epdf.pub_nanotechnology-and-nanoelectronics-materials-devic

14 2 Quantum Mechanical Aspects
2
q
(2.2)
2 h c
0
can be measured with great accuracy, as developed in [13] ( 0 is the dielectric constant
of vacuum, c the velocity of light).
2.5.2 Tunneling Currents
Other systems manufactured are sandwich structures (e.g., GaAlAs–GaAs–GaAl
As). They are based on the fact that GaAlAs for instance, has a band gap of 2.0 eV
while GaAs has a band gap of only 1.4 eV. By applying a voltage, the band structure
is bent as schematically presented in Fig. 2.12. In a conventional consideration, no
current is allowed to flow between the contacts (x < 0, x > c) irrespective of an applied
voltage because the barriers (0 < x < a and b < x < c) are to prevent this. However,
by assuming considerably small values of magnitudes a, b, and c, a tunneling
current can flow when the external voltage places the energy levels outside and inside
(here E'') on the same value (in resonance). It should be noted that after exceeding
this condition, the current sinks again (negative differential conductivity).
This sandwich structure is the basis for a good number of devices such as lasers,
resonant tunneling devices or single-electron transistors. They will be treated
in the section on electrical nanodevices.
2.6 Evaluation and Future Prospects
The state of the available molecule and cluster simulation programs can be described
as follows: the construction of a molecule occurs under strict ab initio
rules, i.e., no free parameters will be given which must later be fitted to experiment;
instead, the Schrödinger equation is derived and solved for the determination
of eigenenergies and eigenfunctions in a strictly deterministic way. The
maximum manageable molecular size has some 100 constituent atoms. The limitation
is essentially set by the calculation time and memory capacity (in order to
prevent difficulties, semi-empirical approximations are also used. This is done at
the expense of the accuracy). Results of these calculations are
Molecular geometry (atomic distances, angles) in equilibrium,
Electronic structure (energy levels, optical transitions),
Binding energy, and
Paramagnetism.
The deficits of this treatment are the prediction of numerous desired physical
properties: temperature dependency of the above-named quantities, dielectric behavior,
absorption, transmission and reflection in non-optical frequency ranges,
electrical conductivity, thermal properties. However, there are attempts to acquire
these properties with the help of molecular mechanics and dynamics [14–16].