Confinement Effectson Electronic Properties ofNano Scale Semiconductors

Abstract

The behavior of macroscopic electronic components can be easily understood using classical electric and electronic relations. Unfortunately such classical relations can no longer capable of describing nano electronic components. This is due to the fact that nano particles can not be described by classical laws, but one needs quantum laws in this case. This needs new quantum electronic model that can describe nano electronic components behavior. Using quantum uncertainty principle and statistical distribution current, one can find conductivity, conductance and resistance in terms of Plank constant, density of energy states and diffusion constant. These quantities are shown to be quantized. These relations enables writing ohms law as a sum of classical part sensitive to the conductor length beside a quantum part sensitive to chemical energy and diffusion current at diode interface. The formal definition of resistance and conductance in terms of current and volt has been used to find the quantum resistance. The energy density of states manifests it self through the statistical distribution function, while the plank constant was incorporated through the chemical potential. The statistical nature of these parameters manifests itself through the diffusion constant which is related to the current density. The same arguments were used to obtain quantum capacitance in terms of the energy density of states, for non-equilibrium systems. The Boltzman transport equation has been written in terms of a chemical potential variation instead of the statistical distribution function, which has been smeared out using simple mathematical tricks. The Boltzman equation was thus used to obtain conductance and resistance for quantum non equilibrium systems.