Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

although this term is not rigorously correct because of electron–hole interactions),photogenerated electrons and holes (usually in the form of excitons)are created with excess energy above the lowest exciton energy; these energeticcarriers are termed ‘‘hot carriers’’ The fate of this excess energy can followseveral paths: (1) It can be dissipated as heat through electron–phononinteractions or Auger processes as the carriers relax to their lowest state; (2)a second electron–hole pair can be created by the process of impact ionizationif the excess energy is at least twice the QD bandgap; (3) the electrons andholes can separate and the excess energy can be converted to increasedelectrical free energy via a photovoltaic effect or stored as additional chemicalfree energy by driving more endoergic electrochemical reactions at the surface[11]. The efficiency of photon conversion devices, such as photovoltaic andphotoelectrochemical cells, can be greatly increased if path 2 or 3 can dominateover path 1. Path 1 is generally a fast process in bulk semiconductorsthat occurs in a few picoseconds or less if the photogenerated carrier densityis less than about 5 10 17 cm 3 [77–79]. The hot electron relaxation, orcooling time can be increased by two orders of magnitude in semiconductorsquantum wells when the photogenerated carrier density is increased aboveabout 5 10 18 cm 3 by a process termed ‘‘hot phonon bottleneck’’ [77,79,80].QDs are intriguing because it is believed that slow cooling of energeticelectrons can occur in QDs at low photogenerated carrier densities [81–87],specifically at light intensities corresponding to the solar insolation on Earth.The first prediction of slowed cooling at low light intensities in quantizedstructures was made by Boudreaux et al. [81]. They anticipated thatcooling of carriers would require multiphonon processes when the quantizedlevels are separated in energy by more than phonon energies. They analyzedthe expected slowed cooling time for hot holes at the surface of highly dopedn-type TiO 2 semiconductors, where quantized energy levels arise because ofthe narrow space charge layer (i.e., depletion layer) produced by the highdoping level. The carrier confinement is this case is produced by the bandbending at the surface; for a doping level of 1 10 19 cm 3 the potential wellcan be approximated as a triangular well extending 200 A˚ from the semiconductorbulk to the surface and with a depth of 1 eV at the surface barrier. Themultiphonon relaxation time was estimated froms c x 1 exp DE ð2ÞkTwhere H c is the hot carrier cooling time, N is the phonon frequency, and DE isthe energy separation between quantized levels. For strongly quantizedelectron levels, with DE > 0.2 eV, H c could be >100 ps according to Eq. (2).However, carriers in the space-charge layer at the surface of a heavilydoped semiconductor are only confined in one dimension, as in a quantumCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.