|
Poly(ether sulfone)
Sample preparation
PES films were prepared by spin coating
(Laurell Tech. Corp. WS-400A-6NPP/LITE) of a polymer solution
at 1500 rpm (in air) and were kept for 1 hour under vacuum at 100
oC to ensure complete evaporation of the solvent. The polymer
solution was obtained by complete dissolution of a 25-micron Goodfellow
PES film in N,N-Dimethylformamide (DMF) and was prepared by Dr.
K. Kuriki.
Measurement and analysis
We performed a three-angle measurement (at
72, 75 and 78 incident angle). To extract the thickness of the
deposited film, the ellipsometric parameters were fitted using
the Levenberg-Marquardt regression method with a Cauchy-like dispersion
relation:
n=A+B/λ2+c/λ4
k=D/λ+E/λ3+F/λ5
where λ is
the wavelength and A,B,C,D,E,F are
fitting parameters. Additional Lorentzian absorption peaks were
used in the infrared. The deduced dispersion relation was used
to generate starting values in the Levenberg-Marquardt regression
method to calculate the n and k values at every wavelength (independently
of any model). The standard deviation of the fit was equal to 4.10
-3 and the corresponding film’s thickness to 820 nm. The
n-k curves exhibit absorption due to the electronic bandgap above 4.08
eV and many absorption peaks due to bond resonances at wavelengths above
6 mm. Very few values of the refractive index are reported in the litterature
(1.65 ref.1) but transmission spectra are available in the literature
(see ref.2 for the 25-micron thick (Goodfellow) PES film). Using the Transfer
Matrix Method (TMM, see ref.3) with the measured n-k values, we calculated
the corresponding transmission spectrum for a 25-micron thick PES film
and obtained very good agreement in the position and the shape of the
absorption peaks with the experimental spectra (from our own measurement
as well as from literature - see insert: red curve = simulation, blue curve
= experimental).
1. Goodfellow http://www.goodfellow.com/csp/active/gfMaterialInfo.csp?MATID=SU30&material=1
2. P.K. Nair, J. C., O.G. Daza, M.T.S. Nair, Polyethersulfone
foils as stable transparent substrates for conductive copper sulfide
thin film coatings , Thin Solid Films 401, 243-250 (2001).
3. Ajoy K. Ghatak, K. T., M.R. Shenoy, Numerical
Analysis of Planar Optical Waveguides Using Matrix Approach
, Journal of Ligthwave Technology LT-5, 660-667 (1987).
Results
|
Wavelength (microns)
|
n
|
k
|
|
0.25
0.251
0.252
0.253
0.2541
0.2551
0.2562
0.2572
0.2583
0.2594
0.2605
0.2616
0.2627
0.2638
0.2649
0.2661
0.2672
0.2684
0.2695
0.2707
0.2719
0.2731
0.2743
0.2755
0.2768
0.278
0.2792
0.2805
0.2818
0.2831
0.2844
0.2857
0.287
0.2883
0.2897
0.291
0.2924
0.2938
0.2952
0.2966
0.298
0.2995
0.3009
0.3024
0.3039
0.3054
0.3069
0.3084
0.31
0.3115
0.3131
0.3147
0.3163
0.3179
0.3195
0.3212
0.3229
0.3246
0.3263
0.328
0.3297
0.3315
0.3333
0.3351
0.3369
0.3388
0.3406
0.3425
0.3444
0.3463
0.3483
0.3502
0.3522
0.3542
0.3563
0.3583
0.3604
0.3625
0.3647
0.3668
0.369
0.3712
0.3734
0.3757
0.378
0.3803
0.3827
0.385
0.3875
0.3899
0.3924
0.3949
0.3974
0.4
0.4025
0.4052
0.4078
0.4105
0.4133
0.4161
0.4189
0.4217
0.4246
0.4275
0.4305
0.4335
0.4366
0.4397
0.4428
0.446
0.4492
0.4525
0.4558
0.4592
0.4626
0.4661
0.4696
0.4732
0.4769
0.4806
0.4843
0.4881
0.492
0.4959
0.4999
0.504
0.5081
0.5123
0.5166
0.5209
0.5254
0.5299
0.5344
0.5391
0.5438
0.5486
0.5535
0.5585
0.5636
0.5687
0.574
0.5794
0.5848
0.5904
0.5961
0.6019
0.6078
0.6138
0.6199
0.6262
0.6326
0.6391
0.6458
0.6526
0.6595
0.6666
0.6738
0.6812
0.6888
0.6965
0.7045
0.7126
0.7208
0.7293
0.738
0.7469
0.756
0.7653
0.7749
0.7847
0.7948
0.8051
0.8157
0.8266
0.8377
0.8492
0.861
0.8731
0.8856
0.8984
0.9117
0.9253
0.9393
0.9537
0.9686
0.984
0.9999
1.0163
1.0332
1.0507
1.0688
1.0876
1.107
1.1271
1.148
1.1697
1.1922
1.2155
1.2399
1.2652
1.2915
1.319
1.3477
1.3776
1.4089
1.4417
1.476
1.512
1.5498
1.5896
1.600416222
1.601449815
1.602277652
1.603313652
1.604350992
1.605389676
1.606221592
1.6072627
1.608305159
1.60934897
1.610394138
1.61123125
1.612278865
1.613327842
1.614378186
1.615219446
1.616272255
1.617326437
1.618381996
1.619438933
1.620285477
1.621344902
1.622405714
1.623467915
1.624531508
1.625383386
1.626449491
1.627516995
1.628585901
1.629442038
1.630513476
1.631586323
1.632660583
1.633736259
1.63459782
1.635676051
1.636755705
1.637836786
1.638702679
1.639786334
1.640871422
1.641957948
1.643045914
1.643917325
1.64500789
1.646099903
1.647193366
1.648069184
1.649165266
1.650262807
1.65136181
1.652462277
1.653343708
1.65444682
1.655551404
1.656657465
1.657765004
1.658652103
1.659762312
1.660874008
1.661987194
1.662878818
1.663994694
1.665112069
1.666230946
1.667351327
1.668248717
1.669371815
1.670496425
1.671622552
1.672524547
1.673653411
1.6747838
1.675915716
1.677049164
1.677957026
1.679093238
1.680230989
1.681370283
1.682511123
1.683424911
1.684568542
1.685713728
1.686860472
1.687778991
1.688928548
1.690079671
1.691232365
1.692386632
1.693311181
1.694468289
1.695626979
1.696787254
1.697716619
1.698879757
1.70004449
1.701210822
1.702378754
1.703314256
1.704485079
1.705657514
1.706831562
1.708007228
1.708948927
1.710127513
1.711307725
1.712489567
1.713436217
1.714621002
1.715807427
1.716995495
1.718185209
1.719138168
1.720330854
1.721525197
1.722721199
1.723679198
1.724878195
1.726078862
1.727281202
1.728485218
1.72944964
1.730656682
1.73186541
1.733075827
1.734287938
1.735258848
1.736474015
1.737690885
1.738909463
1.739885555
1.741107214
1.742330589
1.743555684
1.744782503
1.745765202
1.746995134
1.7482268
1.749460204
1.750448181
1.751684723
1.752923013
1.754163054
1.755404852
1.756399556
1.757644523
1.758891257
1.76013976
1.761390037
1.762391538
1.763645017
1.76490028
1.766157332
1.767164263
1.768424543
1.769686621
1.770950503
1.77221619
1.773230044
1.774498994
1.775769761
1.777042349
1.778061734
1.77933761
1.780615319
1.781894865
1.78317625
1.784202686
1.785487395
1.786773954
1.788062369
1.78909444
1.790386205
1.791679836
1.792975339
1.794272716
1.79531197
1.796612733
1.797915381
1.79921992
1.800526353
1.801572867
1.80288272
1.80419448
1.80550815
1.806560465
1.807877584
1.809196625
1.810517592
1.811840489
1.8129002
1.814226583
1.815554908
1.81688518
1.817950802
1.819284588
1.820620333
1.821958041
1.823297716
1.824370875
1.825714102
1.827059309
1.828406499
1.829755677
1.830836454
1.832189222
1.833543991
1.834900765
1.83598763
1.837348024
1.838710436
1.840074869
1.841441329
1.842535959
1.843906078
1.845278236
1.846652438
1.847753274
1.849131166
1.850511115
1.851893124
1.8532772
1.854385951
1.855773757
1.857163641
1.858555609
1.859949665
1.861066417
1.862464243
1.863864171
1.865266206
1.866389352
1.86779519
1.869203146
1.870613227
1.872025437
1.873156741
1.874572795
1.875990992
1.877411337
1.878549162
1.879973384
1.881399768
1.882828317
1.884259038
1.885405181
1.886839822
1.888276648
1.889715663
1.891156874
1.892311427
1.893756601
1.895203985
1.896653582
1.897814858
1.899268454
1.900724278
1.902182336
1.903642633
1.904812485
1.906276825
1.907743417
1.909212268
1.910388978
1.911861907
1.913337109
1.91481459
1.916294354
1.917479813
1.9189637
1.920449887
1.921938377
1.923429176
1.924623482
1.926118451
1.927615744
1.929115368
1.930316747
1.931820578
1.933326753
1.934835279
1.936346161
1.937556566
1.939071703
1.940589211
1.942109096
1.943326719
1.944850897
1.946377468
1.947906436
1.949437809
1.950664643
1.952200357
1.953738492
1.955279052
1.956822044
1.958058191
1.959605574
1.961155405
1.962707688
1.963951286
1.965508001
1.967067185
1.968628845
1.970192987
1.971446091
1.973014715
1.974585837
1.9746
1.9761
1.9776
1.9791
1.9806
1.9821
1.9836
1.9851
1.9867
1.9882
1.9897
1.9912
1.9928
1.9943
1.9958
1.9974
1.9989
2.0005
2.002
2.0036
2.0051
2.0067
2.0082
2.0098
2.0113
2.0129
2.0145
2.016
2.0176
2.0192
2.0207
2.0223
2.0239
2.0255
2.0271
2.0286
2.0302
2.0318
2.0334
2.035
2.0366
2.0382
2.0398
2.0414
2.043
2.0446
2.0463
2.0479
2.0495
2.0511
2.0527
2.0544
2.056
2.0576
2.0593
2.0609
2.0625
2.0642
2.0658
2.0675
2.0691
2.0708
2.0724
2.0741
2.0757
2.0774
2.0791
2.0807
2.0824
2.0841
2.0858
2.0874
2.0891
2.0908
2.0925
2.0942
2.0959
2.0976
2.0993
2.101
2.1027
2.1044
2.1061
2.1078
2.1095
2.1112
2.113
2.1147
2.1164
2.1181
2.1199
2.1216
2.1233
2.1251
2.1268
2.1286
2.1303
2.1321
2.1338
2.1356
2.1373
2.1391
2.1409
2.1426
2.1444
2.1462
2.148
2.1498
2.1515
2.1533
2.1551
2.1569
2.1587
2.1605
2.1623
2.1641
2.1659
2.1677
2.1695
2.1714
2.1732
2.175
2.1768
2.1787
2.1805
2.1823
2.1842
2.186
2.1879
2.1897
2.1916
2.1934
2.1953
2.1971
2.199
2.2009
2.2027
2.2046
2.2065
2.2084
2.2102
2.2121
2.214
2.2159
2.2178
2.2197
2.2216
2.2235
2.2254
2.2273
2.2292
2.2312
2.2331
2.235
2.2369
2.2389
2.2408
2.2427
2.2447
2.2466
2.2486
2.2505
2.2525
2.2544
2.2564
2.2584
2.2603
2.2623
2.2643
2.2663
2.2682
2.2702
2.2722
2.2742
2.2762
2.2782
2.2802
2.2822
2.2842
2.2862
2.2883
2.2903
2.2923
2.2943
2.2964
2.2984
2.3004
2.3025
2.3045
2.3066
2.3086
2.3107
2.3128
2.3148
2.3169
2.319
2.321
2.3231
2.3252
2.3273
2.3294
2.3315
2.3336
2.3357
2.3378
2.3399
2.342
2.3441
2.3462
2.3484
2.3505
2.3526
2.3548
2.3569
2.3591
2.3612
2.3634
2.3655
2.3677
2.3698
2.372
2.3742
2.3764
2.3785
2.3807
2.3829
2.3851
2.3873
2.3895
2.3917
2.3939
2.3961
2.3983
2.4006
2.4028
2.405
2.4072
2.4095
2.4117
2.414
2.4162
2.4185
2.4207
2.423
2.4253
2.4275
2.4298
2.4321
2.4344
2.4367
2.439
2.4412
2.4435
2.4459
2.4482
2.4505
2.4528
2.4551
2.4574
2.4598
2.4621
2.4645
2.4668
2.4691
2.4715
2.4739
2.4762
2.4786
2.481
2.4833
2.4857
2.4881
2.4905
2.4929
2.4953
2.4977
2.5001
2.5025
2.5049
2.5074
2.5098
2.5122
2.5147
2.5171
2.5195
2.522
2.5244
2.5269
2.5294
2.5318
2.5343
2.5368
2.5393
2.5418
2.5443
2.5468
2.5493
2.5518
2.5543
2.5568
2.5593
2.5619
2.5644
2.5669
2.5695
2.572
2.5746
2.5771
2.5797
2.5823
2.5849
2.5874
2.59
2.5926
2.5952
2.5978
2.6004
2.603
2.6056
2.6083
2.6109
2.6135
2.6161
2.6188
2.6214
2.6241
2.6268
2.6294
2.6321
2.6348
2.6374
2.6401
2.6428
2.6455
2.6482
2.6509
2.6536
2.6564
2.6591
2.6618
2.6645
2.6673
2.67
2.6728
2.6755
2.6783
2.6811
2.6839
2.6866
2.6894
2.6922
2.695
2.6978
2.7006
2.7034
2.7063
2.7091
2.7119
2.7148
2.7176
2.7205
2.7233
2.7262
2.7291
2.7319
2.7348
2.7377
2.7406
2.7435
2.7464
2.7493
2.7522
2.7552
2.7581
2.761
2.764
2.7669
2.7699
2.7728
2.7758
2.7788
2.7818
2.7848
2.7877
2.7907
2.7938
2.7968
2.7998
2.8028
2.8058
2.8089
2.8119
2.815
2.818
2.8211
2.8242
2.8273
2.8304
2.8334
2.8365
2.8397
2.8428
2.8459
2.849
2.8521
2.8553
2.8584
2.8616
2.8648
2.8679
2.8711
2.8743
2.8775
2.8807
2.8839
2.8871
2.8903
2.8935
2.8968
2.9
2.9033
2.9065
2.9098
2.913
2.9163
2.9196
2.9229
2.9262
2.9295
2.9328
2.9361
2.9395
2.9428
2.9461
2.9495
2.9529
2.9562
2.9596
2.963
2.9664
2.9698
2.9732
2.9766
2.98
2.9834
2.9869
2.9903
2.9938
2.9972
3.0007
3.0042
3.0077
3.0112
3.0147
3.0182
3.0217
3.0252
3.0287
3.0323
3.0358
3.0394
3.043
3.0465
3.0501
3.0537
3.0573
3.0609
3.0645
3.0682
3.0718
3.0754
3.0791
3.0828
3.0864
3.0901
3.0938
3.0975
3.1012
3.1049
3.1086
3.1124
3.1161
3.1199
3.1236
3.1274
3.1312
3.135
3.1387
3.1426
3.1464
3.1502
3.154
3.1579
3.1617
3.1656
3.1694
3.1733
3.1772
3.1811
3.185
3.1889
3.1929
3.1968
3.2007
3.2047
3.2087
3.2126
3.2166
3.2206
3.2246
3.2286
3.2327
3.2367
3.2408
3.2448
3.2489
3.253
3.257
3.2611
3.2652
3.2694
3.2735
3.2776
3.2818
3.2859
3.2901
3.2943
3.2985
3.3027
3.3069
3.3111
3.3154
3.3196
3.3239
3.3281
3.3324
3.3367
3.341
3.3453
3.3496
3.354
3.3583
3.3627
3.367
3.3714
3.3758
3.3802
3.3846
3.389
3.3935
3.3979
3.4024
3.4068
3.4113
3.4158
3.4203
3.4248
3.4294
3.4339
3.4385
3.443
3.4476
3.4522
3.4568
3.4614
3.466
3.4707
3.4753
3.48
3.4847
3.4894
3.4941
3.4988
3.5035
3.5083
3.513
3.5178
3.5226
3.5274
3.5322
3.537
3.5418
3.5467
3.5515
3.5564
3.5613
3.5662
3.5711
3.576
3.5809
3.5859
3.5909
3.5958
3.6008
3.6058
3.6109
3.6159
3.621
3.626
3.6311
3.6362
3.6413
3.6464
3.6516
3.6567
3.6619
3.667
3.6722
3.6775
3.6827
3.6879
3.6932
3.6984
3.7037
3.709
3.7143
3.7197
3.725
3.7304
3.7357
3.7411
3.7465
3.752
3.7574
3.7629
3.7683
3.7738
3.7793
3.7848
3.7904
3.7959
3.8015
3.8071
3.8127
3.8183
3.8239
3.8295
3.8352
3.8409
3.8466
3.8523
3.858
3.8638
3.8696
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