Scanning quantum dot microscopy (SQDM) is a scanning probe microscopy (SPM) that is used to image nanoscale electric potential distributions on surfaces. 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 to 10 nm 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).
Working principle 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. The boundary S {\displaystyle {\mathcal {S}}} is given by the surfaces of sample and probe assumed to be connected at infinity. Then, the potential Φ QD = Φ ( r ) {\displaystyle \Phi _{\text{QD}}=\Phi (\mathbf {r} )} of a point-like QD at r {\displaystyle \mathbf {r} } can be expressed using the Green's function formalism as a sum over volume and surface integrals, where V {\displaystyle {\mathcal {V}}} denotes the volume enclosed by S {\displaystyle {\mathcal {S}}} and n ′ {\displaystyle \mathbf {n} '} is the surface normal.
Φ QD = Φ ( r ) = ∭ V G ( r , r ′ ) ρ ( r ′ ) e d 3 r ′ + ϵ 0 e ∮ S [ G ( r , r ′ ) ∂ Φ ( r ′ ) ∂ n ′ − Φ ( r ′ ) ∂ G ( r , r ′ ) ∂ n ′ ] d 2 r ′ . {\displaystyle \Phi _{\text{QD}}=\Phi (\mathbf {r} )=\iiint \limits _{\mathcal {V}}G(\mathbf {r} ,\mathbf {r} '){\frac {\rho (\mathbf {r} ')}{e}}d^{3}\mathbf {r} '+{\frac {\epsilon _{0}}{e}}\oint \limits _{\mathcal {S}}{\bigg [}G(\mathbf {r} ,\mathbf {r} '){\frac {\partial \Phi (\mathbf {r} ')}{\partial \mathbf {n} '}}-\Phi (\mathbf {r} '){\frac {\partial G(\mathbf {r} ,\mathbf {r} ')}{\partial \mathbf {n} '}}{\bigg ]}d^{2}\mathbf {r} '.}
In this expression, Φ QD {\displaystyle \Phi _{\text{QD}}} depends on the charge density ρ {\displaystyle \rho } inside V {\displaystyle {\mathcal {V}}} and on the potential Φ {\displaystyle \Phi } on S {\displaystyle {\mathcal {S}}} weighted by the Green's function
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