Analysis of surface texturization of solar cells by molecular dynamics simulations

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Volume 2008, Article ID 540971,5pages doi:10.1155/2008/540971

Research Article

Analysis of Surface Texturization of Solar Cells by

Molecular Dynamics Simulations

Hsiao-Yen Chung, Chiun-Hsun Chen, and Hsin-Sen Chu

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan

Correspondence should be addressed to Hsin-Sen Chu,[email protected]

Received 11 April 2008; Revised 18 May 2008; Accepted 4 June 2008 Recommended by Mohamed Sabry Abdel-Mottaleb

The purpose of this paper is to develop a simple new model, based on the classic molecular dynamics simulation (MD), alternative to complex electron-photon interactions to analyze the surface texturization of solar cells. This methodology can easily propose the absorptance differences between texturing and nontexturing solar cells. To verify model feasibility, this study simulates square, pyramidal, and semicircular texturization surfaces. Simulations show that surface texturization effectively increases the absorptance of incident light for solar cells, and this paper presents optimal texturization shapes. The MD model can also be potentially used to predict the efficiency promotion in any optical reflection-absorption cases.

Copyright © 2008 Hsiao-Yen Chung et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

Achieving higher eﬃciency in solar cells is one of the

most important issues in recent studies on the topic, and researchers have examined many methods for achieving this goal. Surface texturing of solar cells is a common approach to reduce incident light reflection and, consequently, increase

solar cell eﬃciency.

Dry etching and wet etching are commonly used to apply surface texturization to solar cells. Dry etching means texturing without wet solutions. A plasma texturing tech-nique using reactive ion etching, with advantages of low cost consumption and independence from crystallographic

orientation, was previously proposed [1, 2]. A selective

surface texturing technique using lasers recently gained some

interest. Tan et al. [3] performed femtosecond pulsed laser

induced forward transfer on a quartz substrate. A trench-like texturing was ablated on the donor substrate using a pulsed laser. This method exhibits good controls on the depth and width of ablated trenches.

Wet etching means surface texturing with chemical solutions. In a general surface texturing process on crystalline silicon, alkaline solutions form pyramids. This pyramidal surface shape occurs because alkaline solutions etch silicon along crystallographic orientations.

Some researchers use acid solutions to produce surface texturization. Due to the character of acid solutions, the etching rates in the diﬀerent orientations are similar. Thus

a semicircular structure is formed [4].

Most texturing studies focus on wet etching processes.

Hylton et al. [5] conducted many experiments to compare

the eﬃciency increase of saw-damage etching and texture

etching processes using alkaline solutions on multicrystalline silicon wafers. That paper also explained the geometrical paths of incident light which defined the absorption and reflection on the pyramid structures. Nishimoto and Namba

[6] developed a low-cost wet etching manufacturing process

and reported the texturization of a monocrystalline silicon

surface with low-cost alkaline solutions, Na2CO3. Recently,

Gangopadhyay and his colleagues [7] further developed

a new texturing method with tribasic sodium phosphate solution, claiming it was superior to the conventional method because it used less isopropyl alcohol for texturing.

The most previous studies focused on the manufacturing process. However, if we can simulate the behaviors of absorption and reflection before fabricating a new surface texturizaion on a solar cell, it is helpful to reduce the time and fabricating wastes. Therefore, it is necessary to develop a simulation methodology to govern this issue.

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Molecular dynamics simulation is a technique well suited to nanoscale phenomena and mechanical behaviors. However, few studies use MD to examine solar-cell issues.

One such study [8] explores the photo-induced

electron-transfer phenomena on a dye-sensitized titanium solar cell with nonadiabatic MD simulations, which is based on the ab-initio functional theory. The study found that approximately 20% of the acceptor state was located on a titanium atom of the first surface layer. This simulation also predicted a complex non-single-exponential time-dependence of the electron-transfer process. However, many unknown factors in photon-electron interactions prevent studies from being conducted on the issue of photon absorption.

This paper presents a simple photon-atomic model with molecular dynamics simulations to explore the eﬀects of three shapes of solar cell surface texturization. This paper also includes an estimation of the optimum texturization.

2. METHODOLOGY

First of all, if the de Broglie wavelength of a photon and an atom is smaller, we can make assumption that the absorption and reflection are closely represented as a series of collision behaviors between photons and atoms.

To avoid complications in photon-electron transforma-tion, a rough and simple MD model was devised to govern this problem. In the classic mechanical MD simulations, a two-body attractive-repulsive potential model governs the interaction between two particles. For one particle, short-range repulsive forces rebound the too close particles from itself, and long-range attraction catches other particles closer to itself in attractive force field. Assuming that the force field between an atom and photon is spherical, the 12-6 Lennard-Jones potential model with an undetermined parameter k, which is a short-range multiple, is adopted,

U(r)=4 k 1 r 12 − 1 r 6 . (1)

When photons reach the substrate, attraction and repul-sion behaviors occur between silicon’s atoms and photons.

Figure 1shows the mechanism of photon-atom interactions. When a photon enters the attractive field of an atom, the photon should be attracted to the center of the atom. But

the repulsive force pushes the photon oﬀ center if the photon

is too close to the atom center. The substrate is maintained as an NVE model (fixing particle numbers, system’s volume, and total energy) in the heat-transfer process, so the photons which enter the substrate are constrained because of forces among atoms and decay of motive energy of themselves. Due to the actions of attractive and repulsive forces and the photon energy dissipation, the velocity of a photon which enters the substrate deeply tends toward zero. This behavior is considered photon absorption in a solar cell. However, some photons are repulsed at the substrate surface due to the repulsive force. This is considered reflection. The photons whose velocity decreases to zero were removed to avoid the

increasing of particle numbers, and then aﬀect the system

energy. Photon Constraint Repulsive field Attractive field Rebound (a) Rebound Photon Constraint Constraint Constraint Atom (b)

Figure 1: Illustrations of attractive and repulsive interaction of atoms and photons. (a) The photons move toward repulsive force field is probably rebound out, and the other photons move through attractive field is constrained or decelerated. (b) The rebounded behavior is as same as reflection. The constraint behavior is as same as absorption.

Note that the eﬃciency of monocrystalline silicon is, at

most, 24.7% [9]. This study attempts to make a model with

an absorptance reaching 24.7% in a smooth, nontextured substrate by simply adjusting k. In our simulation, k is determined to be 3.86. After this calculation, simulations of varying surface texturization with this potential model can proceed. The smooth surface model is a reference, and the other texturing models in this paper, which are simulated with the same conditions, can then be compared with the reference model. This methodology not only reasonably avoids the complexity of photon-atom interaction but also

achieves the goal of trying to evaluate the eﬃciency of two

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Photon θ v d h x y z (a) Photon θ α (b) Photon θ _O r H (c)

Figure 2: Physical model (a) square (b) pyramid (c) semicircle, the geometric variables are also shown in this figure.

Following this concept, monocrystalline silicon was selected as the solar cell material. This is because silicon is the most common material in all types of solar cells, and its structure is simpler for using with an MD model. The results and conclusions of this study can also be extended to other solar cells, GaAs, InGaAs, InGaP, and so forth. According to the reviews of previous studies, square, pyramidal, and

semicircular texturing were demonstrated. Figure 2 shows

the physical models of the three samples in this paper. A single silicon cell has a diamond structure with 8 atoms. Under the texturing surface, three layers absorb the motion

Table 1: Parameters. Fundamental quantities

Mass 4.65×10−23g/atom in silicon

Lengthα 5.431 ˚A

Energyε 1.792×10−19J

Timet 1.77×10−3ps/step

Normalized quantities

Light speed (photon’s speed)c∗ _4.8_×₁₀6

TemperatureT∗ _0.0231

Massm∗ 0.54

energy of photons. To avoid the eﬀects of diﬀerent lengths in the x- and y-directions, the substrate of solar cells is set as a square. Periodic boundary conditions are imposed in the

x- and y-directions. Due to the periodic texturing shapes,

diﬀerent period lengths lead to diﬀerent numbers of atoms.

In the case of diﬀerent intervals of square texturization,

at least six periods are chosen. So in the case of distance

d = 1 cell, the number of silicon atoms is 144352. The

longer the distance, the more atoms are present in the substrate. The photon incident angle varies at x-z plane.

The system temperature keeps at 300 K. Table 1 shows the

physical parameters of this model.

3. RESULTS AND DISCUSSION

Figure 3shows the relationship between the height of square texturing and absorptance for the square surface case. When

h = 0, the surface of solar cells is smooth, and the

absorptance is 0.247 at an incident angle of 0 degrees. When surface texturing exists, the specimen with a greater square height has higher absorptance. However, the rate of increase becomes smaller as the height increases. Photons can easily drop into the holes with higher walls, so the substrate absorbs more photons. If the incident angle of photons increases, the absorptance lessens because more photons rebound.

Figure 4 shows how the various distances aﬀect the absorptance. As the distance increases, the absorptance

obviously decreases when the square height is 2.31 ˚A. As

inFigure 3, the absorptance decreases as the incident angle of the photons increases. The absorptance decreases slowly

when the distance surpasses 6.94 ˚A. In other words, the eﬀect

decreases as the distance increases.

The next example simulates a pyramidal surface.Figure 5

shows the influence of the facet tilt angleα. In this figure, the

absorptance increases as the tilt angleα increases. Moreover,

the rate rises quickly when α is more than 30 degrees.

This result indicates that a more acute pyramid structure

causes a decrease in reflection. Hylton et al. [5] discussed the

possible path of light incident upon geometrically textured surface in air and concluded that a blunter facet tilted angle (sharp pyramid) facilitates light double-bounce incidence, thereby reducing surface reflection. Our results agree with that conclusion. However, the current results are totally

contrary to the research by Xi et al. [4]. This is because the

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16 14 12 10 8 6 4 2 0 h (angstrom) 0◦ 30◦ 45◦ 60◦ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ab so rp ta n ce 0.247

Figure 3: The relation among absorptance, h and photon’s

incidence angleθ. 16 14 12 10 8 6 4 2 0 d (angstrom) 0◦ 30◦ 45◦ 60◦ 0 0.1 0.2 0.3 0.4 0.5 Ab so rp ta n ce 0.247

Figure 4: The relation among absorptance, distance and photon’s

incidence angleθ.

pyramids become sharper and taller with increasingα. This

supposition leads to this phenomenon. As expected, a larger

incident angle causes lower absorptance.Figure 5shows this

result.

Finally,Figure 6shows the case of a semicircular surface.

Varying the ratio of H/r, the absorptance shows a clear

rising trend from 0.247 at H/r = 0, at which the surface

of substrate is smooth, to a semicircular hole,H/r = 1, if

vertical light meets the substrate. Obviously, the increasing

rate of absorptance decreases if H/r rises. The same trend

occurs at 30, 45, and 60 degrees of the incident angle, but the magnitude of absorptance is lower than that exposed by vertical light. This trend of absorption agrees well with the

findings of Xi et al. [4]. 80 60 40 20 0

Facet tilt angleα (deg)

0◦ 30◦ 45◦ 60◦ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ab so rp ta n ce 0.247

Figure 5: The relation among absorptance, facet titled angleα, and

photon’s incidence angleθ.

1 0.8 0.6 0.4 0.2 0 H/r 0◦ 30◦ 45◦ 60◦ 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Ab so rp ta n ce 0.247

Figure 6: The dependence of absorptance onH/r in the case of

semicircular texturing surface.

4. CONCLUSION

In conclusion, this study proposes a new and simple MD model alternative to complex electron-photon interactions in quantum scale to analyze surface texturization of solar cells. Three surface texturization shapes are simulated with various angles of incident light. This methodology can easily

determine the absorptance diﬀerences of various surface

tex-turizations, and suggest better texturization shapes. Increas-ing the trench depth, shortenIncreas-ing the distance between two trenches, sharpening pyramids, and adding more circling to

the semicircular structure all help improve the eﬃciency of

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In this study, we ignore the wave behavior of photons and atoms. In fact, according to the wave-particle duality, the wave behaviors aﬀect, either more or less, the absorption and reflection of solar cells. However, this study is a beginning to simulate the absorption by molecular dynamics. Our results also agree well with previous studies. This MD model can

potentially be used to predict the eﬃciency promotion in any

optical reflection-absorption cases.

REFERENCES

[1] T. Sakoda, K. Matsukuma, Y.-M. Sung, K. Otsubo, M. Tahara, and Y. Nakashima, “Additional plasma surface texturing for single-crystalline silicon solar cells using dielectric barrier discharge,” Japanese Journal of Applied Physics. Part 1, vol. 44, no. 4A, pp. 1730–1731, 2005.

[2] W. A. Nositschka, C. Beneking, O. Voigt, and H. Kurz, “Texturisation of multicrystalline silicon wafers for solar cells by reactive ion etching through colloidal masks,” Solar Energy Materials and Solar Cells, vol. 76, no. 2, pp. 155–166, 2003. [3] B. Tan, K. Venkatakrishnan, and K. G. Tok, “Selective surface

texturing using femtosecond pulsed laser induced forward transfer,” Applied Surface Science, vol. 207, no. 1–4, pp. 365–371, 2003.

[4] Z. Xi, D. Yang, W. Dan, C. Jun, X. Li, and D. Que, “Investigation of texturization for monocrystalline silicon solar cells with diﬀerent kinds of alkaline,” Renewable Energy, vol. 29, no. 13, pp. 2101–2107, 2004.

[5] J. D. Hylton, A. R. Burgers, and W. C. Sinke, “Alkaline etching for reflectance reduction in multicrystalline silicon solar cells,” Journal of the Electrochemical Society, vol. 151, no. 6, pp. G408– G427, 2004.

[6] Y. Nishimoto and K. Namba, “Investigation of texturization for crystalline silicon solar cells with sodium carbonate solutions,” Solar Energy Materials and Solar Cells, vol. 61, no. 4, pp. 393– 402, 2000.

[7] U. Gangopadhyay, K. H. Kim, S. K. Dhungel, et al., “A novel low cost texturization method for large area commercial mono-crystalline silicon solar cells,” Solar Energy Materials and Solar Cells, vol. 90, no. 20, pp. 3557–3567, 2006.

[8] W. Stier and O. V. Prezhdo, “Non-adiabatic molecular dynamics simulation of ultrafast solar cell electron transfer,” Journal of Molecular Structure: THEOCHEM, vol. 630, no. 1–3, pp. 33–43, 2003.

[9] M. A. Green, K. Emery, D. L. King, Y. Hishikawa, and W. Warta, “Solar cell eﬃciency tables (version 29),” Progress in Photovoltaics: Research and Applications, vol. 15, no. 1, pp. 35– 40, 2007.

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