Gaps. Retrieved September 3, 2019, from Solar Cell Central:
http://solarcellcentral.com/junction_page.html
Solar Cell Central. (n.d.). Solar Efficiency Limits. Retrieved September 3, 2019, from Solar Cell Central:
http://solarcellcentral.com/limits_page.html
SparkFun. (n.d.). Diodes. Retrieved September 4, 2019, from SparkFun Electronics:
https://learn.sparkfun.com/tutorials/diodes/all
Study.com. (n.d.). Incident Ray: Definition & Overview. Retrieved September 4, 2019, from Study.com:
https://study.com/academy/lesson/incident-ray-definition-lesson-quiz.html
Sustainia. (2016, November 3). Global Challenge, Global Solutions: Thin-Film Solar Cells. Retrieved from Global Daily:
http://globaldaily.com/climasphere/global-challenge-global-solutions-efficient-flexible-thin-film-solar-cells/
The Editors of Encyclopaedia Britannica. (n.d.). Photoelectric Effect. Retrieved September 4, 2019, from The Encyclopaedia Britannica:
https://www.britannica.com/science/photoelectric-effect
The Editors of Encyclopaedia Britannica. (n.d.). Photovoltaic effect. Retrieved September 4, 2019, from The Encyclopaedia Britannica:
https://www.britannica.com/science/photovoltaic-effect
The International Energy Agency (IEA). (2018). World Energy Outlook (WEO) 2018. IEA. Retrieved from
https://webstore.iea.org/world-energy-outlook-2018
The Physics Classroom. (n.d.). Charge Interactions. Retrieved September 4, 2019, from Static Electricity – Lesson 1 – Basic Terminology and Concepts:
https://www.physicsclassroom.com/class/estatics/Lesson-1/Charge-Interactions
The World Bank. (201). Life expectancy at birth, total (years). Retrieved from The World Bank Data:
https://data.worldbank.org/indicator/sp.dyn.le00.in
The World Bank. (2017). Number of infant deaths. Retrieved from The World Bank Data:
https://data.worldbank.org/indicator/SH.DTH.IMRT
The World Bank. (2018). GDP (current US$). Retrieved from The World Bank Data:
https://data.worldbank.org/indicator/NY.GDP.MKTP.CD
Tokyo Chemical Industry UK Ltd. (n.d.). Organic Solar Cell (OPV) Materials. Retrieved September 4, 2019, from Tokyo Chemicl Industry UK Ltd – Materials Science:
https://www.tcichemicals.com/eshop/en/gb/category_index/12802/
Top Alternative Energy Sources. (n.d.). The Czochralski Process. Retrieved September 3, 2019, from Top Alternative Energy Sources:
http://www.top-alternative-energy-sources.com/Czochralski-process.html
United Nations. (2018, October 22). The Paris Agreement. Retrieved from United Nations Framework Convention on Climate Change:
https://unfccc.int/process-and-meetings/the-paris-agreement/the-paris-agreement
University of Cambridge. (n.d.). Direct and Indirect Band Gap Semiconductors. Retrieved September 4, 2019, from Teaching & Learning Packages Library – Introduction to Semiconductors:
https://www.doitpoms.ac.uk/tlplib/semiconductors/direct.php
University of Oxford . (2016, October 5). Non-toxic solvent removes barrier to commercialisation of perovskite solar cells. Retrieved from University of Oxford News:
http://www.ox.ac.uk/news/2016-10-05-non-toxic-solvent-removes-barrier-commercialisation-perovskite-solar-cells
Weinberg, I., & Brinker, D. J. (1986). Indium Phosphide Solar Cells – Status and Prospects for Use in Space. NASA. San Diego: 21st Intersociety Energy Conversion Engineering Conference (IECEC). Retrieved September 4, 2019, from
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19860017048.pdf
Wikipedia. (n.d.). Amorphous Silicon. Retrieved September 4, 2019, from Wikipedia:
https://en.wikipedia.org/wiki/Amorphous_silicon
Wikipedia. (n.d.). Cadmium Selenide. Retrieved September 4, 2019, from Wikipedia:
https://en.wikipedia.org/wiki/Cadmium_selenide
Wikipedia. (n.d.). Shockley-Queisser Limit. Retrieved September 4, 2019, from Wikipedia:
https://en.wikipedia.org/wiki/Shockley%E2%80%93Queisser_limit
William Shockley, H. J. (1961). Detailed Balance Limit of Efficiency of p-n Junction Solar Cells. Journal of Applied Physics, 32(3). doi:
https://doi.org/10.1063/1.1736034