Characterisation of Random Pyramid Surfaces Using Laser Scanning

Transcription

Characterisation of
random pyramid surfaces
using laser scanning microscopy
Dr. Eckard Wefringhaus
International Solar Energy Research Center Konstanz e.V.
Overview
• Motivation
• Methods
• Applying different textures
• Determination of surface profiles
• Definition and determination of topographical parameters
• Evaluation of topographical parameter distribution
• Results
• Parameter distributions
• Pertinence of parameters for reflection
• Conclusions
16. Juni 2011
Dr. Eckard Wefringhaus, ISC Konstanz
Freiberger Forschungsforum
62. Berg- und Hüttenmännischer Tag
2. Fachkolloquium Materialien/Werkstoffe
2
Motivation
KOH/IPA
and new
methods,
T, t, c, …
Anisotropic
texturing
Performance of
solar cells
Surface
topography
Light
trapping
Reflection
Short circuit
current,
efficiency
16. Juni 2011
(Uniformity
of) pyramid
height /
density /
coverage
3
Motivation
KOH/IPA
and new
methods,
T, t, c, …
Anisotropic
texturing
Performance of
solar cells
Surface
topography
Light
trapping
Reflection
Short circuit
current,
efficiency
16. Juni 2011
(Uniformity
of) pyramid
height /
density /
coverage
4
Motivation
Surface
topography
(Uniformity of)
pyramid
height /
density /
coverage
Up to now, only qualitative statements or very rough classifications
- “a more uniform pyramid geometry” [1]
- “inhomegenous pyramidal texture with pyramid size 1-6 µm” [2]
- “homogeneous collocation of pyramids (base length 2-5 µm)” [3]
- “uniform pyramids ( 2-5 µm )” [4]
=> Define and derive quantitative parameters describing (uniformity of)
pyramid height / size / density
[1] Vazsonyi et al., Solar Energy Materials & Solar Cells 57, 179-188, 1999.
[2] Ximello et al., Proc. 25th EU PVSEC, Valencia, Spain, 1761-1764, 2010.
[3] http://www.gpsolar.de/materials/chemikalien/gp-alka-tex-plus/
[4] http://de.rena.com/fileadmin/img/Produkte/200_Solartechnik/230_Batch/232_BatchTex/RENA_DB_monoTex_201011214.pdf
16. Juni 2011
5
Methods
Applying different textures
(by KOH/IPA and other methods)
Determination of surface profiles
(by confocal laser scanning microscope)
Definition and determination of pyramid height and distances
(topographical parameters) (by MountainsMaP)
Evaluation of topographical parameter distribution
(by EasyFit)
Pertinence of parameters for reflection
16. Juni 2011
6
Applying different textures
#
pre-cleaning
texture
refl. [%]*
#
pre-cleaning
texture
refl. [%]*
1
as-cut
GP AlkaTex Plus
11,64
11
as-cut
KOH/IPA **
n.d.
2
as-cut
KOH/IPA **
11,37
12
as-cut
KOH/IPA **
n.d.
3
as-cut
KOH/IPA **
11,25
13
as-cut
RENA monoTex
12,31
4
as-cut
KOH/IPA **
11,87
14
as-cut
RENA monoTex
12,61
5
as-cut
KOH/IPA **
11,88
15
as-cut
RENA monoTex
13,81
6
as-cut
KOH/IPA **
11,92
16
as-cut
RENA monoTex
13,16
7
as-cut
KOH/IPA **
11,96
17
O3
KOH/IPA **
13,41
8
as-cut
KOH/IPA **
11,99
18
O3
RENA monoTex
12,31
9
as-cut
KOH/IPA **
11,89
19
SC1
KOH/IPA **
13,69
10
as-cut
KOH/IPA **
11,67
20
SC1
RENA monoTex
12,35
* unweighted mean 400-1100 nm / mean out of 3 measurements; ** different etching times and temperatures
16. Juni 2011
7
Determination of surface profiles by LSM
Olympus
OLS4000
LEXT
http://www.physics.emory.edu/~weeks/confocal/
16. Juni 2011
8
Definition and determination of pyramid height
and distances by MountainsMap
(x,y,z)-coordinates of
pyramid tips
S-filter 0.6 µm
[5, 6]
LEXT picture
(height layer)
F-filter
transformed
picture
Watershed
analysis
[5] ISO/DIS 25178-2:2008. Geometrical product
specifications (GPS) – surface texture: Areal – Part 2:
Terms, definitions and surface texture parameters.
[6] ISO/DIS 25178-3:2008. Geometrical product
specifications (GPS) – surface texture: Areal – Part 3:
Specification operators.
L-filter 100 µm
16. Juni 2011
9
Definition and determination of pyramid height
and distances by MountainsMap
(z)-coordinates of
pyramid tips
H1
Z1
(x,y)-coordinates of
pyramid tips
H2
CF3
Z2
- pyramid height H (and pyramid base length
a(H) = 1.414 H)
- minimum distance to neighbours
(minimum pitch, MinP)
- pyramid height Z (and pyramid base length
a(Z) = 1.414 Z)
- mean distance to neighbours (pitch, P)
- Coflatness CF
16. Juni 2011
- maximum distance to neighbour
(maximum pitch, MaxP)
10
Evaluation of parameter distribution by EasyFit
37 bounded, non-negative distributions considered and ranked
according to significance: example pitch P (clipping from table)
(SoR = sum of ranks, appl. = distribution applicable in n out of 20 cases)
distribution
Kolmogorow Smirnow
Anderson Darling
Chi-square
SoR
appl.
mean
rank
SoR
appl.
mean
rank
SoR
appl.
mean
rank
Beta
156
20
7,80
90
20
4,50
138
20
6,90
Chi-Squared (2P)
600
20
30,00
556
20
27,80
510
20
25,50
Fatigue Life (3P)
209
20
10,45
177
20
8,85
170
20
8,50
Gen. Extreme Value
148
20
7,40
142
20
7,10
157
19
8,26
Gen. Gamma (4P)
171
20
8,55
98
20
4,90
142
20
7,10
Gen. Logistic
358
20
17,90
350
20
17,50
334
20
16,70
Johnson SB
58
18
3,22
79
18
4,39
117
16
7,31
Kumaraswamy
256
20
12,80
221
20
11,05
259
20
12,95
16. Juni 2011
11
Results: parameter distributions
0,4
0,14
0,36
Height H:
Fatigue life
distribution
(α, β, γ)
0,32
0,28
0,24
0,2
0,16
0,12
0,1
0,08
0,06
0,04
0,08
0,02
0,04
0
Height Z:
Burr
distribution
(α, β, γ, κ)
0,12
1
2
3
4
0
4
0,11
0,1
0,09
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0
6
8
10
Z [µm]
H [µm]
Coflatness:
Johnson SB
distribution
(γ, δ, λ, ξ)
2
4
6
8
CF [µm]
16. Juni 2011
12
Results: parameter distributions
0,22
0,2
0,18
0,16
0,14
0,12
0,1
0,08
0,06
0,04
0,02
0
Minimum Pitch:
Dagum distribution?
(α, β, γ, κ)
1
2
3
4
5
0,12
0,11
0,1
0,09
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0
Pitch:
Johnson SB
distribution
(γ, δ, λ, ξ)
2
MinP [µm]
4
6
8
P [µm]
0,1
Maximum Pitch:
Gen. extreme
value distribution
(µ, σ, κ)
0,09
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0
2
4
6
8
10
MaxP [µm]
16. Juni 2011
13
Results: Pertinence of parameters for reflection
Partition-Model (all data)
- 18 parameters included : H FL (α, β, γ), Z B (α, β, γ, κ), CF JSB (γ, δ, λ, ξ),
P JSB (γ, δ, λ, ξ), MaxP EV (µ, σ, κ)
- most significant split parameters: MaxP EV σ & H FL β
14
texture
KOH/IPA
RENA monoTex
Refl. (mean 3) [%]
13,5
13
12,5
12
H FL b<0,17527
Alle Zeilen
MaxP EV s<1,8578
H FL b>=0,17527
11,5
11
H FL b>=0,17527
H FL b<0,17527
MaxP EV s<1,8578
MaxP
EV s>…
Alle Zeilen
16. Juni 2011
14
Partition-Model (only KOH/IPA)
- 18 parameters included : H FL (α, β, γ), Z B (α, β, γ, κ), CF JSB (γ, δ, λ, ξ),
P JSB (γ, δ, λ, ξ), MaxP EV (µ, σ, κ)
- most significant split parameters: MaxP EV σ & H FL α & H FL β
Refl. (mean 3) [%]
13,5
13
12,5
12
H FL b<0,21831
Alle Zeilen
H FL a>=1,0743
MaxP EV s<1,7392
11,5 H FL a<1,0743
11
H FL
a<1,0743
H FL a>=1,0743
MaxP EV s<1,7392
H
H FL
F… b>=0,21831
MaxP EV
s>=1,7392
Alle Zeilen
16. Juni 2011
15
Model: Multiple regression
(stepwise)
- 18 parameters included : H
FL (α, β, γ), Z B (α, β, γ, κ),
CF JSB (γ, δ, λ, ξ), P JSB (γ,
δ, λ, ξ), MaxP EV (µ, σ, κ)
Refl. (mean 3)
[%] Beobachtet
13,5
13
12,5
12
11,5
11
- Significant parameters /
interactions:
Term
Achsenabschnitt
H FL a
H FL b
MaxP EV s
(H FL a-1,27117)*(H FL b-0,21038)
16. Juni 2011
11
11,5
12
12,5
13
13,5
14
Refl. (mean 3) [%] Vorhergesagt
P<.0001 r2 =0,80 RMSE=0,3335
Schätzer
7,6723558
1,3319155
7,6240757
0,6747285
18,434615
Std.-Fehler
0,302014
0,208166
0,934756
0,249044
4,551556
t-Wert
25,40
6,40
8,16
2,71
4,05
Wahrsch.>|t|
<,0001*
<,0001*
<,0001*
0,0077*
<,0001*
VIF
.
2,5814877
1,4181388
3,1679742
1,5978012
16
Refl. (mean
3) [%]
12,06008
±0,05853
13,5
13
12,5
12
11,5
2,2
2
1,8
1,6
1,4
1,7983
13
H FL a
12
0,7299
11
0,2969
13
H FL b
12
0,1384
0,3
0,2
2
1,7
1,4
0,8
11
1,1
Refl. (mean
3) [%]
16. Juni 2011
1,61642
MaxP EV s
H FL b
Refl. (mean
3) [%]
0,21038
H FL b
H FL a
Interaction plot
1,2712
H FL a
0,3
1,2
0,2
1,9
1,7
1,5
1,3
1,1
0,9
0,7
11
17
Meaning of
parameters
H FL α and
H FL β
α = 0,9843
β = 0,1976
γ = 0,0133
α = 1,4157
β = 0,2626
γ = 0,0337
declining α (for α = 0
symmetric function)
declining β
16. Juni 2011
18
Meaning of
parameter
MaxP EV σ
κ = -0.0488
σ = 1,2806
µ = 4,1815
declining σ
κ = -0.0978
σ = 1,8955
µ = 4,7413
16. Juni 2011
19
Refl. (mean
3) [%]
12,06008
±0,05853
13,5
13
12,5
12
11,5
1,2712
H FL a
less very
small and
more
medium
sized
pyramids
0,21038
H FL b
less very
small and
less very
big
pyramids
2,2
2
1,8
1,6
1,4
0,3
1,2
0,2
1,9
1,7
1,5
1,3
1,1
0,9
0,7
11
1,61642
MaxP EV s
narrow
distribution
of
maximum
pitch
Aims to achieve low reflection
16. Juni 2011
20
13
H FL a
12
0,7299
11
0,2969
13
H FL b
12
0,1384
0,3
0,2
2
1,7
1,4
1,1
11
0,8
16. Juni 2011
H FL b
Refl. (mean
3) [%]
1,7983
H FL a
Refl. (mean
3) [%]
Interaction:
If H FL α is small, a high H FL β can be tolerated
(and the other way around)
21
Summary & Conclusions
• Surface topography of anisotropic textures was characterised by LSM
• Parameters, describing the surface topography, were defined and
determined (pyramid heights H and Z, coflatness CF, minimum, mean and
maximum pitch MinP, P, and MaxP)
• These topographical parameters follow different distributions, which are to be
described by specific distribution parameters (e.g. height H is distributed
according to Fatigue life, described by H FL α, H FL β, and H FL γ)
• It was shown that only few of these topographical / distribution parameters
are relevant for reflection of textured wafers (height H and maximum pitch
MaxP, with H FL α, H FL b α, and MaxP EV σ).
16. Juni 2011
22

Characterisation of Random Pyramid Surfaces Using Laser Scanning

Transcription

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