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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.
The particles, sometimes called thermions in early literature, are now known to be ions or electrons. Thermal electron emission specifically refers to emission of electrons and occurs when thermal energy overcomes the material's work function.
The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, ψ(r 1, r 2) = −ψ(r 2, r 1), where the variables r 1 and r 2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal ...
Because the binding energy of electrons in solids is conveniently expressed with respect to the highest occupied state at the Fermi energy , and the difference to the free-space (vacuum) energy is the work function of the surface, the kinetic energy of the electrons emitted from solids is usually written as =.
In this case, the chemical potential of a body is the infinitesimal amount of work needed to increase the average number of electrons by an infinitesimal amount (even though the number of electrons at any time is an integer, the average number varies continuously.): ( ,) = ( ), where F(N, T) is the free energy function of the grand canonical ...
In 1928 J. Robert Oppenheimer published two papers on field emission, i.e. the emission of electrons induced by strong electric fields. Nordheim and Fowler simplified Oppenheimer's derivation and found values for the emitted currents and work functions that agreed with experiments. [10]
However, meaningful investigations had to wait until after J.J. Thomson's [3] identification of the electron in 1897, and until after it was understood – from thermal emission [4] and photo-emission [5] work – that electrons could be emitted from inside metals (rather than from surface-adsorbed gas molecules), and that – in the absence of ...
The two charge carriers, electrons and holes, will typically have different drift velocities for the same electric field. Quasi-ballistic transport is possible in solids if the electrons are accelerated across a very small distance (as small as the mean free path), or for a very short time (as short as the mean free time). In these cases, drift ...