The two-dimensional profiling of light ions into crystal

Using a computer simulation we examine the dependence of the incident tilt angle θ and the incident energy E₀ on two-dimensional concentration profiles of implanted ions into crystalline targets. For each profile, the quantity called the 'microscopic lateral straggling' ΔR_L( z) is evaluated as a function of depth z. The values ΔR_L( z) produced in the case of aligned incidence definitely differ from those of random incidence, in the peak height, the peak depth, and the peak width. When implanted into random direction, the depth at the maximum of ΔR_L( z) and the FWHM (full width at half maximum) are very close to the mean projected range R_p and its straggling ΔR_p, respectively. In the case of aligned incidence, however, such a correlation is not seen. In addition, the detailed behavior of ΔR_L( z) is shown by an exponential function whose exponent is the third-order polynomial of z. It expresses the whole profile of ΔR_L( z), including asymmetry due to either channeling- or random-tail, without connecting the two functions. Our expression is available for B ions into (100) Si with energies up to 500 keV. Four coefficients involved in the equation carres the dependence of both θ and E₀.