Abstract
A model-independent approach based on Gauss’ theorem for measuring the local charge in a specimen from an electron-optical phase image recorded using off-axis electron holography was recently proposed. Here, we show that such a charge measurement is reliable when it is applied to determine the total charge enclosed within an object. However, the situation is more complicated for a partial charge measurement when the integration domain encloses only part of the object. We analyze in detail the effects on charge measurement of the mean inner potential of the object, of the presence of induced charges on nearby supports/electrodes and of noise. We perform calculations for spherical particles and highlight the differences when dealing with other object shapes. Our analysis is tested using numerical simulations and applied to the interpretation of an experimental dataset recorded from a sapphire particle.
Highlights
Off-axis electron holography is a powerful technique for measuring projected electrostatic potentials in materials in the transmission electron microscope (TEM) [1,2,3,4,5]
Where z is the incident electron beam direction, Vtot is the total electrostatic potential within and around the specimen and CE is a constant that depends on the microscope accelerating voltage
Information about how charges are distributed within the specimen is often more valuable than a measurement of the projected electrostatic potential, as the distribution of charges reflects the response of the object to an external stimulus and boundary conditions
Summary
Off-axis electron holography is a powerful technique for measuring projected electrostatic potentials in materials in the transmission electron microscope (TEM) [1,2,3,4,5] It makes use of the superposition of an object wave and a reference wave to form an interference pattern in the image plane, from which the phase of the object electron wavefunction can be recovered. Many of these studies approach the interpretation of the measured projected electrostatic potential by fitting a recorded phase image to a model that depends on a number of unknown free parameters, including electron-optical para meters (the interference distance, accelerating voltage, position of the sample in the column, illumination characteristics, etc), geometrical parameters (the shape of the object, presence or absence of a support, distance to a grounded electrode, etc) and physical parameters (the properties of the material, temperature, environment, etc). Our conclusions are applicable to phase images retrieved using other approaches, such as ptychography [33] or the application of the transport of intensity equation to a defocus series of brightfield images [34, 35], as well as to the interpretation of phase gradient images recorded using techniques such as Foucault imaging [36, 37] and differential phase contrast imaging in the scanning TEM [38,39,40]
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