Interband Transitions in Si Quantum Wires grown in {100} plane
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Interband Transitions in Si Quantum Wires grown in {100} plane X. Zianni and A.G. Nassiopoulou IMEL, NCSR “Demokritos”, 153 10 Aghia Paraskevi, Attiki, GREECE. ABSTRACT We present calculations on the spontaneous emission rates of Si rectangular quantum wires grown in the {100} plane. The electron and holes states are calculated within an effective mass approximation model. For holes, the minimum of the one-dimensional sub-bands is at the point. For electrons, the six anisotropic valleys at the conduction band minimum of bulk Si are not equivalent in the quantum wires and so, the minima of the energy sub-bands depend on the growth direction of the wire. For some wire directions in the {100} plane, the minimum of the ground electron sub-band is at the -point. The directional dependence of the electron states is reflected on the spontaneous emission of the quantum wires. Light emission from Si quantum wires of diameters of a few nanometers can have direct transition character in the visible range. Phonon assisted transitions are then also present, but their intensity is three orders of magnitude smaller than the intensity of direct transitions. In Si quantum wires with indirect band gap the intensity and the peak position of the phonon assisted transitions exhibit dependence on the wires direction.
INTRODUCTION The properties of low dimensional semiconductors show dramatic changes with respect to their bulk counterpart. The progress in the fabrication of the nanoelectronic devices based on this kind of structures has stimulated intensive research in the electrical, optical and other properties of silicon nanostructures. Zero-, one- and two- dimensional structures were fabricated and their properties were widely studied. Silicon quantum wires were fabricated by using lithography and highly anisotropic silicon etching [1] and light emission was observed from those wires at room temperature in the visible range both under optical and under electrical excitation due to quantum confinement [2]. Theoretical calculations predict discrete quantum confined states in the conduction and valence band and a size dependent band gap opening responsible for light emission in the visible range [3-5]. Here, we discuss the dependence of the inter-band transitions in Si quantum wires grown in {100} plane on the wire growth direction.
THEORETICAL MODEL We consider an infinitely long and homogeneous quantum wire of rectangular cross section. It is useful to define the wire direction in a system of coordinates (x,y,z), that is defined as follows: the z axis is along the [001] direction and the x and y axes are rotated anticlockwise by an angle relative to the [100] and [010] directions respectively. The quantum wire infinite length is along the y-axis. Electron and hole eigenstates are obtained by solving Schröndinger equation. In Si quantum wires, the six anisotropic valleys are not equivalent and in order to find F14.20.1
the electron states, an effective mass equation must be solved for each pair of valleys. Horigushi et al. [3] have
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