Electric charging of thin films measured using the contrast transfer function

The phase shift of electron waves due to charging of thin films is investig ated using the contrast transfer properties of the microscope. We take two photos. one with film at the back focal plant and the: other one without fi lm. The phase difference between the contrast transfer functions of the two photos is evaluated using our theoretical predictions, The theoretical mod el is based on an analytical solution of the Laplace equation with appropri ate boundary conditions. From the resulting electrostatic potential functio n the phase shift of electron waves is derived in a weak lens approximation . With this method, information about the radius of the electron beam and t he magnitude of the electrostatic potential at the thin film is obtained. T he excellent agreement between the theoretical model and experimental resul ts is observed. (C) 2001 Elsevier Science B.V. All rights reserved.