Energy straggling

Energy straggling, which is a phenomenon common to all particles, is discussed first. Then the other effects are analyzed separately for each particle group. 

Consider a monoenergetic beam of particles with kinetic energr Tq (Fig. 

1) going throi a thickness Ax that is a fraction of the particle range. The average energy T of the emerging particles is 

The shape of the energy distribution shown in Fig. 13.1 is determined by the parameter k. 

All the symbols in Eqs. 13.3 and 13.4a have been defined in Sec. 4.3, except Z, the charge of the incident particle, and Z2, the atomic number of the stopping material. For nonrelativistic particles (/3 - 1), which are much heavier than electrons, Eq. 13.4a takes the form 

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Figure 7 shows a contribution from ion energy straggling in the sample. This, of course, is zero for near-surface layers and gets rapidly worse for layers several thousand A deep, or for (a, <[)) in grazing configurations. 

Straggling effects become more dominant further into the sample. They are most pronounced with proton beams, because the ratio of energy straggling to energy loss decreases with increasing ion mass. For protons, these effects may be quite substantial for example, depth resolutions in excess of 1000 A are typical for 1-MeV protons a few pm into a material. 

The depth resolution of ERDA is mainly determined by the energy resolution of the detector system, the scattering geometry, and the type of projectiles and recoils. The depth resolution also depends on the depth analyzed, because of energy straggling and multiple scattering. The relative importance of different contributions to the depth resolution were studied for some specific ERDA arrangements [3.161, 3.163]. 

Gaussian-shaped depth profiles of P with three parameters of maximum concentration (Cmax), projected range (Rp) and range straggling (ARp). The energy loss (dE/dx) and energy straggling ( 2 square root of the variance) of the a beam in the Si layer were taken into account ... 

The variance of the energy straggling distribution was first calculated by Bohr using a classical model. Bohr s result is... 

Figure 13.3 The experimental setup used in the study of energy straggling.

Figure 13.4 Alpha-particle energy straggling for (a) thin, and (b) thick foils of silver, [(a) Data ( )...

Range straggling is a phenomenon related to energy straggling by the equation... 

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