Thin Film Calculations (STRATAGem vs. Armstrong)

[UofO EPMA Lab]

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:



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...

[UofO EPMA Lab]

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:



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.