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In heterogeneous electron transfer, an electron moves between a chemical species present in solution and the surface of a solid such as a semi-conducting material or an electrode. Theories addressing heterogeneous electron transfer have applications in electrochemistry and the design of solar cells.
One component is the difference in the work function (also called the electron affinity) between the two materials. [48] This can lead to charge transfer as, for instance, analyzed by Harper. [ 49 ] [ 50 ] As has been known since at least 1953, [ 37 ] [ 51 ] [ 52 ] [ 53 ] the contact potential is part of the process but does not explain many ...
The work function W for a given surface is defined by the difference [1] =, where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and E F is the Fermi level (electrochemical potential of electrons) inside the material.
In theoretical chemistry, Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). [1]
where J is the emission current density, T is the temperature of the metal, W is the work function of the metal, k is the Boltzmann constant, q e is the Elementary charge, ε 0 is the vacuum permittivity, and A G is the product of a universal constant A 0 multiplied by a material-specific correction factor λ R which is typically of order 0.5.
Electron escape through the surface barrier into free-electron-like states of the vacuum. In this step the electron loses energy in the amount of the work function of the surface, and suffers from the momentum loss in the direction perpendicular to the surface.
where Ψ(x) is the electron wave-function, expressed as a function of distance x measured from the emitter's electrical surface, [62] ħ is the reduced Planck constant, m is the electron mass, U(x) is the electron potential energy, E n is the total electron energy associated with motion in the x-direction, and M(x) = [U(x) − E n] is called ...
This is because there is an energy to be paid to extract the electron from the medium (work function). Ballistic conduction is typically observed in quasi-1D structures, such as carbon nanotubes or silicon nanowires , because of extreme size quantization effects in these materials.