Peltier Effect
Most recent answer: 9/22/2012
Q:
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
- Tony Hue (age 22)
Northridge, California
A:
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.
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)
Follow-Up #1: how do holes carry heat?
Q:
If movements of holes result from electrons moving in the opposite direction,how do holes carry heat away in the p-type semiconductor? Is it from lattice vibration?
- Tony Hue (age 23)
Northridge, Calif. USA
- Tony Hue (age 23)
Northridge, Calif. USA
A:
There are a couple of ways of thinking about this. One is just to retrace the steps of the previous answer. Making carriers (holes and electrons) soaks up some thermal energy. Letting them recombine gives off some energy. So you can think of the carriers as carrying energy from where they're made to where they annihilate.
Another way is to think of the flow of entropy. Now entropy isn't a conserved quantity, so "flow" isn't always a good way to think of how it changes, but it's ok here. The reason is that for small currents the entropy generation due to Joule heating is small compared to the entropy flow. So why would a charge carrier, even a hole, carry entropy? Entropy is a measure of how many different ways (quantum states) things can be arranged. A hole is a missing electron in an almost filled band of states. Which state is empty? There are lots of choices, so there's entropy associated with each hole. As the holes flow, they carry entropy with them. (Conduction electrons are filled states in an almost empty band, again with lots of choices, so they too carry entropy.)
So either way you look at it, the holes carry "heat" with them. (The two ways better agree, otherwise we'd have screwed something up.) The lattice vibrations are not directly involved in this transport. The heat transport does of course end up cooling one side and heating the other, so it ends up affecting the lattice vibrations, which increase with the temperature.
Mike W.
Another way is to think of the flow of entropy. Now entropy isn't a conserved quantity, so "flow" isn't always a good way to think of how it changes, but it's ok here. The reason is that for small currents the entropy generation due to Joule heating is small compared to the entropy flow. So why would a charge carrier, even a hole, carry entropy? Entropy is a measure of how many different ways (quantum states) things can be arranged. A hole is a missing electron in an almost filled band of states. Which state is empty? There are lots of choices, so there's entropy associated with each hole. As the holes flow, they carry entropy with them. (Conduction electrons are filled states in an almost empty band, again with lots of choices, so they too carry entropy.)
So either way you look at it, the holes carry "heat" with them. (The two ways better agree, otherwise we'd have screwed something up.) The lattice vibrations are not directly involved in this transport. The heat transport does of course end up cooling one side and heating the other, so it ends up affecting the lattice vibrations, which increase with the temperature.
Mike W.
(published on 09/22/2012)