Contact resistance

The term contact resistance refers to the contribution to the total resistance of a material which comes from the electrical leads and connections as opposed to the intrinsic resistance, which is an inherent property, independent of the measurement method. Placing the test probes of an ohmmeter onto the leads of an 100 ohm resistor, a scientist might observe a total resistance of 1 megohm, 1 kilohm or 101 ohms, depending on exactly how the connection is made. The contact resistance is then the difference between the measured resistance and 100 ohms.

Origin of contact resistance
There are two major determinants of contact resistance: geometry and insulating layers between the contacting surfaces (better known as "dirt.")   The resistance of a contact is inversely proportional to its area, which is in turn dependent on the force holding the two surfaces together and their stiffness. Joining methods like soldering or wire bonding keep the force between two halves of a contact constant. Softer metals like gold tend to form larger area contacts and are therefore preferred for bonding pads. Gold also has the advantage of being non-reactive, which prevents the formation of oxides or other poorly conducting reaction products.

Experimental characterization
The specific contact resistance is experimentally defined as the slope of the I-V curve at V=0:


 * $$r_c = \left\{ \frac{\partial V}{\partial J} \right\} ^{-1} _{V=0}$$.

where J is the current density = current/area. The units of specific contact resistance are typically therefore in $$\Omega.cm^2$$ where $$\Omega$$ stands for ohms. When the current is a linear function of the voltage, the device is said to have ohmic contacts.

The resistance of contacts can be crudely estimated by comparing the results of a four terminal measurement to a simple two-lead measurement made with an ohmmeter. In a two-lead experiment, the measurement current causes a potential drop across both the test leads and the contacts so that the resistance of these elements is inseparable from the resistance of the actual device, with which they are in series. In a four-point probe measurement, one pair of leads is used to inject the measurement current while a second pair of leads, in parallel with the first, is used to measure the potential drop across the device. In the four-probe case, there is no potential drop across the voltage measurement leads so the contact resistance drop is not included. The difference between resistance derived from two-lead and four-lead methods is a reasonably accurate measurement of contact resistance assuming that the leads resistance is much smaller. Specific contact resistance can be obtained by multiplying by contact area.

For development of integrated circuit fabrication processes, far more sophisticated measurements of contact resistance are used, the most popular being the transmission line measurement. The basic idea of the transmission line measurement is to plot the resistance of strips of constant width and varying length that are terminated by similar contacts. The slope of the resulting line is a function of the bulk film resistivity while the intercept is the contact resistance.

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.

Quantum limit
When a conductor has spatial dimensions close to $$(2*\pi)/k_F$$, where $$k_F$$ is Fermi wavevector of the conducting material, Ohm's law does not hold any more. These small devices are called quantum point contacts. Their conductance must be an integer multiple of the value $$2e^2/h$$, where $$e$$ is the electronic charge and $$h$$ is Planck's constant. Quantum point contacts behave more like waveguides than the classical wires of everyday life and may be described by the Landauer scattering formalism. Point-contact tunneling is an important technique for characterizing superconductors.

Other forms of contact resistance
Measurements of thermal conductivity are also subject to contact resistance. Similarly, a drop in hydrostatic pressure (analogous to electrical voltage) occurs when fluid flow 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 jumper cable clamps can frustrate attempts to start a vehicle that has a dead battery. Dirty or corroded contacts on a fuse or its holder can give the false impression that the fuse is blown. A sufficiently high contact resistance can cause substantial heating in a high current device. Unpredictable or noisy contacts are a major cause of the failure of electrical equipment. An intermittent contact which alternates rapidly between a high and low resistance is the worst nightmare of anyone who has to troubleshoot equipment.