Strong confinement of charges in few-electron systems such as in atoms, molecules, and quantum dots leads to a spectrum of discrete energy levels often shared by several degenerate states. Because the electronic structure is key to understanding their chemical properties, methods that probe these energy levels in situ are important. We show how electrostatic force detection using atomic force microscopy reveals the electronic structure of individual and coupled self-assembled quantum dots. An electron addition spectrum results from a change in cantilever resonance frequency and dissipation when an electron tunnels on/off a dot. The spectra show clear level degeneracies in isolated quantum dots, supported by the quantitative measurement of predicted temperature-dependent shifts of Coulomb blockade peaks. Scanning the surface shows that several quantum dots may reside on what topographically appears to be just one. Relative coupling strengths can be estimated from these images of grouped coupled dots.nanoelectronics | single-electron charging | shell structure | electrostatic force microscopy T he ability to confine single charges at discrete energy levels makes semiconductor quantum dots (QDs) promising candidates as a platform for quantum computation (1, 2) and singlephoton sources (3). Tremendous progress has been made not only in understanding the properties of single electrons in QDs but also in controlling their quantum states, which is an essential prerequisite for quantum computation (4). Single-electron transport measurements have been the main experimental technique for investigating electron tunneling into QDs (5). Charge sensing techniques using built-in charge sensors, such as quantum point contacts (6), complement transport measurements because lower electron tunneling rates can be monitored with even real-time detection being possible (7). It is instrumentally challenging to study self-assembled QDs via conventional transport and charge sensing methods because of the difficulty in attaching electrodes. Although progress is being made (8-12), these techniques have very small yield and therefore make it difficult to assess variation in QD electronic properties. Compared to typical QDs studied via transport measurements, in particular lithographically defined QDs, self-assembled QDs can be fabricated to have smaller sizes, stronger confinement potentials, and a more scalable fabrication process, all of which make them attractive for practical applications.In this paper, we focus on an alternative technique for studying QDs that is better suited for self-assembled QDs: charge sensing by atomic force microscopy (AFM). Charge sensing by AFM is a convenient method to study the electronic structure of QDs because nanoelectrodes are not required and large numbers of QDs can be investigated in one experiment. Termed single-electron electrostatic force microscopy (e-EFM), this technique relies on the high force sensitivity of AFM to detect the electrostatic force resulting from single electrons tunneling into ...

We present theoretical and experimental results on the mechanical damping of an atomic force microscope cantilever strongly coupled to a self-assembled InAs quantum dot. When the cantilever oscillation amplitude is large, its motion dominates the charge dynamics of the dot which in turn leads to nonlinear, amplitude-dependent damping of the cantilever. We observe highly asymmetric lineshapes of Coulomb blockade peaks in the damping that reflect the degeneracy of energy levels on the dot, in excellent agreement with our strong coupling theory. Furthermore, we predict that excited state spectroscopy is possible by studying the damping versus oscillation amplitude, in analogy to varying the amplitude of an ac gate voltage.Coupling a nanomechanical object to quantum electronics provides a system that can be used to probe both the mechanics and the electronics with extreme sensitivity. It has been predicted that the electronics may be used to measure the quantum nature of the mechanical object [1], and the reverse-using the mechanics to measure the quantum nature of mesoscopic electronics-was recently demonstrated with superconducting qubits [2]. Electromechanical systems that have attracted considerable attention recently include quantum shuttles [3], and mechanics coupled to single electron transistors [4,5] or tunnel junctions [6,7]. In most systems studied both experimentally and theoretically, the interaction between the electronic and mechanical components is weak.In this paper we study strong coupling effects, both theoretically and experimentally, in an electromechanical system consisting of a quantum dot capacitively coupled to an atomic force microscope (AFM) cantilever. Electrons tunneling on and off the dot effectively damp the cantilever, and this damping exhibits Coulomb blockade peaks as a function of bias voltage similar to those well known in the dot conductance, even in the limit of weak coupling [8,9,10]. It has long been predicted that level degeneracy on the dot leads to lineshape asymmetry of Coulomb blockade peaks in the conductance [11]. Recently, we observed corresponding temperaturedependent peak shifts in the damping at weak coupling [10], but the lineshape asymmetry was far too small to be measured before now. However, by driving the cantilever to large oscillation amplitudes we enter a regime of strong coupling where its motion strongly modifies the tunneling rates on and off the dot, and leads to a dramatic enhancement of the lineshape asymmetry. This enhancement is much greater than expected from simply extrapolating the weak coupling theory; it is a non-adiabatic effect that stems from the similarity of timescales for dynamics of the cantilever and the dot. Furthermore, we predict that by measuring the damping versus bias voltage and oscillation amplitude, strong coupling provides a means to perform excited state spectroscopy on the dot. Note that very different strong coupling effects unrelated to degeneracy were recently reported for a driven carbon nanotube coupled to an embedded do...

Experiments and theoretical calculations of conservative forces measured by frequency modulation atomic force microscopy (FM-AFM) in vacuum are generally in reasonable agreement. This contrasts with dissipative forces, where experiment and theory often disagree by several orders of magnitude. These discrepancies have repeatedly been attributed to instrumental artifacts, the cause of which remains elusive. We demonstrate that the frequency response of the piezoacoustic cantilever excitation system, traditionally assumed flat, can actually lead to surprisingly large apparent damping by the coupling of the frequency shift to the drive-amplitude signal, typically referred to as the "dissipation" signal. Our theory predicts large quantitative and qualitative variability observed in dissipation spectroscopy experiments, contrast inversion at step edges and in atomic-scale dissipation imaging, as well as changes in the power-law relationship between the drive signal and bias voltage in dissipation spectroscopy. The magnitude of apparent damping can escalate by more than an order of magnitude at cryogenic temperatures. We present a simple nondestructive method for correcting this source of apparent damping, which will allow dissipation measurements to be reliably and quantitatively compared to theoretical models.

We present a new charge sensing technique for the excited-state spectroscopy of individual quantum dots, which requires no patterned electrodes. An oscillating atomic force microscope cantilever is used as a movable charge sensor as well as gate to measure the single-electron tunneling between an individual self-assembled InAs quantum dot and back electrode. A set of cantilever dissipation versus bias voltage curves measured at different cantilever oscillation amplitudes forms a diagram analogous to the Coulomb diamond usually measured with transport measurements. The excited-state levels as well as the electron addition spectrum can be obtained from the diagram. In addition, a signature which can result from inelastic tunneling by phonon emission or a peak in the density of states of the electrode is also observed, which demonstrates the versatility of the technique.

We demonstrate a method to fabricate a high-aspect ratio metal tip attached to microfabricated cantilevers with controlled angle, length, and radius, for use in electrostatic force microscopy. A metal wire, after gluing it into a guiding slot that is cut into the cantilever, is shaped into a long, thin tip using a focused ion beam. The high-aspect ratio results in considerable reduction of the capacitive force between tip body and sample when compared to a metal coated pyramidal tip.