Advanced Physical Models for Silicon Device Simulation by Andreas Schenk

By Andreas Schenk

Device simulation has major reasons: to appreciate and depict the actual approaches within the inside of a tool, and to make trustworthy predictions of the habit of an expected new gadget new release. in the direction of those pursuits the standard of the actual versions is decisive. The introductory bankruptcy of this publication incorporates a severe evaluate on types for silicon gadget simulators, which depend on moments of the Boltzmann equation. almost about basic experimental and theoretical paintings an intensive choice of popular versions is mentioned by way of actual accuracy and alertness effects. This assessment exhibits that the standard and potency of the phys­ ical versions, that have been constructed for the aim of numerical simulation during the last 3 a long time, is enough for lots of purposes. however, the elemental realizing of the microscopic methods, in addition to the individuality and accuracy of the versions are nonetheless unsatisfactory. for this reason, the next chapters of the booklet take care of the derivation of physics-based versions from a microscopic point, additionally utilizing new methods of "taylored quantum-mechanics". each one version is in comparison with experimental information and utilized to a few simulation examination­ ples. the issues while ranging from "first ideas" and making the types compatible for a tool simulator can also be confirmed. we are going to exhibit that calls for for fast computation and numerical robustness require a compromise among actual soundness and analytical simplicity, and that the possible accuracy is restricted by way of the complexity of the problems.

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This requires that the electron energy must be larger than the average of the smoothed potential. 2 Review of Physical Models for Drift-Diffusion Equations 19 states deep in the tails, but gains accuracy with increasing energy. Kane averaged the electrostatic energy over a fixed sphere, taking the number of impurity atoms in that sphere as random. Weighting the local density of band states, in which the random potential was included with the corresponding probability distribution, led to a statistical damping of the ideal (square root) density of states and consequently to the occurrence of tail states.

7 shows that the Matthiessen rule overestimates the mobility with a maximum error of about 40%. At room temperature the failure is less than 5% up to a density of 10 17 cm- 3 . This may illustrate why the Matthiessen rule is so successful. SURFACE SCATIERING (EXPERIMENTAL AND THEORETICAL FINDINGS) Especially in MOSFETs the motion of the carriers near the interface is strongly influenced by surface scattering processes. These comprise scattering from charged interface states, fixed oxide charges, bulk impurities, surface and bulk phonons, and from surface roughness.

The first relation applies to heavy doping conditions, where strong screening weakens the Coulomb potential sufficiently, so that the screening length is much smaller than the Bohr radius. The second condition is a demand for sufficient kinetic energy, which cannot be fulfilled if the temperature is too low, or if the carriers are slowed down too much by strong scattering. 29]. It appears that at low carrier energies the Born approximation greatly overestimates the cross section. At high energies the results of the two methods converge.

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