OPTICAL MODELING OF ORGANIC PHOTOVOLTAIC SOLAR CELLS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Maithili Ghamande August, 2011 OPTICAL MODELING OF ORGANIC PHOTOVOLTAIC SOLAR CELLS Maithili Ghamande Thesis Approved: Accepted: Advisor Dean of the College Dr. Jutta Luettmer-Strathmann Dr. Chand Midha Faculty Reader Dean of the Graduate School Dr. Robert R. Mallik Dr. George R. Newkome Faculty Reader Date Dr. Yu-Kuang Hu Department Chair Dr. Robert R. Mallik ii ABSTRACT Organic photovoltaic devices consist of several thin layers of material with different electro-optical properties. Since the conversion of incident photons to charge carriers occurs only in the active layers, the intensity distribution of light within the device has an important effect on the efficiency of a solar cell. The intensity in turn depends upon properties of the layers, such as refractive index, absorption coefficient, and thickness, as well as on properties of the incident light, such as angle of incidence and spectral distribution. In this work, we investigate the absorption of light in thin-film organic solar cells with computational methods. Since interference effects play an important role in thin-films, we implement a transfer matrix method to calculate the complex amplitude of the electric field at the interfaces and propagate the electromagnetic wave within the layers. We apply the method to conjugated polymer/fullerene bilayer solar cells and investigate devices of two planar geometries for the relevant part of the solar spectrum and a range of angles of incidence. Our results show that the angle of incidence has a small effect on the distribution of the electric field in the active layers for a wide range of angles. For normal incidence, we confirm that the thickness of one of the layers, the layer adjacent to the metal electrode, has a large effect on the electric field distribution and find that the absorbance of light in the iii active layers depends strongly on the wavelength of the incident light. A reweighting of the absorbance with the solar irradiance illustrates that optimizing the design of solar cells requires a compromise between materials properties and device geometry. iv ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my advisor, Dr. Jutta Luettmer- Strathmann, for her constant support, patience and especially her guidance through- out this work. I would also like to thank Dr. Hu and Dr. Mallik for being on my committee and giving valuable advice and encouragement. Special thanks to my re- search group members and my friend Kiran Khanal for valuable assistance. I am grateful to the faculty and staff in the Department of Physics for their direct or in- direct help during my study and research. Finally, I would like to thank my parents and sister, for their support during this work. v TABLE OF CONTENTS Page LIST OF TABLES . viii LIST OF FIGURES . ix CHAPTER I. INTRODUCTION . 1 1.1 Organic Solar Cells . 1 1.2 Sunlight . 3 1.3 Thesis Outline . 6 II. MAXWELL'S EQUATIONS . 8 2.1 Maxwell's Equation and Boundary Conditions . 8 2.2 Time Harmonic Maxwell's Equations . 9 2.3 Electromagnetic Waves in Media . 10 III. LIGHT PROPAGATING THROUGH STRATIFIED MEDIA . 15 3.1 Boundary Conditions at a Plane Interface . 15 3.2 Transfer Matrix for a Single Interface . 19 3.3 Multilayer System . 24 IV. ORGANIC SOLAR CELL MODEL AND CHARACTERISTICS . 34 vi 4.1 Organic Solar Cell Model . 34 4.2 Modeling Parameters . 36 V. RESULTS . 41 VI. SUMMARY AND CONCLUSION . 55 BIBLIOGRAPHY . 57 vii LIST OF TABLES Table Page 3.1 Parameters for the example of an air/glass interface with light inci- dent from air with θi = 0. 22 4.1 Thickness of layers in the solar cell for two different geometries. 39 viii LIST OF FIGURES Figure Page 1.1 Schematic drawing of the working principle of an organic photo- voltaic cell. Illumination of the donor material through the trans- parent ITO electrode has created an exciton, which diffuses to the interface between the donor material and the acceptor material. The curved arrow indicates the path of the exciton. At the interface, the exciton dissociates, and the electron is transferred to the acceptor material, leaving a hole in the donor material. These charged car- riers are then transported to and collected at their respective electrodes. 2 1.2 Standard AM 1.5 G solar irradiation spectrum [10]. 5 1.3 Absorption coefficients of active materials (left axis) and the AM 1.5 standard solar spectrum (right axis). MDMO-PPV and P3HT are conjugated polymers that act as donor materials, PCBM is a soluble derivative of the fullerene C60 and an acceptor material. Absorption of sunlight occurs only for wavelengths of about 300 nm to 700 nm [11]. 6 1.4 Orientation of a solar cell array. A ray from the sun (solid line) at midday is normal to the panel when the panel is tilted by an angle β to the horizontal. For the state of Ohio, the angle is approximately 400. 7 3.1 Two media with indices of refraction n1 and n2 are separated by a plane interface perpendicular to the z-axis. An electromagnetic with wave vector k, electric field E, and magnetic field H is incident at point P of the interface with angle of incidence θi. The wave is partially reflected in the same medium with angle θr = θi and fields E0 and H0 and partially transmitted with angle of refraction 00 00 θt and fields E and H . The symbol n denotes the unit vector perpendicular to the interface, and k, k0, and k00 are the wave vectors of the incident, reflected, and refracted rays, respectively. 16 ix 3.2 A planar interface I0ba at z = 0 separates media 0 and 1 with indices of refraction n0 and n1. A TE wave is incident on I0ba with ampli- tude E0bp and angle of incident θ0, and is reflected with amplitude E0bn. The transmitted wave has amplitude E0ap at the interface and angle of refraction θ1. E0i, E0r and E1t are the z-position dependent electric fields of the incident, reflected, and transmitted waves. 20 0 3.3 A wave of wavelength λ = 480 nm traveling from z0 = 0 is incident on a planar interface at z = 0 between medium 0 (air) and medium 1 (glass) with angle of incidence θ0 = 0 and amplitude E0bp = 1. The lines in the top and bottom panel show the real and imaginary contributions of the total electric field amplitudes, respectively. 23 0 3.4 A wave of wavelength λ = 480 nm traveling from z0 = 0 is incident on a planar interface at z = 0 between medium 0 (air) and medium 1 (glass) with angle of incidence θ0 = 0 and amplitude E0bp = 1. The incident (blue), reflected (red) and transmitted (black) intensities in medium 0 and 1 are shown. 24 3.5 A TE wave is incident on the planar interface between medium 0 and medium 1 with complex amplitude E0bp. The wave is partially reflected in the same medium with amplitude E0bn and partially transmitted into medium 1 with amplitude E1ap. The wave is par- tially reflected from interface I1ba into medium 1 with amplitude E1bn and partially transmitted into medium 2 with amplitude E2ap. 25 3.6 Layer system consisting of ambient (0) and substrate (m) semi- infinite layers and m − 1 finite layers. Layer j has thickness dj, refractive index nj, and forward and backward traveling waves with amplitudes Ejbp and Ejbn, respectively, at the interface Ij+1. Ejap and Ejan are the corresponding amplitudes at the interface Ij. 27 3.7 The absolute square value jEj2 of the electric field inside an air- glass-air system for normal incidence and light of wavelength λ = 480 nm. 29 3.8 Reflected amplitudes E0r, E01r and E2r in the air (40nm)-glass (160nm)-air (50nm) system for a wavelength of λ = 480 nm and normal incidence. The top and bottom panel show the real and imaginary contributions, respectively. 31 3.9 The absolute square value jEj2 of the electric field inside the air- glass-air system for θ0 = π=3 and light of wavelength λ = 480 nm. 32 x 3.10 The absolute square value jEj2 of the electric field as a function of position z for a range of angles of incidence θ0 for the air-glass-air system. (a) The contour lines tagged by values represent lines of constant jEj2; the vertical lines show the interfaces. (b) In the col- ormap of jEj2, the shades represent values indicated in the colorbar on the right. 33 4.1 The arrangement of layers in the solar cell. At the top is the ITO electrode, in the middle are the PEOPT and C60 active layers, and at the bottom is the aluminum electrode. A PEDOT layer is placed between ITO and PEOPT; light is incident from the ITO side. 35 4.2 Chemical composition of the active material poly(3-(4'- (1",4",7"-trioxaoctyl)phenyl)thiophene) (PEOPT), of poly(3,4- ethylenedioxythiophne)-poly(styrenesulfonate) (PEDOT), and of the anion (PSS) [3] . 36 4.3 The absorption coefficient χ as function of wavelength λ for PEOPT (solid line) and C60 (dashed line) calculated from index of refraction data of Ref. [3]. 37 4.4 Complex refractive indices of PEOPT and C60 as a function of wavelength λ. The nr (dashed lines) and ni (solid lines) represent the real and imaginary part of the refractive index n, respectively. [3] . 38 4.5 Complex refractive indices of ITO, PEDOT and Al as a function of wavelength.