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(3.85) |
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(3.86) |
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(3.89) |
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(3.90) |
Setting and
yields the values of the wave function in the
whole simulation domain for an incident wave from the left side like in the
transfer-matrix method. The method is easy to implement, fast, and more robust
than the transfer-matrix method. A further advantage of this method is its
suitability for two- and three-dimensional problems. It thus represents a much
more powerful method than the transfer-matrix based methods which are limited
to one-dimensional problems only. Note that the QTBM is closely linked with
the non-equilibrium GREEN's function formalism (NEGF, see Section 2.4.3.4): The
matrix in expression (3.91) is the inverse of the retarded
GREEN's function (2.25) for an open system without
scattering. However, the values of
and
are complex, so the
matrix admits complex eigenvalues and complex solving routines are necessary.
A. Gehring: Simulation of Tunneling in Semiconductor Devices