It's time someone wrote up a short tutorial on performing thin film corrections.
Currently the "gold standard" for thin film calculations is STRATAGem, though it will be interesting to see how the new BadgerFilm software from Moy compares. STRATAGem is based on the method of Pouchou and Pichoir and performs a full fluorescence correction for each layer including the substrate. It can also handle multiple layers of films and also correct for coating effects. For example, Si substrates can significantly fluoresce thin films containing P or S, and with very thin films (<50 nm), coating effects can become significant.
In this comparison I will compare the results from STRATAGem to the extremely simple thin film/particle correction method from Armstrong that is implemented in PFE. First it should be noted that the Armstrong correction is not really a thin film correction, it is really a particle correction with an option for films without a substrate, or at least a substrate that does *not* fluoresce any elements in the film. So it should be used with care and all results should be taken with a very large "grain of salt". Still it is interesting to compare.
Let's start by looking at results from STRATAGem for a Bi, Dy, Fe oxide thin film that has intensities measured at 10, 15 and 20 keV:
(https://smf.probesoftware.com/gallery/360_24_09_19_11_25_49.png)
As you can see the iterated totals on this film (integrating intensities from 10, 15 and 20 keV measurements) came to almost 99% (I usually accept thin film totals between 95 and 105%) and the K vs. HV model fit the measured intensities nicely. And assuming a density of 5, the linear thickness is around 200 nm or 0.2 um.
This gives us a normalized values of Bi = 75 wt%, Dy = 1.6 wt%, Fe = 11 wt% and O = 12 wt% in round numbers.
Now let's perform some analyses in PFE assuming a bulk composition and including Si, since that is the substrate, and here are results for 10, 15 and 20 keV:
ELEM: Bi Dy Fe O Si SUM
254 51.649 1.598 10.021 12.019 25.058 100.345
255 52.108 1.613 10.408 12.022 24.850 101.001
256 51.640 1.461 10.175 12.063 24.860 100.199
257 51.785 1.510 10.078 12.061 25.020 100.453
258 51.912 1.762 9.856 12.081 24.903 100.514
259 52.062 1.637 10.288 12.004 24.978 100.969
260 51.375 1.590 10.151 12.132 24.957 100.205
261 51.830 1.593 10.116 12.139 25.028 100.706
AVER: 51.795 1.596 10.137 12.065 24.957 100.549
SDEV: .241 .089 .166 .051 .079 .316
ELEM: Bi Dy Fe O Si SUM
262 30.227 .677 4.478 10.543 50.527 96.452
263 30.396 .746 4.462 10.642 50.763 97.009
264 30.379 .648 4.435 10.614 50.688 96.764
265 30.230 .717 4.466 10.601 50.688 96.702
266 30.174 .699 4.477 10.598 50.565 96.512
267 30.314 .693 4.406 10.659 50.682 96.755
268 30.065 .746 4.425 10.631 50.769 96.636
269 30.372 .708 4.511 10.597 50.761 96.947
AVER: 30.270 .704 4.457 10.611 50.680 96.722
SDEV: .116 .033 .034 .035 .091 .193
ELEM: Bi Dy Fe O Si SUM
270 20.546 .320 2.398 10.361 65.624 99.249
271 20.439 .387 2.341 10.263 65.519 98.949
272 20.610 .328 2.353 10.333 65.701 99.325
273 20.596 .344 2.364 10.338 65.672 99.313
274 20.613 .335 2.351 10.272 65.510 99.080
275 20.611 .337 2.343 10.337 65.729 99.357
276 20.836 .360 2.339 10.340 65.659 99.534
277 20.525 .332 2.353 10.344 65.498 99.053
AVER: 20.597 .343 2.355 10.323 65.614 99.233
SDEV: .114 .021 .019 .036 .092 .192
The totals actually look reasonable, but the concentrations are completely different from STRATAGem. Note that there is an interference correction on Dy from Bi and Fe. And even if we disable the quantification for Si so it doesn't get included in the matrix correction, the totals are of course low, but the values are again completely different, even if they are normalized to 100%. Here are the unnormalized and normalized results *without* Si in the matrix corrections, first for 10 keV:
ELEM: Bi Dy Fe O Si-D SUM
254 46.803 1.447 9.027 11.658 --- 68.935
255 47.288 1.463 9.389 11.664 --- 69.804
256 46.827 1.325 9.175 11.703 --- 69.031
257 46.937 1.369 9.082 11.700 --- 69.088
258 47.075 1.594 8.884 11.721 --- 69.274
259 47.219 1.483 9.275 11.646 --- 69.623
260 46.579 1.441 9.153 11.764 --- 68.936
261 46.994 1.443 9.120 11.774 --- 69.331
AVER: 46.965 1.446 9.138 11.704 --- 69.253
SDEV: .232 .079 .153 .048 --- .322
ELEM: Bi Dy Fe O Si-D SUM
254 67.894 2.099 13.095 16.911 --- 100.000
255 67.743 2.096 13.451 16.710 --- 100.000
256 67.835 1.920 13.292 16.953 --- 100.000
257 67.938 1.981 13.146 16.935 --- 100.000
258 67.955 2.301 12.824 16.920 --- 100.000
259 67.821 2.131 13.322 16.727 --- 100.000
260 67.569 2.090 13.277 17.065 --- 100.000
261 67.782 2.082 13.154 16.982 --- 100.000
AVER: 67.817 2.087 13.195 16.900 --- 100.000
SDEV: .124 .112 .189 .122 --- .000
15 kev:
ELEM: Bi Dy Fe O Si-D SUM
262 24.417 .610 3.961 9.874 --- 38.862
263 24.566 .670 3.947 9.964 --- 39.147
264 24.536 .585 3.923 9.943 --- 38.987
265 24.423 .645 3.950 9.923 --- 38.941
266 24.379 .629 3.960 9.918 --- 38.887
267 24.490 .625 3.898 9.980 --- 38.992
268 24.284 .670 3.914 9.943 --- 38.811
269 24.540 .637 3.990 9.922 --- 39.089
AVER: 24.454 .634 3.943 9.933 --- 38.964
SDEV: .096 .029 .030 .032 --- .114
ELEM: Bi Dy Fe O Si-D SUM
262 62.832 1.569 10.192 25.408 --- 100.000
263 62.752 1.713 10.083 25.452 --- 100.000
264 62.934 1.501 10.062 25.504 --- 100.000
265 62.718 1.658 10.143 25.481 --- 100.000
266 62.692 1.618 10.184 25.506 --- 100.000
267 62.806 1.602 9.997 25.595 --- 100.000
268 62.569 1.727 10.084 25.620 --- 100.000
269 62.781 1.629 10.207 25.383 --- 100.000
AVER: 62.761 1.627 10.119 25.494 --- 100.000
SDEV: .108 .074 .074 .083 --- .000
And finally 20 keV:
ELEM: Bi Dy Fe O Si-D SUM
270 14.939 .331 2.190 9.117 --- 26.577
271 14.867 .391 2.137 9.037 --- 26.432
272 14.983 .338 2.148 9.104 --- 26.573
273 14.978 .352 2.159 9.105 --- 26.594
274 14.988 .344 2.146 9.058 --- 26.537
275 14.985 .346 2.139 9.108 --- 26.577
276 15.164 .367 2.135 9.129 --- 26.795
277 14.924 .342 2.149 9.106 --- 26.521
AVER: 14.978 .351 2.150 9.096 --- 26.576
SDEV: .086 .019 .018 .031 --- .102
ELEM: Bi Dy Fe O Si-D SUM
270 56.210 1.245 8.240 34.306 --- 100.000
271 56.247 1.480 8.084 34.190 --- 100.000
272 56.384 1.273 8.084 34.260 --- 100.000
273 56.320 1.325 8.117 34.238 --- 100.000
274 56.481 1.298 8.087 34.134 --- 100.000
275 56.382 1.301 8.049 34.268 --- 100.000
276 56.591 1.371 7.969 34.069 --- 100.000
277 56.273 1.288 8.103 34.336 --- 100.000
AVER: 56.361 1.322 8.091 34.225 --- 100.000
SDEV: .128 .074 .075 .089 --- .000
So lots of different results and none of them even close to the STRATAGem thin film corrected results! Next we'll try using the Armstrong method...
Alright, let's recall the results from STRATAGem for comparison (we're assuming the STRATAGem results are correct of course!):
This gives us a normalized values of Bi = 75 wt%, Dy = 1.6 wt%, Fe = 11 wt% and O = 12 wt% in round numbers.
So now we go to the Analyze! window in Probe for EPMA, select our samples (remember we already disabled quant for Si since it's in the substrate and the Armstrong particle/thin film cannot handle substrate physics), and click the Calculation Options button, then we click the Use Particle/Film Calculations button as seen here:
(https://smf.probesoftware.com/gallery/360_24_09_19_11_32_25.png)
What we do is first check the Use Particle or Thin Film calculations checkbox, then enter the thin film thickness in microns in the Particle Diameter field (0.2 um for our ~200 nm film), then 5 for our assumed density, and optionally we can decrease the Numerical Integration Step (size) by 10 for very thin films, though at 200 nm this is a fairly normal thickness film. Then OK, and OK.
Now let's see our results for 10 keV:
ELEM: Bi Dy Fe O Si-D SUM
254 75.483 1.566 10.793 14.357 --- 102.199
255 76.265 1.583 11.227 14.368 --- 103.444
256 75.511 1.430 10.966 14.416 --- 102.323
257 75.701 1.479 10.857 14.409 --- 102.445
258 75.931 1.732 10.625 14.431 --- 102.719
259 76.161 1.607 11.092 14.343 --- 103.203
260 75.077 1.559 10.936 14.502 --- 102.075
261 75.774 1.563 10.901 14.505 --- 102.743
AVER: 75.738 1.565 10.925 14.416 --- 102.644
SDEV: .387 .089 .183 .062 --- .483
Well that's actually not too bad, the oxygen is a little high, but the other elements are pretty darn good for a simple numerical integration!
Now let's look at the 15 keV data:
ELEM: Bi Dy Fe O Si-D SUM
262 71.188 1.092 9.748 14.402 --- 96.430
263 71.599 1.234 9.715 14.537 --- 97.085
264 71.552 1.034 9.653 14.502 --- 96.740
265 71.190 1.176 9.720 14.482 --- 96.568
266 71.067 1.138 9.745 14.480 --- 96.429
267 71.401 1.129 9.591 14.566 --- 96.687
268 70.774 1.237 9.630 14.526 --- 96.168
269 71.534 1.154 9.820 14.473 --- 96.982
AVER: 71.288 1.149 9.703 14.496 --- 96.636
SDEV: .286 .069 .074 .050 --- .303
Well the wheels are starting to come off, but when normalized not quite as bad:
ELEM: Bi Dy Fe O Si-D SUM
262 73.824 1.132 10.109 14.935 --- 100.000
263 73.749 1.271 10.007 14.973 --- 100.000
264 73.962 1.069 9.978 14.991 --- 100.000
265 73.720 1.218 10.066 14.996 --- 100.000
266 73.698 1.180 10.106 15.016 --- 100.000
267 73.848 1.167 9.920 15.065 --- 100.000
268 73.595 1.287 10.013 15.105 --- 100.000
269 73.760 1.190 10.126 14.924 --- 100.000
AVER: 73.769 1.189 10.040 15.001 --- 100.000
SDEV: .110 .071 .073 .061 --- .000
And now for the 20 keV data:
ELEM: Bi Dy Fe O Si-D SUM
270 68.179 -.506 9.456 15.256 --- 92.386
271 67.777 -.233 9.228 15.099 --- 91.871
272 68.368 -.471 9.275 15.213 --- 92.385
273 68.329 -.413 9.321 15.218 --- 92.455
274 68.375 -.445 9.266 15.119 --- 92.315
275 68.370 -.438 9.236 15.219 --- 92.386
276 69.148 -.364 9.219 15.220 --- 93.223
277 68.103 -.453 9.280 15.231 --- 92.161
AVER: 68.331 -.415 9.285 15.197 --- 92.398
SDEV: .388 .084 .077 .056 --- .383
And here normalized to 100%:
ELEM: Bi Dy Fe O Si-D SUM
270 73.799 -.547 10.236 16.513 --- 100.000
271 73.775 -.254 10.044 16.435 --- 100.000
272 74.003 -.510 10.039 16.467 --- 100.000
273 73.905 -.447 10.082 16.459 --- 100.000
274 74.067 -.482 10.037 16.378 --- 100.000
275 74.004 -.474 9.997 16.473 --- 100.000
276 74.175 -.390 9.890 16.326 --- 100.000
277 73.896 -.491 10.069 16.527 --- 100.000
AVER: 73.953 -.449 10.049 16.447 --- 100.000
SDEV: .136 .091 .096 .067 --- .000
And here the wheels have definitely come off at least for the Dy (which is due to over correction from the interference correction from Bi and Fe), though the normalized Bi and Fe numbers aren't too bad really.
So that's one example to ponder. Anyway just wanted to show the steps for using the Armstrong particle/thin film correction in PFE, though I would definitely suggest using STRATAGem (or the new BadgerFilm) if you're serious about thin film corrections.