|
Poly(ether imide)
Sample preparation
PEI 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 partial dissolution of a PEI film in 1-methyl-2-pyrrolidinone
and was prepared by Dr. K. Kuriki. Attempts to completely dissolve
PEI films led to saturation of the solution and precipitation of
a second phase, which tends to indicate that the film is actually made
of more constituents than just PEI and probably contains plasticizers.
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 in the visible-NIR region
(IR region) was equal to 2.6.10 -3 and the corresponding
film’s thickness to 478 nm. The n-k curves exhibit absorption due
to the electronic bandgap above 2.54 eV and many absorption peaks due
to bond resonances above 5.5 mm. In order to confirm these results, in
agreement with the reported values (1.658 ref.1), we used the Transfer
Matrix Method (TMM, see ref.2) with the measured n-k values to calculate
the transmission spectrum of a 13 microns thick film. When comparing it
with the corresponding experimental spectrum, we obtained a reasonably
good agreement in the shape of the absorption peaks but it appeared that
some of the peaks in the IR where slightly shifted, probably due to the
uncertainty on the provided film thickness and roughness effects, and that
some peaks were not common to both spectrum, which could result from the
difference of composition between the two films (see insert: red curve =
simulation, blue curve = experimental).
1. Goodfellow http://www.goodfellow.com/csp/active/gfMaterialInfo.csp?MATID=EI31&material=1
2. 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).
Wavelength
(microns)
|
n
|
k
|
0.25
0.257
0.264
0.271
0.278
0.285
0.292
0.299
0.306
0.313
0.32
0.327
0.334
0.341
0.348
0.355
0.362
0.369
0.376
0.383
0.39
0.397
0.404
0.411
0.418
0.425
0.432
0.439
0.446
0.453
0.46
0.467
0.474
0.481
0.488
0.495
0.502
0.509
0.516
0.523
0.53
0.537
0.544
0.551
0.558
0.565
0.572
0.579
0.586
0.593
0.6
0.607
0.614
0.621
0.628
0.635
0.642
0.649
0.656
0.663
0.67
0.677
0.684
0.691
0.698
0.705
0.712
0.719
0.726
0.733
0.74
0.747
0.754
0.761
0.768
0.775
0.782
0.789
0.796
0.803
0.81
0.817
0.824
0.831
0.838
0.845
0.852
0.859
0.866
0.873
0.88
0.887
0.894
0.901
0.908
0.915
0.922
0.929
0.936
0.943
0.95
0.957
0.964
0.971
0.978
0.985
0.992
0.999
1.006
1.013
1.02
1.027
1.034
1.041
1.048
1.055
1.062
1.069
1.076
1.083
1.09
1.097
1.104
1.111
1.118
1.125
1.132
1.139
1.146
1.153
1.16
1.167
1.174
1.181
1.188
1.195
1.202
1.209
1.216
1.223
1.23
1.237
1.244
1.251
1.258
1.265
1.272
1.279
1.286
1.293
1.3
1.307
1.314
1.321
1.328
1.335
1.342
1.349
1.356
1.363
1.37
1.377
1.384
1.391
1.398
1.405
1.412
1.419
1.426
1.433
1.44
1.447
1.454
1.461
1.468
1.475
1.482
1.489
1.496
1.503
1.51
1.517
1.524
1.531
1.538
1.545
1.552
1.559
1.566
1.573
1.58
1.587
1.594
1.601
1.608
1.615
1.622
1.629
1.636
1.643
1.65
1.657
1.664
1.671
1.678
1.685
1.692
1.699
1.706
1.713
1.72
1.727
1.734
1.741
1.748
1.755
1.762
1.769
1.776
1.783
1.79
1.797
1.804
1.811
1.818
1.825
1.832
1.839
1.846
1.853
1.86
1.867
1.874
1.881
1.888
1.895
1.902
1.909
1.916
1.923
1.93
1.937
1.944
1.951
1.958
1.965
1.972
1.979
1.986
1.993
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
2.1374
2.1391
2.1409
2.1427
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
2.2863
2.2883
2.2903
2.2923
2.2943
2.2964
2.2984
2.3005
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
2.3463
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
2.4073
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
2.4413
2.4436
2.4459
2.4482
2.4505
2.4528
2.4551
2.4574
2.4598
2.4621
2.4645
2.4668
2.4692
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
2.6162
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
2.6646
2.6673
2.67
2.6728
2.6756
2.6783
2.6811
2.6839
2.6866
2.6894
2.6922
2.695
2.6978
2.7006
2.7035
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
2.7878
2.7908
2.7938
2.7968
2.7998
2.8028
2.8059
2.8089
2.8119
2.815
2.8181
2.8211
2.8242
2.8273
2.8304
2.8335
2.8366
2.8397
2.8428
2.8459
2.849
2.8522
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
3.0646
3.0682
3.0718
3.0755
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
3.1388
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
3.2008
3.2047
3.2087
3.2127
3.2166
3.2206
3.2246
3.2287
3.2327
3.2367
3.2408
3.2448
3.2489
3.253
3.257
3.2611
3.2653
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
3.4661
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
3.581
3.5859
3.5909
3.5959
3.6008
3.6059
3.6109
3.6159
3.621
3.626
3.6311
3.6362
3.6413
3.6464
3.6516
3.6567
3.6619
3.6671
3.6723
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
3.8296
3.8352
3.8409
3.8466
3.8523
3.8581
3.8638
3.8696
3.8754
3.8812
3.887
3.8928
3.8987
3.9045
3.9104
3.9163
3.9223
3.9282
3.9342
3.9401
3.9461
3.9521
3.9582
3.9642
3.9703
3.9764
3.9825
3.9886
3.9948
4.0009
4.0071
4.0133
4.0196
4.0258
4.0321
4.0383
4.0446
4.051
4.0573
4.0637
4.07
4.0764
4.0829
4.0893
4.0958
4.1022
4.1087
4.1153
4.1218
4.1284
4.1349
4.1415
4.1482
4.1548
4.1615
4.1682
4.1749
4.1816
4.1884
4.1952
4.202
4.2088
4.2156
4.2225
4.2294
4.2363
4.2432
4.2502
4.2572
4.2642
4.2712
4.2782
4.2853
4.2924
4.2995
4.3067
4.3138
4.321
4.3282
4.3355
4.3427
4.35
4.3573
4.3647
4.372
4.3794
4.3868
4.3943
4.4017
4.4092
4.4167
4.4243
4.4318
4.4394
4.447
4.4547
4.4623
4.47
4.4777
4.4855
4.4933
4.5011
4.5089
4.5167
4.5246
4.5325
4.5405
4.5484
4.5564
4.5645
4.5725
4.5806
4.5887
4.5968
4.605
4.6132
4.6214
4.6297
4.6379
4.6463
4.6546
4.663
4.6714
4.6798
4.6883
4.6968
4.7053
4.7138
4.7224
4.731
4.7397
4.7484
4.7571
4.7658
4.7746
4.7834
4.7923
4.8011
4.81
4.819
4.828
4.837
4.846
4.8551
4.8642
4.8733
4.8825
4.8917
4.901
4.9102
4.9196
4.9289
4.9383
4.9477
4.9572
4.9667
4.9762
4.9858
4.9954
5.005
5.0147
5.0244
5.0342
5.044
5.0538
5.0637
5.0736
5.0836
5.0935
5.1036
5.1136
5.1237
5.1339
5.1441
5.1543
5.1646
5.1749
5.1852
5.1956
5.206
5.2165
5.227
5.2376
5.2482
5.2588
5.2695
5.2803
5.291
5.3019
5.3127
5.3236
5.3346
5.3456
5.3566
5.3677
5.3789
5.39
5.4013
5.4126
5.4239
5.4352
5.4467
5.4581
5.4696
5.4812
5.4928
5.5045
5.5162
5.528
5.5398
5.5516
5.5635
5.5755
5.5875
5.5996
5.6117
5.6239
5.6361
5.6484
5.6607
5.6731
5.6856
5.698
5.7106
5.7232
5.7359
5.7486
5.7614
5.7742
5.7871
5.8
5.813
5.8261
5.8392
5.8524
5.8656
5.8789
5.8923
5.9057
5.9192
5.9328
5.9464
5.96
5.9738
5.9876
6.0014
6.0153
6.0293
6.0434
6.0575
6.0717
6.0859
6.1003
6.1147
6.1291
6.1436
6.1582
6.1729
6.1876
6.2024
6.2173
6.2322
6.2473
6.2624
6.2775
6.2927
6.3081
6.3234
6.3389
6.3544
6.3701
6.3857
6.4015
6.4174
6.4333
6.4493
6.4654
6.4815
6.4978
6.5141
6.5305
6.547
6.5636
6.5802
6.597
6.6138
6.6307
6.6477
6.6648
6.682
6.6993
6.7166
6.7341
6.7516
6.7692
6.7869
6.8048
6.8227
6.8407
6.8588
6.877
6.8952
6.9136
6.9321
6.9507
6.9694
6.9882
7.0071
7.0261
7.0451
7.0643
7.0836
7.1031
7.1226
7.1422
7.1619
7.1818
7.2017
7.2218
7.2419
7.2622
7.2826
7.3031
7.3238
7.3445
7.3654
7.3864
7.4075
7.4287
7.45
7.4715
7.4931
7.5148
7.5367
7.5586
7.5807
7.603
7.6253
7.6478
7.6705
7.6932
7.7161
7.7391
7.7623
7.7856
7.8091
7.8327
7.8564
7.8803
7.9043
7.9285
7.9528
7.9773
8.0019
8.0267
8.0516
8.0767
8.1019
8.1273
8.1529
8.1786
8.2045
8.2305
8.2567
8.2831
8.3097
8.3364
8.3633
8.3903
8.4176
8.445
8.4726
8.5004
8.5283
8.5565
8.5848
8.6133
8.6421
8.671
8.7
8.7293
8.7588
8.7885
8.8184
8.8485
8.8788
8.9093
8.9401
8.971
9.0021
9.0335
9.0651
9.0969
9.1289
9.1612
9.1937
9.2264
9.2593
9.2925
9.326
9.3596
9.3935
9.4277
9.4621
9.4968
9.5317
9.5669
9.6023
9.638
9.6739
9.7102
9.7467
9.7835
9.8205
9.8579
9.8955
9.9334
9.9716
10.0101
10.0489
10.088
10.1274
10.1671
10.2072
10.2475
10.2882
10.3292
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