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

IV.BEYOND CdSeA. Indium Arsenide Nanocrystals and thePidgeon–Brown ModelThe success in both the synthesis and the spectroscopy of CdSe has encouragedresearchers to investigate other semiconductor systems. Although thesynthetic methods used for CdSe can easily be extended to many of the II–VIsemiconductors [7,58], much effort has been focused upon developing newclasses of semiconductor nanocrystals, particularly those that may have hightechnological impact (e.g., silicon [91,92]). Among these, the system that isperhaps best to discuss here is InAs. As a zinc blende, direct-bandgap, III–Vsemiconductor, InAs is in many ways very similar to CdSe. Most importantly,InAs nanocrystals can be synthesized through a well-controlled organometallicroute that can produce a series of different-sized colloidal samples [12].These samples exhibit strong band-edge luminescence such that they are wellsuited to spectroscopic studies. On the other hand, InAs also has severalimportant differences from CdSe. In particular, it has a narrow bandgap(0.41 eV). This implies that the coupling between the conduction and valencebands, which was largely ignored in our theoretical treatment of CdSe, will beimportant.To explore this issue, Banin et al. have performed detailed spectroscopicstudies of high-quality Indium Arsenide nanocrystals [13,93,94]. Figure 6 inChapter 8 shows size-dependent PLE data obtained from these samples. As inCdSe, the positions of all of the optical transitions can be extracted andplotted. The result is shown in Fig. 7 in Chapter 8. However, unlike CdSe,InAs nanocrystals are not well described by a six-band Luttinger Hamiltonian.Rather, the data require an eight-band Kane treatment (also called thePidgeon–Brown model [37]), which explicitly includes coupling between theconduction and valence band [13,41]. With the eight-band model, the sizedependence of the electronic structure can be well described, as shown in Fig.7 of Chapter 8.Intuitively, one expects mixing between the conduction and valenceband to become significant as the bandgap decreases. Quantitatively, thismixing has been shown to be related tosffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDE e;hE s g þ DE ð25Þe;hwhere DE e,h is the confinement energy of the electron or the hole [41]. Asexpected, the value of Eq. (25) becomes significant as DE approaches thewidth of the bandgap (i.e., in narrow-bandgap materials). However, unexpectedly,this equation also predicts that mixing can be significant in wide-gapCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.