Contact resistance

Electrical contact resistance (ECR, or simply contact resistance) is resistance to the flow of electric current caused by incomplete contact of the surfaces through which the current is flowing, and by films or oxide layers on the contacting surfaces. It occurs at

such as switches, connectors, breakers, contacts, and measurement probes. Contact resistance values are typically small (in the microohm to milliohm range).

Contact resistance can cause significant voltage drops and heating in circuits with high current. Because contact resistance adds to the intrinsic resistance of the conductors, it can cause significant measurement errors when exact resistance values are needed.

Contact resistance may vary with temperature. It may also vary with time (most often decreasing) in a process known as resistance creep.

Electrical contact resistance is also called interface resistance, transitional resistance, or the correction term. Parasitic resistance is a more general term, of which it is usually assumed that contact resistance is a major component.

William Shockley^[1] introduced the idea of a potential drop on an injection electrode to explain the difference between experimental results and the model of gradual channel approximation.

Measurement methods

Because contact resistance is usually comparatively small, it can difficult to measure, and Four-terminal measurement gives better results than a simple two-terminal measurement made with an ohmmeter.

• In a two-terminal measurement (as with a typical ohmmeter), the current used to make the measurement is injected through the measurement leads, which causes a potential drop not just across the contact area to be measured but also across the probe contacts and the leads. That means that the contact resistance of the probes and their leads is inseparable from the resistance of the contact area to be measured, with which they are in series.
• In a four-terminal measurement, the current used to make the measurement is injected using a second, separate pair of leads, so the contact resistance of the measurement probes and their leads is not included in the measurement.

Specific contact resistance can be obtained by multiplying by contact area.

Experimental characterization

For experimental characterization, a distinction must be made between contact resistance evaluation in two-electrode systems (for example, diodes) and three-electrode systems (for example, transistors).

In two-electrode systems, specific contact resistivity is experimentally defined as the slope of the

at V = 0:

${\displaystyle r_{c}=\left\{{\frac {\partial V}{\partial J}}\right\}_{V=0}}$

where J is the current density, or current per area. The units of specific contact resistivity are typically therefore in ohms-square meter, or ${\displaystyle \Omega \cdot {\text{cm}}^{2}}$. When the current is a linear function of the voltage, the device is said to have ohmic contacts. Inductive and capacitive methods could be used in principle to measure an intrinsic impedance without the complication of contact resistance. In practice, direct current methods are more typically used to determine resistance.

The three electrode systems such as transistors require more complicated methods for the contact resistance approximation. The most common approach is the

(TLM). Here, the total device resistance ${\displaystyle R_{\text{tot}}}$ is plotted as a function of the channel length:

${\displaystyle R_{\text{tot}}=R_{\text{c}}+R_{\text{ch}}=R_{\text{c}}+{\frac {L}{WC\mu \left(V_{\text{gs}}-V_{\text{ds}}\right)}}}$

where ${\displaystyle R_{\text{c}}}$ and ${\displaystyle R_{\text{ch}}}$ are contact and channel resistances, respectively, ${\displaystyle L/W}$ is the channel length/width, ${\displaystyle C}$ is gate insulator capacitance (per unit of area), ${\displaystyle \mu }$ is carrier mobility, and ${\displaystyle V_{\text{gs}}}$ and ${\displaystyle V_{\text{ds}}}$ are gate-source and drain-source voltages. Therefore, the linear extrapolation of total resistance to the zero channel length provides the contact resistance. The slope of the linear function is related to the channel transconductance and can be used for estimation of the ”contact resistance-free” carrier mobility. The approximations used here (linear potential drop across the channel region, constant contact resistance, …) lead sometimes to the channel dependent contact resistance.^[2]

Beside the TLM it was proposed the gated four-probe measurement

In the semiconductor industry, Cross-Bridge Kelvin Resistor(CBKR) structures are the mostly used test structures to characterize metal-semiconductor contacts in the Planar devices of VLSI technology. During the measurement process, force the current (I) between contact 1&2 and measure the potential deference between contacts 3&4. The contact resistance Rk can be then calculated as ${\displaystyle Rk=V34/I}$ .[7]

Mechanisms

For given physical and mechanical material properties, parameters that govern the magnitude of electrical contact resistance (ECR) and its variation at an interface relate primarily to

, contact mechanics and charge transport mechanisms needs to be considered in the mechanistic evaluation of ECR phenomena.

Quantum limit

When a conductor has spatial dimensions close to ${\displaystyle 2\pi /k_{\text{F}}}$, where ${\displaystyle k_{\text{F}}}$ is Fermi wavevector of the conducting material, Ohm's law does not hold anymore. These small devices are called quantum point contacts. Their conductance must be an integer multiple of the value ${\displaystyle 2e^{2}/h}$, where ${\displaystyle e}$ is the elementary charge and ${\displaystyle h}$ is

.

Other forms of contact resistance

Measurements of

transitions from one channel to another.

Significance

Bad contacts are the cause of failure or poor performance in a wide variety of electrical devices. For example, corroded

in a high current device. Unpredictable or noisy contacts are a major cause of the failure of electrical equipment.

See also

• Contact cleaner
• Wetting current

References

Further reading

• Pitney, Kenneth E. (2014) [1973]. Ney Contact Manual - Electrical Contacts for Low Energy Uses (reprint of 1st ed.). Deringer-Ney, originally JM Ney Co.
  ASIN B0006CB8BC.^{[permanent dead link}
  ] (NB. Free download after registration.)
• Slade, Paul G. (February 12, 2014) [1999]. Electrical Contacts: Principles and Applications. Electrical engineering and electronics. Vol. 105 (2 ed.).
  ISBN 978-1-43988130-9. {{cite book}}: |work= ignored (help
  )
• ISBN 978-3-540-03875-7
  . (NB. A rewrite of the earlier "Electric Contacts Handbook".)
• ISBN 978-3-662-42222-9
  .)
• Huck, Manfred; Walczuk, Eugeniucz; Buresch, Isabell; Weiser, Josef; Borchert, Lothar; Faber, Manfred; Bahrs, Willy; Saeger, Karl E.; Imm, Reinhard; Behrens, Volker; Heber, Jochen; Großmann, Hermann; Streuli, Max; Schuler, Peter; Heinzel, Helmut; Harmsen, Ulf; Györy, Imre; Ganz, Joachim; Horn, Jochen; Kaspar, Franz; Lindmayer, Manfred; Berger, Frank; Baujan, Guenter; Kriechel, Ralph; Wolf, Johann; Schreiner, Günter; Schröther, Gerhard; Maute, Uwe; Linnemann, Hartmut; Thar, Ralph; Möller, Wolfgang; Rieder, Werner; Kaminski, Jan; Popa, Heinz-Erich; Schneider, Karl-Heinz; Bolz, Jakob; Vermij, L.; Mayer, Ursula (2016) [1984]. Vinaricky, Eduard; Schröder, Karl-Heinz; Weiser, Josef; Keil, Albert; Merl, Wilhelm A.; Meyer, Carl-Ludwig (eds.). Elektrische Kontakte, Werkstoffe und Anwendungen: Grundlagen, Technologien, Prüfverfahren (in German) (3 ed.). Berlin / Heidelberg / New York / Tokyo:
  ISBN 978-3-642-45426-4
  .