0
Research Papers: Design Automation

A Spectral Density Function Approach for Active Layer Design of Organic Photovoltaic Cells

[+] Author and Article Information
Umar Farooq Ghumman

Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: umarghumman2018@u.northwestern.edu

Akshay Iyer

Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: akshayiyer2021@u.northwestern.edu

Rabindra Dulal

Physics and Astronomy,
University of Wyoming,
1000 E. University, Dept 3905,
Laramie, WY 82071
e-mail: rdulal@uwyo.edu

Joydeep Munshi

Mechanical Engineering and Mechanics,
Lehigh University,
Packard Lab 367,
19 Memorial Drive West,
Bethlehem, PA 18015
e-mail: jom317@lehigh.edu

Aaron Wang

Physics and Astronomy,
University of Wyoming,
1000 E. University, Dept 3905,
Laramie, WY 82071
e-mail: swang9@uwyo.edu

TeYu Chien

Physics and Astronomy,
University of Wyoming,
1000 E. University, Dept 3905,
Laramie, WY 82071
e-mail: tchien@uwyo.edu

Ganesh Balasubramanian

Mechanical Engineering and Mechanics,
Lehigh University,
Packard Lab 561,
19 Memorial Drive West,
Bethlehem, PA 18015
e-mail: bganesh@lehigh.edu

Wei Chen

Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208
e-mail: weichen@northwestern.edu

1U. F. Ghumman and A. Iyer contributed equally to this work.

2Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 30, 2018; final manuscript received July 11, 2018; published online September 7, 2018. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 140(11), 111408 (Sep 07, 2018) (14 pages) Paper No: MD-18-1265; doi: 10.1115/1.4040912 History: Received March 30, 2018; Revised July 11, 2018

Organic photovoltaic cells (OPVCs), having received significant attention over the last decade, are yet to be established as viable alternatives to conventional solar cells due to their low power conversion efficiency (PCE). Complex interactions of several phenomena coupled with the lack of understanding regarding the influence of fabrication conditions and nanostructure morphology have been major barriers to realizing higher PCE. To this end, we propose a computational microstructure design framework for designing the active layer of P3HT:PCBM based OPVCs conforming to the bulk heterojunction (BHJ) architecture. The framework pivots around the spectral density function (SDF), a frequency space microstructure characterization, and reconstruction methodology, for microstructure design representation. We validate the applicability of SDF for representing the active layer morphology in OPVCs using images of the nanostructure obtained by cross-sectional scanning tunneling microscopy and spectroscopy (XSTM/S). SDF enables a low-dimensional microstructural representation that is crucial in formulating a parametric-based microstructure optimization scheme. A level-cut Gaussian random field (GRF, governed by SDF) technique is used to generate reconstructions that serve as representative volume elements (RVEs) for structure–performance simulations. A novel structure–performance (SP) simulation approach is developed using a physics-based performance metric, incident photon to converted electron (IPCE) ratio, to account for the impact of microstructural features on OPVC performance. Finally, a SDF-based computational IPCE optimization study incorporating only three design variables results in 36.75% increase in IPCE, underlining the efficacy of the proposed design framework.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gleiter, H. , 2000, “Nanostructured Materials: Basic Concepts and Microstructure,” Acta Mater., 48(1), pp. 1–29. [CrossRef]
Lee, W. K. , Yu, S. , Engel, C. J. , Reese, T. , Rhee, D. , Chen, W., and Odom, T. W. , 2017, “Concurrent Design of Quasi-Random Photonic Nanostructures,” Proc. Natl. Acad. Sci. U.S.A., 114(33), pp. 8734–8739. [CrossRef] [PubMed]
Wang, C. , Yu, S. , Chen, W. , and Sun, C. , 2013, “Highly Efficient Light-Trapping Structure Design Inspired by Natural Evolution,” Sci. Rep., 3(1), p. 1025. [CrossRef] [PubMed]
Yu, S. , Wang, C. , Sun, C. , and Chen, W. , 2014, “Topology Optimization for Light-Trapping Structure in Solar Cells,” Struct. Multidiscip. Optim., 50(3), pp. 367–382. [CrossRef]
Yu, S. , Wang, C. , Zhang, Y. , Dong, B. , Jiang, Z. , Chen, X. , Chen, W., and Sun, C. , 2017, “Design of Non-Deterministic Quasi-Random Nanophotonic Structures Using Fourier Space Representations,” Sci. Rep., 7(1), p. 3752. [CrossRef] [PubMed]
Yu, S. , Zhang, Y. , Wang, C. , Lee, W. K. , Dong, B. , Odom, T. W. , Sun, C. , and Chen, W. , 2017, “Characterization and Design of Functional Quasi-Random Nanostructured Materials Using Spectral Density Function,” ASME J. Mech. Des., 139(7), p. 071401. [CrossRef]
Sanchis, L. , Håkansson, A. , López-Zanón, D. , Bravo-Abad, J. , and Sánchez-Dehesa, J. , 2004, “Integrated Optical Devices Design by Genetic Algorithm,” Appl. Phys. Lett., 84(22), pp. 4460–4462. [CrossRef]
Gondarenko, A. , Preble, S. , Robinson, J. , Chen, L. , Lipson, H. , and Lipson, M. , 2006, “Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures,” Phys. Rev. Lett., 96(14), p. 143904. [CrossRef] [PubMed]
Jensen, J. S. , and Sigmund, O. , 2011, “Topology Optimization for Nano-Photonics,” Laser Photonics Rev., 5(2), pp. 308–321. [CrossRef]
Imboden, M. , and Bishop, D. , 2014, “Top-down Nanomanufacturing,” Phys. Today, 67(12), pp. 45–50. [CrossRef]
Kinoshita, S. , Yoshioka, S. , and Miyazaki, J. , 2008, “Physics of Structural Colors,” Rep. Prog. Phys., 71(7), p. 076401. [CrossRef]
Vukusic, P. , and Sambles, J. R. , 2003, “Photonic Structures in Biology,” Nature, 424(6950), p. 852. [CrossRef] [PubMed]
Dufresne, E. R. , Noh, H. , Saranathan, V. , Mochrie, S. G. , Cao, H. , and Prum, R. O. , 2009, “Self-Assembly of Amorphous Biophotonic Nanostructures by Phase Separation,” Soft Matter, 5(9), pp. 1792–1795. [CrossRef]
Dong, B. Q. , Zhan, T. R. , Liu, X. H. , Jiang, L. P. , Liu, F. , Hu, X. H. , and Zi, J. , 2011, “Optical Response of a Disordered Bicontinuous Macroporous Structure in the Longhorn Beetle Sphingnotus Mirabilis,” Phys. Rev. E, 84(1), p. 011915. [CrossRef]
Walker, B. , Tamayo, A. B. , Dang, X. D. , Zalar, P. , Seo, J. H. , Garcia, A. , Tantiwiwat, M. , and Nguyen, T. Q. , 2009, “Nanoscale Phase Separation and High Photovoltaic Efficiency in Solution-Processed, Small-Molecule Bulk Heterojunction Solar Cells,” Adv. Funct. Mater., 19(19), pp. 3063–3069. [CrossRef]
Peet, J. , Heeger, A. J. , and Bazan, G. C. , 2009, “Plastic Solar Cells: Self-Assembly of Bulk Heterojunction Nanomaterials by Spontaneous Phase Separation,” Acc. Chem. Res., 42(11), pp. 1700–1708. [CrossRef] [PubMed]
Lee, W.-K. , Jung, W.-B. , Nagel, S. R. , and Odom, T. W. , 2016, “Stretchable Superhydrophobicity From Monolithic, Three-Dimensional Hierarchical Wrinkles,” Nano Lett., 16(6), pp. 3774–3779. [CrossRef] [PubMed]
Zhang, Y. , Dong, B. , Chen, A. , Liu, X. , Shi, L. , and Zi, J. , 2015, “Using Cuttlefish Ink as an Additive to Produce Non-Iridescent Structural Colors of High Color Visibility,” Adv. Mater., 27(32), pp. 4719–4724. [CrossRef] [PubMed]
Biswas, A. , Bayer, I. S. , Biris, A. S. , Wang, T. , Dervishi, E. , and Faupel, F. , 2012, “Advances in Top–down and Bottom–Up Surface Nanofabrication: Techniques, Applications and Future Prospects,” Adv. Colloid Interface Sci., 170(1–2), pp. 2–27. [CrossRef] [PubMed]
Brabec, C. , Scherf, U. , and Dyakonov, V. , 2011, Organic Photovoltaics: Materials, Device Physics, and Manufacturing Technologies, Wiley, Hoboken, NJ.
Brabec, C. J. , 2004, “Organic Photovoltaics: Technology and Market,” Sol. Energy Mater. Sol. Cells, 83(2–3), pp. 273–292. [CrossRef]
Kippelen, B. , and Brédas, J.-L. , 2009, “Organic Photovoltaics,” Energy Environ. Sci., 2(3), pp. 251–261. [CrossRef]
Brabec, C. J. , Dyakonov, V. , Parisi, J. , and Sariciftci, N. S. , 2013, Organic Photovoltaics: Concepts and Realization, Springer Science & Business Media, New York.
Heeger, A. J. , 2001, “Nobel Lecture: Semiconducting and Metallic Polymers: The Fourth Generation of Polymeric Materials,” Rev. Mod. Phys., 73(3), p. 681. [CrossRef]
Berger, P. , and Kim, M. , 2018, “Polymer Solar Cells: P3HT:PCBM and Beyond,” J. Renewable Sustainable Energy, 10(1), p. 013508. [CrossRef]
Grancini, G. , Polli, D. , Fazzi, D. , Cabanillas-Gonzalez, J. , Cerullo, G. , and Lanzani, G. , 2011, “Transient Absorption Imaging of P3HT:PCBM Photovoltaic Blend: Evidence for Interfacial Charge Transfer State,” J. Phys. Chem. Lett., 2(9), pp. 1099–1105. [CrossRef]
Dang, M. T. , Hirsch, L. , and Wantz, G. , 2011, “P3HT:PCBM, Best Seller in Polymer Photovoltaic Research,” Adv. Mater., 23(31), pp. 3597–3602. [CrossRef] [PubMed]
McDowell, D. L. , Panchal, J. , Choi, H.-J. , Seepersad, C. , Allen, J. , and Mistree, F. , 2009, Integrated Design of Multiscale, Multifunctional Materials and Products, Butterworth-Heinemann, Oxford, UK.
Mistree, F. , 2002, “Robust Concept Exploration Methods in Materials Design,” Ninth AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, p. 5568.
Olson, G. B. , 1997, “Computational Design of Hierarchically Structured Materials,” Science, 277(5330), pp. 1237–1242. [CrossRef]
Matthews, J. , Klatt, T. , Morris, C. , Seepersad, C. C. , Haberman, M. , and Shahan, D. , 2016, “Hierarchical Design of Negative Stiffness Metamaterials Using a Bayesian Network Classifier,” ASME J. Mech. Des., 138(4), p. 041404. [CrossRef]
Liu, K. , Detwiler, D. , and Tovar, A. , 2017, “Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis,” ASME J. Mech. Des., 139(10), p. 101401. [CrossRef]
Seepersad, C. C. , Allen, J. K. , McDowell, D. L. , and Mistree, F. , 2006, “Robust Design of Cellular Materials With Topological and Dimensional Imperfections,” ASME J. Mech. Des., 128(6), pp. 1285–1297. [CrossRef]
McDowell, D. L. , and Olson, G. , 2008, “Concurrent Design of Hierarchical Materials and Structures,” Sci. Model. Simul., Springer, 15(1), pp. 207–240.
Fullwood, D. T. , Niezgoda, S. R. , Adams, B. L. , and Kalidindi, S. R. , 2010, “Microstructure Sensitive Design for Performance Optimization,” Prog. Mater. Sci., 55(6), pp. 477–562. [CrossRef]
Şopu, D. , Soyarslan, C. , Sarac, B. , Bargmann, S. , Stoica, M. , and Eckert, J. , 2016, “Structure-Property Relationships in Nanoporous Metallic Glasses,” Acta Mater., 106, pp. 199–207. [CrossRef]
Gupta, A. , Cecen, A. , Goyal, S. , Singh, A. K. , and Kalidindi, S. R. , 2015, “Structure–Property Linkages Using a Data Science Approach: Application to a Non-Metallic Inclusion/Steel Composite System,” Acta Mater., 91, pp. 239–254. [CrossRef]
Çeçen, A. , Fast, T. , Kumbur, E. , and Kalidindi, S. , 2014, “A Data-Driven Approach to Establishing Microstructure–Property Relationships in Porous Transport Layers of Polymer Electrolyte Fuel Cells,” J. Power Sources, 245, pp. 144–153. [CrossRef]
Cecen, A. , Dai, H. , Yabansu, Y. C. , Kalidindi, S. R. , and Song, L. , 2018, “Material Structure-Property Linkages Using Three-Dimensional Convolutional Neural Networks,” Acta Mater., 146, pp. 76–84. [CrossRef]
Xu, H. , Li, Y. , Brinson, C. , and Chen, W. , 2014, “A Descriptor-Based Design Methodology for Developing Heterogeneous Microstructural Materials System,” ASME J. Mech. Des., 136(5), p. 051007. [CrossRef]
Zhang, Y. , Zhao, H. , Hassinger, I. , Brinson, L. C. , Schadler, L. S. , and Chen, W. , 2015, “Microstructure Reconstruction and Structural Equation Modeling for Computational Design of Nanodielectrics,” Integrating Mater. Manuf. Innovation, 4(1), p. 14. [CrossRef]
Bostanabad, R. , Zhang, Y. , Li, X. , Kearney, T. , Brinson, L. C. , Apley, D. W. , Wing, K. L. , and Chen, W. , 2018, “Computational Microstructure Characterization and Reconstruction: Review of the State-of-the-Art Techniques,” Prog. Mater. Sci., 95, pp. 1–41. [CrossRef]
Liu, Y. , Greene, M. S. , Chen, W. , Dikin, D. A. , and Liu, W. K. , 2013, “Computational Microstructure Characterization and Reconstruction for Stochastic Multiscale Material Design,” Comput. Aided Des., 45(1), pp. 65–76. [CrossRef]
Yeong, C. , and Torquato, S. , 1998, “Reconstructing Random Media—II: Three-Dimensional Media From Two-Dimensional Cuts,” Phys. Rev. E, 58(1), p. 224. [CrossRef]
Yeong, C. , and Torquato, S. , 1998, “Reconstructing Random Media,” Phys. Rev. E, 57(1), p. 495. [CrossRef]
Xu, H. , Dikin, D. A. , Burkhart, C. , and Chen, W. , 2014, “Descriptor-Based Methodology for Statistical Characterization and 3D Reconstruction of Microstructural Materials,” Comput. Mater. Sci., 85, pp. 206–216. [CrossRef]
Bostanabad, R. , Bui, A. T. , Xie, W. , Apley, D. W. , and Chen, W. , 2016, “Stochastic Microstructure Characterization and Reconstruction Via Supervised Learning,” Acta Mater., 103, pp. 89–102. [CrossRef]
Sundararaghavan, V. , and Zabaras, N. , 2005, “Classification and Reconstruction of Three-Dimensional Microstructures Using Support Vector Machines,” Comput. Mater. Sci., 32(2), pp. 223–239. [CrossRef]
Cang, R. , Xu, Y. , Chen, S. , Liu, Y. , Jiao, Y. , and Ren, M. Y. , 2017, “Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design,” ASME J. Mech. Des., 139(7), p. 071404. [CrossRef]
Breneman, C. M. , Brinson, L. C. , Schadler, L. S. , Natarajan, B. , Krein, M. , Wu, K. , Morkowchuk, L. , Li, Y. , Deng, H. , and Xu, H. , 2013, “Stalking the Materials Genome: A Data-Driven Approach to the Virtual Design of Nanostructured Polymers,” Adv. Funct. Mater., 23(46), pp. 5746–5752. [CrossRef] [PubMed]
Hassinger, I. , Li, X. , Zhao, H. , Xu, H. , Huang, Y. , Prasad, A. , Schadler, L. , Chen, W. , and Brinson, L. C. , 2016, “Toward the Development of a Quantitative Tool for Predicting Dispersion of Nanocomposites Under Non-Equilibrium Processing Conditions,” J. Mater. Science, 51(9), pp. 4238–4249. [CrossRef]
Xu, H. , Liu, R. , Choudhary, A. , and Chen, W. , 2015, “A Machine Learning-Based Design Representation Method for Designing Heterogeneous Microstructures,” ASME J. Mech. Des., 137(5), p. 051403. [CrossRef]
van Lare, M.-C. , and Polman, A. , 2015, “Optimized Scattering Power Spectral Density of Photovoltaic Light-Trapping Patterns,” ACS Photonics, 2(7), pp. 822–831. [CrossRef]
Jin, R. , Chen, W. , and Sudjianto, A. , 2005, “An Efficient Algorithm for Constructing Optimal Design of Computer Experiments,” J. Stat. Plann. Inference, 134(1), pp. 268–287. [CrossRef]
Kleijnen, J. P. , 2009, “Kriging Metamodeling in Simulation: A Review,” Eur. J. Oper. Res., 192(3), pp. 707–716. [CrossRef]
Zhang, X. Y. , Trame, M. , Lesko, L. , and Schmidt, S. , 2015, “Sobol Sensitivity Analysis: A Tool to Guide the Development and Evaluation of Systems Pharmacology Models,” CPT: Pharmacometrics Syst. Pharmacol., 4(2), pp. 69–79. [CrossRef] [PubMed]
Brigham, E. O. , 1988, The Fast Fourier Transform and Its Applications, Prentice Hall, Englewood Cliffs, NJ.
Chatfield, C. , 1996, The Analysis of Time Series: An Introduction, 5th ed., Chapman and Hall, London; New York.
Panchal, J. H. , Kalidindi, S. R. , and McDowell, D. L. , 2013, “Key Computational Modeling Issues in Integrated Computational Materials Engineering,” Comput. Aided Des., 45(1), pp. 4–25. [CrossRef]
Fullwood, D. T. , Niezgoda, S. R. , and Kalidindi, S. R. , 2008, “Microstructure Reconstructions From 2-Point Statistics Using Phase-Recovery Algorithms,” Acta Mater., 56(5), pp. 942–948. [CrossRef]
Kadem, B. , Cranton, W. , and Hassan, A. , 2015, “Metal Salt Modified PEDOT: PSS as Anode Buffer Layer and Its Effect on Power Conversion Efficiency of Organic Solar Cells,” Org. Electron., 24, pp. 73–79. [CrossRef]
Zhao, W. , Li, S. , Yao, H. , Zhang, S. , Zhang, Y. , Yang, B. , and Hou, J. , 2017, “Molecular Optimization Enables Over 13% Efficiency in Organic Solar Cells,” J. Am. Chem. Soc., 139(21), pp. 7148–7151. [CrossRef] [PubMed]
Li, M. , Gao, K. , Wan, X. , Zhang, Q. , Kan, B. , Xia, R. , Liu, F. , Yang, X. , Feng, H. , Ni, W. , and Wang, Y. , 2017, “Solution-Processed Organic Tandem Solar Cells With Power Conversion Efficiencies >12%,” Nat. Photonics, 11(2), p. 85. [CrossRef]
Wang, A. , and Chien, T. , 2018, “Perspectives of Cross-Sectional Scanning Tunneling Microscopy and Spectroscopy for Complex Oxide Physics,” Phys. Lett. A, 382(11), pp. 739–748. [CrossRef]
Shih, M. C. , Huang, B. C. , Lin, C. C. , Li, S. S. , Chen, H. A. , Chiu, Y. P. , and Chen, C. W. , 2013, “Atomic-Scale Interfacial Band Mapping Across Vertically Phased-Separated Polymer/Fullerene Hybrid Solar Cells,” Nano Lett., 13(6), pp. 2387–2392. [CrossRef] [PubMed]
Yost, A. J. , Pimachev, A. , Ho, C. C. , Darling, S. B. , Wang, L. , Su, W. F. , Dahnovsky, Y. , and Chien, T. , 2016, “Coexistence of Two Electronic Nano-Phases on a CH3NH3PbI3–x Cl x Surface Observed in STM Measurements,” ACS Appl. Mater. Interfaces, 8(42), pp. 29110–29116. [CrossRef] [PubMed]
Tumbleston, J. R. , Ko, D.-H. , Samulski, E. T. , and Lopez, R. , 2010, “Nonideal Parasitic Resistance Effects in Bulk Heterojunction Organic Solar Cells,” J. Appl. Phys., 108(8), p. 084514. [CrossRef]
Mikhnenko, O. V. , Azimi, H. , Scharber, M. , Morana, M. , Blom, P. W. M. , and Loi, M. A. , 2012, “Exciton Diffusion Length in Narrow Bandgap Polymers,” Energy Environ. Sci., 5(5), p. 6960. [CrossRef]
Mihailetchi, V. D. , Xie, H. X. , De Boer, B. , Koster, L. J. A. , and Blom, P. W. M. , 2006, “Charge Transport and Photocurrent Generation in Poly(3-Hexylthiophene): Methanofullerene Bulk-Heterojunction Solar Cells,” Adv. Funct. Mater., 16(5), pp. 699–708. [CrossRef]
Park, S. H. , Roy, A. , Beaupré, S., Cho, S. , Coates, N. , Moon, J. S. , Moses, D. , Leclerc, M. , Lee, K. , and Heeger, A. J. , 2009, “Bulk Heterojunction Solar Cells With Internal Quantum Efficiency Approaching 100%,” Nat. Photonics, 3(5), p. 297. [CrossRef]
Reyes-Reyes, M. , Kim, K. , and Carroll, D. L. , 2005, “High-Efficiency Photovoltaic Devices Based on Annealed Poly(3-Hexylthiophene) and 1-(3-Methoxycarbonyl)-Propyl-1-Phenyl-(6,6)C61 Blends,” Appl. Phys. Lett., 87(8), p. 083506. [CrossRef]
Park, J.-S. , 1994, “Optimal Latin-Hypercube Designs for Computer Experiments,” J. Stat. Plann. Inference, 39(1), pp. 95–111. [CrossRef]
Jin, R. , Chen, W. , and Simpson, T. W. , 2001, “Comparative Studies of Metamodelling Techniques Under Multiple Modelling Criteria," Computer-Aided Optimal Design of Stressed Solids,” Struct. Multidiscip. Syst., 23(1), pp. 1–13. [CrossRef]
Sun, Y. , Han, Y. , and Liu, J. , 2013, “Controlling PCBM Aggregation in P3HT/PCBM Film by a Selective Solvent Vapor Annealing,” Chin. Sci. Bull., 58(22), pp. 2767–2774. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

A framework for designing active layer nanostructure in BHJ OPVC via SDF

Grahic Jump Location
Fig. 2

Two sample microstructures (a) and (b) along with their Fourier spectrum in the insets; (c) and (d) are the final 1-D SDFs of each image. Dashed line represents the approximated SDF.

Grahic Jump Location
Fig. 1

Variables of interest in processing–structure–performance framework and design scope: (a) A schematic representation of OPVC with BHJ architecture; (b) a four-step energy conversion mechanism

Grahic Jump Location
Fig. 10

(a) Initial image (of size 450 pixels × 450 pixels) (b) Reconstructed (of size 450 pixels × 450 pixels)

Grahic Jump Location
Fig. 11

(a) SDF of original image in comparison with the SDF of reconstructed 3D image/structure and (b) 3D realization of the reconstruction

Grahic Jump Location
Fig. 4

(a) dI/dV mapping of P3HT:PCBM active layer: 100 nm × 100 nm scan size. Brightness and contrast are set arbitrarily. (b) Histogram fitted with two Gaussian functions. Dashed lines indicate the positions of the two Gaussian peaks. Solid line indicates the midpoint between the two Gaussian peak values. (c) Digital values (1 and 0) are assigned based on the dI/dV values in each pixel compared to the solid line in (b).

Grahic Jump Location
Fig. 5

Comparing SDF of the two cases mentioned in Table 1. (a) and (b) are binarized STM images of sizes 100 nm × 100 nm, for cases 1 and 2, respectively. (c) and (d) are the SDFs (solid line) of cases 1 and 2, respectively. In (c) and (d), the dotted line represent the approximations of the SDFs for each case.

Grahic Jump Location
Fig. 12

A sample structure with an excited particle at the center (shaded cell). Yellow arrow represents light's path toward the prospective region; blue represents exciton's path; orange represents electron's path; red represents hole's path. For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.

Grahic Jump Location
Fig. 6

Comparison of CRFs of an original image with a reconstructed image using SDF

Grahic Jump Location
Fig. 7

Two-point CRF observed at different window sizes. The sizes of the windows vary from 100% (i.e., 160 nm) to 40% (i.e., 64 nm).

Grahic Jump Location
Fig. 9

SDF of original image along with two reconstructed images

Grahic Jump Location
Fig. 8

The effect of increasing sampling on accuracy of reconstruction with the time consumed for reconstruction at the bottom. N = 103 is taken the reference, and the other two reconstruction times are in comparison to the first one.

Grahic Jump Location
Fig. 15

The effect of VF and decay on performance with peak point fixed

Grahic Jump Location
Fig. 13

Testing our performance model. (a1–a3) are input parameters: SDF and volume fraction; (b1–b3) are random cross-sectional slices of the reconstructed structure.

Grahic Jump Location
Fig. 14

SDF curves are plotted using the upper bounds and lower bounds of design variables of SDF. SDF of case 1 is also plotted for reference.

Grahic Jump Location
Fig. 16

The SDF and 3D slices of nanostructures with highest (a) and (c) and lowest (b) and (d) IPCE ratio. White regions comprise PCBM while black regions are occupied by P3HT.

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In