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CORM 2016, Gaithersburg, MD, May 17, 2016
Diffuse Reflectance and Light Trapping from Textured Silicon Surfaces in Photovoltaic Applications
Thomas A. Germer1, Martin Foldyna2,3, Zuzana Mrazkova2,4, Guillaume Fischer3, Etienne Drahi5,3
1NIST, Sensor Science Division, Gaithersburg, Maryland USA2LPICM, CNRS, Ecole Polytechnique, Université Paris Saclay, 91128, Palaiseau, France3IPVF (Institut Photovoltaïque d’Ile-de-France) - 8, rue de la renaissance, 92160 Antony, France4Nanotechnology Centre and Department of Physics, Technical University of Ostrava, 708 33, Ostrava-Poruba, Czech Republic5 TOTAL – New Energies, 24 cours Michelet, 92078 Paris La Défense
Photovoltaics
2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60.0
0.2
0.4
0.6
0.8
1.0
Abso
rpta
nce
Wavelength (µm)
With texturingJsc = 42.1 mA/cm
2
Without texturingJsc = 36.2 mA/cm
2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Spec
tral I
rradi
ance
(W/m
2 /nm
)
Effect of texturing on short-circuit current density
3
multiplereflections
longer paths and
total internal reflection
Yablonovitch limit (1982):enhancement = 4n2
Approach
4
We’d like to measure the radiance distribution inside the silicon, but we can’t.
So, instead, we measure the radiance distribution outside the material
We sometimes use non-normal incidence, even though this isn’t how a device is intended to be used.
Use polarization (Mueller matrix), since the polarization is sensitive to scattering details the intensity alone is not sensitive to.
Surface texturing
5
Pyramidal Silicon
Reactive ionetching
Black silicon grass
From Wikipedia/Christoph Kubasch (2005)
On a (100) Si surface, KOH-based etching creates pyramids with faces close to (111).
45°
54.7°
Pyramidal silicon samples
Isopropyl Alcohol (IPA) RENA monoTEX® Surfactant (RT)
Details of the pyramid formation depend upon additives in the alkali etching solution, as well as concentrations and temperature.
Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology nor our collaborators, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.
Monte Carlo Ray Tracing Modeling
Single scattering microfacet model has an analytic solution• BRDF is proportional to the slope distribution• Polarimetric properties (Mueller matrix) are simple
We developed a MC microfacet, multireflection scattering code• Multiple interfaces • Dynamically creates realizations of surfaces
• Numerous algorithms for surface generation• Full Mueller matrix propagation• Each interface can have thin films associated with it.• Periodic boundary conditions• Calculates BRDF, BTDF, and absorption in each layer.• Issues:
• Ignores diffraction• Ignores coherent effects
Reflections for pyramidal silicon as function of incident angle
8
Ray tracing from 52.5° pyramids with θi = 60°
9
Measurements from pyramidal silicon
10
θi = 60°θi = 5°
-1 0 1-1
0
1
y
x
1.000E-03
0.01000
0.1000
1.000
-1 0 1-1
0
1
y
x
1.000E-03
0.01000
0.1000
1.000
-1 0 1-1
0
1
y
x
1.000E-03
0.01000
0.1000
1.000
-1 0 1-1
0
1
y
x
1.000E-03
0.01000
0.1000
1.000
IPA
RT
Color scale is BRDF (sr-1)
Diffraction from triangles
11
Normal incidence
Diffraction will occur perpendicular to edges of
triangle.
Non-normal incidence
Diffraction directions will conserve component of
direction vector along the edges.
Also, as the size of the triangles are reduced the main diffraction lobe gets broader.
Near-Retroreflection Measurements
12
θ5°
These measurements were recorded as Mueller matrices.
The intent was to see if the facet slope distribution, which can be determined in the geometric optics approximation from this measurement, was consistent with the other scatter measurements.
But, the results, as we will see, actually require physical optics and/or multiple bounces to understand.
Along (110): Along (100):
Retro-reflection measurements
13
-10° 0° 10° 20° 30° 40° 50° 60° 70° 80°
10-3
10-2
10-1
100
101
~14° ~23° 36.5° 45.5°
f r (s
r-1)
θ
IPA (100) RT (100)
42.5°
-10° 0° 10° 20° 30° 40° 50° 60° 70° 80°10-3
10-2
10-1
100
101
~12° ~20°
51.5°
f r (s
r-1)
θ
IPA (110) RT (110)
52.5°
A combination of a few diffraction/reflection events
+ other
Pyramids are not really pyramidal
14
Retroreflection along 110 is sensing the average face angle.Retroreflection along 100 is sensing the average edge angle.
When the pyramids are simple there is a simple relationship between the edge angle and the face angle.
45°
54.7°
𝜃𝜃𝜃 = atan [tan 𝜃𝜃 /√2]
There is evidence in the literature that the faces are not (111) but something else.
𝜃𝜃𝜃𝜃𝜃
Brief Polarimetry Primer
15
Polarization state is characterized by a 4-element Stokes vector.
An optical path (or sum of paths) is characterized by a 4x4-element Mueller matrix.
11
11
−
−
01
01
22 23
23 22
11
mm
m mm m
−
01 02 03
11 12 1300
21
10
20 22 23
3 310 32 33
1 m m mm m m m
Mm m m mm m m m
×
For normal-incidence reflection:
For non-normal incidence reflection:
Mueller matrix retroreflection measurements
16
-10° 0° 10° 20° 30° 40° 50° 60° 70° 80°-1.0
-0.5
0.0
0.5
1.0
m22
m23 m32
m11
m33 m10
RT along (100)
Nor
mal
ized
Mue
ller m
atrix
ele
men
ts
θ
m01
-10° 0° 10° 20° 30° 40° 50° 60° 70° 80°-1.0
-0.5
0.0
0.5
1.0 RT along (110)
Nor
mal
ized
Mue
ller m
atrix
ele
men
ts
θ
m33m01
m22
m10
m11
m23
m32
-10° 0° 10° 20° 30° 40° 50° 60° 70° 80°-1.0
-0.5
0.0
0.5
1.0
m23
m11
m01
m10
m22m32
N
orm
aliz
ed M
uelle
r mat
rix e
lem
ents
θ
IPA along (110)
m33
-10° 0° 10° 20° 30° 40° 50° 60° 70° 80°-1.0
-0.5
0.0
0.5
1.0
Nor
mal
ized
Mue
ller m
atrix
ele
men
ts
θ
IPA along (100)
m22
m33
m11m32
m23
m10m01
IPA
RT
Along (110) Along (100)
Scattering by microrough silicon
17
-1
0
1
-1
0
1
-1
0
1
-1 0 1-1
0
1
-1 0 1 -1 0 1 -1 0 1
1E-27
1E-16
1E-05
1E+06
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1 0 1-1
0
1
-1 0 1 -1 0 1 -1 0 1
1E+11
1E+12
1E+13
1E+14
-1
0
1
C
4
theory measurement
Theory based upon first-order vector perturbation theory.
Angle of incidence 60°, Wavelength 351 nmShown in projected-cosine spacePlane of incidence is a horizontal segment.
Scattering by as-cut silicon
18
-1
0
1
-1
0
1
-1
0
1
-1 0 1-1
0
1
-1 0 1 -1 0 1 -1 0 1
1E-27
1E-16
1E-05
1E+06
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1 0 1-1
0
1
-1 0 1 -1 0 1 -1 0 1
1E+11
1E+12
1E+13
1E+14
-1
0
1
C
4
Theory based upon single reflection microfacet model.
theory measurement
Angle of incidence 60°, Wavelength 351 nmShown in projected-cosine spacePlane of incidence is a horizontal segment.
Pyramidal silicon – Mueller matrix
19
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
C4
y
1.000E-03
0.01000
0.1000
1.000
y
y
-1.000
-0.7500
-0.5000
-0.2500
0.000
0.2500
0.5000
0.7500
1.000
y
x
C4
x
x
C4
x
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
C4
y
1.000E-03
0.01000
0.1000
1.000
y
y
-1.000
-0.7500
-0.5000
-0.2500
0.000
0.2500
0.5000
0.7500
1.000
y
x
C4
x
x
C4
x
IPA Sample
5° incident angle 60° incident angle
Pyramidal silicon – Mueller matrix
20
RT Sample
5° incident angle 60° incident angle
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
C4
y
1.000E-03
0.01000
0.1000
1.000
y
y
-1.000
-0.7500
-0.5000
-0.2500
0.000
0.2500
0.5000
0.7500
1.000
y
x
C4
x
x
C4
x
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
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C4
y
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y
x
C4
x
x
C4
x
As Cut (R=23.6%) Etched (R=19.8%) Etched more (R=14.4%)
Etched even more (R=11.8%) Etched the most (R=7.17%)
Incident angle 5°Scattering Plane Basis633 nm
Evolution of Mueller matrix with ion etching
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y
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C4
y
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-1.000
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x
C4
x
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C4
x
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-1.000
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C4
x
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x
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-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
C4
y
1.000E-03
0.01000
0.1000
1.000
y
y
-1.000
-0.7500
-0.5000
-0.2500
0.000
0.2500
0.5000
0.7500
1.000
y
x
C4
x
x
C4
x
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
C4
y
1.000E-03
0.01000
0.1000
1.000
y
y
-1.000
-0.7500
-0.5000
-0.2500
0.000
0.2500
0.5000
0.7500
1.000
y
x
C4
x
x
C4
x
As Cut (R=24.8%) Etched (R=21.73%) Etched more (R=18.4%)
Etched even more (R=16.0%) Etched the most (R=12.2%)
Incident angle 60°Scattering Plane Basis633 nm
Evolution of Mueller matrix with ion etching
Summary/Conclusions
• We have carried out a number of light scattering measurements to better understand light trapping in photovoltaics.
• Many of the features observed cannot be explained by ray optics alone.
• However, most of these features are weakly scattering. They have little impact on the light trapping, but have impact on the use of light scattering in characterizing these materials.
23
Thank you.
24
Diffuse Reflectance and Light Trapping from Textured Silicon Surfaces in Photovoltaic ApplicationsPhotovoltaicsEffect of texturing on short-circuit current densityApproachSurface texturingPyramidal silicon samplesSlide Number 7Reflections for pyramidal silicon as function of incident angleRay tracing from 52.5° pyramids with qi = 60°Measurements from pyramidal siliconDiffraction from trianglesNear-Retroreflection MeasurementsRetro-reflection measurementsPyramids are not really pyramidalBrief Polarimetry Primer Mueller matrix retroreflection measurementsScattering by microrough siliconScattering by as-cut siliconPyramidal silicon – Mueller matrixPyramidal silicon – Mueller matrixEvolution of Mueller matrix with ion etchingEvolution of Mueller matrix with ion etchingSummary/ConclusionsThank you.