Simulation In Photovoltaics: From Solar Cells To Full-Scale Arrays


Simulation provides key insights into the physics of solar cell operation, enabling engineers to explore the full range of design alternatives. At the module and system levels, behavioral models allow engineers to examine design trade-offs that can affect system performance.

This article examines the current role that simulation plays in the development of photovoltaic technologies, from solar cell design to system performance, and provides an outlook for future work. We will focus on silicon bulk cells, because the technology's long history is a good example of the interlock between device development and simulation.

Several studies are used to illustrate the value of simulation. Other technologies not discussed here, notably III-V multijunction and thin-film solar cells, also benefit from simulation, although the physical models and material parameters are not as well known as those of silicon.

The first solar cell intended for commercial use was developed in 1954 by researchers at the Bell Telephone Laboratories. This cell was based on a diffused p-n junction fabricated in silicon. At that time, silicon – along with germanium – was already a prominent semiconductor used in electronic devices, and its selection as the semiconductor for the first generation of solar cells was justified in view of its rapidly advancing manufacturing technology and its excellent electronic and optical properties.

These factors established silicon solar cells as the dominant technology, and many of the mainstream technological advancements in silicon electronics eventually found their way into silicon photovoltaics.

Among these was the tremendous progress made since the 1980s in the simulation of the fabrication processes and electro-optical behavior of silicon devices. Programs such as Stanford University's SUPREM and PISCES launched the field of technology computer-aided design (TCAD), and solar cell engineers, much like their counterparts in semiconductor electronics, used the new simulation technology to gain a better understanding of the internal behavior of solar cells and to refine their designs.

Because the structural simplicity of most first-generation solar cells made them conducive to one-dimensional simulation, simplified programs targeting solar applications also emerged and were instrumental in establishing a solid foundation for simulation within the photovoltaic community.

A solar cell is designed to convert as many incident photons into electrical current as possible. Gradual refinements of the first generation of silicon solar cells eventually led to designs with surfaces employing texturing and anti-reflective coatings to minimize light reflection across the solar spectrum, as seen in Figure 1.

Figure 1:


The base layer of this design is around 250 micrometers thick. Structural and process variables – such as the pitch of the front contact, the doping of the base layer, minority carrier lifetime, and the surface recombination velocities of the front and back contacts – have been shown to significantly impact cell performance.

These variables have been subjected to extensive simulation studies, with optimized designs achieving 15% to 16% conversion efficiency. One of the critical factors limiting the performance of these cells is the thick base layer, which provides ample opportunity for photon-generated carriers to recombine before reaching the contacts.

Although advanced gettering techniques can reduce carrier recombination in the base layer and improve efficiency by lowering the concentration of heavy metal recombination centers, ultimately, a thinner base layer, combined with new design concepts at the front and back surfaces, led to significant performance improvements.

The structure of the highest-efficiency silicon solar cell (shown in Figure 2), known as PERL (passivated emitter, rear locally diffused), features phosphorus-diffused emitters to reduce recombination losses, thick and narrow metallization to minimize ohmic shading losses, and the surface texturing and anti-reflective coatings already employed in earlier cell designs.

Figure 2:

One of the key design aspects is the optimum spacing and size of the rear point contacts – a problem that has been well addressed with 3-D simulation. Compared to traditional stripe contacts, the current flow into point contacts has a pronounced 3-D character. 3-D simulation shows a steep efficiency versus pitch relation for point contacts compared to stripe contacts, which are less sensitive to pitch.

This means that simulation is important in order to find the optimum efficiency as a function of contact pitch in point-contacted cells.

More recently, back-contact back-junction solar cells have been actively investigated because of the promise of further performance improvements. When both contacts are placed on the back, they eliminate optical shading losses and have resulted in increased efficiencies exceeding 22% in production.

When combined with low-cost structuring techniques – such as screen printing in lieu of the more expensive photolithography used in conventional microelectronics – these cells are effective in balancing high performance with low manufacturing cost. Their basic structure is shown in Figure 3.

Figure 3:
In this type of cell, the n-type float zone starting material has a high minority carrier lifetime. The locally doped emitter, back-surface field and front-surface field (FSF) help to minimize recombination losses.

An interesting characteristic of the FSF is that it enhances the lateral current transport when the relatively large pitches of screen printing contacts are used, as reported in a simulation study conducted by the Fraunhofer Institute for Solar Energy Systems.

Another simulation study at the same institute systematically analyzed the optical, recombination and series resistance losses in the structure, all of which reduced the efficiency by 5.48%. This type of analysis, which quantifies the main loss mechanisms as a function of cell structural parameters, is a requirement for the subsequent optimization of the design.

Simulation of the influence of the primary cell design parameters (base width, contact pitch, base resistivity, fraction of emitter coverage, etc.) on the cell performance showed an excellent match with measurement, resulting in an optimum simulated efficiency of 21.1% (20.8% plus or minus 0.6% measured).

As the complexity of solar cell designs has evolved, so has the need for ever more sophisticated 2-D and 3-D simulation tools to help engineers optimize the cell design in order to achieve the required performance and cost target.

Purely experimental approaches are no longer sufficient for modern solar cell development because of the large number of structural and process variables at play, and the detailed and often highly nonlinear ways through which these variables affect cell performance.

Once a cell design has been optimized, the next step is to combine the cells into efficient, reliable and manufacturable modules. At the module level, the behavior of the cell can be simplified to a one- or two-diode model, including the resistive shunt and series connections between the individual cells.

By taking into account the physical properties of the materials used in the cell design and either measured or simulated performance data, researchers can establish mathematical relationships between the design parameters (e.g., absorber layer thickness, cell width, module width and length, etc.) and the simpler diode model with series and shunt resistances.

Using this type of equivalent circuit model to describe the cell, system-level simulation tools can optimize the module performance for overall power efficiency over a variety of irradiance conditions, accounting for factors such as diurnial or seasonal variation of the solar spectrum and the geographical location where the module will be used.

Other system-level effects, such as the impact on performance due to thermal variation and manufacturing tolerances, can be included using behavioral models implemented in standard hardware description languages (HDLs), such as MAST and VHDL-AMS.

Once the photovoltaic module is characterized in a form amenable to system-level simulation, it can be incorporated into the overall system design, including inverters, energy-storage systems and realistic loads, enabling important metrics like overall efficiency and hardware robustness to be examined.

Mixed-domain simulation tools allow for inclusion and optimization of control algorithms for maximum power point tracking (MPPT), battery charging and rectifier/inverter control methodologies to be tested against energy-conserving hardware simulation models.

With the flexibility of HDLs, manufacturing tolerance information and safe operation area envelopes are included in the hardware models, allowing for analyses beyond simple steady-state or time domain to statistical and stress analysis. Modeling of the system at this level of abstraction enables robust design methodologies to be applied, such as Six Sigma or Taguchi methods, to optimize system performance, reliability and cost based upon particular targeted performance metrics.

The solar panel to load-impedance matching circuit is a DC/DC converter controlled by the algorithm in the digital signal processer (DSP). The algorithm calculates the voltage of the solar panels where the peak or maximum power is produced and controls the DC/DC converter to match the solar panel voltage to the load or battery voltage.

The MPPT governs the DC/DC converter by generating a pulse width modulation signal that switches the metal-oxide-semiconductor field-effect transistors at a particular set frequency. The transfer ratio of voltage ‘in’ versus voltage ‘out’ is based on the duty cycle of the PWM signal coming from the DSP.

Such a simulated system could be used for the following research: comparison and optimization of different control algorithms; validation of system stability and performance over an arbitrary range of different irradiance conditions (e.g., hourly, daily, weekly, seasonally, etc.) and load conditions; and examining any of the aforementioned scenarios while including production tolerances and thermal effects for a statistically meaningful representation of actual production performance.

In summary, simulation tools have been used for many years to help optimize solar cell performance. With recent improvements in technology from the cell level to the system level, coupled with an increasingly competitive market landscape, the need for early product design and validation data has become a market differentiator.

Simulation now provides a virtual path from raw cell technology to an optimized power system in a fraction of the time and cost necessary to prototype and validate the physical systems – allowing a seamless technology flow from device to end product.

Kurt Mueller is research and development manager for the modeling and consulting services groups for the Saber product line at Synopsys, a provider of electronic design automation for semiconductor design and manufacturing. Ricardo Borges is senior manager of TCAD product marketing at Synopsys. The authors can be contacted at (650) 584-5000.

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