1. Photovoltaic Solar Cells

2. Solar Conversion
Thermal – absorb suns energy to raise temp and use DT (relative to environment) to perform work.
Photovoltaic – absorb photons that promote electrons to higher energy (excited state).

3. How does a ideal crystalline semiconductor solar cell work
Assume there are no recombination events and we shine a pulse of light
What is the potential energy we can now extract from this material? S0 S1 E
Molecular picture
Remember, we are going to attach electrodes that will interact with both excited and non excited electrons (equilibrium say there are back and forth reactions). Dm
EFe
EFh Eg Dm
The fact that not all electrons (molecules) are excited is accounted for by the electrochemical potential (Dm)

4. How does ideal crystalline or molecular semiconductor solar cell work
Now we shine a second pulse of light
During the second light pulse we allow for radiative recombination
During the second light pulse we open another recombination channel Dm Dm Dm
The less recombination the better.
Unfortunately, absorption is always accompanied by probability for emission and we can’t switch off the radiative recombination.  We must minimize non-radiative channels

5. How does ideal crystalline or molecular semiconductor solar cell work
Under steady state there are both excitation and emission events.
The energy of an excited state (Eg) serves as an upper bound for VOC that due to the existence of radiative recombination is never reached. Dm
Since absorption and emission are related through thermodynamic considerations it is possible to derive an upper bound that is more realistic  Shockley’s paper

6. Detailed balance Detailed balance and reciprocity in solar cells
Thomas Kirchartz and Uwe Rau
phys. stat. sol. (a) 205, No. 12, 2737–2751 (2008)

7. How does ideal semiconductor solar cell work
Shockley’s paper in simple terms
Denote the density of electron-hole pairs as ne, the absorption rate of the sun light as I, and the excitation lifetime as t.
Ideal: The lifetime is dictated by radiative emission only Eg Dm
Denote the effective density of states for electron-hole pairs as ND and assume the semiconductor to be non degenerate (Boltzmann approximation holds):
Ideal: Boltzmann approximation holds

8. Max VOC of Solar Cell EEx Dm
In the ultimate case (only radiative loss):
To find the maximum Dm we recall that we started with:
We also recall that at any temperature there must be a finite black body radiation or a finite electron density. This requires that as T0 also (Eg - Dm) will approach zero or DmEg.
EEx
Loss Dm
Excitation Energy.
Here it is Eg
In the ideal case the only voltage “loss” is due to:
limited excitation (I) or recombination (t)
Feel free to blame the temperature (T) too

9. Losses t + Energy or Charge transfer to lower gap states
To define losses we first set the reference level or define the ideal case t I
In the ultimate case the solar cell collects all photons emitted by the sun
and
all these photons are converted to free charges.
In the ultimate case the only charge decay channel is due to radiative emission (this can not be avoided).
Losses
Not all the photons are being absorbed by the cell or
Not all absorbed photons are converted to free charges
Charge recombination that is different from the radiative rate of the absorbing material (this will always be on top of radiative).
+ Energy or Charge transfer to lower gap states

10. Attributing VOC loss to Sun-Semiconductor not being a closed system I
We have seen that which means that there would be loss in Voc if either the sun intensity (I) is reduced or the radiation rate (t-1) is enhanced. The notion of a closed system means that the Sun and solar cell only emit towards each other. This is obviously not the case and we can say that this is because the sun is not filling the sky to surround the solar cell or that this is because the solar cell is emitting also outside the sun’s solid angle.
If you want to be impressive you may call this “entropy loss”
For isotropic emitter
For ideal planar emitter (lambertian emission)
qSun
qSun Eg Dm

11. VOC loss due to the Sun-Semiconductor not being a closed system - II
If the solar cell is partially transparent or some of the light is being reflected we effectively lose I and hence also Dm.
Not all impinging light is absorbed by the active layer Eg Dm
qSun
If s is the fraction of impinging light that gets absorbed
by the active layer the loss is:

12. Loss due to shorter recombination time (non radiative loss)Eg Dm
Internal Luminescence Efficiency (h) below one reduces VOC by kT*ln(h-1)
Generating charges through total luminescence quenching is not ideal

13. The STRANGE Organics

14. What might be different in organic semiconductor
Organics have two band gaps:
Electronic band gap which is the difference between LUMO HOMO levels
Optical band gap which is smaller than the electronic by the exciton binding energy
Organics have vibronic structure
Energy of luminescence is 1 to 2 vibration energy below the optical band gap.
LUMO
EEx
Loss Dm
Excitation Energy.
Is ??? EL Ee Eg
HOMO
If you use the “standard” crystalline approach – which band gap will you choose?
Relative to the optical gap or absorption gap – does the binding energy constitute a loss?

15. Vibronic relaxation Mirror Image Absorption-Emission NO Stokes shift2 2 1 1
Mirror Image
Absorption-Emission
NO Stokes shift 2 2 1 1
The spacing is due to:
C—C, C—N, C—O   à   800 – 1300cm^-1
C=C, C=N, C=O      à   1500 – 1900cm^-1
C—H, N—H, O—H  à   2850 – 3650cm^-1
A spacing of ~0.2eV.
Eg ; ELum
0-0
1-0
0-1
0-2
Extinction coefficient
Fluorescence Intensity
2-0
Which energy should we choose as the “excitation energy”
Prior to recombination where are the electrons/holes

16. Loss due to reorganization2 2 1
Mirror Image
Absorption-Emission
With Stokes shift Eg
Eg* 1 2 2 1 1
Eg-Eg* =~0.2eV
Eg is the 0-0 transition 
Stokes shift or Marcus reorganization energy will affect the energy difference between electrons and holes prior to recombination
1-0
0-1
0-0
Extinction coefficient
Fluorescence Intensity
2-0

17. “Loss” due to broad density of state (or where is the band edge?)
LUMO
The higher the expectations
The bigger the disappointment C B
A=E0
HOMO

18. Loss due to broad density of state (or where is the band edge?)
Grabitz, P. O.; Rau, U.; Werner, J. H, Phys. status solidi 2005, 202 (15), 2920–2927.
J. C. Blakesley and N. C. Greenham, Journal of Applied Physics, vol. 106, p , 2009.

19. What might be different in organic semiconductor
ELum Eg
ELum Eg
P3HT
Since we are interested in the energy of excitations in organics it might be better to let ELum replace Eg as the upper bound that is never reached.
Eg - ELum may be due to: coulomb binding , vibronic relaxation , stokes shift, Broad DOS

20. Device structures

21. PN Junction based Photo-Cell
(See BASICS OF SEMICONDUCTOR DEVICESׁ ) N P + -
Depletion
EC2 -
Vbi=Vt
EC1 EF
EV2 +
EV1
Relevant points:
Plus on the left and minus on the right  relative to the center: bands on the right
go up (left down)
Electron-hole pair may be broken in a region where EC(x) <> EC(x+Dx)

22. If we continuously shine light what will happen (in open circuit)?-
Vbi=Vt
EC1 EF
EV2 +
EV1
If we continuously shine light what will happen (in open circuit)?
1. Accumulation of negative Q on left and positive Q on right
2. Flattening of the bands
3. Reduced charge separation until band are flat!
EC1
EF2
EC2
EV2
EV1
EF1
VOC=EF1-EF2

23. EC2 EC1 EV2 EV1 V - + Maximum available potential energy = ?
Electron contribution = ?
Hole contribution = ?

24. Another way to create EC(x) <> EC(x+Dx)
Before physical contact between metals and organic Semiconductor M1 M2
After physical contact & equilibration: M2 M1 EF

25. Yet another method (hetero-structure)
Operation of a simple plastic cell nm
Light Absorption
Separate the charges
Transport /
recombination I M T E O T A
Glass L

26. Thanks to J.J.M. Halls for the slide

27. Self Assembly of Bulk Heterojunction
HOMO
Glass
ITO
PEDOT:PSS Mg Ag
Donor
Acceptor
Donor
Acceptor

28. Characteristic equations of ideal solar cell
Under applied voltage
and illumination
Current
VOC
Voltage
JSC

29. Characteristic equations of ideal solar cell
Under applied voltage
and illumination
The open circuit Voltage:
And the Power conversion efficiency :

30. The Fill Factor (non ideal diode)

31. Equivalent circuit

32. Equivalent circuit (of a diode type solar cell)
Ideal
Current J V
Jdark
JSC
VOC
Voltage
JSC

33. Equivalent circuit (of a diode type solar cell)
Ideal V
Jdark
JSC RS
RSH J V
Jdark
JSC

34. Equivalent circuit (of a diode type solar cell)
Jdark
JSC RS
RSH
Current
Current
VOC
VOC
Voltage
Voltage
JSC
JSC RS
RSH
What about fill factor of 25%

35. (Is this) The End
בסוף הכל יהיה בסדר.
אז אם הכל בסדר זה הסוף.

36. The energy source

37. Solar Spectrum at a point outside the Earth’s atmosphere (AM0)
It resembles radiation spectrum of a black body at 5760K.

38. Solar radiation
The surface of the sun, is at a temperature of about 6000K and closely approximates a blackbody.
A blackbody absorbs all radiation incident on its surface and emits radiation based on its temperature. H=σT4 (where σ is the Stefan-Boltzmann constant)
The spectral irradiance from a blackbody is given by Plank's radiation law, shown in the following equation:

39. Solar radiation
The solar radiation outside the earth's atmosphere is calculated using the radiant power density at the sun's surface Hsun =5.961 x 107 W/m2, the radius of the sun (Rsun), and the distance between the earth and the sun.
The calculated solar irradiance at the Earth's atmosphere is about 1.36 kW/m2.

40. Solar radiation
Black 6000K
AM0

41. Solar Spectrum reaching Earth’s surface

42. Black 6000K
AM0
AM1.5

43. Quantifying the attenuation by the atmosphere – Air Mass factor
datm X nAirMass
datm gs
AM1.5  angle of elevation is 42O
Such atmospheric thickness would attenuate the irradiance to ~900Wm-2 but for convenience the AM1.5 is defined for irradiance of 1000Wm-2.

44. Results For Ideal case
Jsc:

45. Results
PCE:

46. Loss of Voc
If we assume that under short circuit conditions all the sun photons are converted to current and that the cell’s recombination is purely radiative so that we can use Plank’s formulas to calculate the loss of Voc as a function of band gap.
Note: In practical cells J0 is only part of the leakage current and in the general case:
Jsc/J0≠Jsc/Jleakage

48. Max VOC of Solar Cell In the ultimate case (only radiative loss):
To find the maximum Dm we recall that we started with:
We also recall that at any temperature there must be a finite black body radiation of a finite electron density. This requires that as T0 also (Eg - Dm) will approach zero or DmEg.
If we now raise the temperature while keeping Dm close to Eg we find that the entire DOS is full of electrons (ne=ND) which is not physical. Namely as we raise the temperature we are losing in term of Dm. Since ne=It this implies that as T is raised t becomes shorter (for fixed sun intensity I).
The above discussion can also be carried out with the aid of the current voltage characteristics that defines VOC as:
Here J0 is dark. Spontaneous recombination, current.