How do holes in semiconductor carry heat?

[davidvu]

This question is about seebeck effect.
If the movement of hole(positive charge) happens because of electrons moving in opposite direction, how is the heat carried by hole when one side of p-type semiconductor is heated?
Is it from lattice vibration?

 

[PhysTech]

This question is about seebeck effect.
If the movement of hole(positive charge) happens because of electrons moving in opposite direction, how is the heat carried by hole when one side of p-type semiconductor is heated?
Is it from lattice vibration?

When you have an electrically conductive medium (doped semiconductor or metal), conduction of heat occurs by motion of electrons/holes as well as lattice vibrations. The relative contributions depends on the electrical ($\sigma$) and thermal ($\kappa$) conductivities. Energy does not necessarily flow in the direction of the flow of electrons. In the absence of an external voltage, the only way electrons and holes in semiconductors can move around is through "diffusion." In other words, they migrate from a region of high concentration to a region of low concentration.

The concentration of the holes, produced as a result of thermal excitations, is higher on the hotter side of the p-type semiconductor. Since holes are nothing but electron vacancies in the valence band, there are more vacancies on the hotter side. Electrons in the valence band on the colder side "see" these vacancies and hence move to the hotter side, thus leaving vacancies in the colder side. As you may have already realized, I just described the propagation of a hole, in terms of explicit electron motion, from the hotter side to the colder side.

One thing to note is that the electrons go from a higher energy to a lower energy. This means that the electrons which traveled from the colder side to the hotter side went from a higher energy state to a lower energy state; i.e. they lost the excess energy to the colder side. This effectively led to a transfer of energy from the hotter to colder side.

 

[davidvu]

One thing to note is that the electrons go from a higher energy to a lower energy. This means that the electrons which traveled from the colder side to the hotter side went from a higher energy state to a lower energy state; i.e. they lost the excess energy to the colder side. This effectively led to a transfer of energy from the hotter to colder side.

Your explanation that "The concentration of the holes, produced as a result of thermal excitations, is higher on the hotter side of the p-type semiconductor" and "electrons on the colder side moving to the hotter side" is really nice and helps me a lot in understanding the flow of electrons in the p-type semiconductor. But it's the hot side that is heated, and that heat travels to the cold side(some say it's carried by holes) in the opposite direction of electrons. My question is whether that heat travels to cold side from lattice vibration. Could you please expand on your explanation in quote once more? Thank you very much for your help!

 

[PhysTech]

Your explanation that "The concentration of the holes, produced as a result of thermal excitations, is higher on the hotter side of the p-type semiconductor" and "electrons on the colder side moving to the hotter side" is really nice and helps me a lot in understanding the flow of electrons in the p-type semiconductor. But it's the hot side that is heated, and that heat travels to the cold side(some say it's carried by holes) in the opposite direction of electrons. My question is whether that heat travels to cold side from lattice vibration.

Yes, it does. I already mentioned this in the first line "When you have an electrically conductive medium (doped semiconductor or metal), conduction of heat occurs by motion of electrons/holes as well as lattice vibrations." It's possible that you missed it because it was not the focus of my post. Also, I was under the impression that you were only having trouble thinking of heat conduction in terms of holes.

Could you please expand on your explanation in quote once more? Thank you very much for your help!

Here're the explanations for the lines in quotes:

(1) "The concentration of the holes, produced as a result of thermal excitations, is higher on the hotter side of the p-type semiconductor"

At finite temperatures any kind of semiconductor, intrinsic or doped, has a certain amount of electrons and holes in the conduction and valence bands respectively. These electron-hole pairs are the result of the electrons in the valence band gaining sufficient energy to overcome the band gap. Therefore, it makes sense that as temperature increases the number of such electron-hole pairs created would also increase. If you want a more rigorous analysis you can refer to equations (23) and (24) in chapter 1 of:

https://www.amazon.com/dp/0471143235/?tag=pfamazon01-20

For the sake of convenience I will repeat it here. The density of holes ($p$) is given by

p = 2\left(\frac{2\pi m^* k_B T}{h^2}\right)^{3/2} \exp\left(-\frac{E_F - E_V}{k_B T}\right)

where $m^*$, $k_B$, $T$, $h$, $E_F$, and $E_V$ are effective mass of the hole, Boltzmann constant, temperature, Planck's constant, Fermi energy, and energy at the edge of the valence band respectively. You don't need to worry about the full expression or where it comes from (in case you don't already know). The important thing to note is the dependence of $p$ on temperature. It can be very easily verified that $p$ monotonically increases with $T$. This expression holds for both intrinsic and p-doped semiconductors. You can demonstrate that to yourself by taking appropriate limits of $E_F - E_V$.

(2) "electrons on the colder side moving to the hotter side"

Since the concentration of holes on the hotter side is larger than the colder side, as is clearly evident in the above equation, the holes diffuse from the hotter side to the colder side. But as you know, since holes moving in one direction is nothing but valence electrons moving in the other direction, electrons will move from the colder side to the hotter side.