Calculation of the thermal effect of an electron probe on a sample of GaN
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Stationary temperature fields due to the interaction of an electron probe with a GaN sample are examined. In order to calculate the density of generated heat, the process of electron energy loss is modeled by the Monte Carlo method. The heat generation region is assumed to have the shape of a half-ellipsoid. In the case of uniform heat generation in the ellipsoid, an analytical solution to the heat conduction problem is found and expressed in terms of elementary functions. It is shown that the maximum heating temperature and the temperature field distribution depend only slightly on the shape of the heat generation region. An approximation of the density of heat sources by a uniform distribution over a hemisphere of radius equal to the ultimate range of electrons leads to a considerably underestimated maximum heating temperature. An expression is derived for determining the characteristic size of the heat generation region in GaN; this expression allows one to calculate the maximum heat temperature with an accuracy of 3% in a wide range of electron beam energies.
KeywordsMonte Carlo Method Heat Source Temperature Field Heat Generation Beam Energy
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