Calculations straggling

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%. 

Straggling. The essence of RBS is to measure the energy of the scattered beam and to calculate thereby the depth and/or mass from which scattering occurs. Any uncertainty in particle energy leads to a reduction in the precision with which mass and depth analysis can be achieved. 

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 ... 

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

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

Figure 2 shows the reference coordinates and nomenclature of this geometry. Theoretical calculations of the projected range and straggle for various dopants and substrates have been calculated and shown in graphical form (4, 21-26). Some common dopant ions for silicon and gallium arsenide are shown in Figures 3, 4, 5, and 6. 

Figure 4. Theoretical calculations of projected straggle for B, P, As, and Sb in silicon. (Adapted with permission from Reference 27, copyright 1983, John Wiley and Sons).

Stepwise creation of Gaussian implantation profiles, where the projected ranges are calculated with the stopping powers given by Kalbitzer [85] and convoluted with a width due to straggling. 

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