# Contact Potential

## contact potential

[′kän‚takt pə′ten·chəl]
(electricity)

## Contact Potential

a difference in electric potentials arising between two bodies that are in contact and in thermo-dynamic equilibrium. The concept of contact potential is most important for solid conductors (metals and semiconductors). If two solid conductors are brought into contact, an exchange of electrons takes place between them; at first the electron transfer will occur predominantly from the conductor with a lower work function to the conductor with a higher work function. As a result, the conductors acquire electric charges of opposite sign, which causes the appearance of an electric field that impedes the flow of electrons. Ultimately a state of equilibrium is attained; in this state the electron flow in one direction becomes equal to the flow in the opposite direction, and a contact potential is established between the conductors.

The value of the contact potential is equal to the difference in work functions divided by the charge of an electron. In an electric circuit consisting of several conductors, the contact potential between the conductors at the ends of the circuit is determined solely by their work functions and does not depend on any of the intermediate components of the circuit (Volta’s rule). The contact potential may attain values of several volts and depends on the structure of the conductor and the condition of its surface. Therefore, the value of the contact potential can be changed by treatment of the surface (coatings, adsorption, and so on), by the introduction of impurities (in the case of semiconductors), and by alloying with other substances (in the case of metals).

Since the work performed by electric forces arising because of the contact potential in moving charges within a closed circuit consisting of several conductors is equal to zero, direct measurement of the contact potential is impossible. One of the most widely used methods of measuring the contact potential is the method using Kelvin’s vibrating capacitor. The distance between the plates of a capacitor made from the pair of conductors being investigated is changed periodically. The capacitance of the capacitor is thus varied, and an alternating current caused by the contact potential difference is generated in the circuit. Thus, the contact potential may be determined by measuring the current.

The electric field of the contact potential is concentrated in the conductors near the boundary surface and in the gap between the conductors. The linear dimensions of the region are of the order of the screening length, which increases with decreasing concentration of conduction electrons within the conductor. The screening length in metals has atomic dimensions (10−8 to 10−7 cm); in semiconductors it varies within wide limits and can attain values of 10−4 to 10−5 cm. Two conclusions may be drawn from this fact: (1) Of the two bodies in contact, a greater part of the contact potential occurs on the conductor having the greater resistance; (2) for semiconductors, the density of charge carriers is changed markedly in the region of concentration of the contact potential.

The contact potential plays an important role in solid-state physics and its applications. It significantly affects the operation of electrovacuum instruments. In electron tubes the contact potential difference between electrodes is added to the applied external voltages and influences the shape of the current-voltage characteristic curve. In thermionic generators the contact potential is used for direct conversion of thermal energy to electric power. Electrons are “evaporated” from a hot cathode that has a high work function and are “condensed” on an anode with a low work function. The difference in the potential energy of electrons is converted into work, which is performed in the external electric circuit.

In cases where the contact is between a metal and a semiconductor, the contact potential is almost wholly concentrated in the semiconductor. At sufficiently large values it markedly changes the current carrier concentration in the area of the semiconductor adjacent to the contact; hence, the resistance of the layer is also changed. If a high-resistance layer is formed by depletion of current carriers, then, upon application of an external potential difference the current-carrier concentration in this layer will change markedly and asymmetrically (the asymmetry will depend on the sign of the applied voltage). Thus, the contact potential causes the nonlinearity of the current-voltage characteristics of metal-semiconductor contacts, which therefore have rectifier properties.

If the contact is between two semiconductors consisting of the same material but with different types of conductivity, the con-tact potential leads to the formation of a space-charge transition region with nonlinear dependence of resistance on the external voltage.

### REFERENCES

Pikus, G. E. Osnovy teorii poluprovodnikovykh priborov. Moscow, 1965.
Tsarev, B. M. Kontaktnaia raznost’ potentsialov i ee vliianie na rabotu elektrovakuumnykh priborov, 2nd ed. Moscow, 1955.

V. B. SANDOMIRSKII

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