Design of Moth Eye Anti-Reflective Surfaces for Nano-Satellites
A passive method for increasing power production over orbit by as much as 10%
Hugh Podmore Regina Lee, PhD
Moth-Eye Surfaces
Transmission Properties
Application to Nano Satellites
Moth-Eye surfaces are used at an interface
between two media to produce perfect
index matching, virtually eliminating light
loss due to reflection. In this work we
demonstrate that increased transmission
from the use of Moth-Eye surfaces would
be highly advantageous for nano-satellites.
It is possible to model a Moth-Eye surface as a
many layered stack of infinitely thin films each
with different refractive index defined by the
fill factor, f, defined according to the formulae:
We have designed a Moth-Eye surface to operate over the same wavelengths
as commercially available Triangular Advanced Solar Cells purchased from
Spectrolab. The surface is designed to operate between the wavelengths
of 350nm to 1800nm; the nanocones will have a pyramidal profile with a base
width of 100nm and height of 550nm. [3]
n1
n2
...
nN-2
nN-1
Nanocone
Array
The entire system may then be modeled using
thin film transfer matrices, yielding the fresnel
transmission and reflection coefficients for both
s and p-type polarizations. [2] By calculating
these coefficients across a broad spectrum of
wavelengths and incident angles from 0 to 90°
it is possible to design a Moth-Eye surface for
commercial triple junction solar cells.
{
Λ
{ d = 0.25λ
n
1.5
1
x0
GaInP2, n > 3
{
d > 0.4λ
n
{
x
{
d > 0.4λ
n
1800
1800
1600
1600
1400
1400
1200
1200
1000
1000
800
1.5
1
1.5
1
x0
400
50
2
1.8
1.6
1.4
1.2
600
60
70
400
80 90
50
θ(° )
2
Using the transmission
coefficient contours as well
as the AM0 solar spectrum
and the known EQE values
of the TASC Solar Cells we
can calculate the effect of
the Moth-Eye surface on
power production.
Pyramidal SWG
Parabloid SWG
Conventional ARC
1.9
1.8
1.7
1.6
1.5
Here we compare the
parabloid and pyramidal
nanocones to bare SiO2
note the marked increase
in power production above
50°.
1.4
1.3
1.2
1.1
1
45
49.5
54
58.5
63
67.5
θ(° )
72
76.5
60
70
80 90
1
Ratio of transmission coefficients between Moth-Eye structures and bare glass
surface for parabloidal nanocones (left) and pyramidal nanocones (right). At high
angles of incidence Moth-Eye surfaces show significantly increased transmission.
81
85.5
90
Knowing the expected power at each incident angle allows us to determine the
increase in power over orbit by analyzing the sun vector as seen by a typical
nadir pointing 3-U cubesat. We find that for the pyramidal Moth-Eye surface the
power production over orbit may be increased by as much as 10%.
14
800
600
x0
Λ
λ ( nm )
Substrate
(SiO2, Si, Ge, etc)
As light passes through the nanocone array
the index of refraction gradually changes
to match the index of the substrate. This
transition occurs as a function of height
and is controlled by the “fill factor” of the
nanocone array. Controlling the profile
of the nanocones will yield different
gradients.
Where n0 is the
index of refraction
of the incident
medium and nN is
the index of the
bulk material.
Power Production By AR−Type
vs. Uncoated Coverglass
n0
The cones will be fabricated on the surface of an SiO2 substrate which will be
mounted to solar cells as a conventional coverglass layer. Simulation results
suggest that the Moth-Eye surface will increase transmission for all incident
angles of light, particularly at angles above 50°.
Excess Power Production
vs. Uncoated Coverglass ( % )
2
2
Moth-Eye surfaces consist of an array of
nanocones smaller than light. Incident light
is unable to resolve these small cones and
instead perceives only a change in the
effective refractive index of the media. [1]
MgF2, n = 1.38
SiO2, n = 1.54
1/2
n =[n f+n (1-f)]
1/2
2
2
n = [ (1 / n 0 ) f + ( 1 / n2 ) ( 1 - f ) ]
2
0
Pyramidal SWG
Parabloid SWG
Conventional ARC
12
10
Solar incidence angles for
twenty different orbits at
inclinations between 0° and
100° were determined over
one week of operation. The
orbital height was 600km
and the satellite was
oriented such that the long
axis was aligned with the
nadir, as would be typical
during earth observation.
8
6
4
2
Using the calculated values
for increased power
production as a function of
incident angle we analyze
the solar angles experienced
by a typical nadir pointing
3-U Cubesat.
0
10
20
30
40
50
60
70
Inclination of Orbit, i ( ° )
80
90
100
References:
[1] P. Clapham & M. Hutley, “Reduction of Lens Reflexion by the “Moth Eye” Principle”, Nature, Vol. 224, Iss. 5414, 1973
[2] E. Grann et al., “Optimal Design for Antireflective Tapered Two Dimensional Subwavelength Grating Structures”, Journal of the Optical Society of America A, Vol. 12, Iss. 2, 1995
[3] H. Podmore & R. Lee, “Increasing Power Production on Micro and Nano Satellites using Sub-Wavelength Gratings”, Aerospace Conference, 2015 IEEE, 2015