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Thermodynamics and Solar Energy

By Edmund Blackadder in Edmund Blackadder's Diary
Fri Oct 31, 2014 at 09:55:05 PM EST
Tags: solar energy, delft, thermodynamics, shockley-queisser limit, heat losses, recombination losses, up converters, down converters, quantum dots (all tags)

From the Delft Solar Energy MOOC, Video 6.1 "Third Generation PV Technologies":


The Shockley-Queisser limit as discussed in week 3, is a kind of thermodynamic approach to estimate the maximum performance of a single junction solar cell.

The AM1.5 spectrum is incident on a solar cell.

We don't allow the solar cell to increase in temperature.

This means that all energy in the incoming AM1.5 spectrum can escape the system of the solar cell by either the current density generated or by the radiative recombination of charge carriers.

As a result the maximum efficiency which can be achieved is around 33% in the band gap range from 1.0 eV up to 1.8 eV as indicated by the black area in the shown graph.

Now we are going to look at a very fundamental limitation of the photovoltaic effect as we have discussed it so far.

What physical principles are limiting the extent of photogeneration?


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[...]

Tackling these fundamental limitations means that we can develop PV concepts with conversion efficiencies that can surpass the Shockley-Queisser limit.

[...]

As a result, the highest conversion efficiencies of 44% have been achieved.

This exceeds the Shockley-Queisser limit by more than 10%.

---

Professor Arno Smets goes on to describe how single photons incident upon a solar cell can result in the generation of more than one electron-hole pair. A high-energy photon can produce two, or more, electron-hole pairs, thus raising the External Quantum Efficiency over 100%.

IBM's solar concentrator reports 80% overall efficiency. Combined with some of the theoretical gains from up or down conversion of photons (so that each photon creates more than one electron-hole pair in the solar cell) can create overall efficiencies that exceed the power of the solar input.

Was Solyndra working on advanced solar technologies such as up-conversion and down-conversion? We should be investing in such research. Market signals might prefer to allocate all resources to cheap panels that get 20% efficiency; government should create the money to research the technology that will get us greater than 100% efficiency.

The reason thermodynamic-derived limits can be overcome is that the new technologies rely on nanoscale exploitation of quantum effects. If charge carriers can be multiplied, i.e. a single photon can produce more than one charge carrier, why can't the output of the solar cell exceed the input? Do the charge carriers care where they came from when they create a current?

If you can increase the EQE over 1, can't you increase the current density without limit?

From one of the Solar Energy MOOC's questions:


The short-circuit current density can be calculated from the EQE and the photon flux by:

Jsc=q∫λ2λ1ΦAM1.5(λ)EQE(λ)dλ

The bounds of the first integral, and the "sc" and "AM1.5" subscripts, are mangled by the copy-paste (such is the brittleness of mathematics), but basically if you increase the EQE, can't you increase the Jsc (short-circuit current density), even if the photon flux remains the same?

 

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Related Links
o Delft Solar Energy MOOC
o Shockley-Q ueisser limit
o External Quantum Efficiency over 100%
o IBM's solar concentrator
o quantum effects
o Edmund Blackadder's Diary


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Thermodynamics and Solar Energy | 24 comments (24 topical, editorial, 0 hidden)
s/can create/we can create (none / 0) (#1)
by Edmund Blackadder on Fri Oct 31, 2014 at 09:57:10 PM EST



---
MAY I SUCK YOUR PENIS? - Nimey
Hi! I fail at basic sig technology! En plus, je suis pédé! - smegko
s/first integral/integral (none / 0) (#2)
by Edmund Blackadder on Fri Oct 31, 2014 at 09:58:53 PM EST



---
MAY I SUCK YOUR PENIS? - Nimey
Hi! I fail at basic sig technology! En plus, je suis pédé! - smegko
Consider this practice question: (none / 0) (#3)
by Edmund Blackadder on Sat Nov 01, 2014 at 12:40:58 AM EST

http://subbot.org/edx/solarenergy/EQE_question.png


PRACTICE QUESTION 3.3.3  (1/1 point)

After the characterization of a solar cell under standard test conditions (STC), the efficiency is 18.6%. What would the efficiency of the solar cell be (in %) if the EQE were halved and all the other external parameters remained the same?

[...]

EXPLANATION

The efficiency depends on the short-circuit current density as:

η=VocJscFFPin

And the short-circuit current density depends on the EQE as:

Jsc=q∫ΦAM1.5(λ)EQE(λ)dλ

Therefore, if the EQE were halved, the Jsc would be halved, and the efficiency would also be halved to η=9.3%.

So, if the EQE is doubled, the efficiency doubles. If you can split an incoming photon into 3 or 4 charge carriers, the efficiency triples, or quadruples. A tripling would already take it past 100% efficiency, if you started at the Shockley-Queisser limit.

So theoretically, conservation of energy doesn't apply. There is no theoretical barrier to getting over 100% efficiency.

---

Note: k$5 turned the equations into escape sequences. Once again, the brittleness of the mathematical language is demonstrated.

eta = (V_oc * J_sc * FF) / P_in

J_sc can be increased without theoretical limit, by quantum dots or down conversion or up conversion or hot carriers, etc. Since EQE can go over 100%, J_sc can be doubled, tripled, quadrupled.

If J_sc increases, then eta (the efficiency) increases.

If J_sc triples, and eta started at 33%, eta can go over 100%. In such a case, how is energy conserved? The multiplication of charge carriers seems to create more than the photon on its own could provide.

---
MAY I SUCK YOUR PENIS? - Nimey
Hi! I fail at basic sig technology! En plus, je suis pédé! - smegko

Concentrators kill birds too :( (none / 0) (#5)
by Edmund Blackadder on Sat Nov 01, 2014 at 01:04:25 AM EST

I was looking up concentrator bird kills, and found this article about a bird-friendly wind turbine: http://www.gizmag.com/bird-friendly-wind-turbine/23961/

$550 / per unit. I wonder how much the state payed to put up those giant windmill monstrosities near Ellensburg and Cle Ellum, and in south central Washington.

We should make sure solar concentrators are bird-safe, too :(

---
MAY I SUCK YOUR PENIS? - Nimey
Hi! I fail at basic sig technology! En plus, je suis pédé! - smegko

More on efficiency and quantum dots (none / 0) (#6)
by Edmund Blackadder on Sat Nov 01, 2014 at 01:15:14 AM EST


The particles are at a very close distance from each other, in the order of a nanometer.

In one particle an electron is excited into the conduction band.

It appears that in such nanoparticle systems the quantized rest energy is not necessarily lost as heat to the lattice, but can be transferred as a quantized energy package to a neighboring quantum dot.

Here a second electron is excited into conduction band of the second quantum dot.

Now we have generated two electron-hole pairs out of one photon.

No excess heat is lost. No entropy produced. It's essentially an adiabatic process. And you get more out of it than you put in!

---
MAY I SUCK YOUR PENIS? - Nimey
Hi! I fail at basic sig technology! En plus, je suis pédé! - smegko

Holy shit you're fucking stupid... (none / 0) (#7)
by procrasti on Sat Nov 01, 2014 at 02:00:27 AM EST

If you could create an energy efficiency of over 100%, just tie one of these up to a photon emmitter powered by it, then shine one photon onto it, it will produce two charge carriers, which will produce two photons, which will produce 4 charge carriers, which will produce 4 photons... in an exponential cascade until your single device can create more power than all the world's nuclear, fossil and renewable sources combined.

It's obvious idiocy.

On a note about External Quantum Efficiency... it's the number of charge carriers produced per incident photon... the total energy of these produced charge carriers is LESS THAN the energy of the photon.

You are looking for a perpetual motion device... either make one, show one, or shut the fuck up because you're fucking hopeless.

<-- kr5ddit
-------
if i ever see the nickname procrasti again on this site or anywhere in my life, i want it to be in an OBITUARY -- CTS
doing my best at licking arseholes - may 2015 -- mirko
-------
Winner of Kuro5hin: April 2015
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kr5ddit.com - You're front page to the internettm.

Also note, the Shockley-Queisser limit is never (none / 0) (#10)
by procrasti on Sat Nov 01, 2014 at 03:03:04 AM EST

broken, UNDER THE ASSUMPTIONS of the Shockley-Queisser limit.

Ie, where it is broken, it isn't broken, because the limit doesn't apply to those situations (concentrated light, multiple junctions etc)...

This is where you're lack of understanding of what assumptions mean comes into play.

None of this will ever get you more energy out a system than you put into it... to think so means you are living in crack fantasy land... but we knew that already under the trane is a fucking crazy crack head assumption.

<-- kr5ddit
-------
if i ever see the nickname procrasti again on this site or anywhere in my life, i want it to be in an OBITUARY -- CTS
doing my best at licking arseholes - may 2015 -- mirko
-------
Winner of Kuro5hin: April 2015
-------
kr5ddit.com - You're front page to the internettm.

Thermodynamics and Solar Energy | 24 comments (24 topical, 0 editorial, 0 hidden)
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