Density of States and Group Velocity Calculations for SiO2
Ab initio calculations of the electron group velocity for SiO2 are worked out. The conduction bands are calculated by means of two different techniques: Hartree-Fock (HF) and Density-Functional Theory (DFT). Eight energy bands have been used to calculate
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Density of States and Group Velocity Calculations for Si0 2 E. Gnani, S. Reggiani, and M. Rudan Dipartimento di Elettronica, Universita di Bologna, viale Risorgimento 2, 40136 Bologna, Italy [email protected] Abstract
Ab initio calculations of the electron group velocity for Si0 2 are worked out. The conduction bands are calculated by means of two different techniques: Hartree-Fock (HF) and Density-Functional Theory (OFT). Eight energy bands have been used to calculate the density of states and group velocity for the energies of interest. Two different crystal structures of Si0 2 , built-up by the same fundamental unit, namely, the Si0 4 tetrahedron, are investigated: they are the a-quartz, and the /3-cristobalite.
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Introduction
The interest in silicon dioxide as material for technological applications in electronic devices is growing steadily. In modern semiconductor technology, Si02 films grown on silicon have been employed in the construction of integrated circuits in various devices. Thus, especially in recent years, experimental and theoretical investigations focused on microscopic properties of this material related with reliability problems. Electron transport in silicon dioxide has already been tackled in the frame of the spherical-harmonics expansion (SHE) method applied to the solution of the Boltzmann transport equation (BTE), using the parabolic-band approximation [6]. In particular, the first conduction band was assumed to be a spherical and parabolic function terminating at 6 eV, this limiting the validity of the analysis when high electric fields are considered. A more accurate description of the bands at higher energies has already been achieved by tackling the calculation of the full-band structure of Si02. In [5] the solution of the Schroclinger equation has been carried out by means of two different ab initio techniques (Hartree-Fock (HF) and Density-Functional Theory (DFT)). In this paper, the same techniques are exploited to determine the coefficients of the SHE method, namely the density of states (DOS) and group velocity (Gv) as a function of energy, along the same line already worked out for silicon [7]. As in the SHE scheme the band structure of the material appears through these electronic properties, the calculations reported in this work constitute the basis for an accurate description of the transport properties for Si02 at higher energies. In the authors' knowledge, such calculations have not been carried out before.
D. Tsoukalas et al. (eds.), Simulation of Semiconductor Processes and Devices 2001 © Springer-Verlag Wien 2001
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Theory and Implementation
In VLSI-CMOS technology, the gate oxide is grown on a silicon crystal in its amorphous phase. Early investigations [1] showed that the amorphous Si0 2 is constituted by Si0 4 tetrahedra with bond-length and bond-angle distortions; as a consequence, the calculation of the transport properties of the crystalline phases of Si02 can be exploited to understand the main aspects of the amorphous phase as well. The analysed sys
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