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

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

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## Abstract

The purpose of this paper is to explore the relations between surface texturization and absorptance of multicrystalline silicon solar cells by a simple new model, based on the classic molecular (MD) dynamics simulation, alternative to complex electron-photon interactions to analyze the surface texturization of solar cells. In this study, the large tilted angle leads to the lower efficiency of solar cell. To consider the effect of incident angle, a range of high efficiency exists due to the increasing probability of second reflection. Furthermore, the azimuth angle of incident light also affects the efficiency of solar cells. Our results agree well with previous studies. This MD model can potentially be used to predict the efficiency promotion in any optical reflection-absorption cases.


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## Body

## 1. Introduction

The solar cell technology has attracted recent
attention due to the price rising of petroleum. In recent studies,
achieving higher efficiency in solar cells is the one of most important issues
on the topic. Surface texturing of solar cells is a common approach to reduce
incident light reflection and, consequently, increase solar cell efficiency.Wet etching is commonly used to produce texturization on surface of solar
cells. Generally, pyramidal structure formed on the surface of silicon solar
cells by alkaline solutions etching. This pyramidal surface shape occurs
because alkaline solutions etch silicon along crystallographic orientations. Hylton et
al. [1] 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 [2] 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 [3] 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.New solutions are also applied. Marrero et al. [4] describe a texturization method for
monocrystalline silicon solar cells based on a mixture of sodium carbonate and
sodium hydrogen carbonate solutions. A specific solution has been found that results
in an optimal etching rate, the lowest surface reflectance, and a homogeneous
density of pyramidal structures on the silicon surface. The subsequent
phosphorus diffusion with rapid thermal processes has been modified in order to
drastically reduce the process time and, simultaneously, to obtain a high
homogeneity of the sheet resistance values and improved photocarriers
lifetimes. 100×100 mm solar cells with an efficiency of 15.8% have been
obtained compared to an efficiency of 14.7% for the reference cell.Usual step during PV cell production is surface texturization, which is
performed to reduce the reflection losses from the front surface of solar
cells. Conventional chemical and electrochemical methods are efficient in
texturing monocrystalline silicon
[5]. Unfortunately, these methods
are inefficient for multicrystalline silicon due to the presence of random
crystallographic grain orientations and high selectivity of etching along
specific directions. Consequently, it is impossible to obtain texturization of
homogeneous structure on the whole surface [6–10]. Another possibility is mechanical texturization [11].
Unfortunately, it is also not satisfactory due to possible mechanical damages,
resulting in breakability and fragility of silicon and additionally very small
thickness of silicon wafers. Therefore, there is a real need for a versatile
gentle process that is capable of producing the layer of regular texture. The
possible way of overcoming these difficulties is laser texturization [8, 12, 13].Molecular dynamics simulation
is a well-suited technique to nanoscale phenomena and mechanical behaviors [14–16]. However,  few studies use MD
to examine solar-cell issues. Stir and Prezhdo [15] explore the photoinduced
electron-transfer phenomena on a dye sensitized titanium solar cell with
nonadiabatic MD (NAMD) simulations, which is based on the ab-initio functional theory. The
system under study is typical of the dye sensitized semiconductor nanomaterials
used in solar cells, photocatalysis, and photoelectrolysis. The electronic
structure of the dye-semiconductor system and the adiabatic dynamics is simulated by ab-initio density functional theory MD,
while the NA effects are incorporated by the quantum-classical mean-field
approach. A novel procedure separating the NA and adiabatic ET pathways is
developed. The simulation provides a detailed picture of the ET process. For
the specific system under study, ET occurs on a 30-femtosecond-time scale, in agreement with the
ultrafast experimental data. Both adiabatic and NA pathways for the ET are
observed. The NA transfer entirely dominates at short times and can occur due
to strong localized avoided crossing as well as extended regions of weaker NA
coupling. Although the adiabatic ET contribution accumulates more slowly, it
approaches that of the NA ET pathway asymptotically. The electron acceptor
states are formed by the d-orbital of Ti atoms of the semiconductor and are
localized within the first 3-4 layers of the
surface. About 20% of the acceptor state density is localized on a single Ti
atom of the first surface layer. The simulation predicts a complex nonsingle-exponential
time dependence of the ET process.However, many unknown factors in photonelectron
interactions prevent studies from being conducted on the issue of photon
absorption. On the other hand, this
issue is deserved to study.The above literature review shows that there is still much
necessity to investigate the problem of enhancing solar cells’ efficiency.
Also, the relations of surface texturization effects are still not well
understood. In this study, a simple
photonatomic model with molecular dynamics simulations to explore the effects
solar cell surface texturization is developed and numerically solved to
enhance the understanding of the underlying characteristics of different shapes
of surface texturization by wet or dry etching.The scope of this paper
is mainly focused on the issue of relations of pyramidal
structure and light absorptance. A real-closely pyramid texturization on the
surface of multicrystalline silicon substrate etching by alkaline solutions is
simulated by the molecular dynamics model to explore the influences of
incident, azimuth and tilted angles with absorptance. The optimal shapes of
this model are also discussed in our studies.


## 2. Mathematical and Physical Model

As mentioned, the
molecular dynamics simulation is a well-suited numerical method to calculate reflection
caused by texturization of solar cells. The classical
molecular dynamics scheme considers ann-atomic nonquantum system. Each atom i in this system is of its position ri, velocity vi and mass M. Thus, the motion of a particle can be described as Newton’s second law:
(1)Md2ridt2=∑j=1,j≠iNFij,
where Fij is
the force exerted by atom j on atom i. The force term is derived
from the interatomic potential that must satisfy both nanoscopic and
macroscopic requirements. The potential function generally forms with a
short-distance repulsive term and a long-distance attractive term. Given
initial conditions, (1) can be solved to provide the position and the velocity
of each particle as a function of time, which will be used to compute the
system temperature, heat flux, and thermal conductivity.Under the condition that the de Broglie wavelength of a photon and an
atom is smaller, the assumption that the absorption and reflection closely represented as a series
of attraction and repulsion behaviors between photons and atoms is reasonable.To avoid complications in photonelectron 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 themselves, 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:
(2)U(r)=4[k(1r)12−(1r)6].When photons reach the substrate with the nondimensional light speedc*
and the impact angle θ,
attraction and repulsion behaviors occur between silicon’s atoms and photons. Figure 1 shows the mechanism of photonatom interactions. When a photon enters the
attractive field of an atom, the photon should be attracted to the center of
atom. But the repulsive force pushes the photon off center if the photon is too
close to the atom center.Illustrations of attractive and repulsive interactions of atoms and photons. (a) The photons
moves toward repulsive force field are 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)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. The system’s temperature can be
readily calculated from the velocity of each individual atom in the simulation
domain since the Boltzmann distribution function allows the straightforward
derivation of the mean kinetic energy〈Ec〉 in the following way:
(3)〈Ec〉=12M∑i=1Nv2=32NkBTMD,
where kB is the Boltzmann constant and N is the number of particles in the system.The initial temperature of the system was determined by
Maxwell-Boltzmann distribution. During the indentation process, the velocity of
every atomυnew was scaled as
(4)υnew=υ*TDTA,
where TD is the desired
temperature, TA is the
actual temperature, and υ* is the calculated velocity of atom. In
this paper, the temperature was set as 300 K.Due to the actions of attractive and repulsive forces and the photon’s
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’s energy.Note that the efficiency of monocrystalline silicon is, at most, 24.7% [17]. This study attempts to make a model with an
absorptance reaching to this theoretic value, 24.7% in a smooth nontextured
substrate by simply adjusting k. In
our simulation, k is determined to be
3.86 in silicon. 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 photonatom
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 a MD model. The results and conclusions
of this study can also be extended to other solar cells, GaAs, InGaAs, InGaP, and
so forth. The structure of monocrystalline silicon is an fcc diamond structure,
showed in Figure2. According the reviews of previous studies, square,
pyramidal, and semicircular texturing structures were demonstrated. 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’s incident angle varies at x-z planes.Figure 2
The model of mc-silicon by alkaline etching. The tilted angle isα.All the simulations were executed with the computer of AMD
Althlon64X2 3800+ CPU, Fedora Core Linux 6, and the GNU project FORTRAN
compiler g77.


## 3. Results and Discussion

The variety of light absorptance  of multicrystalline Si
substrate etched by alkaline solutions is discussed in Figures3–5.  According the
discussion by Xi et al. [18], the tilted pyramids usually formed on the surface of
mc-Si substrate etching by alkaline solution. If the orientation of the grains
tends to (100), the pyramid will form a triangle with 70° on the top, tilted angle α and 110°−α on the other angles. So, we
try to make simulation with this model, and the results can easily compare with
the results of Xi et al. [18].Figure 3
Schematic illustration of reflection on the surface of mc-silicon after
alkaline etching.Figure 4
The relation of absorptance and the tilted angle, agreeing with the
result of Xi et al. [18].Figure 5
The relation of absorptance and incident angle.Figure4 shows that the reflection hardly changes when
the tilted angle is less than 20°.
That is because the most light reflects from O1 plane to O2 plane in Figures 3–5. More second
reflection means that more light will be absorbed by the substrate. But if the
tilted angle surpasses 20°,
the reflectance increases quickly.  Therefore, the pyramids with a large tilted
angle lead to the lower efficiency. To compare with the results of Xi et al.
[18], these two results are with a
good agreement.Furthermore, we try to change the incident angleθ, shown
in Figure 5. In the case of pyramid with tilted angle α=30° (the three angles
are 70°, 80°, and 30°), more second reflection is produced when the incident angle θ=20°∼85°, so the absorptance
rises higher to almost 60%. But once the incident angle is greater than 80°,
the possibility of second reflection decreased because the incident light is
perpendicular to plane O2. Thus the absorptance quickly decreased.
As the similar situation, when the incident angle is smaller than −20°, the
incident light is also perpendicular to plane O1, the possibility of
second reflection decreased, so the absorptance decreased to almost 20%.We are interested about the effect of azimuth angle of
incident light with absorptance. The surface morphology of the alkaline-etched
wafers is quantified using a spherical polar coordinate system, as was the case
for describing the relationship between different wafer and crystal
orientations, shown in Figure6. However, in this case, the tilt (α) and
azimuth (φ) angles refer to
the positions of the normals to a particular facet of textured surface exposed
by etch. These angles are measured relative to a particular crystal or wafer
orientation, whose surface is parallel to the x-z planes in the coordinate system and whose surface normal is
parallel to the Z axis. The positions of the etch facets formed on a particular
crystal or wafer orientation are thus described in terms of their angles α and φ with respect to the base orientation.Figure 6
The diagram of a spherical polar coordinate system, which is quantified, is used to describe the surface morphology of the alkaline-etched wafers.The simulation is proceeding with the conditions of the
incident angleθ=30°, isosceles
pyramid of tilted angle α=55°,
and the azimuth angle φ=0° to 90°, to explore the influence of azimuth angle on the absorptance of
solar cells with pyramid surface. In Figure 7, it is found that the absorptance
is the greatest when the azimuth angle φ=0° or 90°, the incident light is perpendicular to the (100)
plane for the azimuth angle. The reflective light is usually reflected by
planes of another pyramid. The higher probability of second reflection leads to
the higher absorptance. But when the azimuth angle is getting larger, more incidents
reflect only once, the probability of second reflection slightly decreased. Thus,
the absorptance also decreased. When the azimuth angle is greater than 45°, the incident light
illuminates the (010) plane. The absorptance slightly increases again.Figure 7
The position of the triangle of
principal orientations. The incident angleθ and the azimuth angle φ are demonstrated.Table 1
Parameters of physical models, the bandgaps of the most important semiconductors for solar-cell applications.
Fundamental quantitiesMulticrystalline siliconMass (density)2.33 g/cm3Lengthσ5.431 ÅEnergyε1.792×10−19 JTimet1.77×10−3 ps/stepNormalized quantitiesLight speed (photon’s speed)c*4.8×106TemperatureT*0.0231Massm*0.54


## 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.In the simulations of multicrystalline
silicon by alkaline etching, the large tilted angle leads to the lower
efficiency of solar cell. To consider the effect of incident angle, a range of
high efficiency exists due to the increasing probability of second reflection. Furthermore,
the azimuth angle of incident light also affects the efficiency of solar cells.In this study, the wave behavior of photons
and atoms is ignored. That means, according to the wave-particle duality, the gap
between our study and real phenomenon possibly exists. However, this study is a
beginning to simulate the absorption by molecular dynamics. Our results also agree
well with previous studies. Thus, the development of this MD model is helpful
to simulate the texturization before solar cells fabrication and can
potentially be used to predict the efficiency promotion in any optical
reflection-absorption cases.



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*Source: 282791-2008-10-21.xml*