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

To explain these results, the following model for the UCPL that invokessurface states was proposed [51]. The model is based on Fu and Zunger’s [50]calculated energy level structure of InP QDs as a function of QD size,including surface states produced by In and P dangling bonds; their resultsare reproduced in Fig. 12a. At QDs sizes above 57 A˚ , the In dangling bond(In-DB) energy level is coincident with the QD conduction-band minimum(CBM); however, below 57 A˚ , the energy separation between the CBM andthe In-DB increases with decreasing size as the conduction-band energymoves up and the In-DP energy remains nearly constant. On the other hand,as seen in Fig. 12a, the P-DB energy level is always above the valence-bandmaximum (VBM) at all QD sizes (0.3 eV for bulk InP), and this separationincreases as the VBM moves down with decreasing QD size.All of the UCPL results can be explained within the context of theenergy levels calculated by Fu and Zunger [50] and the model is shown in Fig.12b. For upconversion of photon energies above the red-shifted trap emissionenergies, the first step in the process is photoexcitation from the P-DB state tothe conduction band; if the QD size is significantly less than 57 A˚ , the electronin the conduction band then relaxes to the In-DB state, which lies below theconduction band. The second step is excitation of the photogenerated hole inthe P-DB state to the valence band, followed by radiative recombination ofthe electrons and holes across the bandgap. For upconversion of the trapemission, the first step is photoexcitation from the P-DB state to the In-DBstate, followed by excitation of the P-DB hole to the valence band andradiative recombination from the In-DB state to the VBM.This model also predicts that as the QD size gets smaller, the UCPLdecreases and goes to zero at the QD size (15 A˚ ) where the quantity (P-DBVBM) equals the quantity (CBM In-DB) (i.e., the relaxation energy ofelectrons from the conduction band to the In-DB cancels out the upconversionenergy of the holes from the P-DB to the VBM). The experimental resultsin Ref. 51 are consistent with this prediction. As seen in Fig. 12a, the differencebetween the theoretically calculated P-DB energy and the CBM In-DBenergy as a function of QD size follows the equivalent experimental value ofthe UCPL shift (DE UC ) added to the VBM energy; also, DE UC goes to zero at15 A˚ , as predicted. However, although the experimental results fit the In-DBand P-DB model of Fu and Zunger [50] very well, there is presently noindependent experimental identification of the actual chemical nature of thesurface states in the InP QD samples.In the UCPL model, the energy of upconversion is produced byexcitation of the In-DP hole to the valence band; this process could be driveneither by phonon absorption or by absorption of a second photon. The formerprocess is favored for several reasons. (1) The upconversion shows a strongdecrease in intensity with decreasing temperature (while the normal Stokes PLintensity increased with decreasing temperature); a sequential two-photonCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.