Chapter 1 Introduction
1.5 Motivation
Therefore, key issues need to be solved:
m=0
Λ
(1) It is necessary to find a way to form the sub-wavelength structure which can reduce reflectance and reduce the damage created by RIE method.
(2) It is necessary to find the way to replace the deposition of second ARC layer so that we can low down the cost of deposition of another layer and thermal mismatch.
(3) It is necessary to develop a low cost and easy fabrication method to form the sub-wavelength structure on antireflection coating.
Therefore, we studied the possibility of sub-wavelength structure on ARC surface instead of semiconductor surface, which may benefit the Si solar cell technologies.
We chose to study the silicon nitride (Si3N4) sub-wavelength structure for this study due to the following reasons:
(1) Si3N4 is a well-known ARC used in semiconductor industry.
(2) No previous studies about solar cell with Si3N4 SWS.
(3) Sub-wavelength structures will act as a second ARC layer with an effective refractive index so that the total structure can perform as a double layer antireflection layer (DLAR) layer.
(4) Si3N4 SWS will avoid or reduce the problem of defects created in Si and will improve the efficiency of Solar Cell.
In this work, we calculate the spectral reflectivity of pyramid-shaped Si3N4
sub-wavelength structures (SWS). A multilayer rigorous coupled-wave approach is advanced to investigate the reflection properties of Si3N4 SWS. We examine the simulation results for single layer antireflection (SLAR) and DLAR coatings with SWS on Si3N4 surface, taking into account effective reflectivity over a range of
wavelengths and solar efficiency. Also we compare the pyramid-shaped structures with cone, parabola, and cylinder-shaped SWS to see the effect of shapes on reflectance property of SWS.
Based upon our theoretical observation efficiency of silicon solar cell with silicon nitride SWS, we develop a simple and scalable approach for fabricating sub-wavelength structures (SWS) on silicon nitride by means of self-assembled nickel nano particle masks and inductively coupled plasma (ICP) ion etching. The size and density of nickel nano particles is optimized by considering different parameters.
Nevertheless, the surface profile of a sub-wavelength structure is strongly dependent on the conditions of the RIE process. So, we investigate the effect of ICP etching conditions on the profile of fabricated sub-wavelength structure on Silicon nitride antireflection coating layers.
1.6 Thesis content
The introduction to solar cell, the need of sub-wavelength structure and the motivation for this work has been described in chapter 1.
In chapter 2, the theory and design of sub-wavelength structure developed in our work has been described. Modeling of sub-wavelength structures via effective medium theories is examined. Also, we will describe about PC1D calculation method of solar cell characteristics and the results in this chapter.
A detail description of our developed fabrication method and results for silicon nitride sub-wavelength structure is given in chapter 3. Furthermore, the description of the instruments used in process and measurement are given in this chapter.
In chapter 4, the fabrication methods of silicon nitride nanocone structures are described with detail fabrication mechanism. Also the results are analyzed in the chapter.
In chapter 5, we will describe the results of fabricated solar cell using silicon nitride sub-wavelength structures in briefly.
Then, in the final chapter, we will summarize and conclude our studies and findings. Some suggestions for future studies will also be given for the improvement of the silicon nitride sub-wavelength structures.
Chapter 2
Design and Simulation of Silicon Nitride SWS
It is necessary to study the reflectance properties of the silicon nitride sub-wavelength structures on silicon substrate with different shapes and optimize the structure height for the better average reflectance before studying the sub-wavelength structures experimentally. So in this chapter, the theory of the developed model for the study of sub-wavelength structures has been described in details with the results and their discussions. Also the procedure of electrical characteristics calculation of a silicon solar cell using the sub-wavelength structure and the results has been reported in this chapter.
2. 1 Sub-wavelength structure design
2.1.1 Theory and Simulation Procedure
For the simplicity, a single pyramidal structure, shown in Fig. 2.1(a), is explored for the reflectance property with respect to the wavelength. The region with brown color of SWS is Si3N4, the region with sky color stands for Si substrate, and the environment of the triangular part is air. The etched Si3N4 (i.e., the height of triangular part) is h and the thickness of the non-etched Si3N4 is s, both of these two parameters are designing parameters for the reflectance optimization.
The studied SWS is a diffractive structure and its reflectance property could be calculated by a rigorous coupled-wave analysis (RCWA) technique. RCWA is an exact solution of Maxwell’s equations for the electromagnetic diffraction by grating structures. A multilayer RCWA method is used in this study, where the effective medium theory (EMT) [24-26] is adopted to calculate the effective refractive index
for each partitioned uniform homogeneous layer, as shown in Fig. 2.1(b).
Figure 2.1: (a) Geometry of sub-wavelength structure studied in this work, where h is the height and s is the non-etched part of SWS. (b) A stack of uniform
homogeneous layers resulting from the partitioned geometry of (a) for the reflection calculation using the multilayer RCWA method and EMT.
Simplifications of Maxwell’s equations are based on the following assumptions:
1. Incident field is an arbitrary linearly polarized monochromatic plane wave
2. Electromagnetic fields are time-harmonic 3. Media are linear, homogeneous and isotropic
4. Gratings are infinitely periodic and are approximated with a layered structure
Reducing the computational domain to one unit-cell, without loss of generality (WLOG), we first divide the pyramidal structure into several horizontal layers with calculated effective refractive index n(zl) for each layer, we can solve the reflectance property of the entire structure including a layer for the non-etched Si3N4 with respect
to the different wavelength.
From the partitioned structure, shown in Fig. 2.1(b), we now consider the reflection and the transmission of a transverse electric (TE) polarized plane wave of free-space wavelength λ, incident at angle θ, on L uniform layers of effective refractive indices nl = n(z1), …, nl, …, nL = n(zL) and thickness d1, …, dl, …, dL. For each layer, the normalized electric field (in the x-y plane) for the input and the output regions is given by, for the air region, i.e., z≤0
l = 1, …, L, I, R and T are the incident, reflected and the transmitted amplitudes of the
electric fields, P and Q are the field amplitudes in the uniform Si3N4 slab, k0=2π/λ
is the wave-vector magnitude, and nair and nSi are the refractive indices of the air and
the silicon regions. Note that now the layer of non-etched Si3N4 has been added into
our simulation structure, where its effective refractive index nSiN = 2.05 is the same
with the original one and f(zL) = 1. The reflected and transmitted amplitudes of the
explored SWS are calculated by matching the tangential electric- and magnetic-field
components at the boundaries among layers [28]. First, for the boundary between the
input air region and the first layer of Si3N4 (i.e., z = 0), we have
matched equations are
The equations (26)-(28) could be solved by using a transmittance matrix method [29].
Using Eq. (28), the field amplitudes PL and QL in terms of the transmitted coefficient
T are determined firstly. They are then substituted into Eq. (27) for the field
amplitudes PL-1 and QL-1. Consequently, the system of equations to be solved for the
reflection properties is given by
T
polarization is considered here for the calculation of the reflection properties [30].For a given number of layers for the SWS including the layer of non-etched
Si3N4, say L in total; a calculation procedure for computing the reflectance properties
of the studied SWS described above is summarized: (i) calculate the effective
refractive index for each zl via Eq. (1); (ii) compute the coefficients using Eqs.
(21)-(25) for a specified wavelength λ; (iii) and solve Eq. (29) to get the unknowns R
and T.
2.1.2 Results and Discussions
First of all, we compare the reflectance with respect to the wavelength of
sunlight for the SWS with Si and Si3N4. As shown in Figure 2.2(a), by assuming a
constant refractive index for Si nSi = 3.875 and for Si3N4 nSiN = 2.05, the reflectance
versus the wavelength for Si SWS with h = 88 nm and Si3N4 SWS with h = 88 nm and
vanished non-etched part of SWS (i.e., s = 0 nm) is simulated and compared.
(a)
Wavelength (nm)
400 500 600 700 800 900 1000
Reflectance (%)
5 10 15 20 25 30 35
Si SWS w/ h = 88 nm
Si3N4 SWS w/ h = 68 nm and s = 20 nm Si3N4 SWS w/ h = 88 nm
(b)
Figure 2.2: (a) The schematic of Si and Si3N4 SWS for the study. (b) The reflectance versus the wavelength for Si SWS with h = 88 nm and Si3N4 SWS
with h = 88 nm and vanished non-etched part of SWS (i.e., s = 0 nm).
Comparison for the Si3N4 SWS with the case of non-zero s, say s = 20 nm is also provided. It is found that it is possible to reduce the reflectance of Si3N4 SWS by
proper selection of h and s.
As seen from Figure 2.2(b), it is found that the non-optimized Si3N4 SWS
possesses a little bit higher reflectance which may not be a plus for ARC. However,
we can design a Si3N4 SWS with the case of non-zero s, say h = 68 nm and s = 20 nm,
which shows that the reflectance is close to the result of Si SWS or even better. This
observation motivates us to explore the morphology-dependent reflectance of Si3N4
SWS with a set of optimized h and s. Note that Si refractive index nSi may depend
upon the wavelength of incident sunlight [31]; our calculation for the Si3N4 SWS with
h = 68 nm and s = 20 nm confirms the reflectance difference between the model with
constant and wavelength-dependent nSi, as shown in Figure 2.3. In this calculation, an
empirically fitted formula for the wavelength-dependent nSi is implemented in our
simulation program [32]
(
12)
2 2 1
2 λ λ
λ ε λ
+ − +
= A B
nSi
, (30) where, λ1 =1.1071µm, ε = 11.6858, A = 0.939816µm2 and B =
8.10461 × 10−3.
Wavelength (nm)
400 500 600 700 800 900 1000
Reflectance (%)
5 10 15 20 25 30 35
nSi = 3.875
nSi is function of λ via Eq. (30)
Figure 2.3: The spectral reflectivity of Si3N4 SWS for h = 68 nm and s = 20 nm with constant Si refractive index and refractive index as a function of lambda
given by Eq. (28).
Using the above empirical fitted formula, the refractive index of silicon is plotted
for wavelength from 400 nm to 1000 nm as shown in Figure 2.4.
Figure 2.4: Refractive index of Si vs wavelength using equation (28)
Instead of considering the reflectance for a certain wavelength, an effective
E(λ) is photon energy and R(λ) is the calculated reflection.
Height of Si SWS (nm)
0.00
Figure 2.5: The effective reflectance for the wavelength varying from 400 nm to 1000 nm; plot is as a function of (a) h for Si SWS and (b) of h and s for
Si3N4 SWS.
Figures 2.5(a) and 2.5(b) show the effective reflectance as a function of h for Si
SWS, and of h and s for Si3N4 SWS. For Si SWS, there is a minimum Reff = 3.89% for
h = 220 nm, and for Si3N4 SWS, the minimum of Reff = 3.43% occurs at h = 150 nm
and s = 70 nm. Compared with Si SWS, the improvement of Reff for Si3N4 SWS is due
to the nature of Si3N4 and an optimal combination of the height of etched part of Si3N4
and the thickness of non-etched part of Si3N4.
It has been reported that SLAR and DLAR were used in solar cell, for a unified
comparison; similarly, we further examine their Reff over the same wavelength, as
shown in Figs. 2.6(a) and 2.6(b).
(a)
(b)
Figure 2.6: Plot of the effective reflectance for the wavelength varying from 400 nm to 1000 nm. (a) is the result as a function of the thickness of Si3N4 ARC
with n = 2.05for SLAR coating on Si. (b) is the result as a function of the thickness of ARC 2 and refractive index of ARC 2 for Si3N4 / ARC 2 DLAR coating on Si. The thickness of Si3N4 ARC 1 is fixed at 80 nm which is optimized
from (a).
For Si3N4 SLAR coating on Si, as shown in the inset of Figure 2.6(a), the
refractive index is equal to 2.05, where the thickness of ARC is varied. For Si3N4 /
ARC 2 DLAR coating on Si, the thickness of ARC 2 and the refractive index of ARC
2 are varied. Note that the thickness of ARC 1 equals 80 nm, as shown in the inset of
Figure 2.6(b), directly comes from the optimal value of Figure 2.6(a), and the lower
bound of refractive index of ARC 2 starts from 1.38 which is the refractive index of
MgF2. The lowest Reff occurs when the refractive index of ARC 2 is 1.38 and its
thickness is 100 nm.
Based upon the investigation of Figs. 2.5 and 2.6, we show the optimal
reflectance spectra among the bulk Si (i.e., the bare Si), the optimized SLAR, DLAR,
Si SWS and Si3N4 SWS for the wavelength from 400 nm to 1000 nm in Figure 2.7.
Wavelength (nm)
400 500 600 700 800 900 1000
Reflectance (%)
0 10 20 30 40 50 60
Bare Si
Si SWS w/ h = 220 nm
Si3N4 SWS w/ h = 150 nm and s = 70 nm SLAR, thickness of Si3N4 = 80 nm
DLAR, thickness of ARC 1 and ARC2 is 80 nm and 100 nm
Figure 2.7: Comparison of the reflectance spectra among the bulk Si (i.e., the bare Si), the optimized SLAR, DLAR, Si SWS and Si3N4 SWS for the
wavelength from 400 nm to 1000 nm.
Table 1 lists the effective reflectivity for those optimized structures of 150 nm Si3N4
SWS and 70 nm non-textured Si3N4 film, compared with the Si SWS, Si3N4 SLAR
(its thickness is 80 nm) and Si3N4 / MgF2 DLAR (its thickness is 80 nm / 100 nm)
structures. The flat silicon substrate exhibits high reflection > 35% for visible and
near infrared wavelengths, Si3N4 SLAR coatings exhibits low reflection < 20% for
long wavelengths 700 nm and high reflection > 35% for shorter wavelengths 400 nm,
and Si3N4 / MgF2 DLAR coatings exhibits low reflection < 10% for long wavelengths
700 nm and high reflection > 20% for short wavelength 400 nm, while the SWS
gratings show reduced reflection of < 10% for whole wavelengths. The Si3N4 SWS
with h = 150 nm and s = 70 nm exhibits lowest effective reflectivity among five
structures; consequently, the optimized morphology of Si3N4 SWS could be a
promising alternative for DLAR in Si solar cell technology.
Table 1. Effective reflectivity for those optimized structures of 150 nm Si3N4 SWS and 70 nm non-textured Si3N4 film, compared with the Si SWS, Si3N4 SLAR (its thickness is 80 nm) and Si3N4 / magnesium fluoride DLAR (its thickness is 80 nm
/ 100 nm) structures.
ARC structure Reff (%) for λλλλ = 400 nm ~ 1000 nm
Si3N4 SWS 3.43
Si SWS 3.89
DLAR 5.39
SLAR 5.41
2.2 Shape Effect
2.2.1 Simulation Procedure
The shape of the SWS may be somewhat variable and, therefore, we performed
reflectance calculations for a few model shapes, a cone, paraboloid and cylindrical,
respectively as shown in Fig. 2.8, assuming a hexagonal nipple lattice.
The RCWA model as described in section 2.1 was used to calculate the reflectance
of the three types of shapes for normally incident light. Therefore, for a cone shape, the
equation (16) and (17) will become
( )
2
3
2 l lf z r
D
= π
(32)1
ll
r r z
h
= −
(33)Figure 2.8: Three model shape types (a) cone (b) parabola and (c) cylinder shape.
Similarly, for paraboloid and cylindrical shape, the fraction of Si3N4 layer and
base width of each layer will be given by equation (34) and (35) respectively.
( )
cylinder) in our simulation is shown in Fig.2.9.The graded index, which is desirable for suppressing the optical reflection, [35] is
observed for pyramid, cone and parabolic shapes—the refractive index changes from
1.0 to 1.5 for pyramid, from 1.0 to 1.4 for cone and from 1.0 to 1.4 at the air/silicon
nitride interface and then changes sharply to the bulk index of silicon nitride. But for a
cylinder shaped SWS, the effective refractive index calculated is 1.4. From the
comparison, it is found that the slope of the change of refractive index is lowest for
cone shaped SWS. Using microwave models, experimentally it has been demonstrated
that the strong reflectance reduction by a nipple array with cone-shaped nipples [36].
So it is believed that cone shaped Si3N4 SWS will give the lowest reflectance compared
to pyramid or parabolic or cylinder shaped SWS. The optimizations of the structures
and the comparison results will be discussed next.
Distance (nm)
0 50 100 150 200
Refractive Index
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Pyramid Parabolic Cone Cylinder
Figure 2.9: Comparison of the change of calculated effective refractive index at λλλλ = 600 nm from the top of the SWS to the bottom of Si3N4 SWS
Similarly, as we varied the “s” and “h” for pyramid structure, we varied the these
two parameters for parabola, cone and cylindrical shapes to see the lowest effective
reflectance and the optimization results are shown in Fig. 2.10, Fig. 2.11 and Fig. 2.12,
respectively. The reflectance spectra of the optimized structures are compared in Fig.
2.13. The lowest effective reflectance of 3.14% has been seen for the optimized cone
shaped SWS as compared to pyramid, parabola and cylinder shape structure.
0.00 100120140160180200
40 20
Figure 2.10: Parabola Shape optimization
0.00
Figure 2.11: Cone Shape Optimization
0.00
Figure 2.12: Cylinder shape optimization
Wavelength (nm)
400 500 600 700 800 900 1000
Reflectance (%)
Figure 2.13: Comparison of optimized structures with different shape But, the comparison of the reflectance spectra of the four shapes as shown in Fig.
2.13 may not be correct as the volumes of the different shapes are different. For this
reason, we keep the volume constant for all the shapes and varied the height and base
width or base diameter of the SWS to see the effect in reflectance. Note that when we
changed the SWS height and base width or base diameter, the thickness of the
non-etched Si3N4 SWS was kept constant at 70 nm. The effective reflectance of the
pyramid, cylinder, parabola, and cone shaped Si3N4 SWS with different volume are
shown in Fig. 2.14. For the volume from 1 × 105 nm3 to 1 × 106 nm3 we found the
cone-shaped SWS had the lowest and cylinder-shaped SWS had the highest effective
reflectance as compared to other shaped SWSs.
Volume (X 105 nm3)
2 4 6 8 10
Effective Reflectance (%)
2 3 4 5 6 7 8
Pyramid Cylinder Parabola Cone
Figure 2.14: The effective reflectance of Si3N4 SWS versus the SWS volume.
V olum e = 100 000 nm3
Volume = 500000 nm3
Diameter (nm)
80 100 120 140 160 180 200 220
Effective reflectance (%)
2 3 4 5 6 7
Pyramid Cylinder Prabola Conel
(c)
Figure 2.15: Effective reflectance Vs Base diameter w / volume (a) 100000 nm3 (b) 300000 nm3 and (c) 500000 nm3.
2.3 The Electrical Characteristics Calculation
To get the electrical data for the solar cell with Si3N4 SWS, the simulated
reflectance of the optimized Si3N4 SWS and single-layer anti-reflection (SLAR)
structures are post-processed using PC1D program. In this section, we will introduce
about the PC1D software and describe the simulation procedure for the calculation of
solar characteristics.
2.3.1 Introduction to PC1D software
PC1D is the simulation program in most widespread use among the photovoltaic
community. It is a software package for personal computers that uses finite-element
analysis to solve the fully-coupled two-carrier semiconductor transport equations in
one dimension. This program is particularly useful for analyzing the performance of
optoelectronic devices such as solar cells, but can be applied to any bipolar device
whose carrier flows are primarily one-dimensional. flexible internal models make it. It
is easy to set up and modify a broad range of one-dimensional problems from MOS
capacitors to bipolar transistors. Heterojunctions, arbitrary doping profiles,
doping-dependent mobility, bandgap narrowing, Auger recombination, interface
recombination, temperature effects, photogeneration of carriers, complex boundary
conditions, and transient solutions are some of the powerful features built into this
program [37].
The development of this program was initiated by Dr. Paul A. Basore while he
was a member of the faculty of electrical engineering at Iowa State University in 1984,
with funding from the photovoltaic technology division of Sandia National
Laboratories. The project was originally intended to take advantage of the interactive
environment of personal computers to help analyze solar cells. Additional funding
from IBM Corporation in the form of a Faculty Development Award made it possible
to expand the program into a full-featured semiconductor analysis package for public
distribution. Later it was developed at UNSW, Australia [38] and distributed freely.
2.3.2 Simulation Procedure
To calculate the solar cell electrical characteristics before measuring realistic
silicon solar cells, we have used the measured reflectance spectra and simulated
reflectance spectra as the input of the PC1D program. Performance of optical system
directly affects the short-circuit current density (JSC) and the conversion efficiency of a
solar cell. The short circuit current density and open circuit voltage of the solar cell
were calculated under the standard AM1.5 global spectrum from its IV characteristics.
were calculated under the standard AM1.5 global spectrum from its IV characteristics.