D. P. Gruber1, G. Meinhardt,2 W. Papousek3

1 Polymer Competence Center Leoben GmbH, Parkstrasse 11, 8700, Leoben,

Austria

gruber@pccl. at

2AustriaMikroSystems AG, Premstatten, Austria 3Institute of Nanostructured Materials and Photonics JOANNEUM RESEARCH

GmbH, Weiz, Austria

In case of an organic photovoltaic device the incident sunlight must be absorbed in a very thin area within the photovoltaic device, which can be assured by a proper choice of material parameters and layer thicknesses. In a recent paper it was shown that the dependence on the absorption within the active layer is not a trivial function of its thickness, but follows a rather complicated behavior [6]. In this paper we carried out methods for the specific optimization of light absorption of an organic photovoltaic device. Numerical simulations of multilayered structures on the nanometer scale show interesting spatial distributions of light absorption depending on the thicknesses and the optical constants of the individual layers. Parameter studies were carried out, in which we varied the coefficient of extinction and the refractive index of each layer. That gave us a suggestion for the optical constants of a photovoltaic device with optimal power conversion efficie ncies. In this paper we also present methods which permit to dispose the maxima of absorption density to the area near the pn-junction. According to our calculations photovoltaic devices were built, which show decisively improved power conversion efficiencies. Furthermore we analyzed the correlation between photo current and absorption density in a given area around the pn-junction, which lead to better understanding of the diffusion range of dissociated charge carriers.

1. Introduction

There are two essential limiting factors for the efficiency of photoelectric devices like solar cells and photo detectors: The absorption of the incident light energy and the transport of the built charge carriers. In this paper we present a method for the optimization of the light absorption efficiency of bilayer pn-junction devices which are built up as a stack of four layers on a glass substrate with two separate homogeneous layers building a pn-junction (active area) and a PEDOT layer between an ITO and an aluminium electrode. At the interface between those materials, a fast electron

transfer from the p-conducting layer to the n-conducting layer occurs upon light excitation [6] and the respective charge carriers are transported to the electrical contacts of the photovoltaic device. To optimize the energy absorption in a bilayer pn-junction solar cell one has to take care that the maximum of the density of light absorption matches the region near the pn-junction. Different publications reported
electroabsorption studies of electric fields in bilayer molecular organic photovoltaic devices made of zinc-phthalocyanine (ZnPC), perylene pigment (MPP) and other materials [11,12,13]. It was figured out that the interface field has a different spectral signature as that of the bulk of the two layers [11] but they accounted the square of the electric field as the deciding value for the optimization of energy conversion which turned out to be not the full truth. Investigations in the behavior of the spatial distribution of energy density inside the devices showed that there is a mismatch between the square of the electric field |E|2 and the absorption density in dependence on the position vector through the photovoltaic device. [1,2,3,4]. Later papers reported modeling of light absorption of organic solar cells emphasizing the great potential which still rests in today’s construction of organic photovoltaic devices [6,7]. Our paper leads to improvements in the proper use of current solar cell materials on the one hand and gives an indication about the optical behavior of new materials providing optimal energy conversion for future device setups on the other hand.

2.

Fig. 1: Electromagnetic wave incident on a multilayer

Theory

Figure 1 shows the electrodynamic setup of an organic solar cell. We assume perpendicular incoming light in counter ‘z’ direction. In the classical model at any interface between two layers the incident light is divided into a transmitted part in ‘ z’ direction and a reflected part in counter ‘z ‘ direction. At l, l +1 reflected parts fall back at l-1,l where they are divided again into a transmitted and a reflected part. Consequently it comes to multiple reflections in every layer. In the model one can substitute multiple reflections by an electric field Em+ in ‘z’ direction and an electric filed in counter ‘ z ‘ direction Em- [1].

incident wave (given): E (r) = Ae

-ik r

(1)

Based on MAXWELL’s equations and the conditions of continuity one gets for the partial waves in the multilayer:

07 — PV Systems and PV Cells
reflected wave: E (r) = Ae-k r	(2)
—■l — — — l — kl-~ wave l — (counter z-direction): E (r) = A e r	(3)
—l + ■» — l + :7l+ r wave l + (z-direction): E (r) = A e	(4)
transmitted wave: E (r) = Ae ~,k r	(5)

(l = 0,1,2,….. m -1)

e

One can set the coordinate system without loss of generality so that k is parallel to the xz-plane what ensures key = 0. Consequently one gets simpler expressions for the wave vectors of the incident, reflected and transmitted wave. From the conditions of continuity

at z = D1, Dm one gets the amplitude vectors of the reflected and the transmitted

waves as well as for the waves l — and l + within the layers. Furthermore one can choose Ay = 0 without loss of generality. With the wave vectors and the amplitude

incident wave: Ee (z) = e-i(kXx+kzz) Ax (6) reflected wave: Erx (z) = — r0me-2ikeeDle-i{kXx-kzz ] Aex (7) wave l -: Elx- (z) = kz tom eikzDl+1 e^ik‘.D1 e~i(keex+kzz) Ae kez tm x (8) wave l +: Elx+ (z) = _ K-lsmr e-ik‘zDi+ie-iktDi Aee-i(kexx-klzz) Ae e lm x x kz tlm (9) transmitted wave: k t Et ( z) = ~^t e~ik‘tDme — ik‘zD1e-i(k‘ex+k‘zz) Ae x e 0m x < (10)

vectors and by the use of the Fresnel coefficients [1] one can calculate the electric field of the incident, reflected and transmitted waves as well as for the wave components within the layers:

a a(z) =T

E

(11)

2

According to the definition of the absorption density in MAXWELL’s electrodynamics

al kl 2 о S 2 2 ke tlm

e 2Im( kl)(Di+i-z)

— 2 Re

+ r 2 e~2Im(kl)(Dl +1+ z) + lm

(Ae )2

r e 2i Re(kl )(Di+i-z) ‘lmc

ai (z)

the absorption density in the layer l turned out as:

(12)

(l = 0,1,2,….. m) where tlm and rlm are the Fresnel coefficients of the part of the layer indicated by the indices.

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