Doping of a quantum dot and self-limiting effect in electrochemical etching

Abstract

The observation of photoluminescence (Canham, 1990) in electrochemically etched porous silicon has launched an intense research activity because this discovery has opened the door for a possible optoelectronic role for silicon, the all important material for electronics. Furthermore, the apparent increase in the fundamental optical absorption energy gap (Lehmann and Gösele, 1991) and the decrease in the Raman phonon frequency with increase of the position of the peak photoluminescence established the role of quantum confinement (Tsu et al., 1992). Fundamentally, quantum confinement pushes up the allowed energies resulting in an increase in the binding energy of shallow impurities such as the cases of quantum well (Bastard, 1981) and superlattice (Ioriatti and Tsu, 1986). Theoretical treatment of the dielectric constant in quantum confined systems (Tsu and Ioriatti, 1986) (Kahen et al., 1985) shows that a significant reduction takes place when the width of the quantum well is reduced to 2 nm and below. In a quantum dot of radius a, the reduction of the size dependent static dielectric constant ε(a) results in a significant increase of the binding energy (Tsu et al., 1993) of shallow impurities. Since electrochemical etching depends on the current, significant increase in the binding energy can cut-off extrinsic conduction leading to a self-limiting process in the electrochemical etching during the formation of the porous silicon (Tsu et al., 1993). The model used in calculating ε(a) is the modified Penn model (Penn, 1962) which replaces the continuous electron energies by the discrete energy states of a quantum dot. The calculated ε(a) agrees (Tsu and Ioriatti, unpublished) with ε(q) in the results of Walter and Cohen (1970) when q is replaced by π/a. Having obtained ε(a), we are in a position to compute the binding energy of the shallow impurity, Eb, in a quantum dot.