The two-dimensional profiling of light ions into crystal

Using a computer simulation we examine the dependence of the incident tilt angle theta and the incident energy E-0 on two-dimensional concentration profiles of implanted ions into crystalline targets. For each profile, the quantity called the 'microscopic lateral straggling' Delta R-L(z) is evaluated as a function of depth z. The values Delta R-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 Delta R-L(z) and the FWHM (full width at half maximum) are very close to the mean projected range R-p and its straggling Delta R-p, respectively. In the case of aligned incidence, however, such a correlation is not seen. In addition, the detailed behavior of Delta R-L(z) is shown by an exponential function whose exponent is the third-order polynomial of z. It expresses the whole profile of Delta R-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 carries the dependence of both theta and E-0.