Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates
Multilayer antireflection coatings have been modeled in visible and IR (3-5μm) bands to reduce reflectance from glass, germanium (Ge), silicon (Si) and zinc selenide (ZnSe) substrates. The transmittance of bare glass substrate is around 95% whereas for Ge 64%, Si 70%, ZnSe 84%. Theses values are enh...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1180772017-05-29T03:05:06Z Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates Asghar, M.H. Khan, M.B. Naseem, S. Multilayer antireflection coatings have been modeled in visible and IR (3-5μm) bands to reduce reflectance from glass, germanium (Ge), silicon (Si) and zinc selenide (ZnSe) substrates. The transmittance of bare glass substrate is around 95% whereas for Ge 64%, Si 70%, ZnSe 84%. Theses values are enhanced reasonably by the application of multilayers films. Starting from a single layer, the layers have been added systematically forming multilayer structures to reduce reflectance considerably with each increasing layer. The designed layers are optimized for their performance by varying their thickness and refractive indices. The analysis of these modals has shown that the proposed multilayer structures are very effective in reducing the reflectance for all the substrates in two spectra. 2003 Article Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates / M.H. Asghar, M.B. Khan, S. Naseem // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 508-513. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS: 42.79.Wc, 78.20.-e http://dspace.nbuv.gov.ua/handle/123456789/118077 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Multilayer antireflection coatings have been modeled in visible and IR (3-5μm) bands to reduce reflectance from glass, germanium (Ge), silicon (Si) and zinc selenide (ZnSe) substrates. The transmittance of bare glass substrate is around 95% whereas for Ge 64%, Si 70%, ZnSe 84%. Theses values are enhanced reasonably by the application of multilayers films. Starting from a single layer, the layers have been added systematically forming multilayer structures to reduce reflectance considerably with each increasing layer. The designed layers are optimized for their performance by varying their thickness and refractive indices. The analysis of these modals has shown that the proposed multilayer structures are very effective in reducing the reflectance for all the substrates in two spectra. |
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Asghar, M.H. Khan, M.B. Naseem, S. Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates Semiconductor Physics Quantum Electronics & Optoelectronics |
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Asghar, M.H. Khan, M.B. Naseem, S. |
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Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates |
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Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates |
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Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates |
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Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates |
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Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates |
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modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Modeling high performance multilayer antireflection coatings for visible and infrared (3-5μm) substrates / M.H. Asghar, M.B. Khan, S. Naseem // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 508-513. — Бібліогр.: 19 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
work_keys_str_mv |
AT asgharmh modelinghighperformancemultilayerantireflectioncoatingsforvisibleandinfrared35mmsubstrates AT khanmb modelinghighperformancemultilayerantireflectioncoatingsforvisibleandinfrared35mmsubstrates AT naseems modelinghighperformancemultilayerantireflectioncoatingsforvisibleandinfrared35mmsubstrates |
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2025-07-08T13:19:34Z |
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2025-07-08T13:19:34Z |
_version_ |
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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2003. V. 6, N 4. P. 508-513.
© 2003, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine508
PACS: 42.79.Wc, 78.20.�e
Modeling high performance multilayer antireflection
coatings for visible and infrared (3�5µµµµµm) substrates
M.H. Asghar1, M.B. Khan1, and S. Naseem2
1Advanced Engineering Research Organization (AERO), Wah Cantt. Pakistan.
2Centre for Solid State Physics, Punjab University, Lahore. Pakistan.
1E-mail: mha_19@yahoo.com
Abstract. Multilayer antireflection coatings have been modeled in visible and IR (3�5µm)
bands to reduce reflectance from glass, germanium (Ge), silicon (Si) and zinc selenide (ZnSe)
substrates. The transmittance of bare glass substrate is around 95% whereas for Ge 64%, Si
70%, ZnSe 84%. Theses values are enhanced reasonably by the application of multilayers
films. Starting from a single layer, the layers have been added systematically forming multilayer
structures to reduce reflectance considerably with each increasing layer. The designed layers
are optimized for their performance by varying their thickness and refractive indices. The
analysis of these modals has shown that the proposed multilayer structures are very effective
in reducing the reflectance for all the substrates in two spectra.
Keywords: antireflection coatings, multilayers.
Paper received 21.07.03; revised manuscript received 02.01.04; accepted for publication 11.12.03.
1. Introduction
Antireflection coatings have had the greatest impact on
optics, and even today, in sheer volume of production,
they still exceed all the other types of coatings. In some
applications antireflection coatings are required for the
reduction of surface reflections. In other not only reflec-
tion is reduced but also transmittance is increased con-
siderably. As it is a known fact that radiations incident
upon the surface of an optical material is separated into
reflected, transmitted, absorbed and scattered fractions.
The fraction of available energy that is distributed
amongst these is determined by the indices of refraction.
Antireflection coatings can range from a single layer
having virtually zero reflectance at just one wavelength,
to a multilayer system of many layers having virtually
zero reflectance over a wide spectral range.
2. Theory of antireflection coatings
The simplest antireflection coating is a single layer de-
posited on a substrate [1]. To achieve antireflection prop-
erties, this layer depends on the cancellation of light at
the upper and lower of the two surfaces. Assuming the
refractive index of air as n0, film as n1 and that of substrate
as ns, then in order to cancel the two reflected beams the
intensity of the radiation reflected at the upper and lower
surfaces of the coating should be equal which means that
the ratios of the refractive indices at each boundary should
be equal, that is:
n0 / n1 = n1/ ns, with film thickness, n1t1 = λ/4
This configuration will give only one minimum in the re-
flectance profile. For more minima, more layers are re-
quired. The same theory is used to calculate the expres-
sions for two- and three- layers antireflection coatings [2].
Similarly, multiple layers are used to achieve more minima
in reflectance profile for broadband antireflection coat-
ings [3, 4]. We have modeled multilayer antireflection coat-
ings for glass and infrared substrates. These coatings are
modeled at a design wavelength of λ0 = 0.55 µm for vis-
ible and λ0 = 4µm for infrared substrates, respectively.
Moreover all the designs have been optimized by varying
the individual layer refractive index and thickness.
2.1 Multilayer matrix calculations
Matrix calculations determine the spectral transmittance
and reflectance profile for multilayer structures on a
M.H. Asghar et al.: Modeling high performance multilayer antireflection coatings for...
509SQO, 6(4), 2003
substrate. Consider a loss free multilayer design, nor-
mally incident radiations, and assume that films are op-
tically homogenous. The electric field vector (Em�1) and
magnetic field and the magnetic field vector (Hm�1) at the
incident boundary of a film are related to the electric
field vector Em and magnetic field vector Hm vectors at
the boundary of the adjacent film by the product of the
following matrices per layer. The matrix is calculated at
each boundary throughout the multilayer as the magni-
tude of electric and magnetic field vectors alter with the
properties of the layer [5]. Application of the appropri-
ate boundary conditions between each layer requires that
the tangential components of E and H vectors are con-
tinuous across each boundary to the equations of wave
propagation.
Let the electric and magnetic field vectors of the wave
traveling in the direction of the incidence are denoted by
symbol �+�, and those waves traveling in the opposite
direction by the symbol ���. At the interface of mth layer,
the tangential component of E and H are given as
Em = Em
+ + Em
�
Hm/H1 = Em/E1
Hm = Em × H1/E1 (1)
Neglecting the common phase factors, and where Em
and Hm represent the resultants then:
+=+
m
m
m E
E
H
H
E
1
1
2/1 (2)
+−=−
m
m
m E
E
H
H
E
1
1
2/1 (3)
+=+
1
12/1
E
HE
HH m
mm (4)
−=−
1
12/1
E
HE
HH m
mm (5)
The fields at other interfaces m�1 are similar to equa-
tions 2�5 at the same instant of time and a position with
identical x and y coordinates. These can be determined
by multiplying by phase difference in z direction given
by eiδ or e�iδ where:
λ
θπ
δ 1
cos2 1dN
= (6)
And θ1 may be complex. The values of E and H at this
interface are therefore:
δδ
η
i
m
mi
mm eE
H
eEE
+== +
−
+
1
1 2/1 (7)
δδ
η
i
m
mi
mm eE
H
eEE
+−== −−
−
−
1
1 2/1 (8)
[ ] δδ η i
mm
i
mm eEHeHH 11 2/1 +== +
−
+ (9)
[ ] δδ η i
mm
i
mm eEHeHH −−−
−
− −== 11 2/1 (10)
Where η1 is the tilted optical admittance given by
η1 = H1/E1
Now
Em�1= E+
m�1 + E�
m�1
1
1
sin
cos
η
δ
δ
i
HEE mmm +=−
δ
η
δ
cos
sin
1
1 mmm H
i
EH +=−
This can be written in matrix form as:
=
−
−
m
m
m
m
H
E
i
i
H
E
δδη
ηδδ
cossin
/)sin(cos
1
1
1
1
Solving the above given expression [6], the matrix
expression for single layer is:
=
DiC
iBA
M1
Where: cos δm = A = D, isinδm/ηm = B, isinδmηm= C
For two successive layers:
Layer 2 Layer 1
=
11
11
23
22
DiC
iBA
DiC
iBA
M (15)
After multiplication we have:
+−
+
+
+
−
=
1212
1212
1212
1212
DDBC
DiBiBA
iCDAiC
CBAA
M (16)
Let AA = A2A1 � B2C1, BB = A2iB1 + B2iD1, CC =
= iÑ1A1 + D2iA1, DD = Ñ2B1 + D2D1
Therefore matrix is written as:
=
DDCC
BBAA
M (17)
Therefore, for a multilayer containing q-layers:
=
∏
= q
q
q
m
m H
E
M
H
E
10
0 (18)
510
SQO, 6(4), 2003
M.H. Asghar et al.: Modeling high performance multilayer antireflection coatings for...
The loss-free transmittance and reflectance for the
multilayer assembly can be calculated from this product
matrix by:
( ) ( )2
0
2
0
0
_
4
CCBBnnDDnAAn
nn
T
ss
s
q
+++
= (19)
( ) ( )
( ) ( )2
0
2
0
2
0
2
0
CCBBnnDDnAAn
CCBBnnDDnAAn
R
ss
ss
q
+++
−+−
= (20)
The reflectance, transmittance and absorptance are
then related by R + T + A = 1. The solution of this ma-
trix theory is a laborious job for multilayer coatings.
Based on the matrix theory, we have developed a soft-
ware program to design and simulate the performance of
multilayer coatings [7].
3. Modeling and analysis
Thin film materials are required to have certain charac-
teristics to become a potential candidate for multilayer
structures. This includes high transparency, homogenei-
ty, high packing density, good adhesion, low stress, hard-
ness and ability to survive in different environmental and
deposition conditions [8, 9]. These materials are then used
to reduce reflection from the surfaces, which are basi-
cally caused by the sharp variation of the refractive in-
dex at the incident medium-substrate interface. Multi-
layer coating structures based on those materials have
wide band of applications in electronics, optoelectronics,
optics and optoelectronics equipments.
(A) visible region: The reflectance from the surface of
bare glass substrate is 4.2%. Starting from single layer
reflectance is reduced by application of five layers. The
design data and reflectance values for all these designs
are given in table 1. Initially single layer of MgF2 has
been employed to reduce the magnitude of this reflect-
ance. The maximum reflectance from the substrate has
reduced from 4.2% to 2.2%, with reduction in average
reflectance to 1.65%. For a single layer coating only one
minimum is achievable. Two layer coating comprising
MgF2 and Al2O3 (Air/MgF2/Al2O3/Glass) has been de-
signed to further reduce the reflectance obtained by sing-
le layer configuration. In this configuration we have two
distinct minima of reflection as compared to one for sin-
gle layer. Earlier we had a maximum reflectance of
2.26%, which has reduced to 1.77% by the addition of
second layer. Further the average reflectance has gone
down to 1.02%. The reflectance profile of three-layer
coating comprising of SiO2, HfO2, and MgO (Air/SiO2/
HfO2/MgO/Glass) is more effective than the previous two
designs. SiO2 is very low index material with a value of
1.46 in the visible spectrum, and HfO2 has a moderately
high index of nearly 2.0 with a good environmental du-
rability [9]. The maximum reflectance from the substrate
has further reduced to 1.37% with average reflectance to
0.91%. Therefore, the performance of the coating is fur-
ther improved by the addition of third layer. The reflect-
ance is further reduced by four-layer design comprising
MgF2, ZrO2, Al2O3 and MgF2 (Air/MgF2/ZrO2/Al2O3/
MgF2/Glass). A slight increase in reflectance at the edges
of the band can be seen, but the important feature of this
design is the zero reflectance at two spectral points. In
this case maximum and average reflectance has appreci-
ably reduced to 1.28% and 0.45%, respectively. On the
application of the fifth layer in the model (Air/MgF2/
ZrO2/Al2O3/Cryolite/MgF2/Glass) maximum and aver-
age reflectance further reduced to 1.11% and 0.42% re-
spectively. The combined reflectance plot of the five con-
figurations is shown in Fig. 1. This application of multi-
ple layers encourages the use of multi-layers to achieve
wide transmission bands. By increasing number of lay-
Table 1. Design data and reflectance values for all configurations on glass.
Configurations Material Refractive Index (n) Thickness (µm) Rp(%) Rave(%)
Single Layer MgF2 1.38 0.099 2.26 1.65
Two-Layers MgF2 1.38 0.099 1.77 1.02
Al2 O3 1.62 0.169
Three-Layers SiO2 1.46 0.087 1.37 0.91
HfO2 1.98 0.128
MgO 1.73 0.073
Four-Layers MgF2 1.38 0.090 1.28 0.45
ZrO2 2.05 0.121
Al2O3 1.62 0.077
MgF2 1.38 0.181
Five Layers MgF2 1.38 0.094 1.11 0.42
ZrO2 2.05 0.126
Al2O3 1.62 0.080
Cryolite 1.35 0.096
MgF2 1.38 0.094
M.H. Asghar et al.: Modeling high performance multilayer antireflection coatings for...
511SQO, 6(4), 2003
ers and optimizing their index and thickness [11], the
reflectance from the substrate can be reduced to a rea-
sonably low value. In other words the transmittance
through the substrate can be increased substantially. It
should be noted from Fig. 1 that decrease is pretty sharp
up to the addition of fourth layer. How ever, the magni-
tude of reduction in reflectance with the addition of fifth
layer is very small. This may suggest the threshold limit
for multilayer configuration in which performance re-
quirements are not very stringent.
(B) infrared region: Ge, Si and ZnSe have been used as
substrates material as they are commonly used in 3�5µm
band for many optical and electro-optical applications
[12�17]. All these substrates exhibit a very high reflect-
ance value in the said spectrum. In most of the applica-
tions, this high value of reflectance is not acceptable as it
reduces the total energy reaching the detector surface
with every increasing optical component in the system or
device. Therefore, it is necessary to reduce their surface
reflectance by appling ARC�s. The materials used as film
layers are ZrO2, Si, SiO, CdTe, BaF2, ZnSe, Y2O3 and
SiO2, LaF3 and YF2. All these materials are suitable for
antireflection films in the desired region of wavelength
[18].
The reflectance of bare germanium substrate in 3�5µm
is 36%. Multilayer coatings can be used to reduce this
value to an appreciably low level [19]. We have modeled
such coatings on germanium substrate at a design wave-
length of 4µm. The process starts from a single layer
model, and the layers are increased to reduce the value of
maximum and average reflectance over the desired band.
Table 2 shows the model data and calculated values of
maximum and average reflectance over the entire band
for a single layer modal. The data shows that the maxi-
mum and average value of reflectance has decreased form
36% to 12.36% and 2.97% respectively. The combined
reflectance plot of all the four designs is shown in Fig. 2.
We have adopted an approach of smooth transition of
layer indices with every increasing layer in all models,
starting from incidence medium right up to the substrate.
This approach helps in avoiding sharp interfaces between
the layers, helping in smooth reduction of reflectance
from the surface of the substrate. The Fig. 2 clearly shows
the reduction of peak and average values with increasing
number of layers.
The reflectance from bare silicon substrate surface is
30%. This value is lower as compared to the germanium,
as it has got a lower refractive index in the given spec-
trum. Similar procedure of layer addition has been em-
ployed to model and analyze multilayer structures for
reducing reflectance from the substrate. Table 3 shows
the model data with maximum and average values of re-
flectance for all configurations. Fig. 3 shows the com-
bined plots for one, two, three and four layer configura-
3
0
3.4
5
10
15
20
25
30
35
40
3.8 4.2 4.6 5
Wavelength, mµ
Single layer
Bare substrate
Two layers
Three layers
R
e
fl
ec
ta
n
ce
,
%
Four layers
Fig. 2. Combined reflectance profiles for all configurations on
germanium.
3
0
3.4
5
10
15
20
25
30
35
3.8 4.2 4.6 5
Wavelength, mµ
Single layer
Bare substrate
Two layers
Three layers
R
ef
le
ct
a
n
c
e,
%
Four layers
Fig. 3. Combined reflectance profiles for all configurations on
silicon.
0.4 0.45 0.5
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0.55 0.6 0.65
Wavelength, mµ
Single layer
Bare substrate
Two layers
Three layers
A
v
e
r
a
g
e
r
ef
le
ct
io
n
,
%
Four layers
Five layers
Fig. 1. Combined reflectance profiles for all configurations on
glass.
512
SQO, 6(4), 2003
M.H. Asghar et al.: Modeling high performance multilayer antireflection coatings for...
tions. The trend in the reduction of reflectance for all the
configurations is similar to that for germanium. How-
ever, in this case the performance for three and four layer
configurations is even better and the curves are more flat
and comparatively closer to the horizontal axis. Only
two materials are used in four layers configuration. This
shows that proper optimization not only helps in getting
good performances but also tend to reduce unnecessary
variety of materials which is very critical in manufactur-
ing process.
The reflectance of bare ZnSe substrate is 16.81%.
Multilayer antireflection coatings are employed on the
substrate to drastically lower this value. Table 4 shows
the model data and calculated values of maximum and
average reflectance for single, two, three and four layer
structures to reduce the reflectance from the substrate.
Fig. 4 shows the combined plots of all the configura-
tions. The sharp fall in the reflectance values is observed,
even with single layer coating configuration due to low
index under lying surface.
Table 2. Design data and reflectance values for all configurations on germanium.
Configurations Material Refractive Index (n) Thickness (µm) Rp(%) Rave(%)
Single Layer ZrO2 2.05 0.487 12.36 2.97
Two-Layers SiO 1.6 0.625 4.19 2.67
CdTe 2.6 0.384
Three-Layers SiO 1.6 0.625 2.37 1.15
CdTe 2.6 0.384
Si 3.42 0.292
Four-Layers BaF2 1.3 0.769 2.37 0.487
ZrO2 2.05 0.487
CdTe 2.6 0.375
Si 3.42 0.292
Table 3. Design data and reflectance values for all configurations on silicon.
Configurations Material Refractive Index (n) Thickness (µm) Rp(%) Rave(%)
Single Layer LaF3 1.6 0.632 11.17 4.46
Two-Layers MgF2 1.38 0.679 4.64 3.26
ZrO2 2.05 0.457
Three-Layers MgF2 1.38 0.724 2.35 1.17
ZrO2 2.05 0.487
CdTe 2.64 0.378
Four-Layers MgF2 1.38 0.679 0.419 0.150
ZnSe 2.39 0.784
MgF2 1.38 1.3587
ZnSe 2.39 0.392
3
0
3.4
4
8
12
16
20
3.8 4.2 4.6 5
Wavelength, mµ
Single layer
Bare substrate
Two layers
Three layers
R
ef
le
ct
a
n
c
e,
%
Four layers
Fig. 4. Combined reflectance profiles for all configurations on ZnSe.
M.H. Asghar et al.: Modeling high performance multilayer antireflection coatings for...
513SQO, 6(4), 2003
4. Conclusions
Multilayer antireflection coatings in visible and IR (3�
5µm) have been modeled, starting from single layer up to
five layer configuration. The performance of each suc-
cessive configuration has been optimized in order to dem-
onstrate efficient use of multiple layers for antireflection
applications. The analysis of these designs reveal that by
increasing number of layers in a judicious manner with
suitable refractive indices and thickness, the maximum
and average reflectance from the surface of the substrate
can be decreased to very low magnitudes .
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Table 4. Design data and reflectance values for all configurations on zinc selenide.
Configurations Material Refractive Index (n) Thickness (µm) Rp(%) Rave(%)
Single Layer YF2 1.4 0.714 5.47 1.99
Two-Layers BaF2 1.3 0.769 2.21 1.49
Y2O3 1.73 0.578
Three-Layers BaF2 1.3 0.769 1.23 0.54
Y2O3 1.73 0.578
ZrO2 2.05 0.487
Four-Layers SiO2 1.4 0.664 0.60 0.34
ZrO2 2.05 0.914
Y2O3 1.73 0.541
ZrO2 2.05 0.457
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