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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.
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. [1]: 2 [2]: 622 The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor.
The carrier particles, namely the holes and electrons of a semiconductor, move from a place of higher concentration to a place of lower concentration. Hence, due to the flow of holes and electrons there is a current. This current is called the diffusion current. The drift current and the diffusion current make up the total current in the conductor.
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.
Nordheim and Fowler simplified Oppenheimer's derivation and found values for the emitted currents and work functions that agreed with experiments. [ 10 ] A great success of the tunnelling theory was the mathematical explanation for alpha decay , which was developed in 1928 by George Gamow and independently by Ronald Gurney and Edward Condon .
e = elementary positive charge (i.e., magnitude of electron charge), m e = electron mass, k = Boltzmann constant = 1.38 × 10 −23 J/K, h = Planck constant = 6.62 × 10 −34 J⋅s, ϕ = work function of the cathode, ~ = mean electron reflection coefficient. The reflection coefficient can be as low as 0.105 but is usually near 0.5.
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 ...
The minimum amount of energy needed for an electron to leave a surface is called the work function. The work function is characteristic of the material and for most metals is on the order of several electronvolts (eV). Thermionic currents can be increased by decreasing the work function.