Simulation of multi-junction solar cells for performance optimization

Recent model development and simulation case studies of multi-junction solar cells show the value of numerical simulation in cell design and optimization


Ricardo Borges, Synopsys Inc., Mountain View, CA, USA

Recent model development and simulation case studies of multi-junction solar cells show the value of numerical simulation in cell design and optimization

Amid a fast-growing interest in green energy production, photovoltaic (PV) energy is undergoing a veritable revolution in terms of deployed production capacity, cost structure, and innovation. Though the majority of solar cells used in today’s modules use mono- and multi-crystalline silicon, with thin-film technologies growing in relative market share, high-efficiency multi-junction solar cells offer an alternative approach to address overall system cost with the use of concentrated PVs (CPV). One example is a recently deployed system in a medium size residential community in Israel, where the CPV system not only delivers electricity but also produces hot water using the heat dissipated by the solar cells under an illumination of ~800 suns concentrated by the system’s parabolic mirrors [1]. Different versions of this system target a wide range of user profiles, from residential installations to large-scale electricity generation projects, attesting to the bright possibilities enabled by high-efficiency multi-junction solar cells.

Figure 1. Smallest symmetry element of a triple-junction solar cell generated by the Sentaurus Structure Editor.

Multi-junction solar cells

Initially developed for satellite solar panels, where high efficiency and area are at a premium and cost is a secondary consideration, multi-junction solar cells hold the world record for efficiency. Earlier this year, the Fraunhofer Institute for Solar Energy (ISE) announced a new efficiency world record of 41.1% for a triple-junction GaInP/GaInAs/Ge cell with a concentration factor of 454 suns [1], surpassing the previous record of 40.8% achieved by the National Renewable Energy Laboratory in Colorado. Beyond the high efficiency, the Fraunhofer ISE work also showed that buffer-substrate defects in metamorphic epitaxial layers do not appreciably degrade cell performance. By relaxing this constraint of having to match the substrate lattice constant, new combinations of ternary and quaternary compounds can be explored to further improve performance.

While triple-junction cells have been receiving a great deal of attention in connection with the reported world record efficiencies, dual-junction cells are also being investigated. Recently, researchers at the Polytechnic University in Madrid have reported a new world record of 32.6% efficiency for lattice-matched GaAs/GaInP cells at a high concentration of 1026 suns [2]. The Madrid research team believes that the lattice-matched design affords them the possibility of higher concentration, even exceeding 1000 suns, helping to lower the overall system cost. Moreover, optimization of the structure to achieve better current matching between the top and bottom cells could boost the efficiency to ~35% [2].

In parallel with these technical and commercial developments, numerical simulation of multi-junction solar cells has been making strides to help optimize the design of these complex structures and reduce the development cost. Relative to silicon and thin-film solar cells, multi-junction solar cells use more expensive GaAs substrates and epitaxial growth techniques. Epitaxial reactors can process several wafers concurrently, but only one type of structure can be grown at a time. This makes experimental splits for structure optimization expensive because of both substrate costs and one-sample-at a time epitaxial growth. Moreover, this type of solar cell typically consists of 20 epitaxial layers or more, most of which play a critical role in the performance of the cell and must be precisely designed with respect to composition and thickness. Considering that for each layer a doping concentration, mole fraction, and thickness variable may be assigned, the total number of process variables to be optimized is large.

To further complicate matters, some of the physical characteristics of these cells are very nonlinear. For example, the I-V characteristics of the tunnel diodes connecting the sub-cells render impractical traditional optimization approaches reliant on polynomial fits to design-of-experiment splits. Instead, structural optimization approaches based on true physical models are required to capture the complex interplay of sub-cell thickness, tunnel junction design, current-matching of the sub-cells, losses affecting external quantum efficiency, temperature-dependent effects, etc. And when we consider that an 0.5% increase in efficiency is a worthwhile improvement for a next-generation multi-junction cell, detailed numerical simulation seems worthwhile indeed.

Simulation environment and model requirements

The simulation of multi-junction solar cells draws on many aspects of generic solar cell simulation, but some physical phenomena are unique to this type of cell—in particular, thermionic emission across heterojunctions and transport across the tunnel diodes that joint each sub-cell. The design of the tunnel diodes requires low electrical resistance, high optical transmissivity, and a high enough peak tunneling current density so as not to restrict current flow in the cell. They are built with highly doped (degenerate) pn-junctions with band-to-band and trap-assisted tunneling contributing to the current density.


Figure 2. Light J-V characteristics of stacked subcells under AM1.5D illumination.

Band-to-band tunneling can be implemented numerically with local or non-local models. With local tunneling models, no actual carrier transport through the barrier takes place, and the tunneling is mimicked by adding an extra generation term to the continuity equation, typically dependent on the electric field or quasi-Fermi level gradient. These models have been successfully applied to MOS devices. Nonlocal tunneling models, on the other hand, involve real spatial carrier transport through barriers and use a quantum mechanical calculation of the tunneling probability along the tunneling path.

A detailed investigation of band-to-band tunneling in the tunnel diodes used in multi-junction solar cells indicates that nonlocal tunneling is necessary to match experimental I-V characteristics [3]. In particular, this work reveals that while the local tunneling model shows a saturation of the derivative of the I-V curve at V=0, in contradiction with the experiment, the nonlocal tunneling model matched the measurement. By calibrating the Richardson constant and the conduction and valence band tunneling masses, the authors were able to obtain a good match of the measured I-V characteristics, particularly in the low forward bias region where these diodes operate within the cell.

Figure 3. Light J-V and P-V characteristics of a triple-junction solar cell under AM1.5D illumination.

Recent simulation projects

The modeling approach for the tunnel diodes has been applied to the simulation of a dual-junction solar cell [4]. The simulation showed excellent match to the measured current-voltage and external quantum efficiency (EQE) versus wavelength characteristics, attesting to the physical comprehensiveness of the model. Using this well-calibrated simulation as a baseline, the authors then carried out further numerical studies to characterize the influence of tunnel diode design on performance, optimize the thickness of the top cell, and assess the impact of a Bragg reflector on EQE.

Another paper tackled the important topic of temperature-dependent behavior of multi-junction solar cells [5]. In view of the high concentrations of sunlight under which these cells are designed to operate, a comprehensive understanding of temperature-dependent behavior is very useful to optimize the structures. By incorporating temperature-dependent absorption coefficient, energy gap, density of states, and carrier densities, the authors were able to closely match simulated and measured EQE versus wavelength curves at three temperatures (200K, 300K, and 400K) and point to the main physical sources of efficiency loss at higher temperatures [6].

These publications, among others, indicate that simulation of multi-junction solar cells has made great progress in the last few years and is ready to play an active role in the research and development of these important devices.

A GaInP/GaAs/InGaAs triple junction solar cell

As an illustration, let’s look at the simulation of a gallium indium phosphide (GaInP)/gallium arsenide (GaAs)/InGaAs triple-junction solar cell. The device structure, shown in Fig. 1 on p. 16, is made up of 17 epitaxial layers and includes an anti-reflective coating of MgF2 and TiOx. The simulations of solar cells can be conveniently grouped into an optical simulation to calculate the optical generation profile and subsequent device simulations to compute relevant performance characteristics such as current-voltage (J-V) characteristics, efficiency, and fill factor under specific illumination conditions. For the simulation of planar devices, the transfer matrix method (TMM) can be used to calculate the optical field in devices consisting of multiple materials. The layers in the monolithic structure comprise various materials such as aluminum InP (AlInP), GaInP, AlGaAs, GaAs, and InGaAs.

Figure 4. EQE spectra of subcells and reflectance spectrum of a GaInP/GaAs/InGaAs triple-junction solar cell.

The light J-V curve can be simulated for standard solar spectra (AM0, AM1.5G, AM1.5D) and arbitrary concentrations. All the solar-cell structures can be simulated either in 1D or 2D simulation mode; 3D simulations are also possible but are typically not required for this type of cell. In 1D simulation mode, a homogenous 2D structure is created with only two or three vertical mesh lines. Simulations performed in 1D simulation mode are relatively faster and are used to quickly achieve an early design of the triple-junction solar cell. The 1D simulation mode can also be useful for faster optimization of the simulation mesh in the vertical or y-direction. This optimized y-direction mesh is then used in 2D simulation mode to optimize the mesh in the horizontal or x-direction.

The J–V curves of all the stacked subcells under AM1.5D illumination are shown in Fig. 2. This plot is useful to verify that each subcell is properly designed to support approximately equal amounts of current so that no subcell limits the total current of the serially stacked subcells. The light J-V and power-voltage (P-V) curves of the triple-junction solar cell under AM1.5D illumination are shown in Fig. 3. Key figures-of-merit for the cell, such as open-circuit voltage and short-circuit current, can be extracted from this plot using a post-processing algorithm.

Finally, the reflectance and EQE spectra are shown in Fig. 4. The EQE of each subcell dominates in a particular wavelength region. The EQE of the GaInP subcell dominates in the lower wavelength (higher energy) region and is zero for higher wavelengths. Similarly, the EQE of the InGaAs subcell dominates in the higher wavelength (lower energy) region and is zero for lower wavelengths. This is due to the fact that each subcell absorbs photons in a different wavelength range. As the figure illustrates, the EQE of all three subcells is >80%.


Multi-junction solar cells hold the world record for efficiency and continue to be developed for deployment in CPV systems. Recent model development and simulation case studies of multi-junction solar cells demonstrate the value of numerical simulation in the design and optimization of these important photovoltaic devices.


1. “High-concentration at home,” PV Magazine, No. 2, 2009.
2. “Madrid team sets dual-junction solar record,” Compound Semiconductor Online, Nov. 2008, news.
3. M. Hemle, G. Letay, S.P. Philipps, A.W. Bett, “Numerical Simulation of Tunnel Diodes for Multi-junction Solar cells,” Progress in Photovoltaics: Research and Applications, 2008.
4. S.P. Philipps, M. Hemle, G. Letay, W. Guter, B.M. George, F. Dimroth, et al., “Numerical Simulation and Modeling of III-V Multi-Junction Solar Cells,” Proc. of the 25th European Photovoltaic Solar Energy Conf. and Exhibition, Sept., 2008.
5. S.P. Philipps, D. Stetter, R. Hoheisel, M. Hemle, F. Dimroth, A.W. Bett, “Characterization and Numerical Modeling of the Temperature-Dependent Behavior of GaAs Solar Cells,” Proc. of the 25th European Photovoltaic Solar Energy Conf. and Exhibition, Sept., 2008.

Ricardo Borges received his MSEE from Tufts U. and is senior manager, product marketing, Silicon Engineering Group, Synopsys Inc., Mountain View, CA;


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