Electrostatic phenomena are practically omnipresent on the nanometer length scale and play an important role for example in electronic devices or molecular biology: Diodes and transistors only function because of the electric potential step at their pn-junctions. In flash memory, information is stored in the form of small amounts of charge and the functionality of biomolecules is heavily influenced by their partially charged functional groups. The understanding and engineering of electric potentials at the nanoscale is hence an important topic in many fields of research and being able to image the distribution of such potentials on a given surface is an important part of this process.
Nanoscale electrostatic surface potentials can be imaged with electron microscopes  or scanning probe microscopes. An example of the latter category is the widely used atomic force microscope (AFM)  which can be modified to perform electrostatic force microscopy (EFM)  or Kelvin probe force microscopy (KPFM) . In both cases, the electric potential variations on the surface create variations in the force (gradient) between the sample and the tip as a whole. The tip apex which is closest to the surface feels a particularly strong force modulation and is therefore primarily responsible for the image contrast. Consequently, the achievable lateral resolution depends on the tip-surface distance and the tip shape and is typically in the range of several tens of nm . While atomic resolution can be obtained at very small tip heights and a slow scanning speed, such an imaging mode is limited to small and very flat sample areas and, as yet, lacks a clear quantitative interpretation [6,7]: Measuring electrostatic potentials via the resulting tip-surface force is problematic at smallest length scales where this force is very difficult to separate from other omnipresent, laterally varying forces like chemical or van der Waals (vdW) forces.
To Make Electric Surface Potentials Visible
Recently, scanning quantum dot microscopy (SQDM) has been developed, it is an imaging technique for electric surface potentials (fig.
1) which is quantitative and achieves a high lateral resolution at comparably large tip-surface separations [8-11], making it also applicable to rougher surfaces or 3D nanostructures like biomolecules. SQDM is also based on (dynamic) AFM but otherwise conceptually different from the established methods EFM and KPFM: The imaging of local surface potentials with SQDM is realized via the gating and charging of a tip-attached quantum dot (QD), a process that is not influenced by, e.g., vdW forces. Hence, the quantitative interpretation of SQDM images is quite straightforward. It can thus be used, for example, to quantify work function changes, even if the surface area of interest is very small, or the surface dipoles of individual adatoms or molecules .
SQDM utilizes a sensor-transducer working principle like several other recently developed scanning probe techniques . The QD “senses” changes in the local potential via gating and “transduces” this information by abruptly changing its charge state by one unit charge, which, in turn, creates a change in tip-surface force that can be detected by the AFM (fig. 2). For integer charging to happen, the QD needs to be electrically separated from the metal tip to which it is mechanically attached. Its potential relative to the (grounded) tip can then be adjusted by applying a gating bias Vb to the (conductive) sample. For SQDM image acquisition, Vb is adjusted such that a previously selected electronic level of the QD is aligned with the Fermi level EF of the tip. A proper alignment causes a distinct signature in the AFM force-gradient channel resulting from the change in the QD charge state as an electron tunnels from the tip onto the QD or vice versa. SQDM imaging then works by the principle of compensation: As the tip + QD is scanned over the surface it encounters varying local surface potentials which change the QD potential by gating in the same way the gating bias does. The impending misalignment of the QD level during scanning is avoided by continuously re-adjusting Vb with a dedicated controller that tracks the force-gradient signature associated to a change in QD charge state (fig. 3). SQDM raw images are thus maps of the changes in Vb which reflect corresponding changes in the surface potential.
Lateral Resolution about 2 nm
The exact relation between SQDM raw images and the actual surface potential can be derived by solving an inverse boundary value problem of electrostatics . In a somewhat simplified picture, we find that the surface potential can be derived from the Vb maps via deconvolution. The corresponding point spread function (PSF) can be estimated very well , which leads to a low level of deconvolution artifacts. Remarkably, the PSF drops exponentially with lateral distance, which explains the high resolution that characterizes already the Vb images. This surprising property (given the fact that we image long-ranged electric potentials which normally decay as 1/r) is the result of the combined screening of these potentials by tip and surface . Ultimately, the lateral resolution of SQDM at a tip-surface distance of about 2 nm allows distinguishing objects in the deconvolved image which are 1-2 nm apart (fig. 1).
Another feature of SQDM is the simultaneous acquisition of the surface potential and the surface topography (fig. 1). SQDM scans are performed at constant height such that the effective tip-sample separation varies with the sample topography during scanning. This affects the gating efficiency: At a small separation, the influence of Vb on the QD levels is strong, while its influence decreases when the separation increases. The principle of compensation thus dictates that not only the variations in surface potential, but also the variations in surface topography have to be compensated by adjusting Vb: Above protrusions (depressions) |Vb| needs to be decreased (increased) to keep the QD level aligned with EF. To disentangle the contributions of topography and potential, two SQDM Vb maps have to be recorded, for which two different QD levels are aligned with EF. In our experiments we have chosen alignments in which the QD either gains or loses one electron (Vb > 0 and Vb < 0, respectively). Combining the information from both maps, the topography and potential of the surface can then be obtained on equal footing by a straightforward calculation .
New Designs for SQDM Sensors
While the theory of SQDM imaging is now well understood , exploring new designs for SQDM sensors (AFM tip + QD) is a worthwhile endeavor with substantial challenges. In our experiments so far, the QD is a PTCDA (3,4,9,10-perylene-tetracarboxylic dianhydride) molecule that is attached via chemical bonding to the silver AFM tip by picking it up from the surface at low temperatures. This procedure leads to a molecule that stands on the tip , a configuration in which a singly occupied molecular orbital is sufficiently close to EF and sufficiently decoupled from the tip to align it with EF using a gating bias voltage of only a few volt  (fig. 3). This molecular SQDM sensor achieves perhaps almost optimal performance for imaging, but the solution has also two drawbacks: The PTCDA-based sensors are tedious to make and, due to their low thermal stability, they can only be used at cryogenic temperatures. Alternative fabrication routes utilizing for example lithographic processes, could hence increase the application range of SQDM substantially. When searching for such alternatives, one has to keep an eye on several design parameters for the sensor which require some fine-tuning for SQDM to work optimally. Those are the size of the QD, its coupling to the tip and the position of its levels relative to EF in the absence of gating. Complications arise since these parameters are dependent on each other: Quantum mechanics dictates that a small QD (desirable) has a large spacing between its energy levels (not desirable). Still, the level spacing should be large compared to kT since otherwise integer occupancy is not possible. At the same time, a weak electronic coupling between QD and tip makes gating the QD easier which would allow using QDs with larger level spacing. But coupling also needs to be strong enough to enable tunneling of electrons between tip and QD. Our PTCDA sensor proves that there exist sweet spots in this design parameter space and we are optimistic that sensor designs will be found which enable plug-and-play-type SQDM imaging, perhaps even at room temperature, thus extending SQDM to a vast range of applications in materials science and beyond.
Matthew F. B. Green1,2,3, Ruslan Temirov1,2,4, F. Stefan Tautz1,2,3, and Christian Wagner1,2
1Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, Jülich, Germany
2Jülich Aachen Research Alliance (JARA)-Fundamentals of Future Information Technology, Jülich, Germany
3Experimentalphysik IV A, RWTH Aachen University, Aachen, Germany
4II. Physikalisches Institut, Universität zu Köln, Köln, Germany
Dr. Christian Wagner
ERC-StG Gruppe “ Controlled Mechanical
Manipulation of Molecules”
Peter Grünberg Institute
Functional Nanostructures at Surfaces (PGI-3)
Forschungszentrum Jülich GmbH
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