The SEENET-MTP Seminar: Trends in Modern Physics 19–21 August 2011, Niš, Serbia Talk by Frederico Corni, Faculty of Education, University of Modena аnd Reggio Emilia, Italy

1. BSS2011: Trends in Modern Physics - Nis RUTHERFORD BACKSCATTERING SPECTROMETRY: A LABORATORY DIDACTIC PATH ABOUT THE BASIC INTERPRETATION MODELS Federico Corni Department of Education and Social Sciences Faculty of Education University of Modena and Reggio Emilia, Italy

2. Why RBS for Physics Education in Secondary School? It represents a bridge between Classical Physics and Modern Physics. Most of the modern techniques of analysis are based on quantum mechanics since matter is studied in terms of interactions of its microscopic components. But for their strong orientation to do measurements they are often interpreted according to (semi)classical models. It supplies an exciting context of application of Classical Physics The application of classical interpretation models allows to obtain microscopic information such thicknesses and composition of thin films. It contributes to learn a physical view of the world New physical quantities founded on very general principles of Physics are introduced, irrespective to the Classical or the Modern Physics context.

3. Why RBS for Physics Education in Secondary School? It supplies a methodological view to investigate the microscopic world It is a modern and very diffused technique extensively used by scientists as research tool in material science It can become object of secondary school student study Experiments and activities that students operatively perform can be designed and proposed for secondary school labs.

4. What is Rutherford Backscattering Spectrometry? RBS provides information about mass and depth distribution of the constituent elements of the first hundreds of nanometers of the surface of a sample 400 nm SiO 2 200 nm Si Si substrate

5. What is Rutherford Backscattering Spectrometry? It exploits the phenomenon of collision between a mono-energetic ion beam with the atoms of the target

6. What is Rutherford Backscattering Spectrometry? It exploits the phenomenon of collision between a mono-energetic ion beam with the atoms of the target For the energies (some MeV) and the ions (light ions such H+, He++) employed, the process can be fairly considered an elastic unscreend interaction between the nucleuses as in the Rutherford experiment

7. What is Rutherford Backscattering Spectrometry? The measurement consists in the collection of the energy spectrum of the ions of the beam which, after a collision with the atoms of the target, are backscattered along a certain direction

8. Example of RBS spectrum Ion beam: He ++ Energy: 2 MeV Scattering angle: 170° 400 nm SiO 2 200 nm Si Si substrate Ion beam

10. Ion elastic collision with a target atom (kinematic factor) What is the energy of an ion after an elastic collision with a heavier nucleus? Or else, conversely, how can the mass of a target element be evaluated from a measure of the energy of the backscatterd ions?

11. The Kinematic factor sample ion beam detector ion beam

13. Coulomb scattering between ions and nucleuses (scattering cross section) What is the probability that an incident ion hits the nucleus of a certain element of the sample and be sent along a certain scattering direction? Or else, conversely, haw can the abundance of an element in the sample be evaluated from the fraction of scattered ions (or its scattering efficiency)?

14. The scattering cross section nucleus ion beam

16. Ion inelastic stopping in traversing matter (stopping cross section) what is the average energy loss of the ion due to its penetration into the matter? Or else, conversely, how can the in-depth distribution of an element be obtained from the energy spectrum of the scattered ions?

17. Due to the superimposition of many microscopic phenomena contributing to the decrease of the ion kinetic energy, the stopping cross section of an element is evaluated through the experimental energy loss per unit thickness d E /d x of traversed material normalized to the element atomic density n E E-  E  x Friction between sliding surfaces

21. M 1 = 0.406 kg Thanks to this activity the students can observe that backscattering occurs only if the target is heavier than the projectile and that the kinetic factor does not depend on the initial velocity (and energy) of the projectile and is a monotonic increasing function of the target mass. M 2 (kg) v 0 v 1 E K1 /E K2 0.406 0.906 1.406 1.906 2.406 3.406

24. Example of measurement 0 2 4 6 8 10 12 0 20 40 60 80 100 120 140 theta eventsi

25. Exterimental data normalization: Theoretical calculation:  y(  )  R y

26. Thanks to this activity the students are induced to reflect upon the meaning of a statistical quantity and can observe that the angular distribution of the trajectories after the collision contains the information on the shape of the form and consequently on the kind of interaction that occurs.

29. The stopping cross section allows to calculate the film thicknesses and the depth-profiles of the various elements. Energy