Page 19 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Introduction
Almost everything becomes quantized, from thermal and electrical resis-
tance to interactions such as the Hall effect.
Time scale considerations are at least as important as length scales. They
are governed by the major processes that take place within the materials.
The shortest technological time scales are found in electron-electron
scattering processes and are on the order of a few femtoseconds, fol-
lowed by the interaction process of lattice vibrations and electronic sys-
tems with a duration of between a few hundreds of femtoseconds to a
picosecond. Direct optical transitions from the conduction band to the
valence band lie in the range of a few nanoseconds to a few microsec-
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onds. For applications in the MHz (10 Hz) and GHz (10 Hz) regime the
details of the electron-electron scattering process are of minor interest
and most scattering events may be considered to be instantaneous. For
some quantum mechanical effects the temporal resolution of scattering is
crucial, for example the intra-collisional field effect.

The same considerations hold for the energy scale. Acoustic electron
scattering may be considered elastic, that is to say, it doesn’t consume
energy. This is true only if the system’s resolution lies well above the few
meV of any scattering process. At room temperature (300 K) this is a
good approximation, because the thermal energy is of the order of 25.4
meV. The level of the thermal energy implies a natural energy scale, at
which the band gap energy of silicon of about 1.1 eV is rather large. For
high energy radiation of several keV the band gap energy again is negli-
gible.

The above discussion points out the typical master property of a compos-
ite system: A system reveals a variety of behavior at different length
(time, energy, …) scales. This book therefore demands caution to be able
to account for the semiconductor as a system, and to explain its building
blocks and their interactions in the light of scale considerations.

18 Semiconductors for Micro and Nanosystem Technology