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• Abstract

SECTION I

## INTRODUCTION

AN important challenge in the development of thin-film solar cells is the optimization of light trapping design. Thin absorber layers can be less expensive to fabricate and can offer electrical advantages over thick devices [1], [2], [3], [4]. In order to achieve the high efficiencies that are required to make such technologies competitive with traditional wafer-based solar cells, it is critical to optimize both their optical and electrical performance. While thin-film silicon solar cells typically rely on randomly textured substrates to achieve light trapping [5], [6], significant attention has recently been directed toward designed nanostructuring of solar cells, which offers increased control of light absorption and propagation in the device [2], [3], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Design of such structures is aided by the use of computer simulations that account for both optical and electrical performance of the device [8], [25].

Many promising nanophotonic designs involve structuring of the active layers themselves [3], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Such approaches can offer enhanced light trapping through antireflection effects, resonant absorption in semiconductor nanostructures, and improved control over the optical mode structure in the active layer [3], [15]. It is important to note thatthe deposition of highly structured active layers can produce localized regions of low material quality, resulting in a tradeoff between enhanced optical design and optimized material quality [20], [22], [26], [27], [28]. Thus, in order to optimize device efficiency, it is, important to consider the effect of morphologically induced local defects when designing and optimizing light-trapping nanostructures [22].

The focus of this study is to demonstrate that such local defects can be accounted for in multidimensional optoelectronic simulations of nanostructured thin-film a-Si:H solar cells. Explicitly accounting for local variations in material quality in these simulations provides physical insight into the microscopic device physics governing operation. In particular, we find that defect location can couple to the optical excitation profile in the device, which results in a spectral response different from that obtained when uniform material quality is assumed.

Our approach is based on coupled optical and electrical simulations in which the optical generation rate is calculated from full-wave electromagnetic simulations and taken as input into a finite-element method (FEM) device physics simulation [8], [29]. This method has been shown to reproduce experimental current–density voltage curves of a-Si:H solar cells that feature light trapping nanospheres [30]. In the electrical simulation step, we address the tradeoff between optical design and electrical material quality by including a localized region within the a-Si:H exhibiting increased dangling bond trap density. This region of degraded material represents a recombination active internal surface (RAIS) that is formed during deposition. Such localized regions of low-density low-electronic-quality material quality are known to form during plasma enhanced chemical vapor deposition (PECVD) when growing surfaces collide with one another during deposition, a process that is particularly likely in the high-aspect ratio features used for light trapping [20], [22], [26], [27].

SECTION II

## SIMULATION DETAILS

The structure we investigated is shown in Fig. 1. The design is based on an n-i-p a-Si:H device in which all layers are conformally deposited over a nanostructured substrate. Our approach is to first carry out single-wavelength full-wave optical simulations with the finite-difference time-domain (FDTD) method. The carrier generation profile in the a-Si:H is extracted from the FDTD results for each wavelength and is weighted by the AM1.5G spectrum. The resulting white-light generation profile is then taken as input into an FEM device physics simulation in which the electrostatic and carrier transport equations are numerically solved in the a-Si:H region to extract the current density–voltage (J–V) characteristics of the device. From the simulated J–V curve, we extract the open circuit voltage $V_{\rm oc}$, the short circuit current density $J_{\rm sc}$, the fill factor FF, and the resulting conversion efficiency. We also use the single-wavelength generation profiles as input into short-circuit calculations to simulate spectral external quantum efficiency (EQE) of the device. This approach accounts for the full microscopic device physics of carrier collection under illumination and bias in complex geometries.

Fig. 1. Schematic showing the geometry of simulated $\hbox {n} \hbox{--} {\hbox {i}} \hbox{--} \hbox {p}$ a-Si:H solar cell. The red regions indicate the doped a-Si:H. The dashed lines indicate the location of RAISs, which are accounted for in the model as local regions of degraded material quality extending vertically through the device.

The structures are based on, from bottom to top, 200 nm of nanostructured Ag, a 130-nm-thick aluminum-doped zinc oxide (AZO) layer, an $\hbox {n-i- p}$ a-Si:H active region with 10-nm-thick $\hbox {n}$ and $\hbox {p}$ layers and 270 nm $i$-layer, and an 80 nm indium-doped tin oxide (ITO) layer. All the upper layers are assumed to conformally coat the textured Ag. The Ag features are 200 nm wide, the AZO and a-Si:H features are 220 nm wide, and the ITO features are 300 nm wide. The pitch of the features is 300 nm, the closest packing achievable without overlap of the ITO features. The height of the raised features is 200 nm in all layers. The simulations in this study are done in 2-D to take advantage of reduced computational demand, but we note that the methods are applicable to full 3-D simulations as well [8]. We note that the schematic in Fig. 1 is three simulation volumes wide. The explicit simulation volume is that between neighboring dashed lines, and Neumann boundary conditions are imposed at the horizontal boundaries to model the periodic structure. In all plots of spatial results that are presented here, we have stitched together three copies of the simulated region in order to help the reader visualize the periodic structure that is implied by the boundary conditions.

SECTION IV

## CONCLUSION

We have demonstrated the use of coupled multidimensional optical and electrical simulations for the study of the optoelectronic device physics of localized defects that are induced by nanostructures in thin-film solar cells. In addition to providing a detailed picture of the microscopic device physics affecting carrier collection, our results highlight the importance of accounting for the specific geometry of the defects themselves along with the full optical absorption profile within the device. In particular, we found that interactions between the geometry of the absorption profile and the RAISs can induce significant variations in carrier collection efficiency. Such effects cannot be fully accounted for without implementing a multidimensional model such as that used here.

It is critical to account for tradeoffs between optical and electrical performances in the optimization of light-trapping structures for solar cells. This prevents the unconstrained optimization of the optical properties of a device from yielding impractical geometries that suffer severe material quality degradation. The method that we present could be coupled to an empirical study on morphologically dependent material quality for a specific process in order to fully understand and optimize the optoelectronic design of thin-film solar cells. Furthermore, our general approach of multidimensional optoelectronic simulations that include local variations in material parameters is applicable to other photovoltaic material systems in addition to a-Si:H. Our approach provides a framework within which light trapping designs for different photovoltaic material systems, which are governed by different practical limitations, can be optimized.

### ACKNOWLEDGMENT

The authors would like to thank M. Kelzenberg and D. Turner-Evans for useful discussions regarding technical aspects of the simulations.

## Footnotes

This work was supported by the “Light–Material Interactions in Energy Conversion” Energy Frontiers Research Center, United States Department of Energy, under grant DE-SC0001293, LBL Contract DE-AC02-05CH11231. The work of M. G. Deceglie was supported by the Office of Basic Energy Sciences under Contract DOE DE-FG02–07ER46405 and the National Central University's Energy Research Collaboration.

M. G. Deceglie and H. A. Atwater are with the Thomas J. Watson Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA 91125 USA (e-mail: deceglie@caltech.edu; haa@caltech.edu).

V. E. Ferry and A. P. Alivisatos are with the Materials Science Division at Lawrence Berkeley National Laboratory and the Department of Chemistry, University of California, Berkeley, CA 94720 USA (e-mail: veferry@lbl.gov; apalivisatos@lbl.gov).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

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