Theory of Electronic, Optical and Transport Properties in Silicon Quantum Wires
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THEORY OF ELECTRONIC, OPTICAL AND TRANSPORT PROPERTIES IN SILICON QUANTUM WIRES G. D. SANDERS*, C. J. STANTON* AND Y. C. CHANG**
*Dept. of Physics, University of Florida, Gainesville, FL 32611 "**Dept. of Physics, University of Illinois, Urbana, IL 61801
INTRODUCTION Recent observation of efficient luminescence in porous silicon has stimulated interest in the electronic and optical properties of Si quantum wires [1,2,3]. If silicon becomes a material suitable for optical applications, techniques for fabricating silicon wires reliably and uniformly will be needed. Once this is achieved, there will be interest not only in optical properties of silicon wires but also transport properties. For instance, to determine the properties of a hypothetical Si LED, one needs to know about both transport and optical properties. In this paper, we present theoretical studies of electronic, optical and transport properties of silicon quantum wires ranging in size from 7.7A to 31A. The electronic and optical properties are treated in an empirical tight-binding approach with excitonic effects included in the effective mass approximation. Carrier transport is treated in a Boltzmann transport framework with nonpolar deformation potential acoustic phonon scattering being the dominant scattering mechanism.
THEORY Electronic Properties We consider an infinitely long silicon wire oriented along (001) with a square cross-section whose faces, of width L, are parallel to the four equivalent (110) planes. Silicon dangling bonds at the surface are passivated by hydrogen (with a single s orbital). We use a secondnearest-neighbor empirical tight-binding model which includes seven atomic orbitals per site with symmetries s, x, y, z, di, d2 , and s*, where d, = (X 2 - y2 )/ v'2 and d2 = (3z 2 - r2)/V6. The s* orbital is added to improve the description of higher conduction bands [2]. The Hamiltonian and optical matrix elements between silicon atomic orbitals on neighboring sites are obtained by adjusting the tight-binding results to agree with pseudopotential calculations for bulk Si. The matrix elements for the surface hydrogen sites are scaled according to Harrison's l1d 2 rule [2]. The quantum wire band structure, En(k), and wavefunctions are found by diagonalizing a tight-binding Hamiltonian. The k-dependent optical matrix elements are momentum matrix elements between these wavefunctions and are related to optical matrix elements between atoms on neighboring sites. Optical Properties The absorption coefficient due to band-to-band transitions in a quantum wire is obtained from the tight-binding bands and optical matrix elements using Fermi's Golden Rule [2]. Exciton effects are included in a two-band effective-mass model with parabolic bands. Since we deal with free standing wires, the confining potential for electrons and holes is the work function (taken to be infinite). The exciton wave function (for an exciton at rest) is written as a product of electron and hole wave functions describing the in-plane motion and an exciton envelope
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