Abstract
Understanding the electronic and phononic transport properties of junctions consisting of a scattering region such as a nanoscale matters or molecules connected to two or more electrodes is the central basis for future nano and molecular scale applications. The theoretical and mathematical techniques to treat electron and phonon transport are leading to model the physical properties of nano and molecular scale junctions. My aim in this paper is to review the theoretical and mathematical techniques to treat electron and phonon transport in nano and molecular scale junctions leading to models of their physical properties. This helps not only to understand the experimental observations but also provides a vital design tool to develop strategies for molecular electronic building blocks, thermoelectric device and sensors.
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