Aluminum Oxide Thickness Measurement

If the metal:oxide ratio can be determined for a thin film oxide sample (~0-9 nm) and if the inelastic mean free path (IMFP, λ) of the metal (λm) and oxide (λox) is known (or can be calculated), the oxide film thickness can be calculated using the calculations of the type developed by Strohmeier [1] and Carlson [2] defined as follows:

d=λoxsinθ ln(((NmλmIox)/(NoxλoxIm))+1) (Eq. 1)

where θ is the photoelectron take-off angle, Iox and Im are the area percentages of the oxide and metal peaks from the high-resolution spectrum, and Nm and Nox are the volume densities of the metal atoms in the metal and oxide, respectively.

For an aluminum oxide film on an aluminum substrate, the Al 2p spectrum has well separated oxide and metal peaks (example shown in Figure 1) and Io and Im values can be readily ascertained. Using the λ and N values proposed by Strohmeier [1], an Excel based aluminum oxide thickness calculator is presented. Just input the percentage of metal from the high-resolution spectrum to get a film thickness in Angstroms. (Note: you must download the file to Excel to use it - it is locked in Google Docs).

Figure 1. Al 2p XPS spectrum of a thin film Al oxide on Al metal with a calculated oxide thickness of 3.7 nm.

References:
1. B.R. Strohmeier, Surf. Interface Anal. 15 (1990) 51.
2. T.A. Carlson, G.E. McGuire, J. Electron Spectrosc. Relat. Phenom, 1 (1972/73) 161.

The Thickogram

Peter Cumpson[1] at NPL in the United Kingdom has developed a useful graphical method for measuring overlayer thickness in samples where the overlayer has a different elemental chemistry than the substrate (for example: a niobium film over a silicon substrate). The method allows for the following:

1) Uniform surface contamination (e.g. adventitious carbon layer) is not important.
2) Unknown instrumental factors common to substrate and oxide cancel out.
3) Uses a simple equation.
4) Works well for large and small film thickness.

Some rules:
1) Emission angle must be between 0 and 60 degrees (ie. Take-off angle of 90 to 30 degrees). Emission angles around 45 degrees are the most accurate.
2) Applicable to a wide range of Kinetic Energies above ~500 eV.
3) Error in result is +/-10% based on accuracy of attenuation lengths obtained by calculations.

Values Needed: o = Overlayer, s= Substrate
Io = Intensity of Overlayer Peak (or Peak Area)
Is = Intensity of Substrate Peak (or Peak Area)
So = R.S.F. of Overlayer Peak
Ss = R.S.F. of Substrate
Eo = K.E. of Overlayer Peak
Es = K.E. of Substrate Peak
Theta = emission angle, (0 for 90 degree take-off)
Cos(Theta) (=1 for 90 degree take-off)
Lambda o = attenuation length of photoelectrons (from the overlayer) in the overlayer.

How to Use It: A printable version of the Thickogram (Figure 1) can be downloaded here. An Excel spreadsheet that is useful for multiple calculations is presented here. (Note: you must download the file to Excel to use it - it is locked in Google Docs).
1) Calculate A = Io/So / Is/So, add point on Thickogram
2) Calculate B = Eo/Es, add point on Thickogram
3) Draw a line from A to B. Point C is found on the curve.
4) Thickness (t) is calculated as t = C(Lambda o)cos(Theta)



Figure 1. The Thickogram showing points A, B and C.
If you wish to use this method I would highly recommend reading through the original paper first [1].

Reference:
[1] Peter J. Cumpson, Surf. Interface Anal. 29, 403-406 (2000).