Advanced TCAD Simulation Helps Optimize Solar Cell Efficiency

The search for renewable sources of electrical power, driven by the need to reduce CO₂ emissions, is rapidly spurring new research avenues in several promising technologies, among them photovoltaics (PV). Although solar cells have been around since the 1960s, the push toward higher-efficiency and lower-cost solar cells has led to the development of new material and structural concepts.

Within the traditional crystalline and multicrystalline material system, novel approaches for improving photon collection and absorption are being investigated to raise efficiency. Newer thin-film materials, such as cadmium telluride (CdTe) and copper indium gallium selenide (CIGS), offer lower production costs, albeit with lower efficiency than silicon-based cells. At the high end of the efficiency curve, multi-junction cells have broken the 40% barrier and, when deployed in solar concentrator systems, have become a true contender in the marketplace. Yet, progress toward achieving higher efficiency continues unabated. This article explores the important role simulation plays in improving cell efficiency.

The reasons limiting the efficiency of today's solar cells are grounded in semiconductor physics, with the energy bandgap playing a vital role. A photon whose energy exceeds the bandgap energy is absorbed by creating an electron-hole pair of the same energy as the bandgap, with the photon's excess energy wasted as heat. A photon with energy below the bandgap does not contribute to charge carrier generation. Solar cells are essentially pn-junction diodes. Under applied voltage, an electric field is set up in the pn-junction depletion region, allowing electrons and holes generated within the field via photon absorption to be swept away to the cell contacts, resulting in electric current. Because the solar energy spectrum covers a wide range of wavelengths — from ~250 nm in the ultraviolet (UV) to 2500 nm in the infrared (IR) — inevitably, low-energy photons will not be absorbed, while high-energy photons will contribute only a portion of their energy to the electrical current. The wasted excess energy of high-energy photons, power dissipated by the finite resistance of the contacts, and processes that annihilate or capture electrons and holes before they get collected at the contacts are all parasitic effects that limit the efficiency of the cell.

In a seminal paper written in 1961, Shockley and Queisser analyzed the photoelectrical conversion process in solar cells and derived an efficiency limit of ~32%.¹ In their analysis, they assumed a single-junction semiconductor structure and a single electron-hole pair created for each absorbed photon. Much of today's research in semiconductor-based solar cells focuses on removing these limiting assumptions, thereby raising the theoretical efficiency above 32%.²

An obvious potential improvement is to use multiple semiconductor junctions, each with an energy gap tailored to absorb a portion of the solar spectrum. Recently, multi-junction solar cells, using a complex stack of epitaxially grown layers based on germanium, gallium arsenide (GaAs) and indium gallium phosphide (InGaP), have achieved efficiencies above 40%.

Other concepts under exploration include hot-carrier designs, whereby a single photon contributes to more than one electron-hole pair; sub-band designs, which allow absorption of photons with below-bandgap energy; and various approaches to improve the collection efficiency of photons. Clearly, the complexity of solar cell design increases when efficiency enhancement concepts are considered. Because many of these concepts are based on well-understood physical phenomena, it is natural to investigate the role of simulation in designing high-efficiency solar cells.

Numerical simulation of semiconductor processes and devices, often referred to as technology computer-aided design (TCAD), is a well-established discipline in the realm of semiconductor process development and optimization currently used by all major semiconductor companies in applications ranging from nanoscale CMOS to power devices and RF compound semiconductor devices. In silicon applications, simulation of key processing steps, such as implantation, diffusion and oxidation, has attained a high degree of sophistication, with today's models accounting for the interaction of dopant atoms, point and extended defects in the lattice, the impact of stress, non-equilibrium thermal activation and diffusion, etc. This body of work is readily applied to crystalline solar cells, enabling engineers not only to simulate and optimize the doping profile of the design, but also to explore ways to improve the cell efficiency by gettering metallic impurities.³ The next section provides an example of this application of TCAD to solar cells.

Device simulation, comprising the solution of the semiconductor transport equations within semiconductor regions with external metal contacts, is more broadly applied to crystalline (c-Si), multicrystalline (mc-Si) and amorphous (a-Si) silicon-based cells, as well as to cells containing compound semiconductor materials. Common outputs include dark and light I-V curves and internal and external quantum efficiencies.

Because of their electro-optical nature, the simulation of solar cells must necessarily take into account many detailed phenomena. From the optics point of view, the simulator must allow the definition of standard solar spectra, such as AM1.5. At interfaces between media — for example, at the air-dielectric interface on top of the cell — reflection and transmission of the light must be treated. If the feature sizes are much larger than the wavelength of the light, a ray-tracing model is sufficient. When interference effects are important, such as in the presence of an antireflective coating (ARC) or when the semiconductor absorption layers are thin, a transfer matrix method (TMM) can be used if the structure is planar or quasi-planar. When the structure combines thin regions, susceptibility to interference, and small features of the same scale as the wavelength of the light, more sophisticated optical models may be needed.

To accurately simulate photon absorption in the semiconductor regions of the cell, a model that includes changes to the energy gap caused by heavy doping effects and mole fraction of the constituent materials should be used. Radiative, Auger and Shockley-Read-Hall (SRH) recombination are also very important because any process removing carriers from collection by the cell terminal ultimately affects the efficiency. The trap levels that form within the energy gap in amorphous semiconductors can be explicitly defined either as discrete energy levels or continuous energy distributions. Moreover, the electrical effect of grain boundaries of multicrystalline materials can be modeled by assigning certain regions of the simulation structure with boundary conditions of carrier trapping and recombination.^4,5

It is also possible to combine the detailed numerical simulations of the cell with lumped circuit elements — known as mixed-mode simulation — essentially allowing the interconnection of physical cell design with larger-scale circuit-level behavior. This feature is important because solar cells use repeated elemental blocks whose interconnection contributes to loss of efficiency due, for example, to ohmic losses.

In summary, solar cell simulation can leverage much of the tremendous progress that has been made in TCAD simulation over the past two decades. The following section illustrates the application of TCAD to solar cell design and optimization with two examples, the first focusing on process and the second on device simulation.

Minority carrier lifetime is very important in solar cells, as longer lifetimes lead to higher cell efficiency caused by enhanced charge collection at the cell terminals. It is well known that the minority carrier lifetime depends on the number and energy levels of recombination centers or traps. Consequently, reduction of recombination centers through processing techniques is a topic of great interest, particularly in c-Si solar cells. Gettering processes are a type of defect engineering whereby the number of metallic impurities in the silicon and their associated recombination centers are reduced in the active regions of devices.

Recently, TCAD has been successfully demonstrated for iron gettering, opening the way to use simulation to optimize the gettering process and improve cell efficiency.⁶ Plekhanov et al. have described an aluminum gettering process that uses the fact that, above the eutectic temperature of 577°C, the solubility of metals in aluminum is very high (10²¹ cm^-3) compared with their solubility in silicon (10¹⁷ cm^-3).⁷ This provides a tremendous driving force for metal atoms to segregate into the aluminum or Al-Si liquid layer. As the segregation process occurs simultaneously with the impurity diffusion, the gettering process can be described by:

• A segregation equation at the Al-Si material boundary
• A diffusion equation for the impurity diffusion in bulk silicon
• Reaction terms for cluster dissolution and formation if impurity clusters, such as metal precipitates, are taken into account in the model

For impurity gettering, the same physics can be applied as for dopant diffusion. Plekhanov et al. developed a set of equations to describe the gettering of the impurities C, taking into account the decreasing size of metal precipitates C* in silicon:

where D is the diffusivity of the impurity, r is the radius of the metal precipitate, and ρ is the precipitate density. This equation was implemented into the Sentaurus Process simulator by its user-defined model interface, which allows users to define new species equations for the diffusion, segregation and reactions of these new species, effectively extending the simulator to new processes beyond those traditionally used in mainstream silicon manufacturing.

For each time step, Sentaurus Process solves this differential equation and provides the spatial distribution of the species. After the reactions and diffusion equations are set up, the process flow with arbitrary temperature ramps is defined. In the first example, a 1-D simulation with a very simple ramp — a constant temperature at 900°C for four different gettering times (10, 20, 30 and 40 min) — is investigated. The rear of the 100-μm-thick silicon wafer is covered by aluminum (at a depth of 100 μm). The main result of the process simulation is the trap distribution shown in Figure 1.

1. Process simulation provides depth-dependent trap distribution within the silicon wafer for different gettering times.

The trap distribution resulting from the simulation of the gettering process can be exported to the device simulator, Sentaurus Device, for electrical analysis. The trap density, N_Trap, is related to the SRH lifetime through the relationship:

τ_{SRH ,n}=1/N_trap v_thσ_n

where σ_n is the capture cross-section and v_th is the thermal carrier velocity. Following an optical simulation to compute light propagation and absorption in the structure, a device simulation of the cell I-V characteristics is performed, and accounts for the trap distribution imported from the process simulation. In this example, after 40 min, all iron atoms are gettered by the aluminum rear side, resulting in a strong increase of the short circuit current and, hence, efficiency.

Figure 2 shows the dependency of the gettering time on external quantum efficiency (EQE). As expected, the curves corresponding to 40 min gettering time show the highest boost of the EQE in the IR part of the spectrum because of enhanced minority carrier lifetimes and, thus, diffusion length.

2. Looking at external quantum efficiency (EQE) vs. wavelength for various gettering times shows that 40 min gettering time provides the highest EQE boost in the infrared.

Device example

Finally, consider an optimization example of a passivated emitter and rear locally diffused (PERL) solar cell. Figure 3 shows a 2-D cross-section of the structure where several process parameters are selected for optimization, with their description and numerical ranges shown in the Table.

3. A 2-D cross-section of a solar device structure shows what process parameters can be selected for efficiency optimization.

A numerical design-of-experiments was done covering the process variable space, and key cell performance figures of merit were extracted from the simulations. The results are shown in Figure 4, where the impact of varying each process variable on the performance figures of merit is visible by the slope of the lines joining the individual simulations.

4. The impact of varying each process variable is shown, comparing simulation results for optimized process variables (dark green). The slope of the line indicates the strength of the parameter’s influence.

Conclusion

The PV industry is experiencing tremendous growth because of the great promise this technology offers to deliver clean and sustainable electrical power, with cost reduction and efficiency gain as the key drivers of today's solar cell research. TCAD simulation plays a key role in the design and optimization of solar cells by providing engineers with insight into the internal physics of solar cell operation.