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Poisson's equation
We have seen that the electric field generated by a set of
stationary charges can be
written as the gradient of a scalar potential, so that
(218)
This equation can be combined with the field equation (213) to
give a partial
differential equation for the scalar potential:
(219)
This is an example of a very famous type of partial differential
equation knownasPoisson's equation.
In its most general form, Poisson's equation is written
WORK FUNCTION
Insolid-state physics, the work function (sometimes spelled
workfunction) is the
minimumthermodynamic work(i.e. energy) needed to remove
anelectronfrom a solid to a point in
thevacuumimmediately outside the solid surface. Here
"immediately" means that the final electron
position is far from the surface on the atomic scale, but still
too close to the solid to be influenced by
ambient electric fields in the vacuum. The work function is not
a characteristic of a bulk material, but
rather a property of the surface of the material (depending on
crystal face and contamination).
Relationship between work function, vacuum electric potential,
andFermi level (voltage)[edit source|editbeta]
http://farside.ph.utexas.edu/teaching/em/lectures/node30.html#e353http://farside.ph.utexas.edu/teaching/em/lectures/node30.html#e353http://farside.ph.utexas.edu/teaching/em/lectures/node30.html#e353http://en.wikipedia.org/wiki/Solid-state_physicshttp://en.wikipedia.org/wiki/Solid-state_physicshttp://en.wikipedia.org/wiki/Solid-state_physicshttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Vacuumhttp://en.wikipedia.org/wiki/Vacuumhttp://en.wikipedia.org/wiki/Vacuumhttp://en.wikipedia.org/w/index.php?title=Work_function&action=edit§ion=1http://en.wikipedia.org/w/index.php?title=Work_function&action=edit§ion=1http://en.wikipedia.org/w/index.php?title=Work_function&action=edit§ion=1http://en.wikipedia.org/wiki/Work_function?veaction=edit&vesection=1http://en.wikipedia.org/wiki/Work_function?veaction=edit&vesection=1http://en.wikipedia.org/wiki/Work_function?veaction=edit&vesection=1http://en.wikipedia.org/wiki/Work_function?veaction=edit&vesection=1http://en.wikipedia.org/wiki/Work_function?veaction=edit&vesection=1http://en.wikipedia.org/w/index.php?title=Work_function&action=edit§ion=1http://en.wikipedia.org/wiki/Vacuumhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Solid-state_physicshttp://farside.ph.utexas.edu/teaching/em/lectures/node30.html#e353
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When the two metals depicted here are in thermodynamic
equilibrium with each other as shown (equalFermi levels), the
vacuumelectrostatic potential is not flat due to a difference in
work function.
If an electron is removed from a solid to a state of zero total
energy, then thethermodynamic
workrequired is given by EF, where EF is theFermi
level(electrochemical potential) in that system. Thework function
is however defined by placing the electron into the vacuum nearby
the surface, where there
is anelectrostatic potential; at this point, the electron's
total energy is not zero but instead Evac= e.
Thus, the work function Wis defined by[1]
In other words, it is the sum of the work required to completely
remove the electron (EF), and the
work required to place it back just outside the surface (e).
The work function is in fact a property of the surface material,
and EF is fixed by the electrode that is
attached to the material. Practically, this means that the
material's work function acts to determine the
value of (rather than the other way around). The electrode's
internal voltage Vcan be defined as V
= EF/e,[2]
giving
In other words, if a battery is used to apply a voltage Vto an
electrode, then the
actual produced in the vacuum will vary depending on the work
function. Wdepends on the
material the electrode is made from. The reason for this
dependence ofWon material can be
attributed to a variety of effects (binding energy, surface
dipoles, etc.), discussed below.
http://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Electrochemical_potentialhttp://en.wikipedia.org/wiki/Electrochemical_potentialhttp://en.wikipedia.org/wiki/Electrochemical_potentialhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Work_function#cite_note-1http://en.wikipedia.org/wiki/Work_function#cite_note-1http://en.wikipedia.org/wiki/Work_function#cite_note-1http://en.wikipedia.org/wiki/Work_function#cite_note-2http://en.wikipedia.org/wiki/Work_function#cite_note-2http://en.wikipedia.org/wiki/Work_function#cite_note-2http://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/File:Work_function_mismatch_gold_aluminum.svghttp://en.wikipedia.org/wiki/Work_function#cite_note-2http://en.wikipedia.org/wiki/Work_function#cite_note-1http://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Electrochemical_potentialhttp://en.wikipedia.org/wiki/Fermi_levelhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Thermodynamic_workhttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Fermi_level
