# XRR Simply Explained?

1. Jun 30, 2010

### IntentKnown

I'm currently an undergrad research assistant in a lab that is experimenting with the interface between ferroelectrics and ferromagnetics. We have many thin film samples with various thicknesses and we often need to find out the thickness of these samples,which are mostly LSMO and PZT, as the sputtering of said samples can be off sometimes.

My question is this:

How can I read our XRR data to find the thickness of our samples? I've not been able to find any resources that explain the reflection peaks in terms of characteristics of the sample, such as layer thickness, density...etc.

Also, we have a sample that is wedge shaped, where the LSMO has a thickness of ~100nm on one side, and tappers off to 0. This wedge is then on top of a constant layer of PZT. Is there any standard and well-proven method to find the changing thickness of this sample.

Lastly, any tips and tricks with GenX would be appreciated also.

THANKS

2. Jun 30, 2010

### Gokul43201

Staff Emeritus
The basic features are easy to remember/derive:

1. The critical angle (below which there are no interference oscillations) depends on the material density,

2. The decay in the signal strength with increasing incidence angle depends on the roughness,

3. The period of oscillations depends on the film thickness.

The expression for the thickness is (utilizing a small angle approximation) what you get from writing the equation for an interference maximum at a particular angle:

$$\alpha_m ^2 - \alpha _0 ^2 = (m \lambda/2t)^2$$,

where $\alpha _m$ it the glancing angle at which the m'th maximum is detected, $\alpha _0$ is the critical angle (described above), t is the film thickness, etc.

Plotting the square of the angle against m^2 allows you to extract the values for the critical angle and thickness.

Usually, however, your XRD system comes with software that will fit your data to extract all three parameters (density, roughness, thickness). Also, the manual for the software will explain the principles of XRR and the fitting expressions.

What is the lateral size of the LSMO/PZT wedge sample?

3. Jun 30, 2010

### IntentKnown

Our sample is around 5mm squared.

4. Jun 30, 2010

### Gokul43201

Staff Emeritus
The following are ideas you can think about:

1. Measure the thickness at different locations along the sample using repeated XRR measurements. The problem with this will be beam width. A micro-XRD would fix that problem, but those are not easy to come by.

2. You might have better luck finding a narrow beam on an ellipsometer. You can calibrate the ellipsometer against an XRR derived thickness from a uniform film sample, and use that to measure thickness at different positions along the wedge sample.

3. TEM - this is usually the standard approach for something like this. May be harder to do, but gives you the best data.

5. Jul 7, 2010

### yoshisoakland

A good reference for XRR is the book "modern X-ray physics" by Als-Nielsen & McMorrow.