Semiconductor quantum dots, due to their small size, mark the transition between molecular and solid-state regimes, and are often described as`arti®cial atoms' (refs 1±3). This analogy originates from the early work on quantum con®nement effects in semiconductor nanocrystals, where the electronic wavefunctions are predicted 4 to exhibit atomic-like symmetries, for example`s' and`p'. Spectroscopic studies of quantum dots have demonstrated discrete energy level structures and narrow transition linewidths 5±9 , but the symmetry of the discrete states could be inferred only indirectly. Here we use cryogenic scanning tunnelling spectroscopy to identify directly atomic-like electronic states with s and p character in a series of indium arsenide nanocrystals. These states are manifest in tunnelling current±voltage measurements as two-and six-fold single-electron-charging multiplets respectively, and they follow an atom-like Aufbau principle of sequential energy level occupation 10 .InAs nanocrystals for this study were prepared using a solutionphase pyrolytic reaction of organometallic precursors. These nanocrystals are nearly spherical in shape, with size controlled between 10 and 40 A Ê in radius 11 . The nanocrystal surface is passivated by organic ligands which also provide chemical accessibility for quantum dot (QD) manipulation: for example, to prepare``nanocrystal molecules'' 12,13 , nanocrystal-based light-emitting diodes 14 , and to fabricate single-electron tunnelling devices 15 . For the tunnelling spectroscopy studies we link the nanocrystals to a gold ®lm via hexane dithiol molecules 16 . Figure 1a (left inset) shows a scanning tunnelling microscope (STM) topographic image of an isolated InAs QD, 32 A Ê in radius. Also shown in Fig. 1a is a tunnelling current±voltage (I±V) curve that was acquired after positioning the STM tip above the QD and disabling the scanning and feedback controls, realizing a doublebarrier tunnel junction (DBTJ) con®guration 17±19 (Fig. 1a, right inset). A region of suppressed tunnelling current is observed around zero bias, followed by a series of steps at both negative and positive bias. In Fig. 1b we show the tunnelling conductance spectrum (that is, dI/dV versus V), which is proportional to the tunnelling density of states (DOS) 20 . A series of discrete single-electron tunnelling peaks is clearly observed, where the separations are determined by both single-electron charging energy (addition spectrum) and the discrete level spacings (excitation spectrum) of the QD. The I±V characteristics were acquired with the tip retracted from the QD to a distance where the bias voltage is dropped largely across the tip±QD junction. Under these conditions, conduction (valence) band states appear at positive (negative) sample bias, and the excitation peak separations are equal to the real QD level spacings 19 .On the positive-bias side of Fig. 1, two closely spaced peaks are observed immediately after current onset, followed by a larger spacing and a group of six nearly equidistant peaks. We ...