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

corresponding to the s-like wave function (Fig. 20c) is localized to the centralregion of the core–shell nanocrystal, whereas the images corresponding to thep-like wave functions extend out to the shell (Figs. 20d–20e), consistent withthe above-discussed model. This can also be seen in the cross sectionspresented in frame (f 1 ) taken along a common line through the center of eachcurrent image and most clearly in (f 2 ), which shows the current normalized toits maximum value along the same cuts. Image 20e, taken at a voltage abovethe p multiplet, manifests a nearly spherical geometry similar to that of image20c for the s state but has a larger spatial extent. Image 20d, taken with V Bnear the middle of the p multiplet, is also extended but has a truncated topwith a small dent in its central region.An illustrative model aids the interpretation of the current images,assuming a spherical QD shape, with a radial core–shell potential taken asshown in the inset of Fig. 20a [90]. The energy calculated for the s state is lowerthan the barrier height at the core–shell interface and has about the samevalues for core and core–shell QDs. In contrast, the energy of the p state isabove the core–shell barrier and it red shifts with shell growth, in qualitativeagreement with our spectroscopic result discussed in Section V. Isoprobabilitysurfaces for the different wave functions are presented in Figs. 20g–20i,with Fig. 20g showing the s state, Fig. 20h showing the in-plane component ofthe p wave functions, p 2 x þ p 2 y , that has a toruslike shape, and Fig. 20i depictingthe two lobes of the perpendicular component, p 2 z . The square of theradial parts of the s and p wave functions are presented in Fig. 20j. Thecalculated probability density for the s state is spherical in shape and mostlylocalized in the core, consistent with the experimental image taken at a biaswhere only this level is probed (Fig. 20c). The p components extend much furtherto the shell, as observed in the experimental images taken at higher bias.Moreover, the different shapes observed in the current images can be assignedto different combinations of the probability density of the p components.A filled torus shape, similar to the current image (Fig. 20d) taken at themiddle of the p multiplet, can be obtained by a combination with larger weightof the in-plane p component p 2 x þ p2 y , parallel to the gold substrate, and asmaller contribution of the perpendicular p z component. The nonequalweights reflect preferential tunneling through the in-plane components. Thismay result from a perturbation due to the specific geometry of the STMexperiment leading to a small degeneracy lifting. A spherical shape for theisoprobability surfaces results from summing all of the p components withequal weights, consistent with the current image measured at a bias above thep manifold (Fig. 20e). This example of wave-function imaging combined withthe tunneling and optical spectra allowed us to visualize the atomiclikecharacter of nanocrystal quantum dots.Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.