Analysis of thermal effects accompanying the interaction of electron beams with ferroelectric crystals (Q619372)

The paper studies the features of the non-stationary temperature distribution in the typical ferroelectric specimen under action of a focused electronic probe based on analytical and numerical method of the heat conductivity theory. Due to that in thermal front propagation through the specimen of finite sizes from the source having a small radius compared to the specimen sizes, the boundary effects will not be important, in order to estimate local heating of the examined samples, it is analyzed a solution of the heat conductivity problem with initial conditions at infinity. The obtained analytical solutions of heat conductivity problems are defined by using approximation of the boundary of the electron energy loss region. As approximations the hemispherical and cylindrical approximations of the heat source are considered. In order to construct the model the thermophysical parameters of the crystal and the test parameters of SEM characteristics are assigned and the Cauchy problem is solved for the inhomogeneous heat conductivity equation in infinity space. Application of the method of sources allows one to obtain temperature distributions for continuously operating surface heat sources of various configurations. The obtained relations for the continuous spherical source and cylindrical surface source allow modeling the process of non-stationary heat conductivity and the maximum specimen overheating in the limit case. Then, it is shown that the problem of simulation of the thermal electronic probe effect on a ferroelectric crystal is reduced to a solution of a boundary heat conductivity problem for a compound solid under present test conditions. In order to carry out numerical analysis, it is considered a hemispherical and cylindrical source for high-voltage and low-voltage SEM, respectively. As a result for the numerical solution of the multidimensional problem of heat conductivity, it is used the implicit finite-difference scheme of the variable component separation technique based on the pass technique. To construct the generalized model, the length and time scales are matched by the Fourier criterion. Finally, it is calculated the thermal effect of the electronic probe on a triglicine sulfate crystal with the silver electrodes deposited on its faces. The numerical results show that the coating considerably reduces the thermal load on the specimen, and the maximum overheating temperature of specimens for low-voltage SEM reaches larger values than for high-voltage SEM.