Range straggling

The range straggling can be calculated using the theory of Lindhard et al. for the condition where nuclear stopping dominates from 

The accurate treatment of ion ranges in compound targets requires extensive calculations, as performed in the PRAL code. However, estimates can be made using 

An estimate of the range straggling in alloys can be made using the empirical expression developed by Kido and Kawamoto (1986) 

---

An estimate of AR ia alloys can be made usiug the empirical expression (12) of equation 10 where the average alloy reduced energy, is defined by equation 11, where C (i = 1, 2,... , n) is the elemental atomic fraction of the /th element, and is the elemental reduced energy defined iu equation 3. Using this formulation, the projected range straggling iu compounds can be calculated to within 20%. 

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 ... 

Figure 17.6 Intensity distribution or attenuation curve is shown as a function of absorber thickness for a typical energetic heavy ion penetrating into a metal. The effect of range straggling is indicated by the Gaussian distribution of ranges. (From Leo, 1987.)...

The electronic stopping does not lead to major deflection and does not contribute very much to the lateral spread Rj. Another important quantity is the range straggling AR or ARp. It contains information about the actual distribution of the implanted ions in a solid. They also have been calculated by various authors, e. g. Schiott ... 

Fig. 6.4. Relationship between range, R, projected range, Rv, and range straggling, ARp, as functions of mass ratio, M2/Mh The range straggling, AR, is in the direction of the incident ion, and ARPJ, is perpendicular to the incident ion. Dashed lines, m = 1/3 solid lines, m = 1/2 (Winterbon et al. 1970)...

Energy Elec. Nuclear Range straggling straggling... 

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

---