A basic goal in molecular electronics is to understand electron transport through a single molecule connected to two electrodes. Substantial progress towards this goal has been made over the past decade, but many fundamentally important and technologically relevant aspects remain to be studied and understood. One example is current-induced local heating in the molecule, which is the subject of this chapter. By measuring the thermal stability of the electrode-molecule contact, the effective temperature of a molecular junction can be determined experimentally. The temperature depends on the molecule and on the applied bias voltage. The results are described in terms of a hydrodynamic theory including both electron-phonon and electron-electron interactions.
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