Abstract

In the high-density excitation limit, as is often probed with ultrafast spectroscopies, spatial and temporal evolution of photogenerated excited states are strongly coupled, giving rise to artifacts that influence experimentally-determined material parameters. The interplay between spatial and temporal degrees of freedom is especially pronounced in pump-probe microscopy, where small laser spot sizes amplify the effects of spatiotemporal coupling on spectroscopic observables. To quantitatively model these effects, a continuum model is developed that accounts for laser spot size as well as nonlinear excited state decay and diffusion. It is shown that effective excitation densities cannot be used to determine quantitatively correct rate constants. Significant error is introduced unless experimental data is fit with a numerical model that accounts for spatial anisotropy in the excitation density. Furthermore, the quantitative determination of material diffusion coefficients is shown to be highly sensitive to experimental parameters.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
    [Crossref]
  2. M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
    [Crossref]
  3. D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
    [Crossref]
  4. T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
    [Crossref]
  5. H. Staleva and G. V. Hartland, “Transient Absorption Studies of Single Silver Nanocubes,” J. Phys. Chem. C 112(20), 7535–7539 (2008).
    [Crossref]
  6. E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
    [Crossref]
  7. G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
    [Crossref]
  8. V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
    [Crossref]
  9. H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
    [Crossref]
  10. C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
    [Crossref]
  11. J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
    [Crossref]
  12. M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
    [Crossref]
  13. S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
    [Crossref]
  14. A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
    [Crossref]
  15. E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
    [Crossref]
  16. Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
    [Crossref]
  17. J. Crank, The Mathematics of Diffusion (Oxford University, 1956).
  18. P. T. Landsberg, Recombination in Semiconductors (Cambridge University, 1991).

2019 (2)

T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
[Crossref]

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

2018 (2)

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

2017 (3)

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

2016 (2)

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
[Crossref]

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

2015 (4)

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
[Crossref]

2014 (1)

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

2011 (1)

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

2008 (1)

H. Staleva and G. V. Hartland, “Transient Absorption Studies of Single Silver Nanocubes,” J. Phys. Chem. C 112(20), 7535–7539 (2008).
[Crossref]

Akimov, D.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

Cabanillas-Gonzalez, J.

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Cahoon, J. F.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Cating, E. E. M.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

Cating, E. M.

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Cerullo, G.

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Christesen, J. D.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Christie, C. A.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

Cogdell, R. J.

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

Cotts, B. L.

C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
[Crossref]

Crank, J.

J. Crank, The Mathematics of Diffusion (Oxford University, 1956).

Davydova, D. y.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

de la Cadena, A.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

Dietzek, B.

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

Doughty, B.

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

Fazzi, D.

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Fischer, M. C.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
[Crossref]

Gabriel, M. M.

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Gardiner, A. T.

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

Ginsberg, N. S.

C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
[Crossref]

Graham, M. W.

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

Grancini, G.

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Grumstrup, E. M.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Guo, Z.

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

Harel, E.

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Hartland, G. V.

H. Staleva and G. V. Hartland, “Transient Absorption Studies of Single Silver Nanocubes,” J. Phys. Chem. C 112(20), 7535–7539 (2008).
[Crossref]

Hill, A. H.

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

Huang, L.

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
[Crossref]

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

Jansen, T. L. C.

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

Kamat, P. V.

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

Kanatzidis, M.

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Kennedy, C. L.

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

Kim, C. J.

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

Kirschbrown, J. R.

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Landsberg, P. T.

P. T. Landsberg, Recombination in Semiconductors (Cambridge University, 1991).

Lanzani, G.

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Ma, Y. Z.

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

Manser, J. S.

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

Massaro, E. S.

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

Matutes, Y. A.

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

Nah, S.

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Ogilvie, J. P.

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

Papanikolas, J. M.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Park, J.

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

Patel, H.

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

Pinion, C. W.

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Polli, D.

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Robles, F. E.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
[Crossref]

Simpson, M. J.

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

Smyser, K. E.

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

Snaider, J. M.

T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
[Crossref]

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Soe, C. M. M.

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Spokoyny, B.

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Staleva, H.

H. Staleva and G. V. Hartland, “Transient Absorption Studies of Single Silver Nanocubes,” J. Phys. Chem. C 112(20), 7535–7539 (2008).
[Crossref]

Stoumpos, C.

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Tiwari, V.

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

Vallorz, E. L.

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

Van Goethem, E. M.

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

Wan, Y.

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

Wang, T.

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Warren, W. S.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
[Crossref]

Wilson, J. W.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
[Crossref]

Wong, C. Y.

C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
[Crossref]

Wu, H.

C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
[Crossref]

Xiao, K.

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

Yang, B.

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

Yang, M.

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Yuan, L.

T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
[Crossref]

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Zhu, K.

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Zhu, T.

T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
[Crossref]

ACS Energy Lett. (1)

J. M. Snaider, Z. Guo, T. Wang, M. Yang, L. Yuan, K. Zhu, and L. Huang, “Ultrafast Imaging of Carrier Transport across Grain Boundaries in Hybrid Perovskite Thin Films,” ACS Energy Lett. 3(6), 1402–1408 (2018).
[Crossref]

Annu. Rev. Phys. Chem. (1)

T. Zhu, J. M. Snaider, L. Yuan, and L. Huang, “Ultrafast Dynamic Microscopy of Carrier and Exciton Transport,” Annu. Rev. Phys. Chem. 70(1), 219–244 (2019).
[Crossref]

Chem. Phys. (1)

E. M. Grumstrup, M. M. Gabriel, E. E. M. Cating, E. M. Van Goethem, and J. M. Papanikolas, “Pump–probe microscopy: Visualization and spectroscopy of ultrafast dynamics at the nanoscale,” Chem. Phys. 458, 30–40 (2015)..
[Crossref]

J. Phys. Chem. C (2)

H. Staleva and G. V. Hartland, “Transient Absorption Studies of Single Silver Nanocubes,” J. Phys. Chem. C 112(20), 7535–7539 (2008).
[Crossref]

E. M. Grumstrup, M. M. Gabriel, E. M. Cating, C. W. Pinion, J. D. Christesen, J. R. Kirschbrown, E. L. Vallorz, J. F. Cahoon, and J. M. Papanikolas, “Ultrafast Carrier Dynamics in Individual Silicon Nanowires: Characterization of Diameter-Dependent Carrier Lifetime and Surface Recombination with Pump–Probe Microscopy,” J. Phys. Chem. C 118(16), 8634–8640 (2014).
[Crossref]

J. Phys. Chem. Lett. (3)

M. J. Simpson, B. Doughty, B. Yang, K. Xiao, and Y. Z. Ma, “Spatial Localization of Excitons and Charge Carriers in Hybrid Perovskite Thin Films,” J. Phys. Chem. Lett. 6(15), 3041–3047 (2015).
[Crossref]

A. H. Hill, K. E. Smyser, C. L. Kennedy, E. S. Massaro, and E. M. Grumstrup, “Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films,” J. Phys. Chem. Lett. 8(5), 948–953 (2017).
[Crossref]

G. Grancini, D. Polli, D. Fazzi, J. Cabanillas-Gonzalez, G. Cerullo, and G. Lanzani, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence For Interfacial Charge Transfer State,” J. Phys. Chem. Lett. 2(9), 1099–1105 (2011).
[Crossref]

Laser Photonics Rev. (1)

D. y. Davydova, A. de la Cadena, D. Akimov, and B. Dietzek, “Transient absorption microscopy: advances in chemical imaging of photoinduced dynamics,” Laser Photonics Rev. 10(1), 62–81 (2016).
[Crossref]

Nano Lett. (1)

E. E. M. Cating, C. W. Pinion, J. D. Christesen, C. A. Christie, E. M. Grumstrup, J. F. Cahoon, and J. M. Papanikolas, “Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy,” Nano Lett. 17(10), 5956–5961 (2017).
[Crossref]

Nat. Commun. (4)

V. Tiwari, Y. A. Matutes, A. T. Gardiner, T. L. C. Jansen, R. J. Cogdell, and J. P. Ogilvie, “Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria,” Nat. Commun. 9(1), 4219 (2018).
[Crossref]

H. Patel, L. Huang, C. J. Kim, J. Park, and M. W. Graham, “Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene,” Nat. Commun. 10(1), 1445 (2019).
[Crossref]

C. Y. Wong, B. L. Cotts, H. Wu, and N. S. Ginsberg, “Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films,” Nat. Commun. 6(1), 5946 (2015).
[Crossref]

Z. Guo, J. S. Manser, Y. Wan, P. V. Kamat, and L. Huang, “Spatial and temporal imaging of long-range charge transport in perovskite thin films by ultrafast microscopy,” Nat. Commun. 6(1), 7471 (2015).
[Crossref]

Nat. Photonics (1)

S. Nah, B. Spokoyny, C. Stoumpos, C. M. M. Soe, M. Kanatzidis, and E. Harel, “Spatially segregated free-carrier and exciton populations in individual lead halide perovskite grains,” Nat. Photonics 11(5), 285–288 (2017).
[Crossref]

Rev. Sci. Instrum. (1)

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited Review Article: Pump-probe microscopy,” Rev. Sci. Instrum. 87(3), 031101 (2016).
[Crossref]

Other (2)

J. Crank, The Mathematics of Diffusion (Oxford University, 1956).

P. T. Landsberg, Recombination in Semiconductors (Cambridge University, 1991).

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Figures (4)

Fig. 1.
Fig. 1. Kinetic effects of anisotropic excitation density. (a) Solid lines show spatially dependent 1/e lifetimes (plotted on left axis) for 25 fJ (dark blue), 250 fJ (light blue), and 2.5 pJ (green), along the y = 0 profile. The black dashed line shows the excitation profile and is plotted on the right axis. (b) At low fluence, the excitation density, $n({r,\Delta t} )$., and the signal (Eq. (2)) decay with identical kinetics (black solid line). At 2.5 pJ, the center of $n({r,\Delta t} )$ (green, dashed) decays more quickly than the edge (r = .91γpump, where the excitation density is an order of magnitude lower, green dotted). The signal (solid line) decays at a rate between these two limits.
Fig. 2.
Fig. 2. Effective density fitting (a) Dotted lines show numerically modeled kinetics for γpump = 0.4 µm, γprobe = 0.5 µm with pulse energies of 0.125 pJ (blue), 0.25 pJ (brown), 1.25 pJ (red), 2.5 pJ (orange), 12.5 pJ (yellow) and 25 pJ (green). Global best fits to the power dependent kinetics are shown as correspondingly colored solid lines. (b) Normalized rate constants plotted as a function of the normalized probe width, assuming an effective excitation density defined by the 1/e2 width and $1/\alpha $ absorption depth of the pump. (c) and (d) show normalized kinetics assuming a reduced pump-probe width (see text) and differ by zeff. Panel c assumes zeff = 1/α, whereas panel d assumes zeff = 2/α.
Fig. 3.
Fig. 3. Effects of excited state diffusion on measured decay kinetics with a finite probe size. (a) Kinetics traces with ${\gamma _{probe}} = 1.0$ µm and ${\gamma _{pump}}$ = 0.4 µm (dashed) or ${\gamma _{pump}}$ = 0.8 µm (solid) for Dc = 0.0 (dark blue), 0.1(light blue), 1.0 (brown), 10 (orange), and 50 cm2/s (yellow). (b) Kinetics traces with ${\gamma _{pump}} = 0.4$ µm and ${\gamma _{probe}}$ = 0.5 µm (dashed) or ${\gamma _{probe}}$ = 1.0 µm (solid) for Dc = 0 to 50.0 cm2/s (same values and colors as in panel a).
Fig. 4.
Fig. 4. Spatiotemporal coupling in diffusion imaging. (a) Scanning the probe over the photoexcited population density produces a spatially-separated profile at a given delay time. (b) Spatially separated profiles at low fluence (25 fJ, solid) and high fluence (12.5 pJ, dashed) at Δt = 0 ps (dark blue) Δt = 200 ps (light blue) and Δt = 600 ps (maroon). Note the broadening of the high-fluence measurements relative to the low-fluence. (c) A plot of FWHM2 vs. Δt should produce a linear trend in the limit of purely diffusive broadening. However at higher fluences, the trend is nonlinear due to nonlinear recombination. Dark blue, light blue, maroon, and red traces show results from 25 fJ, 2.5 pJ, 12.5 pJ, and 25 pJ, respectively. (d) Such behavior could be interpreted (erroneously) as a time-dependent diffusion process due to non-equilibrated excited states. Trace colors and powers correspond to those in panel c.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

n ( r , z , Δ t ) t = 1 r r , z D c r r , z n k 1 n k 2 n 2 k 3 n 3
I ( Δ t ) 0 R m a x 0 z m a x G p r o b e ( r ; γ ) n ( r , z , Δ t ) r z r
n eff = 0 2 π 0 r e f f 0 z e f f m α L n [ 16 ] π γ p u m p 2 E x p [ L n [ 16 ] r 2 γ p u m p 2 ] E x p [ α z ] r θ r z / ( 0 2 π 0 r e f f 0 z e f f r θ r z )
I ( Δ t ) Δ r = 0 ( γ p u m p 2 + γ p r o b e 2 + 16 L n ( 2 ) D c Δ t ) 1 / 2 E x p ( k 1 Δ t )
I ( Δ x , Δ t ) = a 0 β ( Δ t ) exp ( 4 ln ( 2 ) Δ x 2 β ( Δ t ) 2 )
β ( Δ t ) = ( γ 1 2 + γ 2 2 + 16 D c Δ t l n ( 2 ) ) 1 2

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