“…As features in electronic circuits, especially those based on molecules, shrink to less than 10 nm, the transport of electrons through nominally insulating materials has become of prime interest. Experimentally, the distance dependence of electron transport has been probed in 2D structures using an insulating film, commonly a self-assembled monolayer, on a metal surface and either a redox species attached or in solution − or another metal contact to complete the circuit. − In one dimension, molecular spacers separate donor and acceptor molecules or nanoscale electrodes. − The transport of electrons through nonconductors is historically broken down into coherent tunneling over “short” range (less than about 4 nm) and incoherent hopping over longer ranges. The primary feature used to distinguish between the two is the distance dependence of the electron transfer rate, k , which exhibits an exponential falloff with distance d, characterized by decay length β, k = k o e –βd for tunneling and a more linear inverse dependence on distance for hopping .…”