A NEW SOLAR CELL SIMULATOR: wxAMPS

Yiming Liu1,2, Dan Heinzel2, and Angus Rockett2

1 Institute of Photo-Electronic Thin Film Devices and Technology, Nankai University,

Tianjin 300071, P.R. China 2 Department of Materials Science and Engineering, University of Illinois,

1304 W. Green St., Urbana Illinois 61801, USA

ABSTRACT

A new solar cell simulation program, wxAMPS, is presented in this work. The interface of wxAMPS is developed using a cross-platform library, wxWidgets, and the kernel is based on an updated version of the AMPS (Analysis of Microelectronic and Photonic Structures) code. wxAMPS incorporates two different tunneling models for better simulation of specific types of solar cells. Compared to the drift-diffusion model, the intra-band tunneling model provides more realistic characteristics for heterojunction solar cells. The other tunneling component is trap-assisted tunneling current, which plays an important role in tunneling recombination at junctions. To increase the convergence property of this model, a new algorithm that combines the Newton method and the Gummel method has been developed. The simulation results from different models are compared. A preliminary WIKI has also been set up, which provides a database of materials parameters for various kinds of solar cells to help the PV community share materials data and more easily implement simulations.

OVERVIEW The wxAMPS program is a newly developed solar cell simulation software based on the original AMPS (Analysis of Microelectronic and Photonic Structures) code.[1] The graphical user interface (GUI) of wxAMPS is designed with a cross-platform C++ library, wxWidgets, and allows quick data entry as well as enhanced visualization of results for comparison and analysis. The main physical principles are derived from AMPS [2] and in addition two different tunneling models, intra-band tunneling [3] and trap-assisted tunneling [4], are incorporated to the program. The algorithm of wxAMPS has been modified to combine the Newton and Gummel methods, which improves convergence and stability. The effects of series and shunt resistance unrelated to the main diode are also added. A database-oriented WIKI [5] has been set up for sharing the simulation files of devices and helping users find and discuss the parameters used in solar cell simulations. wxAMPS is a good tool to simulate various kinds and structures of solar cells, which can be made from crystalline and amorphous Si material, as well as CdTe and CIGS thin films, and other materials. Tandem-structured solar cells can also be simulated through using the trap-assisted tunneling model in which carrier motilities

are enhanced as functions of electric fields. The latest runnable version can be obtained at the WIKI website.

UPDATED FEATURES Interface The main user interface (Figure 1) is almost the same as the version described previously [1] with the exception of a “Settings” section under the Run button, allowing users to switch the tunneling models and adjust numerical parameters. In the “Settings” dialog box, users can set up upper limit of iteration times, the convergence precision and the clamping range that is the maximum variables change in one iteration. The variables variation is clamped in order to avoid the overestimation generated by the Newton method.

Figure 1 Main user interface of wxAMPS

Another improvement is in the ambient dialog box where the bias voltages of interest can be loaded from a user-customized text file. The ambient conditions configured previously by the user are cached automatically to help reduce the time spent tweaking the simulation environment. Among these settings, smaller voltage steps and clamping ranges can help improve the convergence property for a specific model, but at a cost of longer calculation time. Two additional slide bars have been added to the results dialog box in order to allow users to modify the values of the series and shunt resistances (Figure 2). Upon adjustment of the slide bars, a new current-voltage curve is calculated and displayed and new device parameters are obtained. The revised results and the new curve are updated simultaneously when changing the slide bars of the shunt and series resistances.

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Figure 2 Display dialog box for simulation results and analysis Algorithm Modifications The Gummel method was used in our previous version of wxAMPS to solve the intra-band tunneling current model. Its range of convergence is broad, and it works well on solar cells with low densities of defect states, such as CIGS and CdTe solar cells. However, it encounters difficulty when treating solar cells with high recombination rates, like amorphous Si solar cells. This leads to heavy coupling of the three basic semiconductor equations (Poisson’s equation and the continuity equations for electrons and holes), which causes divergence issues. The Newton method is able to solve the strong coupling situation, but makes it difficult to add the intra-band tunneling current into the model for the complicated Jacobian matrix [1], and proper initial values are also important to the convergence. To solve these mentioned problems, a new algorithm combining the Newton and Gummel methods has been developed. At first, the variables (local vacuum levels and quasi-Fermi levels for electrons and holes) are initialized through a few Gummel iteration steps. Second, a solution is found by using the Newton method in which the drift-diffusion model is used but the intra-band tunneling effect is not considered. The solution obtained in the second step is then used as input for the final calculation, employing the Gummel method to add the effects of intra-band tunneling current. The trap-assisted tunneling model can be implemented in the Newton method, so the first two steps are enough to achieve the solutions for this model.

SIMULATION COMPARISON

Performance

The Gummel iterations in the first step of the algorithm provide more stability for the convergence of the program. Because of the better-initialized guess, wxAMPS works in some cases where AMPS fails with floating number exceptions. Additionally, users will not lose all their information if the simulation does not converge at a certain

bias voltage. In the current version, the values calculated during the each simulation step are cached so as to be accessible to the user. The convergence speed is mostly determined by the performance of the third step. In the case of low recombination rates, the Gummel method converges fast and wxAMPS consumes less time than AMPS does. In the case of high recombination rates, the Gummel method may need more iterations to attain the model results when the intra-band tunneling current is added. However, in the trap-assisted model the third step is not required, which makes the calculation much faster. Results To compare the simulation differences between these models, a baseline CIGS solar cell [6] was simulated.

Figure 3 Dark IV curves derived from three models

The simulated results of the three models were very close, as seen from Figures 3 and 4. In the dark IV curves, there is only a little difference at high voltage bias, where the current of the intra-band tunneling model is slightly lower. This is because large currents will be limited by the thermionic emission mechanism in the intra-band tunneling model [7]. Large currents will lead to significant discontinuities of quasi-Fermi levels at the heterojunction interfaces in the intra-band tunneling model, which is different from that quasi-Fermi levels at interfaces are continuous in the drift-diffusion model. In the light condition of Figure 4, the current-voltage curves predicted by these models are indistinguishable. This is a result of low working currents and weak electric fields in the device. In the intra-band tunneling model, these low currents will not be limited by thermionic emission through heterojunction interfaces. In the trap-assisted model, the tunneling recombination effect is reduced to the conventional Shockley-Read-Hall

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recombination because of the weak electric fields.

Figure 4 Light IV curves from three models. The default AM1.5 spectrum of AMPS is used. To study the thermionic emission limit to the current and understand the differences better, the band spike between the CdS and CIGS layers was artificially changed. This was implemented by modifying the electron affinity of the CdS layer. It was found that when the band spike is smaller than the one in the baseline device, the results become much closer. However, when the band spike is 0.3 eV higher than in the baseline case, the differences of the current-voltage curves become obvious (Figure 5).

Figure 5 Light IV curves from different spike heights at the CdS/CiGS interface. As seen from the Figure 6, the energy band diagram produced by the intra-band model shows noticeable discontinuities between Efn and Efp at the heterojunction, especially a significant discontinuity of 0.6 eV for the Efp, whereas in the drift-diffusion model quasi-Fermi levels at interfaces are the same. The comparisons show that when simulating abrupt heterojunction solar cells with a high band spike, thermionic emission limits will take effect and cause significant differences among these models.

Figure 6 Energy band diagram of the CdS/CIGS interface with a spike of 0.3eV higher than the baseline, at short-circuit condition under illumination.

SUMMARY

With convenient user interface and the incorporation of the intra-band tunneling model and the trap-assisted tunneling model, wxAMPS is high performance software to simulate the behaviors of heterojunction solar cells. A new algorithm taking advantage of the Newton and Gummel method enhances the convergence property and also makes the program feasible to model the intra-band tunneling effects for devices of heavy-recombination. The solar cell parameters predicted by these two tunneling models and traditional drift-diffusion model are very close if the device works in weak electrical fields as well as low currents, and without a high barrier at the hetero-interface.

ACKNOWLEDGEMENTS The authors would like to thank China Scholarship Council for the support. A.R. and D.H. acknowledge funding from the National Science Foundation under award 0602938-0017756000 Materials World Network. The generous sharing of AMPS software and source code by Prof. Stephan Fonash at Pennsylvania State University is also appreciated.

REFERANCES

[1] Y. Liu, D. Heinzel, and A. Rockett, "A revised version of the AMPS simulation code", in Photovoltaic Specialists Conference (PVSC), 2010 35th IEEE, 2010, pp. 001943-001947. [2] S. Fonash, et al., "A Manual for AMPS-1D for Windows 95/NT", The Pennsylvania State University, 1997. [3] K. Yang, "Modeling of abrupt heterojunctions using a

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thermionic-field emission boundary conditions", Solid-State Electronics, vol. 36, issue 3, pp. 321-330, 1993. [4] G. A. M. Hurkx, D. B. M. Klaassen, and M. P. G. Knuvers, "A new recombination model for device simulation including tunneling", Electron Devices, IEEE Transactions on, vol. 39, pp. 331-338, 1992. [5] https://wiki.engr.illinois.edu/display/solarcellsim/. [6] M. Gloeckler, "NUMERICAL MODELING OF CIGS AND CdTe SOLAR CELLS_SETTING THE BASELINE", 3rd conference on photovoltaic energy conversion, 2003. [7] S. M. Durbin and J. L. Gray, "Considerations for modeling heterojunction transport in solar cells", in Photovoltaic Energy Conversion, 1994., 1994, pp. 1746-1749 vol.2.

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