RBS Theory: Stopping Power

Only a small fraction of the incident particles undergo a close encounter with an atomic nucleus and are backscattered out of the sample. The vast majority of the incident He atoms end up implanted in the sample. When probing particles penetrate to some depth in a dense medium, projectile energy dissipates due to interactions with electrons (electronic stopping) and to glancing collisions with the nuclei of target atoms (nuclear stopping). This means that a particle which backscatters from an element at some depth in a sample will have measurably less energy than a particle which backscatters from the same element on the sample surface. The amount of energy a projectile loses per distance traversed in a sample depends on the projectile, its velocity, the elements in the sample, and the density of the sample material. Typical energy losses for 2 MeV He range between 100 and 800 eV/nm. This energy loss dependence on sample composition and density enables RBS measurements of layer thicknesses, a process called depth profiling.

The majority of energy loss is caused by electronic stopping which behaves (roughly) like friction between the probing particles and the electron clouds of the target atoms. Nuclear stopping is caused by the large number of glancing collisions which occur along the path of the probing atom. Nuclear stopping contributes significant energy losses only at low particle energies. The ratio of energy loss to two-dimensional atom density for a given material is known as its stopping cross section (epsilon), commonly measured in units of eV-cm. Since the majority of energy loss is caused by interactions with electrons, the electronic structure of the target material has a significant affect upon its stopping power.

Theoretical predications of stopping power are both complicated and inaccurate. Therefore, empirical stopping powers are often used in RBS calculations. A polynomial equation and a table of coefficients provides calculations of stopping powers over a wide range of energies and elements. In order to calculate the energy loss per unit of depth in a sample one can multiply stopping cross section times the density of the sample material (atoms/cm2). Sample densities can vary significantly. It is necessary to know the density of the sample material in order to calculate the depth of a feature or the thickness of a layer by RBS.

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