With the continuing
reduction of the minimum feature size of semiconductor devices, the
models used for simulations of these devices need to be updated and
implemented. These updates include quantum corrections as well as
models
considering moments of higher order. Quantum corrections become
increasingly important as the dimensions of the device approach the
mean free path length of the electrons within the semiconductor,
leading to quantization of the electrons' states. This has a profound
influence on the density of states and on thereby the distribution of
charge within the device. This is especially true for the lateral
direction in the channel region but will also become important in
the transversal direction as gate lengths are further reduced.
Boltzmann's
transport equation, the starting point for the derivation of the
drift diffusion transport model, is no longer capable of giving
satisfactory results under these conditions. Wigner's equation
represents an attempt to cope with the effects encountered in these
scaled devices. This method proposes to yield relatively simple
macroscopic models capable of describing the electron transport within
nanometer scale devices.
Beginning at about three hundred nanometers drift diffusion models
predict less current than is actually encountered in devices. Energy
transport and hydro-dynamic models continue to provide useful
results down to a size of about one hundred nanometers, but then the
calculated current starts to deviate from measured data. A model using
six moments promises to remain accurate down to at least thirty
nanometers.
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