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1.3 Entering the Quantum Regime

With decreasing feature size the physical description changes from classical physics to quantum physics. Nanoelectronics is the emerging field of building electronic devices that use quantum effects and harness the small-scale quantum properties of nature.

Nanotechnology offers the possibility of building a new generation of electronic devices in which electrons are confined quantum mechanically to provide superior device performance. Over the past two decades discrete nanoelectronic devices have been proposed and successfully demonstrated in research laboratories, such as resonant tunneling diodes (RTD), single electron transistors (SETs) and a broad class of devices comprised of quantum dots, quantum wires and molecules.

The development of novel devices at the nanometer scale with potential for large-scale integration and room temperature operation is a formidable task. Over the years, many ideas have been proposed on the basis of very qualitative reasoning or simplified physical models: typically, the demonstration of working prototypes is achieved, while the fabrication of complex logic circuits proves to be infeasible. There are often fundamental problems, such as the extreme sensitivity of device operation to the presence of defects, stray charges, and other parasitics, or the need of prohibitively tight fabrication tolerances. In other cases the switching times are inherently slow, or the physical effect is so weak that room temperature operation is prevented. Moreover, there is a gap between device physics and nanoelectronic systems integration. Moore's Law predicts that this gap will be closed around 2015.

Though the age of nanoelectronics is predicted to be still 10 years ahead the change in physics from (semi-)classical to quantum physics has an impact for TCAD much earlier. With ongoing miniaturization quantum effects sometimes come to play a dominant role in conventional devices. Currently most commercially available device simulators are based on classical drift-diffusion modeling and variants thereof. Few years from now these codes will no longer be sufficient to simulate devices which are then in industrial production. The current code base of the TCAD vendors will then have lost much in value and new truly quantum mechanical models must be implemented.

Among the ambitious objectives of the Nanotechnology Information Devices (NID) Initiative of the European Commission are the development of novel devices for an unprecedented scale of integration, and the development of tools and techniques for the fabrication of such devices. The NANOTCAD project within the NID Initiative is a coordinated experimental and theoretical effort aimed at the development and the validation of a software package for the simulation and the design of a wide spectrum of nanoscale devices. However, since technologies for nanoscale devices are still at the early research stage, as opposed to the production stage of ULSI technologies, the project is mainly oriented at device prototyping and early evaluation of the realistic potential of a device structure.

Work package 3 within the NANOTCAD project is entitled ``Quantum Monte Carlo Modeling''. Its goal is to develop models and numerical methods for quantum transport using the Monte Carlo method in far from equilibrium conditions. This work package aims at the inclusion of dissipative processes such as phonon scattering. The goal for the ``Quantum Monte Carlo Modeling'' work package is to extend some techniques of classical Monte Carlo simulation to the quantum mechanical regime. Some of its results are also described in this thesis [NKKS01], [KNS03], [KKNS03].

For the NANOTCAD project this author was set the task to implement a finite difference Wigner equation solver. The solver should be used for comparison and testing of the Monte Carlo code during prototyping. However, it turned out, that the Wigner solver did not perform well on the test cases (resonant tunneling diodes) set by the project. Searching for an alternative we (re)discovered the quantum transmitting boundary method (QTBM) and experimented with a variety of quantum mechanical formulations.

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R. Kosik: Numerical Challenges on the Road to NanoTCAD