Characterisation of random pyramid surfaces using laser scanning microscopy

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1 Characterisation of random pyramid surfaces using laser scanning microscopy Dr. Eckard Wefringhaus International Solar Energy Research Center Konstanz e.v.

2 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 2. Fachkolloquium Materialien/Werkstoffe 2

topographical parameter distribution Results Parameter distributions Pertinence

3 Motivation KOH/IPA and new methods, T, t, c, Anisotropic texturing Surface topography (Uniformity of) pyramid height / density / coverage Performance of solar cells Light trapping Short circuit current, efficiency Reflection 2. Fachkolloquium Materialien/Werkstoffe 3

coverage Performance of solar cells Light trapping Short circuit

4 Motivation KOH/IPA and new methods, T, t, c, Anisotropic texturing Surface topography (Uniformity of) pyramid height / density / coverage Performance of solar cells Light trapping Short circuit current, efficiency Reflection 2. Fachkolloquium Materialien/Werkstoffe 4

5 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, , [2] Ximello et al., Proc. 25th EU PVSEC, Valencia, Spain, , 10. [3] [4] 2. Fachkolloquium Materialien/Werkstoffe 5

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.

6 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 2. Fachkolloquium Materialien/Werkstoffe 6

and distances (topographical parameters) (by MountainsMaP) Evaluation of topographical parameter

7 Applying different textures # pre-cleaning texture refl. [%]* # pre-cleaning texture refl. [%]* 1 GP AlkaTex Plus 11,64 11 n.d. 2 11,37 12 n.d. 3 11,25 13 RENA monotex 12, ,87 14 RENA monotex 12, ,88 15 RENA monotex 13, ,92 16 RENA monotex 13, ,96 17 O3 13, ,99 18 O3 RENA monotex 12, ,89 19 SC1 13, ,67 SC1 RENA monotex 12,35 * unweighted mean nm / mean out of 3 measurements; ** different etching times and temperatures 2. Fachkolloquium Materialien/Werkstoffe 7

11,96 17 O3 13,41 8 11,99 18 O3 RENA monotex 12,31 9 11,89 19 SC1 13,69 10 11,67 SC1 RENA monotex 12,35 * unweighted mean

8 Determination of surface profiles by LSM Olympus OLS4000 LEXT 2. Fachkolloquium Materialien/Werkstoffe 8

9 Definition and determination of pyramid height and distances by MountainsMap S-filter 0.6 µm (x,y,z)-coordinates of pyramid tips [5, 6] LEXT picture (height layer) F-filter transformed picture Watershed analysis L-filter 100 µm [5] ISO/DIS :08. Geometrical product specifications (GPS) surface texture: Areal Part 2: Terms, definitions and surface texture parameters. [6] ISO/DIS :08. Geometrical product specifications (GPS) surface texture: Areal Part 3: Specification operators. 2. Fachkolloquium Materialien/Werkstoffe 9

10 Definition and determination of pyramid height and distances by MountainsMap (z)-coordinates of pyramid tips (x,y)-coordinates of pyramid tips H1 H2 CF3 Z1 Z2 - pyramid height H (and pyramid base length a(h) = H) - pyramid height Z (and pyramid base length a(z) = Z) - Coflatness CF - minimum distance to neighbours (minimum pitch, MinP) - mean distance to neighbours (pitch, P) - maximum distance to neighbour (maximum pitch, MaxP) 2. Fachkolloquium Materialien/Werkstoffe 10

414 H) - pyramid height Z (and pyramid base length a(z) = 1.

11 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 cases) distribution Kolmogorow Smirnow Anderson Darling Chi-square SoR appl. mean rank SoR appl. mean rank SoR appl. mean rank Beta 156 7, , ,90 Chi-Squared (2P) , , ,50 Fatigue Life (3P) 9 10, , ,50 Gen. Extreme Value 148 7, , ,26 Gen. Gamma (4P) 171 8, , ,10 Gen. Logistic , , ,70 Johnson SB , , ,31 Kumaraswamy , , ,95 2. Fachkolloquium Materialien/Werkstoffe 11

mean rank SoR appl. mean rank Beta 156 7,80 90 4,50 138 6,90 Chi-Squared (2P) 600 30,00 556 27,80 510 25,50 Fatigue Life (3P) 9 10,45 177 8,85 170 8,50 Gen.

12 Results: parameter distributions 0,4 0,36 0,32 0,28 0,24 0,2 0,16 0,12 0,08 0,04 0 0,11 0,1 0,09 0,08 0,07 0,06 0,05 0,04 0,03 0,02 0, H [µm] CF [µm] Height H: Fatigue life distribution (α, β, γ) 3 4 Coflatness: Johnson SB distribution (γ, δ, λ, ξ) 6 8 0,14 0,12 0,1 0,08 0,06 0,04 0, Z [µm] Height Z: Burr distribution (α, β, γ, κ) Fachkolloquium Materialien/Werkstoffe 12

(α, β, γ) 3 4 Coflatness: Johnson SB distribution (γ, δ, λ, ξ) 6 8 0,14 0,12 0,1 0,08 0,06 0,04 0,02

13 Results: parameter distributions 0,22 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0, Minimum Pitch: Dagum distribution? (α, β, γ, κ) 3 MinP [µm] 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, P [µm] Pitch: Johnson SB distribution (γ, δ, λ, ξ) 6 8 0,1 0,09 0,08 0,07 0,06 0,05 0,04 0,03 0,02 0, Maximum Pitch: Gen. extreme value distribution (µ, σ, κ) MaxP [µm] Fachkolloquium Materialien/Werkstoffe 13

(α, β, γ, κ) 3 MinP [µm] 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 2 4 P [µm] Pitch:

14 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 Refl. (mean 3) [%] 14 13, ,5 12 Alle Zeilen MaxP EV s<1,8578 H FL b>=0,17527 H FL b<0,17527 texture KOH/IPA RENA monotex 11,5 11 H FL b>=0,17527 H FL b<0,17527 MaxP EV s<1,8578 Alle Zeilen MaxP EV s> 2. Fachkolloquium Materialien/Werkstoffe 14

15 Results: Pertinence of parameters for reflection 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 13,5 Refl. (mean 3) [%] 13 12,5 12 Alle Zeilen H FL a>=1,0743 MaxP EV s<1,7392 H FL b<0, ,5 H FL a<1, H FL a<1,0743 H FL a>=1,0743 MaxP EV s<1,7392 Alle Zeilen H H FL F b>=0,21831 MaxP EV s>=1, Fachkolloquium Materialien/Werkstoffe 15

16 Results: Pertinence of parameters for reflection 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) - Significant parameters / interactions: Refl. (mean 3) [%] Beobachtet 13, , , , , ,5 14 Refl. (mean 3) [%] Vorhergesagt P<.0001 r2 =0,80 RMSE=0,3335 Term Achsenabschnitt H FL a H FL b MaxP EV s (H FL a-1,27117)*(h FL b-0,21038) Schätzer 7, , , , , Std.-Fehler 0,3014 0,8166 0, , , t-wert 25,40 6,40 8,16 2,71 4,05 Wahrsch.> t <,0001* <,0001* <,0001* 0,0077* <,0001* VIF. 2, , , , Fachkolloquium Materialien/Werkstoffe 16

0001 r2 =0,80 RMSE=0,3335 Term Achsenabschnitt H FL a H FL b MaxP EV s (H FL a-1,27117)*(h FL b-0,21038) Schätzer 7,6723558 1,3319155 7,6240757 0,6747285 18,434615 Std.

17 Results: Pertinence of parameters for reflection 13, ,5 12 Refl. (mean 3) [%] 12,06008 ±0, ,5 11 0,7 0,9 1,1 1,3 1,5 1,7 1,9 0,2 0,3 1,2 1,4 1,6 1,8 2 2,2 1,61642 MaxP EV s 0,21038 H FL b 1,2712 H FL a 1, H FL a H FL a 12 0, Refl. (mean 3) [%] 0,2969 H FL b 13 H FL b 0, Interaction plot 11 Refl. (mean 3) [%] 0,8 1,1 1,4 1,7 2 0,2 0,3 2. Fachkolloquium Materialien/Werkstoffe 17

1,61642 MaxP EV s 0,21038 H FL b 1,2712 H FL a 1,7983 13 H FL a H FL a 12 0,7299 11 Refl.

18 Results: Pertinence of parameters for reflection 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 2. Fachkolloquium Materialien/Werkstoffe 18

= 1,4157 β = 0,2626 γ = 0,0337 declining α (for α = 0 symmetric

19 Results: Pertinence of parameters for reflection Meaning of parameter MaxP EV σ κ = σ = 1,2806 µ = 4,1815 declining σ κ = σ = 1,8955 µ = 4, Fachkolloquium Materialien/Werkstoffe 19

0488 σ = 1,2806 µ = 4,1815 declining σ κ = -0.

20 Results: Pertinence of parameters for reflection Refl. (mean 3) [%] 12,06008 ±0, , , ,5 11 0,7 0,9 1,1 1,3 1,5 1,7 1,9 0,2 0,3 1,2 1,4 1,6 1,8 2 2,2 1,2712 H FL a 0,21038 H FL b 1,61642 MaxP EV s less very small and more medium sized pyramids less very small and less very big pyramids narrow distribution of maximum pitch Aims to achieve low reflection 2. Fachkolloquium Materialien/Werkstoffe

1,8 2 2,2 1,2712 H FL a 0,21038 H FL b 1,61642 MaxP EV s less very small and more medium sized pyramids

21 Results: Pertinence of parameters for reflection Interaction: If H FL α is small, a high H FL β can be tolerated (and the other way around) Refl. (mean 3) [%] Refl. (mean 3) [%] H FL a 0,2969 0,1384 H FL b 1,7983 0,7299 H FL a H FL b 0,8 1,1 1,4 1,7 2 0,2 0,3 2. Fachkolloquium Materialien/Werkstoffe 21

22 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). 2. Fachkolloquium Materialien/Werkstoffe 22

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