Chapter 4 - Cross-section

Summary

Introduction

In Chapters 2 and 3 we developed concepts essential to our understanding of ion–solid interactions. In Chapter 3 we derived equations describing the kinematics of binary elastic collisions. These equations enable us to calculate the amount of energy transferred to a target atom in a collision when the scattering angle of the projectile or the target atom is known. Conversely, we could calculate the scattering angles if the amount of energy loss in the collision were known. At the end of Chapter 3 we developed an expression for the center-of-mass scattering angle, θ_c, which is a function of the ion energy, the impact parameter b, and the interatomic potential energy V(r). The details of the interatomic potential energy were discussed in Chapter 2.

In Chapter 4 we will examine the probability of ion–solid scattering events. During ion irradiation and ion implantation experiments, many ions or energetic particles interact with many target nuclei. Due to the large number of interactions, the questions of how much energy will be transferred in a collision or what the scattering angle will be must be answered using statistics and probability. The differential cross-section is the fundamental parameter that we will develop. It gives a measure of either the probability of transferring energy T in the range between T and T + dT to a target atom or of the probability of scattering a projectile into some angle between θ_c and θ_c + dθ_c.