Three-dimensional countour of the wave function in a spherical quantum dot. Click to view the animation (600 KB).




Microelectronics has reached a point where quantum effects have a major impact on the electrical characteristics of miniaturized semiconductor devices since they are reaching dimensions on the scale of the electron coherence length.At the heart of quantum mechanics stands Schrödinger's equation which describes the transport of charges by means of wave functions instead of particles. Based on the system under consideration, open- and closed-boundary Schroedinger solvers for one-, two- and three dimensional structures are being developed at the Institute for Microelectronics.














Two-dimensional plot of the wave function in a rectangular quantum dot.





Applications for quantum mechanical simulations abound in microelectronics. One of the most prominent example is the simulation of tunneling effects.  Especially conventional CMOS devices, which rely on a thin gate dielectric to achieve good control over the inversion charge in the channel, face a sometimes untolerably high gate leakage current which is caused by tunneling. Stacked dielectrics or multi-barrier tunneling devices are examples where advanced tunneling models must be used for the simulation and prediction of tunneling currents.








In the case of high degeneracy, the kinetics is partially or totally reversed.




A possibility to increase the mobility of carriers in silicon is to apply biaxial tensile or compressive strain.  In the case of [001] substrates, for example, such strain shifts the two-fold degenerate ellipsoids down. Since they contribute to the in-plane transport through the transverse effective mass, total mobility is increased.  The Monte Carlo method is used to study the influence of a general conduction band splitting on transport in strained layers grown on arbitrary-oriented relaxed silicon-germanium. Both X and L valley splitting is taken into account.  In the case of high degeneracy a pure quantum mechanical effect stemming from the Pauli exclusion principle appears: The kinetics is partially or totally reversed. This effect is taken into consideration by a proper modification of the scattering operator.







A lateral carbon nanotube - based field effect transistor.





The strong electrical field in the channel of contemporary CMOS devices leads to the quantization of energy. This reduces the surface carrier concentration and has an impact on the carrier mobility in the channel. In the long run, CMOS devices will have to be replaced by advanced structures to allow further device scaling. Carbon nanotube FETs are one of the most prominent candidates, since they allow a very high integration density and have superior electrical characteristics. Research to study carrier transport in carbon nanotubes is performed in cooperation with semiconductor industry.