Semiconductor devices continue to press into the nanoscale regime, and new applications have been proposed for which a single dopant atom acts as the functional part of the device 1-3 . Moreover, because shallow donors and acceptors are analogous to hydrogen atoms, experiments on small numbers of dopants have the potential to be a testing ground for fundamental questions of atomic and molecular physics 4,5 . Although dopant properties are well understood with respect to the bulk, the study of configurations of dopants in small numbers is an emerging field 6,7 . Here we present local capacitance measurements of electrons entering silicon donors in a gallium arsenide heterostructure. To the best of our knowledge, this study is the first example of single-electron capacitance spectroscopy carried out directly with a scanning probe tip 8 . The precise position with respect to tip voltage of the observed single-electron peaks varies with the location of the probe, reflecting a random distribution of silicon within the donor plane. In addition, three broad capacitance peaks are observed independent of the probe location, indicating clusters of electrons entering the system at approximately the same voltages. These broad peaks are consistent with the addition energy spectrum of donor molecules, effectively formed by nearest-neighbour pairs of silicon donors.Electron tunnelling spectroscopy through isolated dopants has been observed in transport studies 9,10 . In addition, Geim and coworkers identified resonances due to two closely spaced donors, effectively forming donor molecules 11 . Rather than measuring transport current, our scanning-probe method is essentially a capacitance technique 8,12 . In contrast to the work of Geim et al., the measurements show discernible peaks attributed to successive electrons entering the molecules.Our method is an extension of scanning charge accumulation imaging 12 . Figure 1a shows the experiment schematically. The key component is a metallic tip with an apex of radius ∼ 50 nm, connected directly to a charge sensor, which achieves a sensitivity of 0.01e/ √ H z (ref. 13). For the capacitance spectroscopy measurements reported here, the tip's position is fixed (that is, not scanned) at a distance of ∼1 nm from the sample surface. We then monitor the tip's a.c. charge q tip in response to an a.c. excitation voltage V exc applied to an underlying electrode, as a function of d.c. bias voltage V tip . As detailed in the Methods section, if the quantum system below the tip can accommodate additional charge, the excitation voltage causes it to resonate between the system and the underlying electrode-giving rise to an enhanced capacitance,The first observations of donor-layer capacitance peaks acquired with our method probed a gallium arsenide heterostructure sample grown by molecular beam epitaxy, for which the donor layer was bulk-doped with Si at a density of 10 24 m −3 . To achieve better characterized results that would be more conducive to analysis, we used a GaAs [001] heterostructure...