# Construction of Peltier tiles

I'm learning about the construction of Peltier tiles from Wikpedia. However, some of the statements in the article are not at all clear.

Two unique semiconductors, one n-type and one p-type, are used because they need to have different electron densities. The semiconductors are placed thermally in parallel to each other and electrically in series and then joined with a thermally conducting plate on each side. When a voltage is applied to the free ends of the two semiconductors there is a flow of DC current across the junction of the semiconductors causing a temperature difference. The side with the cooling plate absorbs heat which is then moved to the other side of the device where the heat sink is. Thermoelectric Coolers, also abbreviated to TECs are typically connected side by side and sandwiched between two ceramic plates. The cooling ability of the total unit is then proportional to the number of TECs in it.

• What does "thermally in parallel to each other and electrically in series" mean for semiconductors? Also, why should they be arranged in this fashion?

• Why does flow of DC current across the junction of semiconductors cause a temperature difference? Which "junction" are they talking about?

Part I:

This voltage produced is very small, around $100\ \mu V$ per degree Kelvin temperature difference. To actually get a big voltage you need to attach many of these pairs of dissimilar metals in series, the same way you would do with batteries to get a bigger total voltage. The Seebeck effect is about using a temperature difference to generate electrical power-- TECs just work in the opposite direction, using electrical power to generate a temperature difference.

If you want to drive the cooling with a relatively big voltage, 5V for example, you would need a lot of junctions in series.

Thermally in parallel just means that the P and N semiconductors are not stacked on top of each other, they are next to each other. Both get hot on the same side so if you stacked them on top of each other you would be placing a cold side against a hot side and negating the useful effect.

Part II:

The gray connection circled in green in the figure below is the junction of the Thermoelectric generator.

Image: by Ken Brazier CC BY-SA 4.0-3.0-2.5-2.0-1.0, via Wikimedia Commons

Hot electrons in the n-type (excess free electrons) semiconductor flow towards the cold side and the same happens with the "holes" in the p-type semiconductor. A way to understand this is by thinking of the free charge carriers as gas molecules (emphasis mine):

To a first approximation, the electrons and holes in a thermoelectric semiconductor behave like a gas of charged particles. If a normal (uncharged) gas is placed in a box within a temperature gradient, where one side is cold and the other is hot, the gas molecules at the hot end will move faster than those at the cold end. The faster hot molecules will diffuse further than the cold molecules and so there will be a net build up of molecules (higher density) at the cold end... If the molecules are charged, the buildup of charge at the cold end will also produce a repulsive electrostatic force (and therefore electric potential) to push the charges back to the hot end.

"The Science of Thermoelectric Materials." Thermoelectrics Group, Northwestern University 2017.

The electric potential that develops is also known as a voltage. V = IR, and there you have your DC current. Running a DC current to create a temperature difference is just the other side of the coin, in the same way an electric generator is essentially an electric motor running in reverse.

The Seebeck coefficient for a metal/metal joint is the temperature-dependence of the interface voltage that reaches thermal equilibrium between two materials, one with higher free charge density than the other. Just as fur and amber result in charge separation when you rub them, so do conductors swap a little bit of charge on contact. The usual kind of electric circuit, with iron wire and copper wire joined in a loop, has no net current resulting from the voltage difference, as long as the two joints are at a common temperature. When, however, you disturb that thermal equilibrium, the voltage at one junction no longer balances that at the other...

OK, now that Seebeck coefficient might be 100 uV/C, a tiny fraction of a volt per Celsius degree. With boiling water and ice, you'd get about 1/100 of a volt total. The effect is reversible, and applying 1/100 of a volt would cause charges to flow, and (like gas being compressed) at one junction the flow causes heat to be generated, while (like gas being expanded) the flow at the other junction causes heat to be absorbed. That's Peltier cooling.

The 'thermally in parallel' claim tells us that a number of dissimilar materials are all connected thermally to a single HOT reservoir at the P-to-N junction, and all connected thermally to a single COLD reservoir at the N-to-P junction.

The 'electrically in series' claim tells us that those junctions are all in series (if there's 100 pairs of them, with 1/100 volt each, you get 1 volt for the device).

It is done in series electrically so drive voltages aren't impractically low for application of significant power, and it is done in parallel thermally so that all the junction pairs pump equal amounts of heat. That makes a (possibly small) temperature difference, but a maximally large heat flow from the apparatus. If all the heat-flow elements WEREN'T thermally in parallel, the cooling would apply somewhere other than your target reservoir.

Now, as to the reason for using semiconductors: the important character of semiconductors is that they can be doped to conduct electricity (and thus complete the electrical circuit that powers the heat pump), AND they can be doped so that the N type has lots of electrons (high concentration of carriers) while the P type has very few N carriers. That maximizes the Seebeck coefficient because it makes a highly asymmetric electron population. Instead of metals and maybe 1 volt power, you can use semiconductors and 10 volt power.

Choosing the 'right' semiconductors also involves mechanical bonding, thermal conductivity (which 'leaks' heat and reduces efficiency), and electrical resistance (which creates waste heat). The electrical bonding is also important, the junctions must carry current in TWO directions, and that requires some ohmic-contact materials wizardry.