Calculation of the thermal effect of an electron probe on a sample of GaN

Stationary temperature fields due to the interaction of an electron probe w ith a GaN sample are examined. In order to calculate the density of generat ed 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-e llipsoid. In the case of uniform heat generation in the ellipsoid, an analy tical solution to the heat conduction problem is found and expressed in ter ms of elementary functions. It is shown that the maximum heating temperatur e and the temperature field distribution depend only slightly on the shape of the heat generation region. An approximation of the density of heat sour ces by a uniform distribution over a hemisphere of radius equal to the ulti mate range of electrons leads to a considerably underestimated maximum heat ing temperature. An expression is derived for determining the characteristi c 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 ran ge of electron beam energies. (C) 2001 MAIK "Nauka/Interperiodica".