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.

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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

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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.

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Fig. 3

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

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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).

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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.

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Fig. 6

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

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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).

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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.

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Fig. 9

SDF of original image along with two reconstructed images

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Fig. 10

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

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Fig. 11

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

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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.

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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.

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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.

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Fig. 15

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

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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.



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