![Carbon-film Resistor Construction](https://upload.wikimedia.org/wikipedia/commons/5/57/Carbon-film_Resistor_Construction.svg)
Sheet resistance, is a measure of
resistance
Resistance may refer to:
Arts, entertainment, and media Comics
* Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm:
** ''Resistance'' (comics), based on the video game of the same title
** ''T ...
of thin films that are uniform in thickness. It is commonly used to characterize materials made by semiconductor doping, metal deposition, resistive paste printing, and
glass coating. Examples of these processes are:
doped semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
regions (e.g.,
silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
or
polysilicon
Polycrystalline silicon, or multicrystalline silicon, also called polysilicon, poly-Si, or mc-Si, is a high purity, polycrystalline form of silicon, used as a raw material by the solar photovoltaic and electronics industry.
Polysilicon is produce ...
), and the resistors that are screen printed onto the substrates of
thick-film hybrid microcircuits.
The utility of sheet resistance as opposed to
resistance
Resistance may refer to:
Arts, entertainment, and media Comics
* Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm:
** ''Resistance'' (comics), based on the video game of the same title
** ''T ...
or
resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
is that it is directly measured using a
four-terminal sensing
Four-terminal sensing (4T sensing), 4-wire sensing, or 4-point probes method is an electrical impedance measuring technique that uses separate pairs of current-carrying and voltage-sensing electrodes to make more accurate measurements than the si ...
measurement (also known as a four-point probe measurement) or indirectly by using a non-contact eddy-current-based testing device. Sheet resistance is invariable under scaling of the film contact and therefore can be used to compare the electrical properties of devices that are significantly different in size.
Calculations
![sheet resistance](https://upload.wikimedia.org/wikipedia/commons/d/d0/Sheet_resistance.svg)
Sheet resistance is applicable to two-dimensional systems in which thin films are considered two-dimensional entities. When the term sheet resistance is used, it is implied that the current is along the plane of the sheet, not perpendicular to it.
In a regular three-dimensional conductor, the
resistance
Resistance may refer to:
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** ''Resistance'' (comics), based on the video game of the same title
** ''T ...
can be written as
:
where
*
is material
resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
,
*
is the cross-sectional area,
*
is the length.
* The cross-sectional area can be split into the width
and the sheet thickness
.
Upon combining the resistivity with the thickness, the resistance can then be written as
:
where
is the sheet resistance. If the film thickness is known, the bulk resistivity
(in
Ω·m) can be calculated by multiplying the sheet resistance by the film thickness in m:
:
Units
Sheet resistance is a special case of resistivity for a uniform sheet thickness. Commonly, resistivity (also known as bulk resistivity, specific electrical resistivity, or volume resistivity) is in units of Ω·m, which is more completely stated in units of Ω·m
2/m (Ω·area/length). When divided by the sheet thickness (m), the units are Ω·m·(m/m)/m = Ω. The term "(m/m)" cancels, but represents a special "square" situation yielding an answer in
ohm
Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm.
Ohm or OHM may also refer to:
People
* Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm''
* Germán Ohm (born 1936), Mexican boxer
* Jörg Ohm (b ...
s. An alternative, common unit is "ohms square" (denoted "
") or "ohms per square" (denoted "Ω/sq" or "
"), which is dimensionally equal to an ohm, but is exclusively used for sheet resistance. This is an advantage, because sheet resistance of 1 Ω could be taken out of context and misinterpreted as bulk resistance of 1 ohm, whereas sheet resistance of 1 Ω/sq cannot thus be misinterpreted.
The reason for the name "ohms per square" is that a square sheet with sheet resistance 10 ohm/square has an actual resistance of 10 ohm, regardless of the size of the square. (For a square,
, so
.) The unit can be thought of as, loosely, "ohms ·
aspect ratio". Example: A 3-unit long by 1-unit wide (aspect ratio = 3) sheet made of material having a sheet resistance of 21 Ω/sq would measure 63 Ω (since it is composed of three 1-unit by 1-unit squares), if the 1-unit edges were attached to an ohmmeter that made contact entirely over each edge.
For semiconductors
For semiconductors doped through diffusion or surface peaked ion implantation we define the sheet resistance using the average resistivity
of the material:
:
which in materials with majority-carrier properties can be approximated by (neglecting intrinsic charge carriers):
:
where
is the junction depth,
is the majority-carrier mobility,
is the carrier charge, and
is the net impurity concentration in terms of depth. Knowing the background carrier concentration
and the surface impurity concentration, the ''sheet resistance-junction depth'' product
can be found using Irvin's curves, which are numerical solutions to the above equation.
Measurement
A
four-point probe is used to avoid contact resistance, which can often have the same magnitude as the sheet resistance. Typically a constant
current
Currents, Current or The Current may refer to:
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* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
is applied to two probes, and the potential on the other two probes is measured with a high-impedance
voltmeter
A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit.
Ana ...
. A geometry factor needs to be applied according to the shape of the four-point array. Two common arrays are square and in-line. For more details see
Van der Pauw method
The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample. Its power lies in its ability to accurately measure the properties of a sample of any arbitrary shape, as long as the sample is a ...
.
Measurement may also be made by applying high-conductivity bus bars to opposite edges of a square (or rectangular) sample. Resistance across a square area will be measured in Ω/sq. For a rectangle an appropriate geometric factor is added. Bus bars must make
ohmic contact
An ohmic contact is a non-rectifying electrical junction: a junction between two conductors that has a linear current–voltage (I–V) curve as with Ohm's law. Low-resistance ohmic contacts are used to allow charge to flow easily in both directi ...
.
Inductive measurement is used as well. This method measures the shielding effect created by
eddy currents
Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magn ...
. In one version of this technique a conductive sheet under test is placed between two coils. This non-contact sheet resistance measurement method also allows to characterize encapsulated thin-films or films with rough surfaces.
[Overview on non-contact eddy current sheet resistance measurement techniques and benefits](_blank)
retrieved 22 November 2013.
A very crude two-point probe method is to measure resistance with the probes close together and the resistance with the probes far apart. The difference between these two resistances will be of the order of magnitude of the sheet resistance.
Typical applications
Sheet resistance measurements are very common to characterize the uniformity of conductive or semiconductive coatings and materials, e.g. for quality assurance. Typical applications include the inline process control of metal, TCO, conductive nanomaterials or other coatings on architectural glass, wafers, flat panel displays, polymer foils, OLED, ceramics, etc.
The contacting four-point probe is often applied for single-point measurements of hard or coarse materials. Non-contact eddy current systems are applied for sensitive or encapsulated coatings, for inline measurements and for high-resolution mapping.
See also
*
ESD materials
Electrostatic discharge materials (ESD materials) are plastics that reduce static electricity to protect against damage to electrostatic-sensitive devices (ESD) or to prevent the accidental ignition of flammable liquids or gases.
Materials
ESD ...
References
Measuring Sheet Resistance
General references
*
*
* {{cite book
, last = Schroder
, first = Dieter K.
, year = 1998
, title = Semiconductor Material and Device Characterization
, url = https://archive.org/details/semiconductormat00schr
, url-access = limited
, pages
1€“55
, publisher = J Wiley & Sons
, location = New York
, isbn = 0-471-24139-3
Measuring Sheet Resistance
Semiconductors
Electrical resistance and conductance