On the achievable field sensitivity of a segmented annular detector for differential phase contrast measurements

Differential phase contrast microscopy measures minute deflections of the electron probe due to electric and/or magnetic fields, using a position sensitive device. Although recently, pixelated detectors have become available which also serve as a position sensitive device, the most frequently used detector is a four-segmented annular semiconducting detector ring (or variations thereof), where the difference signals of opposing detector elements represent the components of the deflection vector. This deflection vector can be used directly to quantitatively determine the deflecting field, provided the specimen's thickness is known. While there exist many measurements of both electric and magnetic fields, even at an atomic level, until now the question of the smallest clearly resolvable field value for this detector has not yet been answered. This paper treats the problem theoretically first, leading to a calibration factor κ which depends solely on simple, experimentally accessible parameters and relates the deflecting field to the measured deflection vector. In a second step, the calibration factor for our combination of microscope and detector is determined experimentally for various combinations of camera length, condenser aperture and spot size to determine the optimum setup. From this optimized condition we determine the minimum change in field which leads to a clearly measurable signal change for both HMSTEM and LMSTEM operation. A strategy is described which allows the experimenter to choose the setup giving the highest field sensitivity. Quantification problems due to scattering processes in the specimen are addressed and ways are shown to choose a setup which is less sensitive to these artefacts.