Purdue University
Purdue e-Pubs Birck and NCN Publications
Birck Nanotechnology Center
12-9-2009
Modeling and Optimization of Polymer based Bulk Heterojunction (BH) Solar cell Biswajit Ray Purdue University - Main Campus,
[email protected]
Pradeep R. Nair Purdue University - Main Campus,
[email protected]
R. Edwin García Purdue University - Main Campus,
[email protected]
Muhammad A. Alam Purdue University - Main Campus,
[email protected]
Follow this and additional works at: http://docs.lib.purdue.edu/nanopub Part of the Electronic Devices and Semiconductor Manufacturing Commons, and the Power and Energy Commons Ray, Biswajit; Nair, Pradeep R.; García, R. Edwin; and Alam, Muhammad A., "Modeling and Optimization of Polymer based Bulk Heterojunction (BH) Solar cell" (2009). Birck and NCN Publications. Paper 521. http://docs.lib.purdue.edu/nanopub/521
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact
[email protected] for additional information.
Modeling and Optimization of Polymer based Bulk Heterojunction (BH) Solar cell * Biswajit Ray, Pradeep R. Nair, R. Edwin García1 and Muhammad A. Alam *Email:
[email protected] ,
[email protected] Phone: 317-494-9035, Fax: 765-494-6441 Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA 1 Department of Materials Engineering, Purdue University, West Lafayette, IN 47906, USA Abstract A polymer phase separation model based on Cahn-Hilliard equation and a three-dimensional (3D) coupled exciton/electron/hole transport model in the disordered, phase-segregated morphology so generated, allow us to predict– possibly for the first time – the morphology dependent performance limits of polymer/fullerene bulk heterostructure (BH) solar cells. We relate the optimum anneal time to polymer sizes, solvent content, film thickness, and anneal temperature and find that a regularization of the morphology can double the efficiency of BH cells. 1.
Introduction
Polymer based organic solar cell remains an intriguing technology option for its promise of low cost, large scale, roll-to-roll manufacture. For economic viability, however, the low-process cost needs to be complemented by more than 50 % improvement in efficiency η (currently pegged at ~ 36% [1]). Such dramatic improvement in η must necessarily rely on theoretical models that can translate the characteristic, irreducible complexity of the process/devices of organic cells to achievable efficiency.
z
Al electrode
4 1 3
2
Temperature (K)
1) Photon Absorption 2) Exciton Diffusion 3) Charge separation 4) Carrier transport
x
ITO
(a)
In this paper, we present a theoretical/computational process/device model of polymer/fullerene solar cells to explore the coupled flow of exciton/electron/hole within the meso-structure of the cell and quantitatively relate -- possibly for the first time -- the process conditions to the performance of BH solar cell. Moreover, 3D process/device simulation results explicitly predict an optimum annealing time as well as optimum film thickness (section 2 & 3). Finally, we free energy (J/m 3)
The cartoon of a BH solar cell in Fig. 1a illustrates four key
processes that dictate its efficiency, i.e., exciton generation rate (Gex), exciton diffusion (Dex) and dissociation at the donor/acceptor interface, and the collection of electrons and holes in their respective contacts. These processes are often encapsulated in simple rate equation models to relate the effective material parameters to the efficiency of the cell [2, 3, 4]. However, the most modern versions of rate equations do not adequately capture the fundamental innovation of BH cells: With 10 20 , acceptable efficiency is achieved only if the donor-acceptor (D-A) polymer blends are spinodally phase-segregated (Fig. 1b) via annealing, so that a photo-excited exciton would find a D-A surface within ~Lex regardless the point of its generation. Obviously the performance of the solar cell is intimately dictated by this morphology and yet we know of no model in the literature that explicitly relates the meso-structure of the phases to the efficiency of the solar cell.
(b)
0.05 f0
0
fsep
-0.05
(c)
-0.1
øA
0
øB
0.5
TC
600
ø0
500
Nucleation & growth
400
Spinodal decomposition
300
0
1
No Phase Sep.
0.5 Volume fraction (φ)
(d) 1
Fig. 1. (a) Schematic of donor acceptor BHJ solar cell. Dark material is fullerene and the yellow indicates polymer. Excitons (e-h pair denoted as red and white dot), generated in polymer, charge separates at the interface. (b) 3D view of simulated phase segregated morphology on a 100x100x40 grid. (c) Free energy density function for the polymer-fullerene pair. A phase of initial composition separates into two phases and , thus lowering the free energy from f0 to fsep. (d) The typical phase diagram shown for the polymer fullerene system. Above the critical temperature TC there will be no phase separation. Below TC phase separation takes place by spinodal decomposition or nucleation and growth depending on initial conc.
Process Model:
$
∆ ∆ ∆ … … … … … 1
!"#
Fig. 2. Eq. 1 shows the entropy and enthalpy contribution in the free energy of the mixture. Eq. 2 is the Cahn-Hilliard eq. used to simulate kinetics of phase separation and Eq. 3 is the free energy density function for the polymer mixture used for simulation [5]. is the volume fraction of one of the polymers, M0 is a positive transport coefficient, κ is gradient energy coefficient, χ is the Flory interaction parameter for the 2 polymers, v is the volume of a single monomer unit and NA, NB are polymer chain lengths. Eq. 4 is exciton diffusion equation where G0 is the effective exciton generation rate at the surface and α is the photon absorption coefficient. We use diffusion equation (Eq. 5) for carrier transport with the e-h generation term obtained from the solution of exciton diffusion (Eq. 4).
$ % 2&"' ( … … … … 2
) ln 1 ln 1 , % % 0 1 1 … . . 3 *+ / /
"# % 4 5 678 … … . . 4
Exciton Diffusion:
/; % 46; 0 … … . . 5 /;
/; "# /;
Electron/Hole Transport:
compare the random morphology with the well-ordered, regular cell structure (section 4) and the analysis shows that regular structure may offer significant improvement in efficiency to justify the additional processing cost and complexity.
the phase segregated BH active layer morphology with ta. Even though the meso-structure lacks any specific order, but it is characterized by an average domain width W(ta) which scales via the Lifshitz-Slyozov law [7] i.e. W(ta )~ [ Deff ta] n with n~1/3. We reproduce this power-law in Fig. 3d to validate the numerical implementation of our model.
2. Process Model 3. Device Modeling and Optimization We use the well-known and broadly validated Cahn-Hilliard (C-H) equation [6] (Eq. 2, Fig. 2) to describe the spinodal phase separation as a function of anneal time, ta. The driving forces of the spinodal phase separation are the competition between entropy of mixing polymers of lengths NA and NB, and the interaction energy between the material pairs (given by Flory parameter χ) and both the factors can be quantitatively expressed through the free energy density function (Eq. 3, Fig. 2) . The kinetic part of the process (as given by C-H equation) depends on the interfacial energy (given by gradient energy coefficient κ), and effective diffusion parameter M0 (dictated by solvent, e.g. Chlorobenzene or Toluene), and these parameters dictate how quickly the mixture eventually settles to the minima of the free energy curve (Fig. 1c). Fig. 1d shows the evolution of
(b) 200s
(c) 2000s
40 Cluster Size, W (nm)
Annealing Time: (a) 40s
Given the morphology at a particular ta, only a fraction of the photo-excited charge-neutral excitons can diffuse to the polymer/fullerene distributed boundary (or charge separating zone) before being lost to bulk self-recombination. We numerically solve the 3D exciton diffusion equation (Eq. 4, Fig. 2) within this phase-segregated geometry – thereby relating the exciton flux (Jex) to the (anneal-time dependent) morphology of the film. Fig. 4 shows the solution of time dependent exciton diffusion on the phase segregated geometry (corresponding to a given ta), once the light source is removed at time t = 0. We also calculate the steady state total exciton flux Jex (t = ∞) per unit area of the interfacial region on the morphologies generated at different anneal times and it is plotted in Fig. 5a. Assuming that all the
Y (nm)
200 150 100 50
W
Tfilm =100, 150, 200nm
30 W ~ tn
20
~ t⅓
(d)
0 50
100
150
X (nm)
200
250
50
100
150
X (nm)
200
250
50
100
150
X (nm)
200
250
0
1
10 10 Annealing Time, ta(min)
Fig. 3. (a), (b), (c) are the 2D X-Y cut for the same 3D morphology at different anneal times. We observe a characteristic cluster size (W), as shown in (c), in each of these morphology which grows with anneal time. The various simulation parameters are: Mo = 1.1x10-32 cm5/J-s; κ = 105 J/cm, NA=40, NB =10 Volume of single monomer unit (v) = 5.23x10-28 m3. (d) Characteristic cluster size growth as a function of anneal time shows a power law dependence (W ~ tn), where n ~ (¼-⅓). This power law validates the numerical implementation of the spinodal phase separation of polymer-fullerene system.
Time:
(a) 0s
(b) 1ns
(c) 5ns 1 0.8
150
0.6
W 100
0.4
50
0.2
0
0
50
100
150
200
250
50
100
X (nm)
150
200
250
50
100
X (nm)
150
anneal time (topt) monotonically increases with the thickness of film as shown in Fig. 6c. Moreover, the maximum value of short circuit current (JSC peak) at optimal annealing increases with film thickness as more and more photons are absorbed (Fig. 6c), but beyond the photon absorption length, the geminate recombination (cross marks in Fig. 5b) [9] ensures that no further improvement in JSC is possible.
Once excitons are charge separated, electrons/holes are transported to the anode (Al electrode)/cathode (ITO) through the percolating pathway provided by the polymer (fullerene) clusters. Figs. 5b and 5c show, however, that only a fraction of the polymer (or fullerene) volume is connected to the correct electrode for electron collection and the carriers are prevented from exiting through the wrong contact by appropriate blocking layers [8]. Moreover, floating islands do not contribute to output current. Obviously, the connectivity increases with anneal time (Fig. 5c), as the width of the phase-segregated region scales as W ~ tan (Fig. 3d). However, Fig. 5b already indicates that Jex decreases rapidly with ta. These two counter-balancing trends results in an optimum anneal time (topt) for maximum Short circuit current, JSC, of solar cell (see Figs. 6a and 6b). This optimum value of the
4. Regular Structure Finally, it is natural to ask if efficiency can be improved by regularizing the morphology [10]. Fig. 7a. shows a well ordered 3D regular finger structure with columns of fullerene (dark) and polymer (bright). Unlike the phase-segregation BH cell discussed above, there are no floating islands in this structure. The 3D simulation for exciton diffusion (Fig. 7b) shows that random morphology may be better for exciton dissociation due to its larger interfacial area but there is more than factor of 2 improvement [11] in overall JSC (Fig. 7c) for regular structure due to its better e-h transport properties.
:
Z
17
250
X (nm)
excitons that come to the interfacial region dissociates into electron hole pairs and all the dissociated electron hole pairs can reach the respective electrodes, the maximum limit for the short circuit current density (JSC) is estimated and is shown in Fig. 5a. as a function of anneal time.
x 10
200
Geminate Recombination
Al electrode
1.5 20 1
T film=100nm
0.5 2
h+ e-
eh+
X
10
1 0.8 0.6 0.4
ITO 0.2
3
10 10 Annealing Time (s)
1.2
30 JSC (mA/cm 2)
Jex (number/cm 2)
T film=200nm
Fractional Useful Area
Y (n m )
200
Fig. 4. (a,b,c) Time dependent exciton diffusion on the X-Y plane (transient response once the light source is removed) obtained by solving Eq. 4. Bright region represents the excitons generated in the polymer and dark regions are fullerene clusters which act as the sink for the generated excitons. (d) For analytical modeling we transform the random geometry to a regular structure having same characteristic width. The various simulation parameters are: Dex = 10-4 cm2/s; tex= 10 ns. Exciton generation rate G0= 2x1028 m-3s-1. Photon absorption coefficient (α) is taken as (100nm)-1.
(a)
(b)
0
(c)
50 100 150 Annealing Time (s)
200
Fig. 5. (a) Integrated exciton flux per unit interfacial area of the cell is plotted against anneal time and the corresponding maximum possible short circuit current density is also shown in the right hand side of the axis. Uniform generation of excitons (Gex = G0) without geminate recombination of charge carriers are assumed. (b) X-Z cut of the 3D structure (Fig. 1b) showing the percolated pathways for electrons and holes provided by fullerene clusters (dark) and polymer phase (bright). Geminate recombination takes place at the interfacial region denoted by x. Note the presence of some isolated floating fullerene clusters which do not take part in current conduction. (c) Fraction of the connected fullerene clusters as a function of anneal time. After 50s almost all fullerene clusters are connected providing percolated pathways for electrons to Al Electrode
30 (a) Tfilm=50 nm
6
No Rec. -αZ
B: Gex=G0e
B
No Rec. C: Gex=G0e-αZ
C 4 topt 3 -1 10
25
0
with Rec.
Exp . Data [7]
20 15
B
10 5
Exp . Data [8] [13]
C
1
0 -1 10
2
10
6 5.5 5
Tfilm(opt)
4.5
20 15 10 5
[12]
10 10 Annealing Time (min)
(c)
A
JSC(peak) (mA/cm 2)
A: Gex=G0 JSC (mA/cm 2)
JSC (mA/cm 2)
A
5
6.5
(b) Tfilm=200 nm
topt 0
1
10 10 Annealing Time (min)
2
50
10
100 150 200 Film Thickness (nm)
Opt. Annel Time (min)
7
0
Fig. 6. Short circuit current obtained by solving diffusion equation (Eq. 6) for electrons in the 3D morphology generated at different anneal times for devices with thickness (a)Tfilm=50nm (b) Tfilm=200nm. The electron and hole generation rate is coupled with the exciton flux on the interfacial boundary. The curves (A, B, C) in both the figures illustrate how JSC gets reduced in various stages. The simulation parameters are: De = 10-9 m2/s; τe = 10 µs and photon absorption coefficient (α) = (100 nm)-1. The simulations accurately predict experimental trends for both thin and thick film devices (experimental data scaled by a constant factor). (c) Peak values of Short circuit current and the corresponding optimum annealing times for different active layer thicknesses of the cell. We observe monotonous increase in JSC peak with film thickness till the photon absorption length (100 nm), beyond which geminate recombination decreases the current.
5. Conclusion
References
We have demonstrated for the first time the possibility to complement the empirical approach to polymer solar cell design by predictive theoretical models of spinodal decomposition and exciton/electron/hole transport for designing better experiments and improved efficiency. We conclude that (i) there is an optimal anneal-time (Figs. 6a & 6b) and film thickness (Fig. 6c) for BH solar cells that is uniquely defined by the polymer blends of the cell, and that (ii) regularized structure like double-gyroids or stamped structures may offer more than 100% improvement (Fig. 7c) in efficiency to justify the additional processing cost. Acknowledgement: We acknowledge Columbia Energy Frontier Research Center and Purdue Network of Computational Nanotechnology for financial support and computational resources for this project.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
G. Dennler, M. C. Scharber, and C. J. Brabec, Adv. Mat., p. 1, 2009. W. Geens, T. Martens, J. Poortmans et al., Thin Solid Films, p. 498, 2004. L. J. A. Koster, E. C. P. Smits, V. D. Mihailetchi, and P. W. M. Blom, Thin Solid Films, p. 498, 2004. H.R. Kerp, H. Donker, R.B.M. Koehorst, T.J. Schaafsma and E.E. Faassen, Chem. Phys. Lett., p.302, 1998. R. A. L. Jones, Soft Condensed Matter, Oxford Univ. Press, 2002. J. W. Cahn and J. E. Hilliard, J. Chem. Phys., p. 258, 1958. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids, p. 35, 1961. W. Hains and T. J. Marks, APL, p.023504, 2008. L. Onsager, Physical Review, p. 554, 1938. K. M. Coakley,Y. Liu, C. Goh, M. D. McGehee, MRS Bull, p. 95, 2009. Z. Fan et al., Nature Materials, p.648, 2009. M. Reyes, K. Kim and D. L. Carroll, APL, 083506, 2005. M. Y. Chiu, U. Jeng, C. H. Su, K. S. Liang, and K. H. Wei, Adv. Mat., p. 2573, 2008.
16
x 10
Spinodal
9
5
8 Regular
7
JSC(Peak) (mA/cm 2)
Jex (number/cm 2)
14
10
6
JSC (mA/cm 2)
(a)
12
(c)
10
Regular
8
Spinodal
6
(b)
4 10
20 30 Cluster Size (nm)
6
4
50
100 150 200 Film Thickness (nm)
Fig. 7. (a) 3D view of a perfect regular structure for the Bulk heterojuction solar cell. (b) Comparison of exciton flux for regular and spinodal structure having same cluster size. Surprisingly spinodal structure is more suited for exciton dissociation for smaller cluster size. But carrier transport in regular structure is much better and hence in (c) the short circuit current density obtained from regular structure is higher than the JSC(peak) of spinodal structure for the same average cluster width.
