Electron beam as a local heat source

The physical principles of LTSEM applied to superconductors were first discussed by Clem Huebener [5.2]. The minimum beam diameter which can be achieved in commercial scanning electron microscopes is typically about 10 nm. On the other hand, the spatial resolution of LTSEM is limited by the spreading of the beam-induced sample perturbation. In thin-film superconductors it is essentially the thermal perturbation (local heating effect) which 

The temporal response is given by the thermal relaxation time C-d 

Here k and C are the heat conductivity and the heat capacity per unit volume of the film, respectively, and a is the heat transfer coefficient describing the heat transfer between the film and the substrate. The range of penetration of the beam electrons into the target material is proportional to about the 1.5 power of the beam energy Eo and inversely proportional to the mass density pm of the 

Next we turn in more detail to the detection of the beam-induced local resistivity change, bp. For simplicity we start with the one-dimensional case shown schematically in Fig. 5.4 with a series connection (part a) and a parallel connection (part b) of regions with different values of Tc. For practical reasons we only consider current-biased operation. The total current and voltage is denoted by /and V, respectively. The direction parallel and perpendicular to the current flow is denoted as the x- and y-direction, respectively. 

For the series connection (Fig. 5.4(a)) the local beam-induced resistivity increment bp x) results in a voltage signal 

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