7 - Si Quantum Dots

Abstract

This chapter presents the calculation of the energy state for a silicon sphere with different effective masses. For a spherical silicon particle, the wave equation with principal masses of mt and ml, satisfying the boundary condition of a sphere, does not have simple solutions, so variational approach is used. The product wave function is consided to calculate the expectation value of the energy. The approach discussed in the chapter is entirely similar to the calculation of the ground state energy for a shallow impurity state in a superlattice. Resonant tunneling via nanocrystalline silicon, nc-Si, embedded in an amorphous silicon dioxide, a-SiO2, matrix has been exploited, using a thin layer of deposited a-Si at low temperature, followed by crystallization after annealing. These nanoscale silicon QDs are then embedded in an oxide matrix after subsequent annealing in an oxygen-rich environment. It has been pointed out that the defect density of the c-Si/a-SiO2 system under metal oxide semiconductor (MOS) technology is really low enough to apply to quantum well structures. There is an important point dealing with tunneling measurements that needs to be emphasized. In normal resonant tunneling via quantum wells, the contacts are n+ -doped leading to the negative differential conductance (NDC) whenever the applied voltage is such that the quantum state of the well moves below the source of electrons, from the contact into the forbidden gap. However, with a metal contact, the Fermi sphere is very large compared to all these quantum states involved. When the applied voltage is such that the state involved moves below the conduction band edge, there is tunneling from the metal contact. This leads to a conductance peak, but no current peak. Therefore, an NDC should never appear.