A simple model for the ionization potential, electron affinity, and aqueous redox potentials of small semiconductor crystallites

Abstract

Large semiconductor crystals have intrinsic electronic properties dependent upon the bulk band structure. As the crystal becomes small, a new regime is entered in which the electronic properties (excited states, ionization potential, electron affinity) should be strongly dependent upon the electron and hole in a confined space. We address the possibility of a shift in the photochemical redox potential of one carrier, as a function of crystallite size. As a semiquantitative guide, one might expect a shift on the order of h2/8em*R2 due to the kinetic energy of localization in the small crystallite. We model the elementary quantum mechanics of a charged crystallite using (a) the effective mass approximation, (b) an electrostatic potential for dielectric polarization, and (c) penetration of the carrier outside the crystallite in a cases of small effective mass. Shifts of several tenths of an eV appear possible in crystallites of diameter 50 Å. The carrier charge density reside near the crystallite surface if the effective mass is very small.

Synthesis, Characterization, and Size Control of Zinc Sulfide Nanoparticles Capped by Poly(ethylene glycol)

“…The optical absorption bands E1 and E2 were shifted to higher energy and the exciton band was blue shifted from the bulk value. This interpretation is agreement with that from theoretical investigations and previous work conducted by Chen et al, [21], Brus [22], and Rossetti et al [23]. Similar behavior was reported by Lippens et al [24], whereby the valence and conduction bands move down and up depending on the relative values of the effective mass of an electron (  e m ) and hole (  h m ).…”

XAFS study of starch-stabilized magnetite nanoparticles and surface speciation of arsenate

“…In addition to size manipulation, particle stabilization can give rise to new types of 'surface sites' and/or sorption sites of altered proportions of edge/corner/step locations, leading to altered surface complexation reactivity and varied crystal chemistry (Zhang et al, 2003;Gilbert et al, 2004;Waychunas et al, 2005). The shifting of molecular orbital/band gap energy levels due to quantum confinement effects (Brus, 1983) can also change the redox characteristics of surface metals of the nanoparticles (Boily et al, 2001).…”

Photocatalytic Activity of TiO2-containing Al-Mesoporous Silica Thin Films

“…This fact shows that the TiO 2 thin films on the surface of Al-MSF are assumed to be highly and homogeneously dispersed and minimized up to nanoorder thickness. This hypsochromic shift of the end absorption of the band gap of the semiconductors are well-known as "quantum size effect", which has sometimes observed in cases of the TiO 2 supported on zeolites (15)(16)(17)(18). Moreover, TiO 2 modification of Al-MSF was confirmed by the stretching vibrations of Ti-O observed at 1087 cm -1 and Ti = O at 975 cm -1 , as shown in Fig.…”