Imaging a single-electron quantum dot

Microwave-Frequency Scanning Gate Microscopy of a Si/SiGe Double Quantum Dot

Conventional transport methods provide quantitative information on spin, orbital, and valley states in quantum dots but lack spatial resolution. Scanning tunneling microscopy, on the other hand, provides exquisite spatial resolution at the expense of speed. Working to combine the spatial resolution and energy sensitivity of scanning probe microscopy with the speed of microwave measurements, we couple a metallic tip to a Si/SiGe double quantum dot (DQD) that is integrated with a charge detector. We first demonstrate that the dc-biased tip can be used to change the occupancy of the DQD. We then apply microwaves through the tip to drive photon-assisted tunneling (PAT). We infer the DQD level diagram from the frequency and detuning dependence of the tunneling resonances. These measurements allow the resolution of ∼65 μeV excited states, an energy consistent with valley splittings in Si/SiGe. This work demonstrates the feasibility of scanning gate experiments with Si/SiGe devices.

Imaging quantum dot formation in MoS2 nanostructures

Among two-dimensional materials, semiconducting ultrathin sheets of MoS₂ are promising for nanoelectronics. We show how a scanning probe microscope (SPM) can be used to image the flow of electrons in a MoS₂ Hall bar sample at 4.2 K allowing us to understand device physics at the nanoscale. The SPM tip acts as a movable gate and capacitively couples the SPM tip to the device below. By measuring the change in device conductance as the tip is raster scanned across the sample, spatial maps of the device conductance can be obtained. We present images showing the characteristic 'bullseye' pattern of Coulomb blockade conductance rings around a quantum dot formed in a narrow contact as the carrier density is depleted with a backgate. These images show that multiple dots are created by the disorder potential in MoS₂. From these SPM images, we estimate the size and position of these quantum dots using a capacitive model.

Mode Specific Backscattering in a Quantum Point Contact

We demonstrate a scanning gate grid measurement technique consisting in measuring the conductance of a quantum point contact (QPC) as a function of gate voltage at each tip position. Unlike conventional scanning gate experiments, it allows investigating QPC conductance plateaus affected by the tip at these positions. We compensate the capacitive coupling of the tip to the QPC and discover that interference fringes coexist with distorted QPC plateaus. We spatially resolve the mode structure for each plateau.

Scanning gate imaging of two coupled quantum dots in single-walled carbon nanotubes

Two coupled single wall carbon nanotube quantum dots in a multiple quantum dot system were characterized by using a low temperature scanning gate microscopy (SGM) technique, at a temperature of 170 mK. The locations of single wall carbon nanotube quantum dots were identified by taking the conductance images of a single wall carbon nanotube contacted by two metallic electrodes. The single electron transport through single wall carbon nanotube multiple quantum dots has been observed by varying either the position or voltage bias of a conductive atomic force microscopy tip. Clear hexagonal patterns were observed in the region of the conductance images where only two sets of overlapping conductance rings are visible. The values of coupling capacitance over the total capacitance of the two dots, C(m)/C(1(2)) have been extracted to be 0.21 ∼ 0.27 and 0.23 ∼ 0.28, respectively. In addition, the interdot coupling (conductance peak splitting) has also been confirmed in both conductance image measurement and current-voltage curves. The results show that a SGM technique enables spectroscopic investigation of coupled quantum dots even in the presence of unexpected multiple quantum dots.

Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by the scanning probe technique

We perform a numerical simulation of the mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps as a function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are compared with the original ones. This study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limiting case. We concentrate on large quantum dots for which strong electron-electron correlations appear. For circular dots the correlations lead to the formation of Wigner molecules that in the presence of a tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for a repulsive tip potential and overestimated for an attractive tip. In lower symmetry quantum dots Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of a tip. These charge densities are well resolved by the mapping. These single-electron islands appear in the laboratory frame provided that the classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.

Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

We evaluate the chemical potential of a one-dimensional quantum dot coupled to an atomic force microscope tip. The dot is described within the Luttinger liquid framework, and the conductance peak positions as a function of the tip location are calculated in the linear and non-linear transport regimes for an arbitrary number of particles. The differences between the chemical potential oscillations induced by the Friedel and Wigner terms are carefully analysed in the whole range of interaction strengths. It is shown that Friedel oscillations, unlike the Wigner ones, are sensitive probes for detecting excited spin states and collective spin density waves involved in the transport.

Transport inefficiency in branched-out mesoscopic networks: an analog of the Braess paradox

We present evidence for a counterintuitive behavior of semiconductor mesoscopic networks that is the analog of the Braess paradox encountered in classical networks. A numerical simulation of quantum transport in a two-branch mesoscopic network reveals that adding a third branch can paradoxically induce transport inefficiency that manifests itself in a sizable conductance drop of the network. A scanning-probe experiment using a biased tip to modulate the transmission of one branch in the network reveals the occurrence of this paradox by mapping the conductance variation as a function of the tip voltage and position.

Scanning gate imaging of quantum dots in 1D ultra-thin InAs/InP nanowires

We use a scanning gate microscope (SGM) to characterize one-dimensional ultra-thin (diameter ≈ 30 nm) InAs/InP heterostructure nanowires containing a nominally 300 nm long InAs quantum dot defined by two InP tunnel barriers. Measurements of Coulomb blockade conductance versus backgate voltage with no tip present are difficult to decipher. Using the SGM tip as a charged movable gate, we are able to identify three quantum dots along the nanowire: the grown-in quantum dot and an additional quantum dot near each metal lead. The SGM conductance images are used to disentangle information about individual quantum dots and then to characterize each quantum dot using spatially resolved energy-level spectroscopy.

Scanning gate microscopy of quantum rings: effects of an external magnetic field and of charged defects

We study scanning gate microscopy (SGM) in open quantum rings obtained from buried semiconductor InGaAs/InAlAs heterostructures. By performing a theoretical analysis based on the Keldysh-Green function approach we interpret the radial fringes observed in experiments as the effect of randomly distributed charged defects. We associate SGM conductance images with the local density of states (LDOS) of the system. We show that such an association cannot be made with the current density distribution. By varying an external magnetic field we are able to reproduce recursive quasi-classical orbits in LDOS and conductance images, which bear the same periodicity as the Aharonov-Bohm effect.

High-aspect ratio metal tips attached to atomic force microscopy cantilevers with controlled angle, length, and radius for electrostatic force microscopy

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.

Imaging electron wave functions inside open quantum rings

Combining scanning gate microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of the electron probability density |Psi|(2)(x,y) in embedded mesoscopic quantum rings. The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wave function interferences. Simulations of both |Psi|(2)(x,y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Psi|(2)(x,y).

Scanned probe imaging of quantum dots inside InAs nanowires

We show how a scanning probe microscope (SPM) can be used to image electron flow through InAs nanowires, elucidating the physics of nanowire devices on a local scale. A charged SPM tip is used as a movable gate. Images of nanowire conductance versus tip position spatially map the conductance of InAs nanowires at liquid-He temperatures. Plots of conductance versus backgate voltage without the tip present show complex patterns of Coulomb-blockade peaks. Images of nanowire conductance identify their source as multiple quantum dots formed by disorder along the nanowire--each dot is surrounded by a series of concentric rings corresponding to Coulomb blockade peaks. An SPM image locates the dots and provides information about their size. In this way, SPM images can be used to understand the features that control transport through nanowires. The nanowires were grown from metal catalyst particles and have diameters approximately 80 nm and lengths 2-3 microm.

Construction of a dilution refrigerator cooled scanning force microscope

We present a scanning force microscope that operates in a dilution refrigerator at temperatures of about 100 mK. We use tuning fork sensors for scanning gate experiments on mesoscopic semiconductor nanostructures. Slip-stick motors allow sample coarse-positioning at base temperature. The construction, thermal anchoring, and a procedure to optimize the settings of the phase-locked loop that we use for sensor control are discussed in detail. We present low-temperature topographic and scanning gate images as examples of successful operation.

Technology and metrology of new electronic materials and devices

Scaling of the metal oxide semiconductor (MOS) field-effect transistor has been the basis of the semiconductor industry for nearly 30 years. Traditional materials have been pushed to their limits, which means that entirely new materials (such as high-kappa gate dielectrics and metal gate electrodes), and new device structures are required. These materials and structures will probably allow MOS devices to remain competitive for at least another ten years. Beyond this timeframe, entirely new device structures (such as nanowire or molecular devices) and computational paradigms will almost certainly be needed to improve performance. The development of new nanoscale electronic devices and materials places increasingly stringent requirements on metrology.