Simulation of an Organic Photovoltaic Cell (OPC) Using ATLAS
Introduction
In recent years, the investigation of Organic Light Emitting Diodes (OLEDs) and photovoltaic devices based on small organic molecules and polymers has attracted significant interest due to their potential for inexpensively generated electricity. ATLAS has been used already to investigate OLEDs [1] and compound material GaInP[2][3] devices.
In this article, we will present the use of the ATLAS simulator for the analysis of a PiN organic photovoltaic cell based on the organic material TPD, blendZnPc/C60(1:1), C60.
Simulation Models
Optical Modeling
The RayTracing Method (RTM), Transfer Matrix Method(TMM)
and Beam Propagation Method(BPM) were implemented in the ATLAS/Luminous simulation
package for optical
modeling. In this article, TMM was employed in which the amplitude of the electromagnetic
field vector is calculated by taking into account the optical constants n and
k.
Figure 1. Refractive index profile of a singlelayer coating 
To enable the transfer matrix method for calculation of intensity distribution and photogeneration rate profiles in thin film detectors, the TR.MATRIX parameter on the BEAM statement should be specified.
Light Absorption and PhotoGeneration
The cumulative effects of the reflection coefficients, transmission coefficients,
and the integrated loss due to absorption over the ray path are saved for each
ray. The generation associated with each grid point can be calculated by integration
of the generation rate over the area of intersection between the ray and the
polygon associated with the grid point. For multispectral source, the generation
rate is given by:
where, _{0} is the internal quantum efficiency.
P() is the power spectral density of the source.
L is a factor representing the cumulative loss due to reflections, transmissions, and absorption over the ray path.
is the wavelength.
h is Planck’s constant.
c is the speed of light.
is the absorption coefficient given by
y is the depth of the device, where x,y forms the twodimensional mesh
Transport in Organic Materials
The following models are support in ATLAS/OTFT for
the disordered organic materials[4].
 Density of state model for disordered organic material
 Hopping mobility model
 PooleFrenkel mobility model
 Bimolecular Langevin recombination model
Simulation Structure and Results
Figure 2 shows the simulation structure used in this article. It is a 5 layer device; the p type MeOTPD, absorption layer ZnPc:C60 and n type Rhodamine BC60 films are sandwiched between the IndiumTinOxide(ITO) larger coated on glass substrate and an Aluminum metal contact. The p and n type layers are doped at 1e18cm^{3}, so the contact with both electrodes can be assumed to be ohmic.
Figure 2. OPC structure PiN type on 50nm/30nm/50nm ITO/pdoped(MeO) TPD/iabsorption blend ZnPc:C60(1:1)/ndoped(RhodamineB) C60/Aluminum 
The material parameters for the disordered organic materials are: electron mobility of 2e5 cm2/Vs hole mobility of 8e5 cm^{2}/Vs and dopant density of 1e18 cm^{3}. For the active absorption layer, we use a mobility of 2.5e6 cm^{2}/Vs for holes and 5e6 cm^{2}/Vs for electrons. The PooleFrenkel mobility model parameters (E0N.PFMOB and E0P.PFMOB) are specified as 2.5e5 V/cm.
The energy levels are given in Table 1.


Table 1. Energy levels for the PiN OPCs. 
In the photovoltaic absorption layer, we calculate the generation rate profile of charges resulting from absorption of the injected light with intensity of 127 mW/cm^{2}. The generation rate distribution is shown in Figure 3. The p and n type layers are not absorbing, so the generation rate is zero. The p and n type transport layers do not contribute to the generation rate.
Figure 3. Generation rate profile of PiN solar cell. 
The distribution of free and trapped carriers and the electric field as a function of position within the device are shown in Figures 4 and 5 Since ohmic contacts are assumed, the number of free carriers in the doped wide gap layer is uniform and equal to the dopant density. But in the intrinsic active absorption layer, depletion regions are formed due to diffusion of the free majority carriers from the doped layers into the intrinsic layer. So the carrier distribution has a profile of free carriers and trapped carriers from the balance of recombination, generation, trapping and transport as shown in Figure 4.
Figure 4. Distribution of the free and trapped carriers without external voltage under illumination. 
Figure 5. Distribution of electric field under illumination of 127mW/cm2. 
The concentration of traps strongly influences the value of the current density at positive and negative bias. This dependence is shown in Figure 6, at trap densities ranging from 1e16 to 1e19 cm^{3}. As the trap concentration is lowered, the current density reaches saturation due to low losses in the active layer. Figure 7 shows the effects of illumination on current density.
Figure 6. IV characteristics due to the concentration of trapping states from 1e16 to 1e19cm3 in the blend layer. 
Figure 7. IV characteristics under illumination with 70 and 127 mW/cm2. 
Figure 8. Current versus applied voltage with the characteristics parameters describing the photovoltaic cell. 
The power conversion efficiency of this photovoltaic cell under illumination conditions depends on Jsc and Voc which are shown in Figure 8. The fill factor is given by:
In this structure, Jsc is 8.9mA/cm2, Voc is 0.63V and max(JpVp) is 2.32 mW/cm^{2}, so the FF is 41.4%
The power conversion efficiency is 1.83%
Conclusion
An organic photovoltaic cell has been analyzed using the ATLAS simulator to simulate the response of a blended photovoltaic device to incident solar light. This model is readily extended to a wide range of disordered organic materials.
Reference
 Simulation Standard Vol.15. No.5. May 2005.
 Simulation Standard Vol.15. No.2. February, 2005.
 Simulation Standard Vol.15. No.11. November, 2005.
 ATLAS User’s
Manual, March 2007.