Modeling Nano-Structure Devices
Fundamental problems of and approaches to modeling nanostructure devices are reviewed. First the requirements for modeling charge transport in classical and nanostructure devices are compared and contrasted. Then the quantum mechanical concepts of transmi
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Edited by S. Selberherr, H. Stippel, E. Strasser - September 1993
Modeling NanD-Structure Devices K. Hess tt and L. F. Register t tBeckman Institute for Advanced Science and Technology and Coordinated Science Laboratory, University of Illinois at Urbana-Champaigne Urbana, IL 61801, USA tDepartment of Electrical and Computer Engineering, University of Illinois at Urbana-Champaigne Urbana, IL 61801, USA
Abstract Fundamental problems of and approaches to modeling nanostructure devices are reviewed. First the requirements for modeling charge transport in classical and nanostructure devices are compared and contrasted. Then the quantum mechanical concepts of transmission probabilities and eigen energies in nanostructures are related back to the classical concepts of resistance and capacitance, respectively. Next a small illustrative sampling of numerical approaches to calculation of the quantum mechanical properties of nanostructures is presented. Finally examples are given of how such theoretical concepts and numerical methods can be applied to modeling existing and future devices.
1. Introduction In conventional semiconductor devices, most quantum transport effects can be treated indirectly. The effects of the rapidly varying crystal potential on electron transport can be modeled via the concepts of effective masses, energy gaps, and the positively charged quasi-particle holes. On the macroscopic level, charge transport can then be modeled using the concepts of classical mechanics, aided sometimes by the Pauli exclusion principle and the Born approximation for scattering problems. Only the possibility of electron-hole recombination across the energy gap and the corresponding non-conservation of particle numbers bears witness to the deeper quantum mechanical character of the problem. Of course, size quantization effects do appear in some conventional devices. The conduction channel of a MOSFET extends only a few nanometers from the Si-Si0 2 interface into the silicon and, thus, the charge carrier motion perpendicular to the interface is quantized. However, charge transport over the oxide barrier is usually negligible, and the carriers can be treated as quasi two-dimensional particles in the plane of the conduction channel and still be modeled semi-classically. Hgw far the dimensions of the conduction channel can be shrunk in this latter plane before quantization leads to prominent effects is currently the subject of speculation. In addition to quantization effects, the current mainstays of semiconductor device technology, electron and hole gases and the formation of homojunctions by doping, aho present barriers to shrillka.ge 11.3 the desired step from the va.cuum to the dense
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K. Hess et al.: Modeling Nano-Structure Devices
solid has not been achieved entirely after the invention of the point contact transistor by Bardeen and Brattain in 1947 [1]. On the nano-scale, doping is inhomogeneous and majority carriers and particularly minority carriers form dilute gases in conventional devices [2]. If shrinkage i
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