Lifetime, Mobility, and Diffusion of Photoexcited Carriers in Ligand ...
Lifetime, Mobility, and Diffusion of Photoexcited Carriers in Ligand-Exchanged Lead Selenide Nanocrystal Films Measured by Time-Resolved Terahertz Spectroscopy Glenn W. Guglietta,a† Benjamin T. Diroll,b† E. Ashley Gaulding,c Julia L. Fordham,c Siming Li,a Christopher B. Murray,b,c and Jason B. Baxtera a
Department of Chemical and Biological Engineering, Drexel University, 3141 Chestnut Street,
Philadelphia, Pennsylvania 19104, United States b
Department of Chemistry, University of Pennsylvania 231 South 34th Street, Philadelphia,
Pennsylvania 19104, United States c
Department of Materials Science, University of Pennsylvania, 3231 Walnut Street, Philadelphia,
Pennsylvania 19104, United States
Figure S1. (a,b) TEM images of 5.5 nm PbSe nanocrystals (NCs) used in this study.
Figure S2. AFM area scan of an NH4SCN-treated NC film.
Figure S3. Cross-sectional SEM of a 3-layer film of PbSe nanocrystals (NCs) prepared on a silicon wafer. The film is observed at the top of a three-layer stack of silicon and silicon oxide (250 nm thermal oxide). Substrates using in time-resolved terahertz spectroscopy (TRTS) must be insulating and therefore we were unable to directly image cross-sections of those films asmade by SEM.
Figure S4. SEM micrograph of NH4SCN-exchanged PbSe NC film.
Figure S5. (a) x4000 and (b) x25000 magnification images of TBAI-treated PbSe NC solids showing cracked granular structure.
Figure S6. Small-angle transmission X-ray diffraction data collected from the ligand-exchanged PbSe NC films.
Index of refraction. The index of refraction in the terahertz (THz) region was estimated using a Maxwell-Garnet effective medium approach described in Murphy et al.1 Under this model, the effective dielectric constant ( = ) in the THz is
⁄ + 1 − ⁄ − 1 − = ⁄ + 1 − ⁄ − 1 −
in which f is the fill fraction (non-void), which we estimate to be between 0.6-0.65 from volume exclusion of spheres and cracking of the film; r1 and r2 are the inorganic and inorganic plus ligand =
radii
(e.g.
5.5
nm
and
5.75-6.0
nm).
A
and
B
are
defined
as
!" #!$ %&
*
' !" ( #!$ %& ) +' #!$ %& + ,!" )' #!$ %& + -./0 ) 12 ⁄1* 3
and =
*
' -./0 ( #!$ %& ) !"
' !" ( #!$ %& ) +' #!$ %& + ,!" )' #!$ %& + -./0 ) 12 ⁄1* 3
. Using = 1, = 250, and
= 15, we obtain values of n ranging from 2.85-3.15 and use a value of 3 for our calculations in this work. Unlike in Murphy et al., we directly used the effective dielectric (n=3) for the medium on the basis of these calculations.
Dependence of Extinction on Dielectric Environment. The extinction (per unit distance) crosssection of small spherical particles with given bulk values of dielectric constant n and absorption coefficient k is 7=
28
9:;
? | 2@
where |>? | =
9B C − @ + 2B + 4 @
Using values of n = 4.9 and k = 1.9 for PbSe at 720 nm,2 we obtain Figure S7.
Figure S7. Theoretical extinction coefficient for PbSe spheres as a function of dielectric environment. The range of dielectric environments implied by the empirical extinction coefficients ranges from 1.6-2.6, although this overstates the dielectric influence because we have not corrected for film densification differences, reflection, or scattering. However, it is clear from the simulated extinction that the range of empirical extinction coefficients extracted from optical absorption measurements and AFM thickness measurements is reasonable within the Maxwell-Garnet framework. Organic ligands typically have dielectrics of ~1.5 and the ligand-exchanges with inorganic ligands can be described as yielding very thin inorganic shells (PbS, n~3.9) mixed with air. More detailed studies have claimed that dipolar coupling enhances absorption even more than the dielectric effects alone, which is possible, but not within the resolution of this experiment.3
Table S1. Treatment, Thickness, Extinction Coefficient, and Optical Thickness Ligand Exchange NH4SCN Na2S EDA EDT TBAI
Thickness (AFM, nm) 264 412 578 699 690
Extinction (×104 cm-1) 25.4 16.8 7.8 8.4 7.0
Optical Thickness (nm) 118 179 386 357 428
Figure S8. Reflectance spectra taken at three positions on the NH4SCN-treated PbSe NC film. Absolute reflectance percentage was collected using a silver reference mirror (100% reflectance) at normal incidence using an Olympus optical microscope equipped with a Craig Microspectrophotometer. The wavelength-resolved reflectivity data reveal little evidence of scattering from the film.
Figure S9. TRTS data for as-synthesized PbSe NCs deposited into thin films via spin-coating or dropcasting. The measured signal from these films is compared with that of the NH4SCNexchanged film. We observe negligible differential transmission of the terahertz signal from unexchanged NC films. Power-dependence. While there is some power dependence (Figure S10a), it is not as strong as would be expected from a dominant Auger recombination mechanism, where F G FI
=
J(KGFI *
EF EG
= −7H so that
. Figure S10b shows fits to the highest and lower powers using an Auger model
with Auger c-parameter determined from the best fit to the high power data and N0 determined by pump fluence. The power-dependence which is observed is inconsistent with Auger recombination and thus we exclude Auger as a primary explanation for the decay in photoconductivity. Other decay mechanisms include first order (e.g. Shockley-Read-Hall) and second order (e.g. radiative recombination of free carriers). See Table S2 for more details. The decay on nanosecond time scales follows first-order decay that is nearly power-independent and consistent with the longer-time component apparent in the data. Linear combinations of the different rate laws can be used to approximately fit power-dependent data if the time-scales of decay are substantially different. In the case of a combination of Auger and first-order decay, the observed power-dependence is still not well-modeled with global parameters over a range of powers. A second order recombination model is closer to capturing the dynamics with a simple one-parameter model, but there are still significant deviations from the data. Although we cannot conclusively determine the cause of the power dependence, Auger recombination that has been reported in other work does not appear to be a dominant factor here at the power used for the analysis of data in the main text.1,4
Figure S10. (a) Normalized TRTS decays for the NH4SCN-treated sample at different pump powers. (b) Short-time fraction of the normalized decays at the higher and lowest powers. The solid black line represents a fit of Auger recombination according to the equation above. Using the same c parameter for Auger in the lower-power sample, the red line shows the predicted decay under an Auger-dominated signal for the sample at ~52% power and the blue line shows the Auger model for the sample at 4% power. Table S2. Tabulated fitting functions for first, second, and third order decay processes Decay Process 1st order 2nd order 3rd order
Differential form LH = −NH LM LH = −RH LM LH = −7H LM
Normalized timedependent solution H M = P +QG HO H M 1 = HO 1 + RMHO H M 1 = HO J1 + 7MHO
Example Trap-assisted recombination Radiative recombination Auger recombination
Figure S11. Plot of charge carrier diffusion length as a function of charge carrier mobility and lifetime. Data points in black are from this report on PbSe NC solids. White circles and arrows indicate other reports from PbE materials.5–10 Blue circles and arrows indicate data from CZTS,11 CdTe,12 CIGS,13–16 GaAs, amorphous silicon (a-Si),17 crystalline silicon (c-Si), organolead halide perovskites,18 organic solar cell materials,19 and dye-sensitized solar cells (DSSC, estimated from reported diffusivities).20 The reference number of publications reporting data for these samples is included on the plot and refers to the supporting information references. For single crystal materials like GaAs and Si and even PbSe, the range of accessible mobilities and lifetimes is particularly large and strongly dependent on purity of materials and processing steps. We provide a range which is roughly consistent with known mobilities and lifetimes. Supporting Information References (1)
Murphy, J. E.; Beard, M. C.; Nozik, A. J. Time-Resolved Photoconductivity of PbSe Nanocrystal Arrays. J. Phys. Chem. B 2006, 110, 25455–25461.
(2)
Adachi, S. Optical Constants of Crystalline and Amorphous Semiconductors; Kluwer Academic Publishers: Norwell, Massachusetts, 1999.
(3)
Sandeep, C. S. S.; Azpiroz, J. M.; Evers, W. H.; Boehme, S. C.; Moreels, I.; Kinge, S.; Siebbeles, L. D. A.; Infante, I.; Houtepen, A. J. Epitaxially Connected PbSe Quantum-Dot Films: Controlled Neck Formation and Optoelectronic Properties. ACS Nano 2014, 8, 11499–11511.
(4)
Gao, Y.; Suchand Sandeep, C. S.; Schins, J. M.; Houtepen, A. J.; Siebbeles, L. D. A. Disorder Strongly Enhances Auger Recombination in Conductive Quantum-Dot Solids. Nat. Commun. 2013, 4, 2329.
(5)
Talgorn, E.; Gao, Y.; Aerts, M.; Kunneman, L. T.; Schins, J. M.; Savenije, T. J.; van Huis, M. A.; van der Zant, H. S. J.; Houtepen, A. J.; Siebbeles, L. D. A. Unity Quantum Yield of Photogenerated Charges and Band-like Transport in Quantum-Dot Solids. Nat. Nanotechnol. 2011, 6, 733–739.
(6)
Gao, Y.; Aerts, M.; Sandeep, C. S. S.; Talgorn, E.; Savenije, T. J.; Kinge, S.; Siebbeles, L. D. A.; Houtepen, A. J. Photoconductivity of PbSe Quantum-Dot Solids: Dependence on Ligand Anchor Group and Length. ACS Nano 2012, 6, 9606–9614.
(7)
Allgaier, R.; Scanlon, W. Mobility of Electrons and Holes in PbS, PbSe, and PbTe between Room Temperature and 4.2°K. Phys. Rev. 1958, 111, 1029–1037.
(8)
Coates, D. G.; Lawson, W. D.; Prior, A. C. Single Crystal Photoconductive Detectors in Lead Selenide. J. Electrochem. Soc. 1961, 108, 1038–1042.
(9)
Jeong, K. S.; Tang, J.; Liu, H.; Kim, J.; Schaefer, A. W.; Kemp, K.; Levina, L.; Wang, X.; Hoogland, S.; Debnath, R.; Brzozowski, L.; Sargent, E. H.; Asbury, J. B. Enhanced Mobility-Lifetime Products in PbS Colloidal Quantum Dot Photovoltaics. ACS Nano 2012, 6, 89–99.
(10)
Johnston, K. W.; Pattantyus-Abraham, A. G.; Clifford, J. P.; Myrskog, S. H.; Hoogland, S.; Shukla, H.; Klem, E. J. D.; Levina, L.; Sargent, E. H. Efficient Schottky-Quantum-Dot Photovoltaics: The Roles of Depletion, Drift, and Diffusion. Appl. Phys. Lett. 2008, 92, 122111.
(11)
Guglietta, G. W.; Choudhury, K. R.; Caspar, J. V.; Baxter, J. B. Employing TimeResolved Terahertz Spectroscopy to Analyze Carrier Dynamics in Thin-Film Cu2ZnSn(S,Se)4 Absorber Layers. Appl. Phys. Lett. 2014, 104, 253901.
(12)
Kanevce, A.; Levi, D. H.; Kuciauskas, D. The Role of Drift, Diffusion, and Recombination in Time-Resolved Photoluminescence of CdTe Solar Cells Determined through Numerical Simulation. Prog. Photovoltaics Res. Appl. 2014, 22, 1138–1146.
(13)
Repins, I. L.; Metzger, W. K.; Perkins, C. L.; Li, J. V.; Contreras, M. A. Correlation Between Measured Minority-Carrier Lifetime and Cu(In,Ga)Se(2) Device Performance. IEEE Trans. Electron Devices 2010, 57, 2957–2963.
(14)
Dinca, S. A.; Schiff, E. A.; Shafarman, W. N.; Egaas, B.; Noufi, R.; Young, D. L. Electron Drift-Mobility Measurements in Polycrystalline CuIn1−xGaxSe2 Solar Cells. Appl. Phys. Lett. 2012, 100, 103901.
(15)
Dinca, S. A.; Schiff, E. A.; Shafarman, W. N. Hole Drift Mobility Measurements in Polycrystalline CuIn(1−x)Ga(x)Se(2). Phys. Rev. B 2009, 80, 235201.
(16)
Lee, J.; Cohen, J. D.; Shafarman, W. N. The Determination of Carrier Mobilities in CIGS Photovoltaic Devices using High-Frequency Admittance Measurements. Thin Solid Films 2005, 480-481, 336–340.
(17)
Street, R. A. Trapping Parameters of Dangling Bonds in Hydrogenated Amorphous Silicon. Appl. Phys. Lett. 1982, 41, 1060–1062.
(18)
Wehrenfennig, C.; Eperon, G. E.; Johnston, M. B.; Snaith, H. J.; Herz, L. M. High Charge Carrier Mobilities and Lifetimes in Organolead Trihalide Perovskites. Adv. Mater. 2014, 26, 1584–1589.
(19)
Garcia-Belmonte, G.; Munar, A.; Barea, E. M.; Bisquert, J.; Ugarte, I.; Pacios, R. Charge Carrier Mobility and Lifetime of Organic Bulk Heterojunctions Analyzed by Impedance Spectroscopy. Org. Electron. 2008, 9, 847–851.
(20)
He, C.; Zhao, L.; Zheng, Z.; Lu, F. Determination of Electron Diffusion Coefficient and Lifetime in Dye-Sensitized Solar Cells by Electrochemical Impedance Spectroscopy at High Fermi Level Conditions. J. Phys. Chem. C 2008, 112, 18730–18733.
Department of Chemical and Biological Engineering, Drexel University, 3141 Chestnut Street,
Philadelphia, Pennsylvania 19104, United States b
Department of Chemistry, University of Pennsylvania 231 South 34th Street, Philadelphia,
Pennsylvania 19104, United States c
Department of Materials Science, University of Pennsylvania, 3231 Walnut Street, Philadelphia,
Pennsylvania 19104, United States
Figure S1. (a,b) TEM images of 5.5 nm PbSe nanocrystals (NCs) used in this study.
Figure S2. AFM area scan of an NH4SCN-treated NC film.
Figure S3. Cross-sectional SEM of a 3-layer film of PbSe nanocrystals (NCs) prepared on a silicon wafer. The film is observed at the top of a three-layer stack of silicon and silicon oxide (250 nm thermal oxide). Substrates using in time-resolved terahertz spectroscopy (TRTS) must be insulating and therefore we were unable to directly image cross-sections of those films asmade by SEM.
Figure S4. SEM micrograph of NH4SCN-exchanged PbSe NC film.
Figure S5. (a) x4000 and (b) x25000 magnification images of TBAI-treated PbSe NC solids showing cracked granular structure.
Figure S6. Small-angle transmission X-ray diffraction data collected from the ligand-exchanged PbSe NC films.
Index of refraction. The index of refraction in the terahertz (THz) region was estimated using a Maxwell-Garnet effective medium approach described in Murphy et al.1 Under this model, the effective dielectric constant ( = ) in the THz is
⁄ + 1 − ⁄ − 1 − = ⁄ + 1 − ⁄ − 1 −
in which f is the fill fraction (non-void), which we estimate to be between 0.6-0.65 from volume exclusion of spheres and cracking of the film; r1 and r2 are the inorganic and inorganic plus ligand =
radii
(e.g.
5.5
nm
and
5.75-6.0
nm).
A
and
B
are
defined
as
!" #!$ %&
*
' !" ( #!$ %& ) +' #!$ %& + ,!" )' #!$ %& + -./0 ) 12 ⁄1* 3
and =
*
' -./0 ( #!$ %& ) !"
' !" ( #!$ %& ) +' #!$ %& + ,!" )' #!$ %& + -./0 ) 12 ⁄1* 3
. Using = 1, = 250, and
= 15, we obtain values of n ranging from 2.85-3.15 and use a value of 3 for our calculations in this work. Unlike in Murphy et al., we directly used the effective dielectric (n=3) for the medium on the basis of these calculations.
Dependence of Extinction on Dielectric Environment. The extinction (per unit distance) crosssection of small spherical particles with given bulk values of dielectric constant n and absorption coefficient k is 7=
28
9:;
? | 2@
where |>? | =
9B C − @ + 2B + 4 @
Using values of n = 4.9 and k = 1.9 for PbSe at 720 nm,2 we obtain Figure S7.
Figure S7. Theoretical extinction coefficient for PbSe spheres as a function of dielectric environment. The range of dielectric environments implied by the empirical extinction coefficients ranges from 1.6-2.6, although this overstates the dielectric influence because we have not corrected for film densification differences, reflection, or scattering. However, it is clear from the simulated extinction that the range of empirical extinction coefficients extracted from optical absorption measurements and AFM thickness measurements is reasonable within the Maxwell-Garnet framework. Organic ligands typically have dielectrics of ~1.5 and the ligand-exchanges with inorganic ligands can be described as yielding very thin inorganic shells (PbS, n~3.9) mixed with air. More detailed studies have claimed that dipolar coupling enhances absorption even more than the dielectric effects alone, which is possible, but not within the resolution of this experiment.3
Table S1. Treatment, Thickness, Extinction Coefficient, and Optical Thickness Ligand Exchange NH4SCN Na2S EDA EDT TBAI
Thickness (AFM, nm) 264 412 578 699 690
Extinction (×104 cm-1) 25.4 16.8 7.8 8.4 7.0
Optical Thickness (nm) 118 179 386 357 428
Figure S8. Reflectance spectra taken at three positions on the NH4SCN-treated PbSe NC film. Absolute reflectance percentage was collected using a silver reference mirror (100% reflectance) at normal incidence using an Olympus optical microscope equipped with a Craig Microspectrophotometer. The wavelength-resolved reflectivity data reveal little evidence of scattering from the film.
Figure S9. TRTS data for as-synthesized PbSe NCs deposited into thin films via spin-coating or dropcasting. The measured signal from these films is compared with that of the NH4SCNexchanged film. We observe negligible differential transmission of the terahertz signal from unexchanged NC films. Power-dependence. While there is some power dependence (Figure S10a), it is not as strong as would be expected from a dominant Auger recombination mechanism, where F G FI
=
J(KGFI *
EF EG
= −7H so that
. Figure S10b shows fits to the highest and lower powers using an Auger model
with Auger c-parameter determined from the best fit to the high power data and N0 determined by pump fluence. The power-dependence which is observed is inconsistent with Auger recombination and thus we exclude Auger as a primary explanation for the decay in photoconductivity. Other decay mechanisms include first order (e.g. Shockley-Read-Hall) and second order (e.g. radiative recombination of free carriers). See Table S2 for more details. The decay on nanosecond time scales follows first-order decay that is nearly power-independent and consistent with the longer-time component apparent in the data. Linear combinations of the different rate laws can be used to approximately fit power-dependent data if the time-scales of decay are substantially different. In the case of a combination of Auger and first-order decay, the observed power-dependence is still not well-modeled with global parameters over a range of powers. A second order recombination model is closer to capturing the dynamics with a simple one-parameter model, but there are still significant deviations from the data. Although we cannot conclusively determine the cause of the power dependence, Auger recombination that has been reported in other work does not appear to be a dominant factor here at the power used for the analysis of data in the main text.1,4
Figure S10. (a) Normalized TRTS decays for the NH4SCN-treated sample at different pump powers. (b) Short-time fraction of the normalized decays at the higher and lowest powers. The solid black line represents a fit of Auger recombination according to the equation above. Using the same c parameter for Auger in the lower-power sample, the red line shows the predicted decay under an Auger-dominated signal for the sample at ~52% power and the blue line shows the Auger model for the sample at 4% power. Table S2. Tabulated fitting functions for first, second, and third order decay processes Decay Process 1st order 2nd order 3rd order
Differential form LH = −NH LM LH = −RH LM LH = −7H LM
Normalized timedependent solution H M = P +QG HO H M 1 = HO 1 + RMHO H M 1 = HO J1 + 7MHO
Example Trap-assisted recombination Radiative recombination Auger recombination
Figure S11. Plot of charge carrier diffusion length as a function of charge carrier mobility and lifetime. Data points in black are from this report on PbSe NC solids. White circles and arrows indicate other reports from PbE materials.5–10 Blue circles and arrows indicate data from CZTS,11 CdTe,12 CIGS,13–16 GaAs, amorphous silicon (a-Si),17 crystalline silicon (c-Si), organolead halide perovskites,18 organic solar cell materials,19 and dye-sensitized solar cells (DSSC, estimated from reported diffusivities).20 The reference number of publications reporting data for these samples is included on the plot and refers to the supporting information references. For single crystal materials like GaAs and Si and even PbSe, the range of accessible mobilities and lifetimes is particularly large and strongly dependent on purity of materials and processing steps. We provide a range which is roughly consistent with known mobilities and lifetimes. Supporting Information References (1)
Murphy, J. E.; Beard, M. C.; Nozik, A. J. Time-Resolved Photoconductivity of PbSe Nanocrystal Arrays. J. Phys. Chem. B 2006, 110, 25455–25461.
(2)
Adachi, S. Optical Constants of Crystalline and Amorphous Semiconductors; Kluwer Academic Publishers: Norwell, Massachusetts, 1999.
(3)
Sandeep, C. S. S.; Azpiroz, J. M.; Evers, W. H.; Boehme, S. C.; Moreels, I.; Kinge, S.; Siebbeles, L. D. A.; Infante, I.; Houtepen, A. J. Epitaxially Connected PbSe Quantum-Dot Films: Controlled Neck Formation and Optoelectronic Properties. ACS Nano 2014, 8, 11499–11511.
(4)
Gao, Y.; Suchand Sandeep, C. S.; Schins, J. M.; Houtepen, A. J.; Siebbeles, L. D. A. Disorder Strongly Enhances Auger Recombination in Conductive Quantum-Dot Solids. Nat. Commun. 2013, 4, 2329.
(5)
Talgorn, E.; Gao, Y.; Aerts, M.; Kunneman, L. T.; Schins, J. M.; Savenije, T. J.; van Huis, M. A.; van der Zant, H. S. J.; Houtepen, A. J.; Siebbeles, L. D. A. Unity Quantum Yield of Photogenerated Charges and Band-like Transport in Quantum-Dot Solids. Nat. Nanotechnol. 2011, 6, 733–739.
(6)
Gao, Y.; Aerts, M.; Sandeep, C. S. S.; Talgorn, E.; Savenije, T. J.; Kinge, S.; Siebbeles, L. D. A.; Houtepen, A. J. Photoconductivity of PbSe Quantum-Dot Solids: Dependence on Ligand Anchor Group and Length. ACS Nano 2012, 6, 9606–9614.
(7)
Allgaier, R.; Scanlon, W. Mobility of Electrons and Holes in PbS, PbSe, and PbTe between Room Temperature and 4.2°K. Phys. Rev. 1958, 111, 1029–1037.
(8)
Coates, D. G.; Lawson, W. D.; Prior, A. C. Single Crystal Photoconductive Detectors in Lead Selenide. J. Electrochem. Soc. 1961, 108, 1038–1042.
(9)
Jeong, K. S.; Tang, J.; Liu, H.; Kim, J.; Schaefer, A. W.; Kemp, K.; Levina, L.; Wang, X.; Hoogland, S.; Debnath, R.; Brzozowski, L.; Sargent, E. H.; Asbury, J. B. Enhanced Mobility-Lifetime Products in PbS Colloidal Quantum Dot Photovoltaics. ACS Nano 2012, 6, 89–99.
(10)
Johnston, K. W.; Pattantyus-Abraham, A. G.; Clifford, J. P.; Myrskog, S. H.; Hoogland, S.; Shukla, H.; Klem, E. J. D.; Levina, L.; Sargent, E. H. Efficient Schottky-Quantum-Dot Photovoltaics: The Roles of Depletion, Drift, and Diffusion. Appl. Phys. Lett. 2008, 92, 122111.
(11)
Guglietta, G. W.; Choudhury, K. R.; Caspar, J. V.; Baxter, J. B. Employing TimeResolved Terahertz Spectroscopy to Analyze Carrier Dynamics in Thin-Film Cu2ZnSn(S,Se)4 Absorber Layers. Appl. Phys. Lett. 2014, 104, 253901.
(12)
Kanevce, A.; Levi, D. H.; Kuciauskas, D. The Role of Drift, Diffusion, and Recombination in Time-Resolved Photoluminescence of CdTe Solar Cells Determined through Numerical Simulation. Prog. Photovoltaics Res. Appl. 2014, 22, 1138–1146.
(13)
Repins, I. L.; Metzger, W. K.; Perkins, C. L.; Li, J. V.; Contreras, M. A. Correlation Between Measured Minority-Carrier Lifetime and Cu(In,Ga)Se(2) Device Performance. IEEE Trans. Electron Devices 2010, 57, 2957–2963.
(14)
Dinca, S. A.; Schiff, E. A.; Shafarman, W. N.; Egaas, B.; Noufi, R.; Young, D. L. Electron Drift-Mobility Measurements in Polycrystalline CuIn1−xGaxSe2 Solar Cells. Appl. Phys. Lett. 2012, 100, 103901.
(15)
Dinca, S. A.; Schiff, E. A.; Shafarman, W. N. Hole Drift Mobility Measurements in Polycrystalline CuIn(1−x)Ga(x)Se(2). Phys. Rev. B 2009, 80, 235201.
(16)
Lee, J.; Cohen, J. D.; Shafarman, W. N. The Determination of Carrier Mobilities in CIGS Photovoltaic Devices using High-Frequency Admittance Measurements. Thin Solid Films 2005, 480-481, 336–340.
(17)
Street, R. A. Trapping Parameters of Dangling Bonds in Hydrogenated Amorphous Silicon. Appl. Phys. Lett. 1982, 41, 1060–1062.
(18)
Wehrenfennig, C.; Eperon, G. E.; Johnston, M. B.; Snaith, H. J.; Herz, L. M. High Charge Carrier Mobilities and Lifetimes in Organolead Trihalide Perovskites. Adv. Mater. 2014, 26, 1584–1589.
(19)
Garcia-Belmonte, G.; Munar, A.; Barea, E. M.; Bisquert, J.; Ugarte, I.; Pacios, R. Charge Carrier Mobility and Lifetime of Organic Bulk Heterojunctions Analyzed by Impedance Spectroscopy. Org. Electron. 2008, 9, 847–851.
(20)
He, C.; Zhao, L.; Zheng, Z.; Lu, F. Determination of Electron Diffusion Coefficient and Lifetime in Dye-Sensitized Solar Cells by Electrochemical Impedance Spectroscopy at High Fermi Level Conditions. J. Phys. Chem. C 2008, 112, 18730–18733.
