define work function of metal
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In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in the vacuum immediately 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).
Definition Edit
The work function W for a given surface is defined by the difference[1]
{\displaystyle W=-e\phi -E_{\rm {F}},} W = -e\phi - E_{\rm F},
where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and EF is the Fermi level (electrochemical potential of electrons) inside the material. The term −eϕ is the energy of an electron at rest in the vacuum nearby the surface.
The work function of solid surfaces can be determined experimentally using absolute or relative approaches. Absolute methods allow one to measure the work function value directly. Here, the electrons in the metal are supplied with sufficient kinetic energy to overcome the barrier at the metal / vacuum interface, and can thus escape the metal, and the work function can be obtained from the resulting electric current. Absolute methods include measurements based on thermionic emission, field emission, and the photoelectric effect. Briefly, in the thermionic emission method electrons are ejected from the material after receiving sufficient thermal energy to overcome the energy barrier at the metal / vacuum interface. The appropriate thermal energy is supplied by incremental heating of the sample to temperatures at which the Fermi-Dirac distribution of the electrons in the metal allows for substantial population of electrons at energies higher than the interface energy barrier. The resulting electric current is measured as a function of temperature; this allows one to extract the work function of the surface. The temperature range used in the thermionic emission method is often very high (thousands of Kelvins), making this method of limited value for studying materials and surfaces which are unstable at high temperatures.4 The field-emission method utilizes an electric field to accelerate the electrons inside of the metal to kinetic energies sufficiently high to overcome the interface barrier. The resulting electric current is analyzed as a function of the applied field and the work function is calculated.[4][5]
Photoelectric-effect-based methods use light, typically in the UV range, as the source of energy for the electrons. As in other absolute methods, the resulting electric current (here called photocurrent) is analyzed. Figure 2 shows the energetics of a photoelectric-effect-based measurement of the work function. In this experiment the electrons are provided with a known energy, hν (red arrows in Figure 2). Electrons with sufficient kinetic energy to overcome the barrier at the interface are able to escape the metal – these are represented with the blue box in Figure 2. These photoelectrons then travel away from the metal surface experiencing the potential depicted with the thick black line in Figure 2. As the electrons move further away from the surface their kinetic energy increases, according to Equation 1. The generated photocurrent is then measured as a function of the photoelectron kinetic energy. Two important features are present in a typical plot of photocurrent – kinetic energy. First, a sharp onset at low photoelectron kinetic energy, Emin is present. As already mentioned, this onset defines the lowest energy electrons able to overcome the work function of the surface.
Figure 2. Energetics of electrons in a photoelectric-effect-based measurement of the work function. The photon energy, hν, is shown as a red arrow. After ejection from the metal the electrons experience the potential shown with the thick black line. The kinetic energies of two photoelectrons originating from different energy levels in the metal are shown with thick green lines.In a real experiment the photoelectron-kinetic-energy analyzer causes an additional drop in the potential, which adds a rigid offset to the kinetic energy of the photoelectrons. More on this can be found in Nieuwenhuys 1974 [6]