# Rutherford Backscattering Spectroscopy, Counting Statistics

• Dan Zar
In summary, the conversation discusses solving a numerical example of an RBS spectrum for an AuAgCu-alloy on a glass-substrate using pen, paper, and a calculator. The question is whether the composition can be determined and the accuracy of the result. The relevant equations and values for Z Au, Z Ag, and Z Cu are provided. The solution involves calibrating the areas and calculating the relative areas for each element, resulting in a stoichiometry of Au0.37Ag0.16Cu0.47. The issue of uncertainty is also discussed, with the suggestion of taking the square root of the counts for each element as uncertainty in the numerator and the uncertainty on the sum of Ag+Cu (excluding the uncertainty on
Dan Zar

## Homework Statement

I am given a numerical example (to be solved with pen, paper and calculator only) of an RBS spectrum of a AuAgCu-alloy on a glass-substrate. The question is "Can you get the composition? How accurate is the result?

## Homework Equations

All the Rutherford Backscattering Spectroscopy equations should be easy for an expert in the field. Z Au= 79, Z Ag = 47, Z Cu = 29. Yield = Area under the peak, Au/Ag=(Yield Au/ Yield Ag)*(charge Ag^2/charge Au^2), etc. Uncertainty of Yield = square root of the area.

## The Attempt at a Solution

I am able to get the yields (total areas) by calibrating the areas; I get the following numbers for the relative areas --> Au: 8371, Ag: 1262, Cu: 1427, which end up getting me to the following stoichiometry: Au0.37Ag0.16Cu0.47. Then I believe the square root of the total number of counts (or yield) is the uncertainty of each peak, so how do I know how accurate the result as a whole is? do I add up the total number of counts with the uncertainties (propagate the error) and then whatever percentage of my total number of counts corresponds to the added uncertainties is the accuracy of the result? or, do I have to propagate the error on the ratios even before I get the stoichiometries, which would require a bit of partial differentiation. I am honestly not able to solve problems about counting statistics in Ion Beam Analysis methods, if you can link me to a good text-book like approach of counting statistics in IBA methods I would appreciate it. P.S I am a chemist, be nice :)

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Did you mark the problem as solved on purpose?

The different mass fractions are not independent. If you want individual uncertainties (let's take Au), you can take the square root of Au counts as uncertainty in the numerator and the uncertainty on the sum of Ag+Cu (added in quadrature, but not including the uncertainty on Au) as uncertainty in the denominator. All multiplied with the masses of the atoms of course, if you want mass fractions.

## 1. What is Rutherford Backscattering Spectroscopy (RBS)?

RBS is a technique used to analyze the composition and thickness of thin films. It involves bombarding a sample with high-energy ions and measuring the energy and angle of the ions that are scattered back. This information can then be used to determine the elements present in the sample and their depth profiles.

## 2. How does RBS work?

In RBS, a beam of high-energy ions is directed at the sample, and a detector measures the energy and angle of the ions that are scattered back. The energy and angle of the scattered ions depend on the mass and charge of the elements in the sample, allowing for identification and quantification of the elements present. The intensity of the backscattered ions is also measured, which can provide information about the thickness of the sample.

## 3. What is the purpose of counting statistics in RBS?

Counting statistics refers to the analysis of the number of ions that are detected during an RBS experiment. This information can be used to determine the statistical uncertainty of the results and to ensure the accuracy and precision of the measurements.

## 4. What are the advantages of using RBS?

RBS has several advantages, including its non-destructive nature, high sensitivity, and ability to analyze thin films with high spatial resolution. It is also a versatile technique that can be used to analyze a wide range of materials, from semiconductors to biological samples.

## 5. Are there any limitations to RBS?

One limitation of RBS is that it is a surface-sensitive technique and cannot provide information about the bulk composition of a sample. It is also time-consuming and requires specialized equipment and expertise. Additionally, the analysis of complex samples with overlapping peaks can be challenging, and the accuracy of the results can be affected by factors such as sample preparation and matrix effects.

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