The point response functions described in Sec. 3.1.1 - Sec. 3.1.3 are only generally valid if the simulation domain consist just of one material which completely fills one half space. Normally the simulation domain consists of various materials which build up the transistor structure, for instance silicon, silicon dioxide, silicon nitride. In that case several point response functions (one for each material) have to be combined in a way that covering layers shift the point response profiles of layers lying underneath.
The numerical range scaling (NRS) technique proposed by Ryssel [67]
has turned out to be a very efficient technique for the generation of
multi-layer point response functions [30], [68]. By using this
method a one-dimensional multi-layer point response function is designed as
the sum of several single layer point response functions
shifted by a
scaling vector
and multiplied by a scaling factor
which
satisfies the normalization conditions (3.1).
![]() |
(3.45) |
![]() |
(3.46) |
![]() |
(3.48) |
Higher dimensional multi-layer point response functions are modeled
equivalently. This means that the vertical function and the moments of the
lateral function are shifted by . Thereby it is assumed that each
material is infinitely extended in the lateral directions. Arbitrary shaped
simulation domains are handled by splitting the simulation domain into small
vertical slices and by calculating a scaled point response function for each of
these slices according to the material composition in the slice
[55], [89]. (3.44) - (3.47)
determine a different point response function for each slice and the total
impurity concentration at position
can be calculated by modifying
(3.2) according to the existence of multiple point
response functions.
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(3.49) |
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