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2.2.1 Numerical Range Scaling

  The numerical range scaling (NRS) method [Rys83] seems to be appropriate to cover the multilayer problem. The probability density functions as well as the partial doses themselves are assembled at the material interfaces according to dose and normalization constraints. Let tex2html_wrap_inline4949 be the position of the material interface starting with tex2html_wrap_inline4951 , the surface coordinate, and tex2html_wrap_inline4953 be the thickness of this given material layer i, two characteristic scaling factors tex2html_wrap_inline4957 , tex2html_wrap_inline4959 have to be calculated for each material layer as given from (2.2-1) to (2.2-3).

    eqnarray595

tex2html_wrap_inline4961 gives the already consumed area of the piecewise assembled probability density functions. The final profile can then be obtained by (2.2-4).

  equation614

   figure618
Figure 2.2-1: Application of the NRS model and dose matching criterion to a one-dimensional multilayer structure. Material layer specific parameters tex2html_wrap_inline4959 , tex2html_wrap_inline4953 , and tex2html_wrap_inline4957 according to (2.2-1) - (2.2-4) are also given.

Figure 2.2-1 explains the NRS method for a one-dimensional arsenic implantation profile. The profile is discontinuous at the material interfaces due to different characteristic parameters of the adjacent material.



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