Harnessing Heat: building a thermoelectric generator

The Science of Thermoelectric Generators

21 min readAug 1, 2023

Heat is all around us. Air conditioners, ovens, computers, light bulbs, engines, water heaters, and even your own body — these all radiate heat.

Unfortunately, this heat comes at a cost of the efficiency of the overall machine.

A lot of the devices I mentioned have efficiencies ranging from 60% to 80%, which isn’t too bad. But air conditioners, the human body, and incandescent light bulbs have only about 10–25% energy efficiency.

That means that a human body, which takes in 100 joules of energy, will use only 25 joules, with the other 75 being radiated as waste heat.

Waste heat is a pressing issue, found in all areas of life. It also directly contributes to climate change.

It’s estimated that 67% of the energy produced worldwide is wasted, mostly in the form of heat.

This is more than half of our energy. Just . . . gone. 🤯

Waste heat has the potential to be a valuable source of clean energy — if we can figure out how to harness it.

Hey! Feel free to check out this video if you prefer video format! I cover everything except the extremely technical stuff, which you can find at the end of this article :)

Current Solutions

Let’s take a look at some of the current solutions to waste heat, and their effectiveness.

🦾Combined Heat and Power Engines (CHP)
CHP systems produce electricity and useful heat (eg to heat water in homes). These can reach efficiencies of 70–90%, which is quite good. However, since they are an engine in themselves, they don’t really solve the problem of waste heat, merely mitigate it.
🌡️Thermal Energy Storage (TES)
Sometimes this heat can be stored in something such as sand or molten salt. And then this can be converted into electricity through the use of steam turbines, which use the stored heat to heat water and produce steam. The steam rises to turn a turbine, and electricity is generated. The efficiency of these is about 30–40%.
❄️District Heating and Cooling
Essentially this is where they capture the excess heat generated and use it for useful things, such as boiling water. This is actually decently effective, at 70%. However, it is limited because heat is much harder to transport than electricity. They work much better in urban areas.

The ideal solution would be able to convert this heat into electricity, which is a much more usable form of energy. Unfortunately, due to the laws of physics, converting between forms of energies can result in a loss of efficiency.

There are two main ways to do this: steam turbines (which we already talked about — efficiency at around 30–40%) or thermoelectric devices.

Thermoelectric devices: what are they?

Basically, they convert heat directly into electricity. Pretty sick, if you ask me. It’s through something called the Seebeck Effect, which says that when one side of a material is heated, electrons will move away from the heated side, creating current.

To expand a bit more on how these work: heat is essentially electrons moving. The hotter it is, the faster they move. When they start to move faster, they take up more space (they’re bumping into each other, kinda like bumper cars).

And so as a result, there’s not enough space for the electrons in the hot side, so they flow to the cold side.

The really cool stuff happens when you put two such materials together. If you’ve got a material with a stronger current on top and one with a weaker current on the bottom, you can actually make a circuit. Which can be harvested as electricity. 👀

The material property behind this phenomenon is creatively named the Seebeck coefficient, after the man who discovered it, Thomas Johann Seebeck.

The Seebeck coefficient is given by the formula:

S = ΔV / ΔT

Where S is the Seebeck coefficient, delta V is the voltage difference (in volts) and delta T is the temperature difference (in Kelvin).

The Seebeck coefficient is a measure of a material’s ability to generate current from temperature difference. Basically, how well it can do the process we just went over.

And if you want a more in depth explanation, check out this video:

There are 4 factors that determine a material’s applicability for thermoelectric devices, the Seebeck coefficient being one of them. Here’s the full list:

🌡️High Seebeck coefficient
⬇️Low Thermal Conductivity
⚡High Electrical Conductivity
🔋Low charge carrier concentration (of one type — holes or electrons).

But why do we need these properties?

A high Seebeck coefficient is essentially a measure of how well a certain material can demonstrate the Seebeck effect. And the Seebeck effect is the basis of thermoelectric devices, so that one should be pretty self explanatory. However, the factors that follow have a strong influence on the Seebeck coefficient.

We need low thermal conductivity to reduce the amount of heat that is lost from the hot side of the material to the cold side. The greater the temperature difference, the higher the output. So we want to maximize and maintain that temperature difference, which requires thermal insulation because the material will naturally want to equilibrate.

High electrical conductivity allows electrons to flow easily through the material, which is important in order to allow the current to actually be generated. If the material has low electrical conductivity, the current will be very weak and as a result the power output will be small.

Low charge carrier concentration directly affects the Seebeck coefficient, materials with lower concentrations tend to have higher Seebeck coefficients. This is because when the carrier concentration is too high, the charge carriers bump into each other and as a result can’t move very fast. Almost like a crowd of people trying to run somewhere.

The charge carrier concentration has to be of one type. Holes have a positive charge and electrons have a negative charge, so if the material had both it would result in a net neutral charge, and no current generated.

However, the carrier concentration still needs to be high enough that the material has high electrical conductivity, so there is a delicate balance that needs to be struck.

The Pros

So, you’ve got these crazy awesome materials that can convert heat directly into electricity. What are the benefits?

Well to start, thermoelectric devices:

have no moving parts,
are silent,
require limited maintenance, and
have a wide operating temperature range.

Seems decent to me. Plus, we already went over how they are in some regards the best solution to directly solve waste heat (in theory).

The Cons

While these are for sure super cool devices, the efficiency of these things is terrible. I’m talking 5–15%, with the 15% being in the top of the top, still-being-created-in-labs type stuff.

And while yeah, sure, you could say that an extra 15% of the wasted energy is great, you have to factor in the cost of these materials, and then determine if it’s worth it.

When it comes to conversion efficiency, there is a maximum efficiency that is determined by thermodynamics. For heat engines (yes, thermoelectric devices count), it’s the Carnot equation. This describes the maximum theoretical efficiency of a heat engine operating between two temperature reservoirs, and is given by:

η = 1 — (T_c / T_h)

Where η is the Carnot efficiency, expressed as a decimal or percentage, T_c is the temperature of the cold reservoir and T_h is the temperature of the hot reservoir, both measured in Kelvin.

The efficiency of a real heat engine is always less than the Carnot efficiency due to things like heat loss and irreversible processes.

The nature of thermoelectric materials is that they need to have the special properties we talked about, and in order to get that it typically takes a complex combination of a variety of materials. Many of these materials are rare and expensive, which makes this very hard to economically scale.

And also, the manufacturing costs would be through the roof as well. They’re just way too expensive for the small benefits they provide. Additionally, a lot of the materials used aren’t even air stable. Think about that — we can’t even put them in the air. That’s just not scalable.

Many of these thermoelectrics have an optimal temperature range, and outside of that, their efficiency is even lower. But in the real world, we’re likely not going to be able to have that optimum temperature range all the time. So maximizing efficiency is just super challenging.

And the final issue is that most heat is low grade waste heat. Think about our bodies: we emit some heat sure, but it’s not really enough to power a thermoelectric device. Plus, there has to be a large temperature difference to get the maximum output.

I know, this was quite crushing to me when I found out too. 😭If you want to learn more about the feasibility of thermoelectrics, check out this podcast episode 👀:

But despite this tragic realization, I still found the concept of thermoelectrics quite interesting. Plus, if we can get some serious advancements, they maybe truly could live up to all the hype they’ve gotten. (maybe this is wishful thinking, but who knows :))

Building a thermoelectric generator: step by step

I wanted to get first hand experience of these crazy devices :)

1. Getting the raw materials

First off, I’m gonna run through the materials I used real quick.

thermoelectric devices (trust me, I was going to make my own but its REALLY hard to find semiconductors for some reason 🤷‍♂️)
tea lights + lighter
double sided thermally conductive tape
voltmeter
twist on wire connectors
metal container (I used a bread pan)
water + ice + salt

2. Attaching the thermoelectric devices to the metal tin

The first thing I did was attach the thermoelectric devices to the bottom of the metal tin. I did this using the thermally conductive tape, by putting two pieces on the bottom of the device and then sticking it on the tin.

The important thing here is to put the words face down. The letters on the device indicate the cold side - the one that will be facing the cold temperature. I’m planning to put my cold water inside the tray.

3. Setting up the circuit

After attaching the thermoelectric devices, I had to connect them to form a circuit. I did this by cutting then stripping the ends of the wires to make them shorter. Then I used orange twist on wire connectors to connect the adjacent red and black wires. I left the wires a bit longer so I could tape them up and out of the way with electrical tape after.

You’ll also see that I added the voltmeter (blue thing) at the end. All the voltage that’s generated from the thermoelectrics will flow to that voltmeter, which will display the voltage on it. For the actual test, this one wasn’t working because it needed a minimum of 5 voltage input, so we switched to a different voltmeter.

4. Building a stand for the trays

So after I had most of the device itself set up, I needed to make a stand for it. To generate the temperature difference, there would be cold water in the tray and tea lights underneath. So I needed a way to raise the tin up a bit.

I opted for the simplest option and stacked a bunch of wooden boards together, which worked quite well actually. If you want to build this at home yourself, you could do something similar (just be careful as there is fire) or you could build an actual stand out of metal.

5. Safety Measures

I coated my wooden blocks with tinfoil, because they would be close to an open flame and I didn’t want anything back to happen. 😅

I also put a piece of tin foil on the bottom of the tin on top of the thermoelectric devices, to prevent the wires from melting.

And finally, I put a piece of cork, as an insulator, under the ends of the wires to prevent charge from flowing into the tin foil.

6. Adding the tea lights and the cold water

Ok so everything is set up: now it’s time to see how much voltage I can generate. I tested the voltmeter before with a battery, so we know it works.

I arranged my stand (the wooden boards), lit the tea lights underneath it, then placed the metal tin in between the boards with the edges resting on the boards. Then I filled the tin with water, and added ice and salt (salt + ice = extra cold).

Then, after adding my cork under the wires, I used the voltmeter to measure the current. I got a high of 2.4 volts, which is way higher than I was expecting!

Note: when I set this up is was very windy outside so I had to make a wind shield, which might look a bit odd. But it worked. :)

Overall, this was a super fun project to work on. I didn’t realize the problems with thermoelectrics initially, but I still think they are super interesting. But building one and getting to see the voltage output was super cool — especially considering that it was solely a temperature difference that created it!

And after building that, and seeing all the energy that was wasted (from the candles), I wondered, what’s holding the efficiency back?

Increasing the Efficiency of Thermoelectric materials

Given than the efficiency is still really low, how can we maximize it as much as possible — get it closer to 15%? Or even higher? 📈

To recap: we need a material with low thermal conductivity, high electrical conductivity, low carrier concentration, and a high Seebeck coefficient. And remember these are all pretty closely intertwined, so it’s going to be a balancing act.

Choosing the best material class

Given all these factors, let’s take a look at what class of materials would be the best. This will filter out a ton of materials very quickly so is a great first step.

Well, metals won’t work very well, because although they have a high electrical conductivity, they’ve got a high thermal conductivity and a low Seebeck coefficient.

Insulators obviously won’t work because they don’t conduct electricity.

So that leaves us with semiconductors, which are indeed the best choice. Semiconductors have moderate electrical conductivity and Seebeck coefficient, but a high thermal conductivity. So while they’re not the most ideal, they are not lacking in anything, technically.

Generally, heavily doped semiconductors work best, for reasons we’ll dive deeper into later (doping is adding an atom of another element into your material).

Maximizing electrical conductivity and limiting thermal conductivity

The best thermoelectric materials have contradicting properties. If we could find a material that was electrically conductive and thermally insulating, it would be a breakthrough for a huge number of fields, not just thermoelectrics.

As we already talked about, semiconductors are probably the best choice. Semiconductors conduct electricity under certain conditions. To understand what determines these conditions, we have to look at the band structure.

The band structure determines primarily the optical and electrical properties of a material. To give you an understanding of the basics, electrons become excited by energy. That energy can come in many forms, including light.

When an electron becomes excited, it can jump energy levels. If it jumps from the valence band to the conduction band, it becomes a free electron and can carry electricity.

Another important thing to note is that an electron cannot jump between states (aka energy levels), because they are discrete and the only allowed energy levels.

In a metal, which has high conductivity, the valence and conduction bands overlap, meaning that very little energy is required for electrons to move into the conduction band.

In insulators, that band gap is really big, meaning electrons need a very large amount of energy to clear it.

And in a semiconductor, the band gap is quite small. So only a small amount of energy is required for an electron to move into the conduction band.

The effectiveness of a material for thermoelectric applications is determined by ZT, or the figure of merit. The larger the ZT value, the better the thermoelectric properties of the material.

The ZT value depends on the factors we went over before: Seebeck coefficient, electrical conductivity, carrier concentration, and thermal conductivity.

ZT = (S²σT) / κ

Where S is the Seebeck coefficient, σ is the electrical conductivity of the material, T is the absolute temperature of the material (in Kelvin), and κ is the thermal conductivity of the material.

The Seebeck coefficient is given by (assuming the dopant didn’t significantly change the scattering or band structure):

Where kB is Boltzmann’s constant, m* is the effective carrier mass (which is a measure how a charge carrier responds to an electric field — some carriers appear to “weigh” more than others), h is Planck’s constant, and n is the carrier concentration. In semiconductor thermoelectric materials, the Hall carrier concentration can be written as

To increase the ZT value, people have mostly been focusing on defect engineering. Defects are an imperfection in the lattice, whether that be a vacancy (missing atom) or an atom of another element (dopant).

The interesting about defects is that they can actually affect the band structure of materials. When you introduce a defect, depending on whether it is an electron donor or an electron acceptor, it will create a new energy level just above/below the conduction/valence band. This makes the band gap just a tiny bit smaller. And thus, can affect the conductive properties of a material.

Now let’s go through each of the factors that affect the ZT value, and determine how we can change those to increase the ZT value.

1. Optimizing carrier concentration

The main strategy here is doping, of various types. Doping can control the amount of charge carriers and their mobility. With N-type doping, you add an atom that serves an electron donor, and therefore there are more charge carriers. P-type doping, on the other hand, adds more holes, which electrons can fall into. This allows you to add and subtract charge carriers as you desire.

If carrier concentration becomes too high, the carriers may start to scatter off each other to the point that it decreases the conductivity (remember, conductivity is how well charge carriers can more through a material).

2. Carrier mobility

In general, electrons have higher mobility than holes. In most cases, the increase of m* (effective carrier mass) will cause the carrier mobility to decrease, and the conductivity will lower. And usually, the smaller the electronegativity difference between the two atoms, the better the mobility of the carriers in the material.

To compare, undoped original samples have low carrier concentration but high mobility, while uniformly and heavily doped samples have high carrier concentration but low mobility.

When doping, there are bound to be some areas that remain undoped. So there is going to be an energy imbalance between the doped and undoped areas, and the carriers in the sample overflow from the heavily doped area to the undoped area. And this enhances the carrier mobility!

3. Improvement of Effective Quality

(This is a measure of the effectiveness of a material is at converting heat to electricity — closely related ZT, which measures thermoelectric efficiency.)

A larger effective mass of charge carriers will increase the Seebeck coefficient and then the ZT value. A high effective mass affects the states available for charge carriers to occupy energy levels in the crystal lattice. A higher density of states means there are more available energy states for charge carriers to move around.

This increased availability of energy states creates a higher Seebeck coefficient (S) because charge carriers have more options to transition between energy levels, and so their is higher voltage generation in response to a temperature difference.

High energy band degeneracy contributes to effective carrier mass, which results in a higher Seebeck coefficient, and has no negative effect on carrier mobility. Energy band degeneracy is when two or more distinct states of the same system can have the same energy. So, multiple electrons can exist at the same energy.

Degeneracy is closely related to symmetry, and high low symmetry has very low KL (lattice thermal conductivity). So, this means that materials with high symmetry have good thermoelectric performance. This method of recreating the cube structure to get a highly symmetrical crystal is considered to be a feasible approach to achieving more degeneracy and a higher Seebeck coefficient.

Something called resonance states can tend to increase degeneracy in the electronic band structure of the material. Resonance states are a specific electronic state introduced into a material by doping. When dopants are added, they can create energy levels that align with the original energy levels of the material, and those energy levels become degenerate.

If the Fermi energy falls near the centre of the resonance band, it creates lots of available states for electrons at or near the Fermi energy. (Fermi energy is the energy level at which electrons have a 50% chance of occupying at room temperature.) And because there are lots of available energy states at the Fermi energy, there are many free charge carriers, which allows for excellent electrical conductivity.

This dramatically increases the Seebeck coefficient, which is very important for thermoelectric materials.

4. Reduction of Lattice Thermal Conductivity

Reducing the thermal conductivity is the most effective way to increase the ZT value. The lattice thermal conductivity is given by:

(where Cv is the constant volume heat capacity, Vg is the group velocity of the phonon vibration mode, l is the mean free path, and τ is the phonon relaxation time). The main factors are heat capacity, speed of sound, and relaxation time, so by reducing any parameter the lattice thermal conductivity can be reduced.

To reduce the thermal conductivity, we essentially need to limit transportation of phonons. Phonons are the carriers of heat, just like electrons carry electricity.

One way to do this is scattering: where the phonon bumps into something and as a result scatters off in another direction. This is also perhaps the most effective.

The atomic point defects created by element substitution (form of doping) can scatter both short and medium wave phonons quite well. When the size of the defect in the material is close to the mean free path (average distance travelled before colliding with other particles) of the phonon, it will cause more scattering of phonons.

There are various types of scattering, including point defect, dislocation, interface, and resonance scattering.

Point defect scattering (exactly what it sounds like) is a great way to reduce thermal conductivity because it’s much more likely to scatter phonons rather than electrons. This is great because we also need high thermal conductivity for thermoelectrics.

Dislocation scattering is a form of line defect (defect many atoms in length), and will scatter mid and high frequency phonons.

Interface scattering is effective at scattering long wave phonons (which the above scattering methods missed). Interface scattering occurs when the interface (point where two materials/grain boundaries meet) is imperfect.

Resonance scattering is used in thermoelectric materials that have a special crystal structure. A very interesting example would be topological materials. It’s basically adding filler atoms to the material, which causes vibrations of specific frequencies that make phonon scattering much more likely. But this is mostly only applicable to these “special materials.”

Due to the changes in the energy bands and structure caused by the combined effects of the above methods will increase the scattering of phonons at different wavelengths simultaneously.

5. Finding materials with inherently low conductivity

Employing the above methods does significantly increase the ZT value of the thermoelectric materials, however it tends to affect the thermal stability of the material and cause other issues. So, it makes more sense to look for materials that already have intrinsically low thermal conductivity. Most of the thermoelectric materials discovered with an intrinsically low thermal conductivity have a few key traits.

Weak Chemical Bond

The thermal conductivity of a lattice is proportional to the speed of sound, so having a low sound speed performance often helps to improve the thermoelectric properties of the material. Materials with weak bonds have lower sound speed, because the atoms have more space for movement and electron cloud diffusion is more diffuse.

2. Non-Resonance Effect

The non-resonance effect contributes to scattering phonons, which helps to reduce thermal conductivity. A “resonance effect” is the balanced transmission of sound waves (phonons) in a material, where the phonons move uniformly forward, how they would in a perfect lattice. The non-resonance effect occurs when the phonon transport is influenced by external factors, and they move from their equilibrium positions. This causes asymmetry in the material’s crystal structure. The asymmetry in the material’s crystal structure leads to anharmonicity, which is the deviation from harmonic behavior. Anharmonicity causes phonons to interact and scatter, which reduces thermal conductivity.

3. Ionic Liquid Characteristics

Materials with liquid properties typically have low thermal conductivity due to their small heat capacity. By introducing some ions with liquid like characteristics into a solid material, we can disrupt the regular lattice. Ions can have liquid like properties when their intermolecular forces aren’t strong enough to form a solid, but still hold them loosely to form a liquid. This can reduce the lattice vibrations (called phonons, which carry heat.) They can also reduce the mean free path (how far they can travel before being scattered) of these phonons as well.

4. Molecular Weight

Heat capacity, Cv, is the most important factor influencing thermal conductivity, and it is proportional to the lattice thermal conductivity. The more atoms in the primary cell (this is the smallest repeating unit in a crystal lattice), the less the contribution of acoustic branches to the heat capacity, and thus the thermal conductivity. Acoustic branches are vibrational motions of atoms in a crystal lattice. So to summarize, when there are lots of atoms in the primary cell, the contribution of acoustic branches (vibrational movements of atoms) to heat capacity (which strongly influences thermal conductivity) is reduced. And to relate this back to molecular weight, heavier atoms or molecules tend to reduce the effects of acoustic branches.

5. Complex Crystal Structure

The main factors that affect thermal conductivity of a material are heat capacity, sound velocity, and phonon relaxation time. Having a complex crystal structure (when atoms are arranged in an intricate, irregular, or non-repetitive way), not only reduces the contribution of the acoustic branches to the total heat capacity, but also the group velocity of the acoustic branches. The group velocity is the speed at which the collective vibrations of atoms (acoustic branches) move through the material. So reducing both of those things reduces the thermal conductivity.

6. Electron phonon decoupling

Electrons and phonons are connected by electron-phonon coupling. This coupling comes from electrons moving through the material and exchanging energy with the phonons (lattice vibrations) as it goes. The interactions can cause the electrons to scatter, changing momentum and energy. And the lattice vibrations can also be affected by the presence of electrons.

We need to decouple phonons and electrons to allow for tailoring of their conductive properties independently. To do this, a common method is to introduce certain chemical or structural modifications that selectively block phonons while allowing electrons to move freely. (Yes I know this is still quite vague, but to understand we would have to essentially do a case study .)

Decoupling phonons and electrons will also allow us to ensure high charge carrier mobility and a wide bandgap while fully regulating the thermal conductivity. A wide bandgap may seem slightly counterintuitive, however it can actually increase the Seebeck coefficient,

Some materials, including heavily doped semiconductors and some nanostructured materials already have strong electron-phonon decoupling. Yet another reason heavily doped semiconductors tend to be a great choice for thermoelectrics!

Conclusion

There is still lots of room for improvement in thermoelectrics. By employing all the above methods, we are pretty much able to limit phonon transport completely. But the thermal conductivity is not yet at zero. This is because electrons can also carry heat too, unfortunately. So to reduce the thermal conductivity further, we’d have to eliminate that heat transfer somehow. Something that may have potential is having a wide bandgap.

As a recap:

Almost all research in thermoelectrics come down to increasing the Seebeck coefficient, increasing the electrical conductivity, increasing carrier mobility, decreasing carrier concentration, and decreasing thermal conductivity. There are a ton of different methods to do all those things, which go down to the root of the limitation and solve from there. If you’d like a brief synapses of all those methods, I’d recommend skimming through the headings. But I do hope you found all this as interesting as I do!

Thank you so much for taking the time to read about thermoelectrics, I hope you enjoyed :)

If you wanna chat about thermoelectrics or anything energy/material science, connect with me on LinkedIn!