1. The document discusses advances in impedance spectroscopy for analyzing solar energy conversion devices like dye-sensitized solar cells. 2. Impedance spectroscopy allows measurement of resistances and capacitances in solar cells, which provides insight into recombination, diffusion lengths, and energetics. 3. Parameters like the chemical capacitance, recombination resistance, and diffusion coefficient can be extracted and related to performance factors like open-circuit voltage, short-circuit current, and fill factor.

1. Advances in impedance spectroscopy of solar energy
conversion devices
Juan Bisquert
Photovoltaic and Optoelectronic Devices Group
Universitat Jaume I
12071 Castelló
Spain
27 10 2012

2. Solar cell concepts

3. Photovoltaics: Light absorber

4. Photovoltaics: Charge separation
Bisquert, J.; Cahen, D.; Rühle, S.; Hodes, G.; Zaban, A. "Physical chemical principles of photovoltaic conversion with
nanoparticulate, mesoporous dye-sensitized solar cells." The Journal of Physical Chemistry B, 108, 8106, 2004.

5. Fundamental model for a solar cell
Infinite mobilities-
no transport resistance
Fermi level straight inside
Perfect selective contacts
1. Generation
2. Recombination Fermi level fixed inside by
3. Extraction external potential, independent
of illumination
Bisquert, J.; Cahen, D.; Rühle, S.; Hodes, G.; Zaban, A. "Physical chemical principles of photovoltaic conversion with
nanoparticulate, mesoporous dye-sensitized solar cells." The Journal of Physical Chemistry B, 108, 8106, 2004.

6. The diode equation for a solar cell
Dark At V = 0 equilibrium of generation and recombination
jr (0) = j0
Rise of the Fermi level enhances recombination
jr (V ) = j0 e qV / mk BT
Sunlight Equilibrium of generation and recombination
j = jsc + j0 − j0 e qV / mk BT
Can be measured directly by
Also can be expressed in terms
of carrier density
recombination resistance

7. Current voltage curves

8. Solar cell concepts

9. Dye Solar Cells

10. Dye-sensitized solar cell
Nayak, Kahn, Garcia.Belmonte, Bisquert, Cahen, Energy and Environmental Science 2012

11. Limitation to efficiency
The DSC
It is a 3 –materials solar cell
There is a price of energy differences, but
more versatile and potentially cheap

12. Influence of energetics: higher Voc
If the conduction band of TiO2 is higher, the Fermi level can rise higher (in
principle) and photovoltage may become larger

13. Influence of energetics: photocurrent
If the conduction band of TiO2 is higher, there is less injection from the
dye molecules, and current decreases

14. The redox potential of the hole
conductor
New redox couples?
The Fermi level of the hole conductor is lower than I-/I3- liquid
electrolyte, which gives higher photovoltage

15. The energy diagram

16. Diffusion-recombination transmission line model
J. Bisquert, J. Phys. Chem. B 106, 325-333 (2002)
F. Fabregat-Santiago, J. Bisquert, G. Garcia-Belmonte, G. Boschloo, A. Hagfeldt Solar En.
Mat. Sol.Cells, 87, 117-131 (2005).

17. Measurement of resistances and
capacitances by Impedance
Spectroscopy

18. DSC device IS model
J. Bisquert, J. Phys. Chem. B 106, 325-333 (2002)
F. Fabregat-Santiago, J. Bisquert, G. Garcia-Belmonte, G. Boschloo, A. Hagfeldt Solar En.
Mat. Sol.Cells, 87, 117-131 (2005).

19. How do we determine energetics?
The chemical capacitance measures the density of states in the bandgap
(DOS) and this provides a reference of the Ec in different cells.
Pt
TCO re d o x
e le c t r o ly t e
T iO 2
E C
E Fn
e le c tr ic p o te n tia l
e le c tr o n e n e r g y
eV
E F0
E re d o x

20. Chemical capacitance
The conduction band of TiO2 is situated at a given level with respect to the Fermi level of hole
conductor. The chemical capacitance measures the density of states in the bandgap (DOS)
and this provides a reference of the Ec in different cells.
TC O re d o x
Pt
Chemical
capacitance
e le c t r o ly t e
T iO 2
E C
∂n
E Fn
Cµ = q 2
e le c t r ic p o t e n t ia l
e le c t r o n e n e r g y
eV ∂E Fn
E F0
E re d o x
Bisquert, J. "Chemical capacitance of nanostructured semiconductors: its origin and significance for heterogeneous solar
cells". Phys. Chem. Chem. Phys. 2003, 5, 5360

21. Interpretation of recombination
resistance
'  q VF 
Rrec = R0 exp − β
 k BT 

The model considers a distribution of
surface states, and charge transfer via
Marcus model
1 T
β= + α s = 0. 5 +
2 T0 s
Q. Wang, M. Grätzel, F. Fabregat-Santiago, J. Bisquert et al., J. Phys. Chem. B. 110, 25210-25221
(2006)
J. Bisquert, F. Fabregat –Santiago, I. Mora-Seró, G. Garcia-Belmonte, S. Giménez,
J. Phys. Chem. C, 113, 17278 (2009).

22. Fill factors
The recombination order β
relates directly to the
diode ideality factor
m = 1.5-2.5
j = jsc + j0 − j0e qβV / k BT
Restrictions on the fill factor

23. Shif of the band changes the diode
factor
Jennings and Wang show that the diode factor
changes when the conduction band is brought
down by the addition of lithium.
m = 1 at high lithium content (low cb position)
Because electron
transfer is from
conduction band and
linear recombination
occurs
J. Jennings, Q. Wang J. Phys. Chem. C, 114, 1715 (2010).

24. The diffusion length
The diffusion coefficient is related only to
resistances
Rrec
Ln = Dnτ n = L
Rtr
J. Bisquert, J. Phys. Chem. B, 106, 325-333 (2002)

25. Variations of the diffusion length
The diffusion length increases with the bias
This is indicating that the free electron lifetime is not a
Ln = Dnτ n = D0τ f constant
Quantitative description is made by Peter et al.
Using nonlinear recombination model
J. Villanueva-Cab, H. Wang, G. OskamL. M. Peter, J. Phys. Chem. Lett. 1, 748, (2010).

26. Phtalocyanine dyes
O O O O
O O O O
N N
N N N N
H
N Zn N N N
H
N N N N
N N
O O O O
O O O O
O O
ZnPc-1 H2Pc-2
Barea, E. M.; Ortiz, J.; Payá, F. J.; Fernández-Lázaro, F.; Fabregat-Santiago, F.; Sastre-Santos, A.; Bisquert, J. "Energetic factors governing
injection, regeneration and recombination in dye solar cells with phthalocyanine sensitizers". Energy and Environmental Science 2010, 3, 1985

27. Phtalocyanine dyes
n at VOC EC EC - EFn
Voc jsc η
Sample FF (cm-3) (eV) (eV)
(V) (mA/cm2) (%)
ZnPc-1 0.44 3.48 0.66 1.01 4.2 x 1017 -4.00 0.31
H2Pc-2 0.35 5.71 0.57 1.14 1.5 x 1018 -4.13 0.27
N719 0.45 10.90 0.51 2.50 3.0 x 1018 -4.11 0.19
Barea, E. M.; Ortiz, J.; Payá, F. J.; Fernández-Lázaro, F.; Fabregat-Santiago, F.; Sastre-Santos, A.; Bisquert, J. "Energetic factors governing
injection, regeneration and recombination in dye solar cells with phthalocyanine sensitizers". Energy and Environmental Science 2010, 3, 1985

28. Phtalocyanine dyes
The band is shifted for ZnPC
We move the potential scale to
compare recombination
ZnPc has more recombination
Recombination in H2Pc is the
same as in N719

29. Phtalocianyne dyes
Recombination in H2Pc is the
same as in N719
With the same current it
would give the same voltage
Barea, E. M.; Ortiz, J.; Payá, F. J.; Fernández-Lázaro, F.; Fabregat-Santiago, F.; Sastre-Santos, A.; Bisquert, J. "Energetic factors governing
injection, regeneration and recombination in dye solar cells with phthalocyanine sensitizers". Energy and Environmental Science 2010, 3, 1985

30. The DOS an essential reference to
explain performance
Explanation of the low
VOC.
1)an inefficient injection
2)the low position of the
conduction band of TiO2,

31. Identifying the role that the dye structure plays in DSC
performance
why YD2 porphyrin dye
Acceptor• Can achieve such a high performance
group close to that of a Ru commercial dye?
Donor
group Besides of the dye structure and
the related photophysical properties.
bridge •What other key parameters in a DSC influence
YD2 strongly the overall power conversion efficiency?
Diau, C.-Y. Yeh, J. Mater. Chem. 2010, 20, 1127
Angew. Chem. Int. Ed. 2010, 49, 6646 –6649

32. YD2
YD0 Sample name YD2 YD0 N719
Current density (mA·cm ) N719 Voc (V)
-2
15
0.66 0.65 0.74
jsc (mA/cm2) 15.4 6.92 12.6
10 FF 0.62 0.73 0.70
Efficiencysame condictions 7% efficiency is the record
* Under
(%)* 6.36 3.29 6.54
5
0
0.0 0.2 0.4 0.6 0.8
Potential (V)
N719
Barea, E. M.; Gonzalez-Pedro, V.; Ripolles-Sanchis, T.; Wu, H.-P.; Li, L.-L.; Yeh, C.-Y.; Diau, E. W.-G.; Bisquert, J. "Porphyrin Dyes with High
Injection and Low Recombination for Highly Efficient Mesoscopic Dye-Sensitized Solar Cells". The Journal of Physical Chemistry C 2011, 115,
10898

33. J. Phys. Chem. B 2006, 110, 25210-25221
10-2 105
(a) (b)
-2
Capacitance / F·cm
104
2
Rrec / Ohms·cm
10-3
103
102
10-4
101
10-5 100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Applied Potential / V Applied Potential / V

34. N719
Sample name YD2 YD0 N719
Voc (V) 0.66 0.65 0.74
jsc (mA/cm2) 15.4 6.92 12.6
FF 0.62 0.73 0.70
Efficiency (%) 6.36 3.29 6.54

35. Sample name YD2 YD0 N719
Voc (V) 0.66 0.65 0.74
jsc (mA/cm2) 15.4 6.92 12.6
FF 0.62 0.73 0.70
Efficiency (%) 6.36 3.29 6.54
β 0.47 0.73 0.70
j0 (mA/cm2) 7.75e-05 6.09e-08 2.09e-08
j0k (mA/cm )
2
54 1406 213
α 0.29 0.30 0.24
∆Ec vs ref (mV) -123 -32.0 Ref
Rseries (ohm) 19.5 19.4 17.9
Internal FF 0.73 0.81 0.81
Internal
efficiency (%) 7.41 3.58 7.54
Barea, E. M.; Gonzalez-Pedro, V.; Ripolles-Sanchis, T.; Wu, H.-P.; Li, L.-L.; Yeh, C.-Y.; Diau, E. W.-G.; Bisquert, J. "Porphyrin Dyes with High
Injection and Low Recombination for Highly Efficient Mesoscopic Dye-Sensitized Solar Cells". The Journal of Physical Chemistry C 2011, 115,
10898

36. • ISTPro Features
- Analyzes IS data of
dye-sensitized solar
cells (DSC).
- Allows to treat
impedance
spectroscopy
parameters to obtain
the essential
parameters of the DSC
performance.
- Display the

37. • ISTPro Features
Main Window:

38. • ISTPro Features

39. Organic solar cells

40. Organic solar cells
Sunflower project: http://sunflower-fp7.eu

41. Organic solar cell
On Voltage, Photovoltage, and Photocurrent in Bulk Heterojunction Organic Solar Cells
Juan Bisquert and Germa Garcia-Belmonte, J. Phys. Chem. Lett. 2011, 2, 1950–1964

42. Organic solar cell
Ratcliff, E. L.; Zacher, B.; Armstrong, N. R. "Selective Interlayers and Contacts in Organic Photovoltaic
Cells". The Journal of Physical Chemistry Letters 2011, 2, 1337.

43. The bands and the Fermi levels
Dielectric (depletion)
capacitance The chemical capacitance

44. Band bending and Fermi levels
Donor LUMO
Acceptor LUMO
EF
Donor HOMO ---
--
--
Cathode
Acceptor HOMO
w
V=0

45. Band bending and Fermi levels
Donor LUMO
Acceptor LUMO
EF
Donor HOMO
--
--
Cathode
Acceptor HOMO
w
V < Vfb

46. Band bending and Fermi levels
Donor LUMO
Acceptor LUMO
EF
Donor HOMO ---
Cathode
Cathode
Acceptor HOMO
w
V < Vfb

47. Band bending and Fermi levels
Donor LUMO
Acceptor LUMO
EF
Donor HOMO -
Cathode
Acceptor HOMO
w
V < Vfb

48. Band bending and Fermi levels
Donor LUMO
Acceptor LUMO
EF
Donor HOMO
Cathode
Acceptor HOMO
V = Vfb

49. Depletion region – Mott Schottky plots
Increase in the capacitance
caused by the reduction of
the depletion zone
Characterization of nanostructured hybrid and organic solar cells by impedance spectroscopyw
Francisco Fabregat-Santiago, Germa Garcia-Belmonte, Ivan Mora-Sero´ and Juan Bisquert
Phys. Chem. Chem. Phys., 2011, 13, 9083–9118

50. Depletion region
-P. P. Boix, G. Garcia-Belmonte, U. Muñecas, M.Neophytou, C. Waldauf, R. Pacios,
Appl Phys. Lett 95, 1, (2009)

51. Depletion region

52. Additional proofs of electrical field confined near the
cathode
FIG. 2. (Color online) (a) The mean-field potential line-profile of the cross-sectional image and (b) the corresponding energy band diagram after contacting of all layers.
Appl. Phys. Lett. 99, 243301 (2011)
© 2011 American Institute of Physics

53. Measured DOS of organic BHJ
Measurement of the DOS
The chemical capacitance
∂nL
Cµ ( E ) = q 2 = qg n ( E Fn )
∂EFn
PCBM-P3HT solar cell
Germà Garcia-Belmonte, Pablo P. Boix, Juan Bisquert, Michele Sessolo, and Henk J. Bolink
Solar Energy Materials and Solar Cells, 94, 366 (2010)

54. Comparison of different fullerenes
with similar reduction potential but different DOS
DPM6
PCBM
Higher Voc related to full occupancy of
intermediate electronic band
G. Gar
Germa Garcia-Belmonte Pablo P. Boix, Juan Bisquert, Martijn Lenes, Henk J. Bolink,
Andrea La Rosa, Salvatore Filippone,and Nazario Martín§,J. Phys. Chem. Lett. 1 (2010) 2566-2571

55. Carrier diffusion in organic BHJ
PCBM-P3HT solar cell
Diffusion-Recombination Determines Collected Current and Voltage in Polymer:Fullerene Solar Cells
Teresa Ripolles-Sanchis, Antonio Guerrero, Juan Bisquert, and Germà Garcia-Belmonte, J. Phys. Chem. C 2012, 116, 16925−16933

56. The Fermi level in the Gaussian distribution
In the presence of a Gaussian distribution, the
carriers do not lie below the Fermi level.
Bisquert, J. "Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions
of states". Physical Chemistry Chemical Physics 2008, 10, 3175

57. Why is Voc less than HOMO-LUMO difference?
This is explained by disorder
qVoc = E Fn − E Fp
σ n2 + σ p2  Nn N p 
qVoc = E g − − k BT ln
 np  
2k BT  
This formula derived by G. Garcia-Belmonte quantifies
the energy loss related to disorder
Garcia-Belmonte, G. "Temperature dependence of open-circuit voltage inorganic solar cells from generation–recombination
kinetic balance". Solar Energy Materials and Solar Cells 2010, 94, 2166

58. Recombination in organic BHJ

59. Energetics of recombination
Guerrero, A.; Marchesi, L. F.; Boix, P. P.; Bisquert, J.; Garcia-Belmonte, G. "Recombination in Organic Bulk Heterojunction Solar Cells: Small
Dependence of Interfacial Charge Transfer Kinetics on Fullerene Affinity". The Journal of Physical Chemistry Letters 2012, 3, 1386

60. Reconstruction of current voltage curves from
recombination resistance data
Boix, P. P.; Guerrero, A.; Marchesi, L. F.; Garcia-Belmonte, G.; Bisquert, J. "Current-Voltage Characteristics of Bulk Heterojunction Organic
Solar Cells: Connection Between Light and Dark Curves". Advanced Energy Materials 2011, 1, 1073

61. Reconstruction of current voltage curves from
recombination resistance data
−1 k BT
 dj  jsc = j rec (Voc ) = L
Rrec = L rec 
 dV  βqRrec (Voc )
 F 
Boix, P. P.; Guerrero, A.; Marchesi, L. F.; Garcia-Belmonte, G.; Bisquert, J. "Current-Voltage Characteristics of Bulk Heterojunction Organic
Solar Cells: Connection Between Light and Dark Curves". Advanced Energy Materials 2011, 1, 1073

62. Quantum dot solar cells

64. Charge Transfer, Transport and
Recombination Processes
T1→ e- transport
R4 T2→ h+ transport
I1→ e- injection from QD CB
I2→ e- injection from QD trap
I1 R5 I3→ e- back injection to QD
T1 I2
I4 → h+ injection from QD CB
Tr3 I3 Tr1 R1
I5 → h+ injection from QD trap
Tr1→ e- trapping in the QD
R2 T2
R3 Tr2 → h+ trapping in the QD
I4 R1→ e-- h+ band-to-band
Tr2 I5 recombination in the QD
R2→ e-- h+ trap mediated
recombination in the QD
Electron QD Hole R3→ recombination of e- in the
Transporter Transporter TiO2 with h+ in the QD
R4→ recombination of e- in the
TiO2 with h+ in the HT
R5→ recombination of e- in the
QD with h+ in the HT
- G. Hodes, J. Phys. Chem. C 2008, 112, 17778–17787

65. Quantum dot solar cells
Boix, P. P.; Larramona, G.; Jacob, A.; Delatouche, B.; Mora-Seró, I.; Bisquert, J., Hole Transport and
Recombination in All-Solid Sb2S3-Sensitized TiO2 Solar Cells Using CuSCN As Hole Transporter. Journal
of Physical Chemistry C 2012, 116, 1579–1587..

66. Sensitizer Material
PbS/CdS
CdS
PbS
Combination of different kinds of
QDS increases dramatically cell
performance.
Braga et al., J. Phys. Chem. Lett. 2011, 2, 454–460

67. Surface treatment Effect
Surface treatments have
a dramatic effect on solar
cell performance
Barea et al.
J. AM. CHEM. SOC.
2010, 132, 6834–6839

68. Water splitting with sunlight

69. Water splitting cell
Energy diagram of a PEC cell for the photo-electrolysis of water. The cell is based on an n-type
semiconducting photo-anode.
Gerischer, H. "The impact of semiconductors on the concepts of electrochemistry". Electrochimica Acta 1990, 35, 1677-1699

70. Semiconductor photoelectrochemistry
Reichman Appl. Phys. Lett. 1980, 36, 574

71. Hematite
GrätZel et al J. AM. CHEM. SOC. VOL. 132, 2010

72. Photogeneration of electrons and holes
Charge transfer via surface states
Carrier density and interfacial kinetics in mesoporous TiO 2 during water splitting determined by impedance
spectroscopy Sixto Giménez, J. Electroanal Chem 2012

73. Water splitting cell
Simple model of a photoelectrochemical cell
Bertoluzzi, L.; Bisquert, J. "Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical
Water Splitting Applications". The Journal of Physical Chemistry Letters 2012, 3, 2517

74. Equivalent circuit
Simple model of a photoelectrochemical cell
Bertoluzzi, L.; Bisquert, J. "Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical
Water Splitting Applications". The Journal of Physical Chemistry Letters 2012, 3, 2517

75. Thin hematite layer
JV curve and impedance model
Klahr, B.; Gimenez, S.; Fabregat-Santiago, F.; Hamann, T.; Bisquert, J. "Water Oxidation at Hematite Photoelectrodes: The
Role of Surface States". Journal of the American Chemical Society 2012, 134, 4294

76. impedance results
Klahr, B.; Gimenez, S.; Fabregat-Santiago, F.; Hamann, T.; Bisquert, J. "Water Oxidation at Hematite Photoelectrodes: The
Role of Surface States". Journal of the American Chemical Society 2012, 134, 4294

77. Impedance model and results
Klahr, B.; Gimenez, S.; Fabregat-Santiago, F.; Hamann, T.; Bisquert, J. "Water Oxidation at Hematite Photoelectrodes: The
Role of Surface States". Journal of the American Chemical Society 2012, 134, 4294

78. Other redox couple
water Fe(CN)6]3-/4-
With [Fe(CN)6]3-/4- in solution, however, the charge transfer resistance is essentially constant
over the measured potential range for a given light intensity as shown in figure 4c. The
absence of a measureable surface state capacitance and absence of a dip in the charge
transfer resistance suggests that photooxidaiton of [Fe(CN)6]4- does not involve surface states
and can be described as a simple outersphere
Klahr, B.; Gimenez, S.; Fabregat-Santiago, F.; Bisquert, J.; Hamann, T. W. "Electrochemical and photoelectrochemical
investigation of water oxidation with hematite electrodes". Energy & Environmental Science 2012, 5, 7626

79. Surface treatment with Co-Pi
Sivula et al., Energy Environ. Sci. 2011, 4, 1759
Durrant, Gratzel, et al JACS 2011

80. Interpretation of Co-Pi
Klahr, B.; Gimenez, S.; Fabregat-Santiago, F.; Bisquert, J.; Hamann, T. W. "Photoelectrochemical and Impedance Spectroscopic Investigation of
Water Oxidation with Co-Pi -Coated Hematite Electrodes". Journal of the American Chemical Society 2012, 134, 16693

81. Thank you