Scanning quantum dot microscopy
Scanning quantum dot microscopy (SQDM) is a scanning probe microscopy (SPM) that is used to image nanoscale electric potential distributions on surfaces.
[1][2][3][4] The method quantifies surface potential variations via their influence on the potential of a quantum dot (QD) attached to the apex of the scanned probe.
SQDM allows, for example, the quantification of surface dipoles originating from individual adatoms, molecules, or nanostructures.
This gives insights into surface and interface mechanisms such as reconstruction or relaxation, mechanical distortion, charge transfer and chemical interaction.
Measuring electric potential distributions is also relevant for characterizing organic and inorganic semiconductor devices which feature electric dipole layers at the relevant interfaces.
The probe to surface distance in SQDM ranges from 2 nm[1][3] to 10 nm[2] and therefore allows imaging on non-planar surfaces or, e.g., of biomolecules with a distinct 3D structure.
Related imaging techniques are Kelvin Probe Force Microscopy (KPFM) and Electrostatic Force Microscopy (EFM).
In SQDM, the relation between the potential at the QD and the surface potential (the quantity of interest) is described by a boundary value problem of electrostatics.
is given by the surfaces of sample and probe assumed to be connected at infinity.
can be expressed using the Green's function formalism as a sum over volume and surface integrals,[5] where
and thus defining the boundary conditions, these equations can be used to obtain the relation between
The combination of a conductive probe and a conductive surface, a situation characterized by Dirichlet boundary conditions, has been described in detail.
links data in the imaging plane, obtained by reading out the QD potential, to data in the object surface - the surface potential.
If the sample surface is approximated as locally flat and the relation between
therefore translationally invariant, the recovery of the object surface information from the imaging plane information is a deconvolution with a point spread function defined by the boundary value problem.
In the specific case of a conductive boundary, the mutual screening of surface potentials by tip and surface lead to an exponential drop-off of the point spread function.
[4][6] This causes the exceptionally high lateral resolution of SQDM at large tip-surface separations compared to, for example, KPFM.
[3] Two methods have been reported to obtain the imaging plane information, i.e., the variations in the QD potential
The influence of the laterally varying surface potentials on
is actively compensated by continuously adjusting the global sample potential via an external bias voltage
is chosen such that it matches a discrete transition of the QD charge state and the corresponding change in probe-sample force is used in non-contact atomic force microscopy[8][9] to verify a correct compensation.
In an alternative method, the vertical component of the electric field at the QD position is mapped by measuring the energy shift of a specific optical transition of the QD[2][10] which occurs due to the Stark effect.
The equivalence of these quantities is given by the Helmholtz equation.
In the compensation technique, the influence of the global sample potential
depends on the shape of the sample surface in a way that is defined by the corresponding boundary value problem.
if only a single charge state transition is tracked.
For example, a protrusion in the surface affects the QD potential since the gating by
If two transitions are used in the compensation technique the contributions of surface topography
can be disentangled and both quantities can be obtained unambiguously.
The topographic information obtained via the compensation technique is an effective dielectric topography of metallic nature which is defined by the geometric topography and the dielectric properties of the sample surface or of a nanostructure.
