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How does carnot efficiency limit manifest itself in solar cells?


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1 hour ago, studiot said:

But if you choose to define efficiency as the conversion of just radiation the correct frequency, then yes 100% conversion efficiency is possible.

My mistake, apologies.

I meant to say "But if you choose to define efficiency as the conversion of just radiation the correct frequency, then yes 100% conversion efficiency is theoretically possible."

Consider a gambler at las Vegas who claimed he could beat the system.

So he put a dime into the slot, pulled the handle and out came a dollar.

Hey this has a 1000% efficiency he says.

 

Now applying that to radiation say you fired one photon at a time at the photocell and got a small burst of current as a result.

After the first photon converted, you could say that is 100% conversion efficiency.

 

57 minutes ago, Matthew99 said:

Originally, I assumed that the cell would be placed on earths surface, in perfect contact with its surrounding which holds it at temperature.

Assumed maybe, but not stated in your description.

It doesn't matter since a photocell that does not absorb heat will not need to be 'held at temperature'.

However you are still allowing the hot object to radiate sort of according to the the laws of Physics, but disallowing the cold object (photocell) from doing the same thing.

 

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1 hour ago, studiot said:

It doesn't matter since a photocell that does not absorb heat will not need to be 'held at temperature'.

Its temperature can go up, since absorbing non-thermal photons will do work on it. And work can get converted to thermal energy quite easily.

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5 hours ago, swansont said:

Its temperature can go up, since absorbing non-thermal photons will do work on it. And work can get converted to thermal energy quite easily.

Perhaps I did not state my case very clearly.

I was just trying to point out the illogicality of stating that a device which cannot increase in temperature needs any form of cooling, which was matthew's proposal not mine.

It has always been my case that in fact the device must increase in temperature, unless something is actively done to cool it.
Of course any such active cooling automatically becomes part of any thermodynamic system and should be included in any thermodynamic consideration.

If the device needs cooling there must be an energy inflow promoting heating.
But such would run contrary to the proposal that the device converts all energy input to electricity.

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Just pointing out that something does not need to absorb thermal radiation, i.e. heat, in order to heat up. (an issue with our colloquial use of the terminology). A microwave oven would be a common example.

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19 hours ago, swansont said:

The thermodynamic treatment of the energy of a monochromatic source would be work

17 hours ago, swansont said:

I never said that the process would be 100% efficient

In practice, of course not. However, is there a fundamental law of physics forbidding a 100% conversion efficiency of monochromatic light? (as you mention that it could be treated as work)

17 hours ago, swansont said:

No. Some absorptions would create phonons.

Aha 💡 This could be the solution to why the proposed device is impossible. Will this always be the case? For example, is it physically impossible to shine 1.8 eV photons at a semiconductor with a band gap of 1.8 eV and 100% absorptivity and solely generate electron hole pairs?

9 hours ago, studiot said:

I was just trying to point out the illogicality of stating that a device which cannot increase in temperature needs any form of cooling, which was matthew's proposal not mine.

It seems I didn't make it clear enough what I meant by "holding at temperature". In no way I meant that the cold object (solar cell) does not radiate heat off, of course it does. However, if this imaginary device could turn all incident radiation into work and discharge it to an external circuit, it would not be heated by the hot emitter. Now, as the device itself emits radiation, it would cool down. But as it is in perfect contact with its surroundings, it will "be held at temperature" by its surroundings. Nevertheless, as I am not arguing that this device is possible, this objection is meaningless.

 

As to the workfunction & threshold frequency @studiot mentioned:

To what extent is this applicable to this problem? Wikipedia says: " in a semiconductor the minimum photon energy would actually correspond to the valence band edge rather than work function". Thus, if you had a material comprised of infinitely many semiconductors with infinitely many band gaps, you have a band gap for every photon and therefore no threshold frequency, do you?

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5 hours ago, Matthew99 said:

Aha 💡 This could be the solution to why the proposed device is impossible. Will this always be the case? For example, is it physically impossible to shine 1.8 eV photons at a semiconductor with a band gap of 1.8 eV and 100% absorptivity and solely generate electron hole pairs?

At that energy there would be no KE left over, so the electron isn’t going anywhere, and you might need more to satisfy conservation of momentum (especially a factor for indirect bandgap materials).  Some electrons would be dropping back to the ground state.

Plus you will have reflection at the surface.

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17 hours ago, swansont said:

At that energy there would be no KE left over, so the electron isn’t going anywhere

Wouldn't this happen in any case? Due to thermalization, the kinetic energy that electrons have when they are excited up a band gap of 1.8eV upon absorbing a 2eV photon (->2eV KE left) would dissipate almost immediately AFAIK and the electron settles down to the CB edge - so there is no difference to being excited by a 1.8eV photon for the electron

18 hours ago, swansont said:

Some electrons would be dropping back to the ground state

So it is physically impossible to completely omit recombination?

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3 hours ago, Matthew99 said:

Wouldn't this happen in any case? Due to thermalization, the kinetic energy that electrons have when they are excited up a band gap of 1.8eV upon absorbing a 2eV photon (->2eV KE left) would dissipate almost immediately AFAIK and the electron settles down to the CB edge - so there is no difference to being excited by a 1.8eV photon for the electron

Two things. 1) I'm thinking of the case where, owing to thermal motion, that the electron needs a little more than 1.8 eV to reach the conduction band. 2) how does an electron with no KE contribute to a current?

To your point about the electron thermalizing, sure - but this represents another loss mechanism you have to worry about

 

3 hours ago, Matthew99 said:

So it is physically impossible to completely omit recombination?

I don't know how you would do that. Electrons dropping to a lower energy is a spontaneous reaction. The only way to prevent it is to somehow make the lower state unavailable

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On 9/1/2021 at 8:07 AM, Matthew99 said:

Thus, if you had a material comprised of infinitely many semiconductors with infinitely many band gaps, you have a band gap for every photon and therefore no threshold frequency, do you?

What on Earth do you mean by that ?

Surely you are not proposing a periodic table with infinitely many different elements ?

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15 minutes ago, studiot said:

What on Earth do you mean by that ?

Surely you are not proposing a periodic table with infinitely many different elements ?

You can get different bandgaps with different combinations of materials, and varying the doping/stoichiometery. GaAs. AlGaAs, AlGaxAs1-x etc. so there are potentially a quite large number of combinations

But the proposal doesn't consider the possibility of e.g. a 2 eV photon being absorbed by a material with a 1 eV bandgap, or that the material has to be thick enough to absorb all the light if you want maximum efficiency

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4 minutes ago, swansont said:

You can get different bandgaps with different combinations of materials, and varying the doping/stoichiometery. GaAs. AlGaAs, AlGaxAs1-x etc. so there are potentially a quite large number of combinations

But the proposal doesn't consider the possibility of e.g. a 2 eV photon being absorbed by a material with a 1 eV bandgap, or that the material has to be thick enough to absorb all the light if you want maximum efficiency

A large number yes, but enough to cover the entire spectrum as claimed ?

I agree there are many real world constraints on the process of conversion of the energy of photons to electron current and have nothing realy to add to your great job describing these.

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16 minutes ago, studiot said:

A large number yes, but enough to cover the entire spectrum as claimed ?

I agree there are many real world constraints on the process of conversion of the energy of photons to electron current and have nothing realy to add to your great job describing these.

AFAIK you can get materials from essentially zero out to 4 eV. I don't know how closely you approximate a continuum, but from a purely hypothetical standpoint of an ideal case it's not IMO more outrageous than other assumptions one can make. But at some point the practicality has to kick in, since your material is infinitely thick.

 

(edit: see e.g.  https://en.wikipedia.org/wiki/Wide-bandgap_semiconductor 
 https://en.wikipedia.org/wiki/Narrow-gap_semiconductor )

Even under the idealized case, though, the efficiency is not 100%, for reasons I've described.

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2 hours ago, swansont said:

how does an electron with no KE contribute to a current

I had in mind that if you had a hypothetical cell with zero resistance, an infinitesimally small voltage difference would be enough to drive the photo-generated current.

2 hours ago, swansont said:

To your point about the electron thermalizing, sure - but this represents another loss mechanism you have to worry about

1 hour ago, swansont said:

But at some point the practicality has to kick in, since your material is infinitely thick

You could theoretically use an ideal spectral splitter and direct each photon to a separate cell with the corresponding band gap.

Please keep in mind that I am not talking about practical feasibility, I just want to find out if there is an inherent physical limit that prohibits such a device with 100% conversion efficiency as there is in thermodynamic cycles with the carnot limit. Now just because the physical upper limit might be a certain figure this does not say anything about technical feasibility. I just want to find out how much is possible without violating any fundamental physical laws.

2 hours ago, swansont said:

I don't know how you would do that. Electrons dropping to a lower energy is a spontaneous reaction

Would this also be the case if the cell were at 0K? The cell should not emit radiation at this temperature so doesn't this exclude each other?

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3 minutes ago, Matthew99 said:

I just want to find out if there is an inherent physical limit that prohibits such a device with 100% conversion efficiency

 

I have already mentioned reflection, recombination and creation of phonons.

 

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23 minutes ago, Matthew99 said:

Would this also be the case if the cell were at 0K? The cell should not emit radiation at this temperature so doesn't this exclude each other?

If the entire cell was at absolute zero then every electron would be in its lowest or ground state, by the definition of absolute zero.

So any change to even the state of a single electron would involve raising the temperature above absolute zero, something you have forbidden.

Edited by studiot
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3 hours ago, Matthew99 said:

Would this also be the case if the cell were at 0K? The cell should not emit radiation at this temperature so doesn't this exclude each other?

It can't be at 0K

Ideal is one thing but violating physical law is another.

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16 hours ago, swansont said:

I have already mentioned reflection, recombination and creation of phonons.

Omitting reflection isn't physically permitted, is it?

But if as you say recombination is inevitable, this could be a real fundamental limiting factor. Do you know if radiative recombination probability of one electron is influenced by temperature or if the reason for higher radiative recombination at higher temperatures is higher population of higher energy levels? Is this radiative recombination the reason for thermal radiation? Sorry if that is a dumb question, I've never thought about this in that way as this exceeds my working field which is in engineering.

16 hours ago, studiot said:

If the entire cell was at absolute zero then every electron would be in its lowest or ground state, by the definition of absolute zero.

So any change to even the state of a single electron would involve raising the temperature above absolute zero, something you have forbidden.

You are right, cell at 0K is a contradiction in itself. However, this thought confuses me a bit. Will this mean that every excitation of an electron increases the temperature of the cell, without having phonons involved?

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3 hours ago, Matthew99 said:

You are right, cell at 0K is a contradiction in itself. However, this thought confuses me a bit. Will this mean that every excitation of an electron increases the temperature of the cell, without having phonons involved?

 

20 hours ago, swansont said:

 

I have already mentioned reflection, recombination and creation of phonons.

 

 

From a thermodynamic point of view per Caratheodory's version of the Second Law is appropriate.

"Not all states are accessible, from a given state."   (the shortened version)

From a QM point of view there are electron orbital (bound) state transitions that are inaccessible.
These are known as 'forbidden transitions'

Edited by studiot
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4 hours ago, Matthew99 said:

Do you know if radiative recombination probability of one electron is influenced by temperature or if the reason for higher radiative recombination at higher temperatures is higher population of higher energy levels?

AFAIK the spontaneous transition is probabilistic. More population in the excited state leads to more transitions because the rate is proportional to the number of electrons.

Plus you have stimulated emission, which is how semiconductor (and all) lasers work. Your incoming photons will induce some excited state electrons to transition to the lower state, which will vary with both the population and the light intensity.

 

4 hours ago, Matthew99 said:

Is this radiative recombination the reason for thermal radiation?

No, since it will not be a blackbody spectrum.

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Thanks for all the inputs so far!

On 9/3/2021 at 12:28 PM, swansont said:

Plus you have stimulated emission

You are right. The more photons there are, the more transitions are induced and the probability of an electron for an up or down transition is the same. Thus, my initial argument of zero recombination is nonsense.

On 9/3/2021 at 12:28 PM, swansont said:

No, since it will not be a blackbody spectrum.

May I raise on last (maybe dumb) question:

In a semiconductor with a band gap of 2eV, how is it possible to emit photons of <2eV which are required for a blackbody spectrum? Is it because there are many different energy levels available near to the surface due to surface effects (loose or different bonds)?

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2 hours ago, Matthew99 said:

In a semiconductor with a band gap of 2eV, how is it possible to emit photons of <2eV which are required for a blackbody spectrum? Is it because there are many different energy levels available near to the surface due to surface effects (loose or different bonds)?

Charges undergoing acceleration (e.g. via collisions) will emit photons

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