Session 3B Using the Gen-Osc Layer to Fit Data

Transcription

1 Session 3B Using the Gen-Osc Layer to Fit Data Andrew Martin UPenn, February J.A. Woollam Co., Inc. 1

2 Using Gen-Osc to Fit Data Pre-built Existing Genosc Layer Library optical constants GENOSC Cauchy Point-by-Point GENOSC Choosing the correct oscillators Fitting out-of-range oscillators Parameter correlation 2014 J.A. Woollam Co., Inc. 2

3 iterate GENOSC Process Overview Pt-by-Pt Fit Tabulated Optical Constants Reference optical constants Existing Oscillator Model Create Oscillator Model Use Oscillator To Fit DATA 2014 J.A. Woollam Co., Inc. 3

4 1 Example_1_a-si_on_glass.dat Use 7059_u.mat for substrate Use a-si_asp.mat as Reference Remember to add surface oxide Very important for semiconductors 2014 J.A. Woollam Co., Inc. 4

5 1 Example_1_a-si_on_glass.dat REPEAT Compare Tauc-Lorentz to Cody- Lorentz. Use pre-existing Genosc layer for a- Si available in the library and repeat the example J.A. Woollam Co., Inc. 5

6 Procedure for UV Absorbing Films 1. Cauchy Fit transparent region only 2. Pt-by-Pt Fit all wavelengths fix thickness, then perform pt-by-pt fit Build Genosc from tabulated cauchy 3. Match n,k using Genosc fit reference first e2, then e1 4. Fit Y & D data using new Genosc model J.A. Woollam Co., Inc. 6

7 2 Example_2_Thin_Dielectric_on_Si.dat Use Si_vuv.mat for substrate Cauchy PBP Gen-Osc 2014 J.A. Woollam Co., Inc. 7

8 Select Transparent Region Example 2: Thin Dielectric on Silicon Build Model with Singlelayer Cauchy Fit thickness and Cauchy parameters Extend range further toward absorbing region until MSE climbs Y in degrees cauchy nm 0 si_vuv 1 mm Generated and Experimental Wavelength (nm) Model Fit Exp E 60 Exp E J.A. Woollam Co., Inc. 8

9 Example 2: Thin Dielectric on Silicon Fix Thickness and Cauchy parameters Select data at ALL wavelengths Fit n & k using Pt-by-Pt fit 70 Generated and Experimental 60 Y in degrees Model Fit Exp E 60 Exp E Wavelength (nm) 2014 J.A. Woollam Co., Inc. 9

10 PBP fit result n,k Example 2: Thin Dielectric on Silicon 2014 J.A. Woollam Co., Inc. 10

11 Example 2: Thin Dielectric on Silicon Shortcut: Build GenOsc from tabulated cauchy 1 genosc nm 0 si_vuv 1 mm If you have tabulated optical constants from any layer you would like to use as reference in Genosc, use right-click menu J.A. Woollam Co., Inc. 11

12 Tabulated n & k is loaded as Reference Material Note this particular dielectric has Tauc- Lorentz absorption shape in UV Example 2: Thin Dielectric on Silicon Select Fit e2 only 2014 J.A. Woollam Co., Inc. 12

13 Example 2: Thin Dielectric on Silicon Add Oscillators to match e 2 shape of Reference material. ~ 5eV 2014 J.A. Woollam Co., Inc. 13

14 Example 2: Thin Dielectric on Silicon Fit Oscillator Parameters to match Reference e J.A. Woollam Co., Inc. 14

15 Example 2: Thin Dielectric on Silicon Select Fit e 1 Only Fit e 1 with poles & offset 2014 J.A. Woollam Co., Inc. 15

16 Example 2: Thin Dielectric on Silicon Generate data before fitting to insure that the new layer agrees with point-bypoint result. Generated curves should be close to Experimental data Y in degrees Generated and Experimental Model Fit Exp E 60 Exp E Wavelength (nm) Generated and Experimental D in degrees Model Fit Exp E 60 Exp E Wavelength (nm) 2014 J.A. Woollam Co., Inc. 16

17 Example 2: Thin Dielectric on Silicon Allow oscillator parameters and thickness to fit. 300 Generated and Experimental D in degrees MSE=1.36 Model Fit Exp E 60 Exp E 75 Watch for correlation between parameters Wavelength (nm) SAVE Model File for FUTURE! 2014 J.A. Woollam Co., Inc. 17

18 3 Example_3_SiNx_on_Si.dat Start from Cauchy to get a Gen-Osc for SiNx layer. Minimize number of Genosc parameters J.A. Woollam Co., Inc. 18

19 Out-of-range oscillators, Correlation & sensitivity Fit with 2 Gaussian Oscillators 2.0 Imag(Dielectric Constant), e ) sion_pbp gaussian near bandgap out-of-range gaussian Measured spectral range Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 19

20 Out-of-range oscillators, correlation & sensitivity Note that 3 different oscillators, all fit the measured spectral range equally well!! The Gen-Osc function insensitive to the out-of-range 10 Gaussian parameters The amplitude, center energy & broadening are correlated!! Imag(Dielectric Constant), e ) sion_pbp out-of-range gaussian, eo=9p4ev out-of-range gaussian, eo=11ev out-of-range gaussian, eo=12ev gaussian near bandgap Measured spectral range Imag(Dielectric Constant), e Photon Energy (ev) ) sion_pbp out-of-range gaussian, eo=9p4ev out-of-range gaussian, eo=11ev out-of-range gaussian, eo=12ev gaussian near bandgap Measured spectral range Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 20

21 4 Example_4_Resist_on_Si.dat Use si_vuv.mat for substrate Cauchy PBP Gen-Osc Gaussians work well to match absorptions from organic film, such as this photoresist J.A. Woollam Co., Inc. 21

22 iterate GENOSC Process Overview Pt-by-Pt Fit Tabulated Optical Constants Reference optical constants Existing Oscillator Model Create Oscillator Model Use Oscillator To Fit DATA 2014 J.A. Woollam Co., Inc. 22

23 Using Genosc to Fit Data Starting with Existing Genosc Layer Cauchy Point-by-Point GENOSC Choosing the correct oscillators Fitting out-of-range oscillators Parameter correlation 2014 J.A. Woollam Co., Inc. 23

24 Advanced Genosc When the pt-by-pt fit fails? 2014 J.A. Woollam Co., Inc. 24

25 5 Example_5_Organic_on_Si.dat Use si_vuv.mat for substrate Is the PBP result KK consistent? Use Gen-Osc to check 2014 J.A. Woollam Co., Inc. 25

26 What to do when Pt-by-Pt Fails? 1. Ask why did it fail? Abrupt n,k changes (try # Pts. To Avg. = 2) Starting model inaccurate (Roughness, Grading, Depolarization?) 2. Match e2 with oscillators (Gaussians) and match e1 at long-l. Fit. Go to #4 if needed. 3. Slowly move into absorbing region with Genosc, adding oscillators as needed. Go to # 4 if needed. 4. After oscillators come close to solution, do Normal Fit for n,k to develop a reference material file. 5. to us! (measurements@jawoollam.com) 2014 J.A. Woollam Co., Inc. 26

27 Example 5 Previous point-by-point fit is not KK consistent. However, we can match e2 at all wavelengths, and e1 at longer wavelengths to get starting point J.A. Woollam Co., Inc. 27

28 Allowing all fit parameters to vary, we get: 100 Generated and Experimental Example 5, continued Y in degrees Model Fit Exp E 65 Exp E Wavelength (nm) Generated and Experimental Model Fit Exp E 65 Exp E 75 D in degrees Wavelength (nm) Watch for oscillators that get lost J.A. Woollam Co., Inc. 28

29 6 Example_6_Organic_on_Si.dat Is the Point-by-Point Fit KK consistent? Try # Pts. To Avg. for next guess = 2 Extra Credit, Alternatively Try: Match e2 with oscillators (Gaussians) and match e1 at long-l. Fit. After oscillators come close to solution, do Normal Fit for n,k to develop a reference material file J.A. Woollam Co., Inc. 29

30 Example 6 Results 1 GenOsc nm 0 si_jaw 1 mm MSE = Generated and Experimental Y in degrees Model Fit Exp E 65 Exp E 70 Exp E Wavelength (nm) 300 Generated and Experimental D in degrees Model Fit Exp E 65 Exp E 70 Exp E Wavelength (nm) 2014 J.A. Woollam Co., Inc. 30

31 7 Example_7_Organic_on_Si How do we get the answer without reference material file? Try: Slowly move into absorbing region with Genosc, adding oscillators as needed. After oscillators come close to solution, do Normal Fit for n,k to develop a reference material file J.A. Woollam Co., Inc. 31

32 Example 7 Point-by-Point Fit FAILS 80 Generated and Experimental Y in degrees Model Fit Exp E 65 Exp E 70 Exp E Wavelength (nm) 2014 J.A. Woollam Co., Inc. 32

33 Cauchy to Sellmeier Cauchy Fit up to 1.75eV Then, convert to Genosc (Sellmeier) 2014 J.A. Woollam Co., Inc. 33

34 Extend Data to 2eV Range-select to 2eV (Generate), don t fit yet. 33 Generated and Experimental Y in degrees Model Fit Exp E 65 Exp E 70 Exp E Photon Energy (ev) Must need absorption at 1.8eV and above 2014 J.A. Woollam Co., Inc. 34

35 Index of Refraction ' n' Extinction Coefficient ' k' Add Gaussian, Fit and Repeat Difficult, take small steps (.2eV) After oscillators come close to solution, do Normal Fit for n,k to develop a reference material file. Build another Genosc with new Ref.Mat file. Y in degrees Model Fit Exp Y-E 65 Exp Y-E 70 Exp Y-E 75 Model Fit Exp D-E 65 Exp D-E 70 Exp D-E 75 MSE = 12 Generated and Experimental D in degrees GenOsc nm 0 si_jaw 1 mm n k GenOsc Optical Constants Photon Energy (ev) Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 35

36 %Depolarization 80 EXTRA CREDIT - Depolarization Film was non-uniform and this is required to fit data better. Generated and Experimental 150 MSE = 3.9 Y in degrees Model Fit Exp Y-E 65 Exp Y-E 70 Exp Y-E 75 Model Fit Exp D-E 65 Exp D-E 70 Exp D-E Photon Energy (ev) D in degrees 1 genosc nm 0 si_jaw 1 mm Model Fit Exp -dpole 65 Exp -dpole 70 Exp -dpole 75 Generated and Experimental Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 36

37 Extra Slides The following slides provide an additional Example J.A. Woollam Co., Inc. 37

38 p-semi Oscillator The Genosc psemi has 9 main variable parameters (11 total*): 1. E Center energy 2. A Amplitude 3. B Broadening 4. WL Left end point 5. WR Right end point 6. PL position left control point 7. AL amplitude left control point 8. PR position right control point 9. AR amplitude right control point. e 2 Psemi-M1 PL=0.75 (fixed) WL B (variable) O2R = 0 (fixed) O2L = 1 (fixed) AL:(variable) ev WR A & E1 (variable) AR:(variable) PR=0.5 (fixed) 2014 J.A. Woollam Co., Inc. 38

39 Psemi-Triangle oscillator Psemi-TRI AL = 0.3, AR = 0.5 B (variable) WL (variable) WR (variable) A, Ec (variable) AR:(variable) e 2 AL:(variable) PL=0.5 (fixed) ev PR=0.5 (fixed) 2014 J.A. Woollam Co., Inc. 39

40 Psemi-M0 oscillator Psemi-M0 WR (variable) A B = 0.05eV O2R = 0 (all variable) AR (variable) = 0.8 e 2 AR = 0.5 AR = 0.3 Eo (variable) ev PR=0.5 PR=0.6 PR (variable) 2014 J.A. Woollam Co., Inc. 40

41 8 Example_8_Direct_gap_film_on_SiC.dat Use SiC_4H_o_g.mat for substrate Try to match with Gaussians. How many does it require? How many PSEMI oscillators are required? Count up the total number of free parameters J.A. Woollam Co., Inc. 41

42 Poly-Silicon The dielectric function of silicon varies with crystallinity. Amorphous films have broad UV absorption: no distinct electronic transitions (E 1, E 2, ) As crystallinity increases, individual peaks separate & become narrower. To quantify crystallinity, optical constants are compared to reference measurements where a film with known crystallinity was measured. Imag(Dielectric Constant), e a-si 70% Poly-Si 85% Poly-Si c-si e 2 for different silicon films from one reference file Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 42

43 Estimating Crystallinity Ellipsometry can be used to estimate the amount of crystallinity by comparing the measured optical constants to the reference files. To improve accuracy, a new reference file can be created for the particular deposition process. Imag(Dielectric Constant), e % Poly-Si 80% Poly-Si 90% Poly-Si Crystalline Si Photon Energy (ev) For high crystalline %, the peak is narrower and eventually separates into two distinct regions J.A. Woollam Co., Inc. 43

44 Estimating Crystallinity - 2 For amorphous films and small-grain poly-si, the absorption peak is broad but there is still a shift of the optical constants as shown below. Imag(Dielectric Constant), e a-si 10% poly-si 20% poly-si 30% poly-si Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 44

45 Log(Absorption Coefficient in 1/cm) Estimating Bandgap The ellipsometer is sensitive to optical constants of film. It will be most sensitive to the shape of absorbing region where e 2 is larger. Although many models such as Tauc-Lorentz and Cody-Lorentz contain a bandgap term, the indirect gap of silicon films is not directly measurable. The bandgap can be estimated by plotting the decrease in a toward zero (logscale). Discussed in Woollam Newsletter article from year a-si 10% poly-si 20% poly-si 30% poly-si Tauc-Lorentz model matches different a-si and poly-si films. Blue area shows the level of absorption that the SE can detect. Values below are extrapolated from T-L shape Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 45

46 Log(Absorption Coefficient in 1/cm) Estimating Bandgap - 2 Cody-Lorentz provides more flexibility for amorphous semiconductors. Similar to the Tauc-Lorentz, SE is sensitive to shape primarily from the more absorbing UV region and the bandgap region just shifts as the overall shape changes. Lesson: T-L and C-L can provide a qualitative bandgap value for comparison, but may not match actual physical property of film a-si 10% poly-si 20% poly-si 30% poly-si Photon Energy (ev) 2014 J.A. Woollam Co., Inc. 46