# Analysis of Surface Texturization of Solar Cells by  Molecular Dynamics Simulations

Authors: Hsiao-Yen Chung; Chiun-Hsun Chen; Hsin-Sen Chu
Journal: International Journal of Photoenergy
 (2008)

---

## Abstract

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.


---

## Body

## 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 technique 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.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 transformation, 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 parameterk, which is a
short-range multiple, is adopted, (1)U(r)=4[k(1r)12−(1r)6].When photons reach
the substrate, attraction and repulsion behaviors occur between silicon’s atoms
and photons. Figure1 shows 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.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.
(a)(b)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 models with different
surface texturization.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. Figure2 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
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.Table 1
Parameters.
Fundamental quantitiesMass4.65×10−23g/atom in siliconLengthα5.431 ÅEnergyε1.792×10−19JTimet1.77×10−3ps/stepNormalized quantitiesLight speed (photon’s speed)c*4.8×106TemperatureT*0.0231Massm*0.54Physical model (a) square (b) pyramid (c) semicircle, the geometric
variables are also shown in this figure.
(a)(b)(c)


## 3. Results and Discussion

Figure3 shows 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 3
The relation among absorptance,h
and photon’s incidence angle θ.Figure4 shows
how the various distances affect the absorptance. As the distance increases,
the absorptance obviously decreases when the square height is 2.31 Å. As in Figure 3, the absorptance decreases as the incident angle of the photons increases. The
absorptance decreases slowly when the distance surpasses 6.94 Å. In other words,
the effect decreases as the distance increases.Figure 4
The relation among absorptance,
distance and photon’s incidence angleθ.The next example
simulates a pyramidal surface. Figure5 shows
the influence of the facet tilt
angle α. In this figure, the absorptance increases as the tilt angle α 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 present study assumes
the pyramid to be isosceles; thus, the pyramids become sharper and taller with
increasing α. This supposition leads to this phenomenon. As expected, a larger
incident angle causes lower absorptance. Figure 5 shows this result.Figure 5
The relation among absorptance,
facet titled angleα, and photon’s incidence angle θ.Finally, Figure6
shows 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].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
texturizations, and suggest better texturization shapes. Increasing the trench depth,
shortening the distance between two trenches, sharpening pyramids, and adding more
circling to the semicircular structure all help improve the efficiency of solar
cells.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.



---

*Source: 540971-2008-07-06.xml*