Differential phase contrast microscopy (DPC) is a measurement technique which is utilized in a scanning transmission electron microscope (STEM) equipped with a special direction sensitive detector [1,2]. It is based on the deflection of the electron beam by an angle α due to either Lorentz or Coulomb force, when the electron probe is scanned over an area with intrinsic magnetic or electric fields. This deflection causes a shift of the diffraction disk (DD) in the detector plane of the microscope, which is proportional to strength and direction of the field within the specimen. By measuring this shift with a direction sensitive segmented ring detector one obtains information about the intrinsic fields.
In this work we present an approach to determine calibration factors relating the qualitative DPC signals to absolute magnetic and electric field strengths or deflection angles just by measuring the size of the DD on the DPC detector. For this we derived a formula for the calibration factor by considering geometrical properties of the annular DPC detector and the DD. With this we can for example describe the absolute electric field strength E(x,y) at a certain specimen position (x,y) by:
E(x,y)[V/m] = ( SDPC(x,y) / Ssum(x,y) ) · ( κel[V] / t(x,y)[m] ) (1)
SDPC(x,y) being the DPC signal normalized with the sum signal Ssum(x,y) of all four detector segments, the specimen thickness t(x,y) and the calibration factor κel for electric fields. The latter can be described by:
κel = [ (R2 – r2) / (R · C) ] · [ (mrel · vrel2) / e ] (2)
with R and r being the radii of the DD in the detector plane and the detector hole (see fig. 1) and C the used camera length of the microscope. The second term describes the energy of the accelerated electrons with their relativistic mass mrel, velocity vrel and elemental charge e.
Equation 2 shows us two important things. Firstly that the calibration factor is highly dependent on the radius R of the DD (see fig. 2 and 3). This means that even a small change of the DD radius due to beam broadening caused by the specimen can lead to significant different field values when they are quantified with a calibration factor determined for the same set of microscope parameters but with a slightly smaller disk radius.
The other one is, that it is possible to calculate κel just by the measurement of R, because all the other variables in eq. 2 are well known parameters of the DPC measurement. The disk size itself can be easily determined e.g. with a CCD camera. This is a convenient way to calibrate a DPC system for quantitative measurements. Further it is possible to obtain individual calibration factors for each DPC measurement performed. The latter allows to minimize the error of the quantification due to disk broadening.
In addition to the theoretical approach we will also present our first experimental results showing the validity of the statements made above.
 Rose H., Phase Contrast in Scanning Transmission Electron Microscopy, Optik 39, 4, 416-436, (1974)
 Chapman J.N., The Investigation of Magnetic Domain-structures In Thin Foils By Electron-microscopy, J. Phys. D: Appl. Phys. 17, 623-647 (1984)
To cite this abstract:Felix Schwarzhuber, Johannes Wild, Josef Zweck; Direct determination of calibration factors for quantitative DPC measurements. The 16th European Microscopy Congress, Lyon, France. https://emc-proceedings.com/abstract/direct-determination-of-calibration-factors-for-quantitative-dpc-measurements/. Accessed: July 6, 2020
EMC Abstracts - https://emc-proceedings.com/abstract/direct-determination-of-calibration-factors-for-quantitative-dpc-measurements/