Q & A: How can the Peltier effect work?

I would like to know the basic physics of the Peltier effect. One source says heat has to be absorbed from environment in order to flow into the conductor of higher electrical energy(IEEE Trans Comp&Packaging Tech Vo.l28, no.2, 2005, 218-229). Wikipedia explains that "Depending on the magnitude of the current, heat must accumulate or deplete at the junction due to a non-zero divergence there caused by the carriers attempting to return to the equilibrium that existed before the current was applied by transferring energy from one connect to another". Other sources pretty much say the same thing. How can I explain this in layman's terms(I still don't understand it) (1)How doen electron gain energy from environment when flowing into conductor of higher energy? And,(2)How doen electron lose energy to environment when flowing into conductor of lower energy? Thank you very much in advance.
- Tony Hue (age 22)
Northridge, California

This is a great question.

For background for other readers, the Peltier effect  is the electric-current-driven transfer of heat from one material to another. It's used in many little devices, including quiet no-moving-parts coolers.

Tony raises a really basic question. Why would electrons flow from a low-energy location to a high-energy location, absorbing energy from the environment? Shouldn't they flow "downhill" from the high-energy to low-energy location, dumping some energy to the environment, just like liquid water flows downhill?

Here's the secret: things don't always flow toward the lowest energy (E) place. They flow toward the lowest free-energy (F) place. F takes into account both energy and entropy (S): F=E-ST, where T is the absolute temperature. S is a measure of how many different microscopic states are available.

Thus if the high-energy place is also a place where adding an electron makes enough more S than it did in the low energy place, electrons flowing down the F slope will flow up the E slope. In order for that to happen, you need a junction of two different materials, so that the electron entropy is different in each part.

OK, that sounds way too abstract. In our analogy, is there any case where water flows up, soaking up energy from the environment? Yes, there certainly is. Think of when water evaporates. It flows up, gaining E, a little from gravity but mostly the energy required to break loose from the other molecules. However, it loses F because single molecules running around loose in the gas have much more S than do ones packed into a liquid.

Let's take the question one more step. Why do things tend to flow downhill in E in the first place? It turns out that the general rule is that nature seeks out as many states as it can get to, maximizing total S. If something flows downhill, it loses E, dumping that E into the environment. Heating up the environment increases its S.  Minimizing F turns out to be equivalent to maximizing the total S of the system plus its environment.

Mike W.

(published on 08/04/2012)

Thank you very much for your kind and detailed answer!! Your answer sure helps a lot, but I have more questions. Entropy concept is too difficult for me. Could you please explain this again without involving the environment? I read from a source on the internet that electons travel at different speeds per material due to crystal orientation changes(Bridgman effect?). And that when electrons slow down, the junction becomes cool since the temperature represents the average speed of the particles. Is this explanation OK? Another explanation involving semiconductor is that electrons moving in one way and hole moving in the opposite way have different amount of energy. And that this creates energy flux from one semiconductor to another, either heating or cooling(a little vague for me). Could you please give comments and more explanation on these explanations? One last question is that does a junction gets hot(heat absorption?) or cold(heat rejection?)when current flows from n-type to p-type semiconductor? I apologize for more questions.
- Tony Hue (age 22)
Northridge, California

Hi Tony- I'm not sure I follow all of that, but here are some comments.
It's not really ok to say that the speed of the electrons gives the temperature. In metals, for example, most of the electrons travel very fast because there are so many that the slower-moving states all get filled up.  Even in materials where there are not so many electrons (not-too-heavily-doped semiconductors) the temperature is only related to the typical speed of random motions, not any speed of the systematic current.

With regard to the p-type and n-type, it may help to look at the picture in this article:

In equilibrium, with no current flowing, two opposite processes are in balance. Sometimes an electron and a hole will combine, releasing energy that heats up the material slightly. Sometimes an electron will absorb energy, popping free and leaving a hole. On the average then in each region the numbers of electrons and holes and the amount of thermal energy stays constant. However, in the n region where there are lots of fixed positive charges there are many more free electrons than holes. In the p region, with lots of fixed negative charges, there are a lot more holes than free electrons.

Now let's say you apply a little voltage to make current flow from n to p.  Since the electron charge is defined as negative. that means electrons in the n region are flowing away from the junction. Holes in the p region also flow away from the junction. Near the junction then the density of electron-hole pairs falls below the equilibrium value. So the process of electron-hole recombination releasing energy becomes less frequent there. The process of electron-hole formation absorbing energy continues unchanged. So that region is cooled.

What if you run current from p to n? Then electrons in the n region are carried toward the junction, as are the holes in the p region. You get a denser batch near the junction, increasing the recombination rate. So the junction heats up.

As you can see, in real Peltier devices the arrangement places all the junctions where the current flows from p to n on one side and the junctions where it goes from n to p on the other, pumping heat from one side to the other.

.Mike W.

(published on 08/05/2012)

Hi. I am asking on behalf of my 10 year old son. Well, I guess on my behalf since neither one of us can figure this out. He is researching thermoelectric generation with peltier tiles for a science fair project. The Seebeck Effect.I have read through several of your prior posts and am still not clear on a couple issues. I hope you can help.We remain confused about how the energy differential is converted to electricity. Our understanding of things so far is that the couples are of dissimilar metals because they are "doped" to have either an extra electron or extra hole (missing electron) making them more conductive to each other.Do the valence electrons and holes in the N and P doped pellets move away from the heat towards the cold (faster than movement in the opposite direction) because the energy is lower in the cooler part – looking to find an energy equilibrium? (is this the following downhill you described in post https://van.physics.illinois.edu/qa/listing.php?id=19853&t=how-can-the-peltier-effect-work). So now that the electrons have moved to the cooler side that end is more negatively charged than the warm side? It is at this point that we have electric potential for a circuit?Also, the p and n doped pellets do not touch each other but are connected by another conductor on either side of the peltier tile. Are the valence electron and hole trying to find each other through the mutual conductive connection – is that attraction creating the electric potential?Lastly and related to all of the above, we found this picture on Wikipedia (http://en.wikipedia.org/wiki/Thermoelectric_effect#mediaviewer/File:Thermoelectric_Generator_Diagram.svg) that suggests electrons and holes move away from the cold side to the warm side and there is only a connection between the pellets at the cold (presumably negative side). My son and I eagerly await your help with understanding these remaining issues. Of course I trust and hope that once he figures this out he’ll ask more question….Kind regards,PhilChicago
- Phillip Torres (age 42)
Chicago

Nice questions. Let's have a first crack at them, then you can come back for more clarification. Notice that in that image you cited (below) the electrons flow from hot to cold. So do the holes. The arrows in the circuit show the direction of current flow, which is the same as the hole-flow direction and opposite to the electron flow direction, because it happens that historically the electron charge got defined as negative.

"Thermoelectric Generator Diagram" by Ken Brazier - self-made, based on w:Image:ThermoelectricPowerGen.jpg by CM Cullen (which is GFDL 1.2 and CC-by 2.5 licensed). Licensed under GFDL via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Thermoelectric_Generator_Diagram.svg#mediaviewer/File:Thermoelectric_Generator_Diagram.svg

If the two parts (n and p) were separate, then the temperature difference would drive electrons to the cold end of the n part until the ordinary electrical potential between hot and cold ends in each becomes big enough to drive an equal current back the other way. The same thing happens with holes in the p part. The hot-to-cold electrical potentials in the n and p parts then have opposite signs, since it takes opposite signs of potential to drive negatively charged electrons and positively charged holes back toward the hot end. That's just what you figured out.

Now when you connect that external circuit, the simple electrical potential differences will cause electrons to flow in that circuit, assuming it's made of typical conductors. I think that's the process you describe as "the valence electron and hole trying to find each other through the mutual conductive connection".  Electrons arriving at the cold side of the p region do allow electron-hole recombination to occur there.

Here's another way to help think of it. Although entropy (S) isn't a conserved quantity, it can still flow around. The entropy flow will be from hot to cold. In the n part, the electrons are the thing that carries the entropy. In the p part, the holes carry the entropy.

I hope that helps your son get started.

Mike W.

(published on 03/05/2015)

Mike W., Thank you. Your explanation is very clear and I think in a format that a 5th grader can understand (something we'd just not been able to find yet).Many thanks and keep up the great work,Phil
- Phil (age 42)
Chicago, IL

Thanks for the note!  The wiki images are a huge help in explainig things like this. We should use them more often.

Mike W.

p.s. Here's another old answer that might have something useful for you guys: .

(published on 03/06/2015)