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Sheet Resistance - Series and Parallel Resistors
Sheet Resistance - Series and Parallel Resistors
Published: 2012/04/21
Channel: booksofscience
EEVblog #732 - PCB Sheet Resistance
EEVblog #732 - PCB Sheet Resistance
Published: 2015/04/10
Channel: EEVblog
sheet resistance
sheet resistance
Published: 2014/03/17
Channel: Robert Murray-Smith
Sheet resistance
Sheet resistance
Published: 2014/10/18
Channel: Audiopedia
Wafer Sheet Resistance and Ohms Per Square - Four Point Probes
Wafer Sheet Resistance and Ohms Per Square - Four Point Probes
Published: 2009/06/10
Channel: Jeri Ellsworth
Resistor, Resistance, Resistivity, Sheet Resistance
Resistor, Resistance, Resistivity, Sheet Resistance
Published: 2016/09/09
Channel: eeKnowHow
How to measure surface resistivity of Linqstat plastic conductive films
How to measure surface resistivity of Linqstat plastic conductive films
Published: 2014/06/23
Channel: Caplinq Corporation
Non-Contact INLINE Sheet Resistance Testing solution by SURAGUS GmbH
Non-Contact INLINE Sheet Resistance Testing solution by SURAGUS GmbH
Published: 2014/07/30
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
What Is Sheet Resistance?
What Is Sheet Resistance?
Published: 2017/07/26
Channel: sparky feel
Non-Contact Inline Sheet Resistance Monitoring SURAGUS GmbH
Non-Contact Inline Sheet Resistance Monitoring SURAGUS GmbH
Published: 2014/06/04
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
Wafer Sheet Resistance and Ohms Per Square - Four Point Probes
Wafer Sheet Resistance and Ohms Per Square - Four Point Probes
Published: 2009/06/10
Channel: GeorgeandJeri
GATE 1995 ECE Sheet resistance of n type germanium film
GATE 1995 ECE Sheet resistance of n type germanium film
Published: 2014/04/02
Channel: GATE paper
Problem on Sheet Resistance (5 Mark) - GATE 1995  ECE (Electronic Devices) - www.egate.ws
Problem on Sheet Resistance (5 Mark) - GATE 1995 ECE (Electronic Devices) - www.egate.ws
Published: 2013/11/05
Channel: Raghu Nandan
Four-Point Resistance Measurement? | When and Why, Yo? | Doc Physics
Four-Point Resistance Measurement? | When and Why, Yo? | Doc Physics
Published: 2017/07/20
Channel: Doc Schuster
sheet resistance -series and parallel resistor
sheet resistance -series and parallel resistor
Published: 2016/04/29
Channel: himayat raees
Copper Sheet Resistance Welds
Copper Sheet Resistance Welds
Published: 2013/12/04
Channel: Sunstone Welders
Non-Contact INLINE Sheet resistance sensors SURAGUS
Non-Contact INLINE Sheet resistance sensors SURAGUS
Published: 2016/04/08
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
Handheld Sheet Resistance Tester SURAGUS EddyCus TF Portable
Handheld Sheet Resistance Tester SURAGUS EddyCus TF Portable
Published: 2016/10/07
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
Non-Contact Sheet Resistance Measurement - SURAGUS EddyCus TF lab 4040
Non-Contact Sheet Resistance Measurement - SURAGUS EddyCus TF lab 4040
Published: 2016/05/11
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
EddyCus TF lab - Sheet Resistance Measurement Device
EddyCus TF lab - Sheet Resistance Measurement Device
Published: 2013/07/17
Channel: suragusDE
Microfabrication: Resistance Calculation
Microfabrication: Resistance Calculation
Published: 2011/04/06
Channel: Hans Mikelson
Non-Contact Sheet Resistance Mapping Tool
Non-Contact Sheet Resistance Mapping Tool
Published: 2016/04/08
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
Size Presses
Size Presses
Published: 2015/07/27
Channel: Convergence Training
CRESBOX
CRESBOX
Published: 2014/11/27
Channel: Napson Resistivity measurement
Non-Contact Sheet Resistance Measurement Device SURAGUS EddyCus TF lab 2020
Non-Contact Sheet Resistance Measurement Device SURAGUS EddyCus TF lab 2020
Published: 2016/04/08
Channel: SURAGUS GmbH - Non-Contact Testing Solutions
Four Point Probe Training
Four Point Probe Training
Published: 2016/12/21
Channel: Minnesota Nano Center
Surface Resistivity Meter
Surface Resistivity Meter
Published: 2016/08/30
Channel: LessEMF
4-point resistance measurement (4-point probe + KEITHLEY 2400 SourceMeter)
4-point resistance measurement (4-point probe + KEITHLEY 2400 SourceMeter)
Published: 2017/03/21
Channel: Jinho Bae
SRM1 - ESD Surface Resistance Checker
SRM1 - ESD Surface Resistance Checker
Published: 2013/01/02
Channel: BondlineESDProducts
Copper to Copper Resistance Sheet Welding
Copper to Copper Resistance Sheet Welding
Published: 2013/12/02
Channel: Sunstone Welders
Mechatronics Sher-10-9000 ShereScan 4 Point Probe Sheet Resistance Measurement System #57777
Mechatronics Sher-10-9000 ShereScan 4 Point Probe Sheet Resistance Measurement System #57777
Published: 2015/01/30
Channel: Bid Servicellc
VK-PA-25 PV Power Analyzer Sheet Resistance Measurement Software Demonstration
VK-PA-25 PV Power Analyzer Sheet Resistance Measurement Software Demonstration
Published: 2015/09/10
Channel: Viraj Vishwakantha Jayaweera Piyankarage
Miller  Resistance Spot Welder- Clean Metal
Miller Resistance Spot Welder- Clean Metal
Published: 2014/09/16
Channel: prudhommejc
Vermason Digital Surface Resistance Meter
Vermason Digital Surface Resistance Meter
Published: 2016/06/01
Channel: DescoEuropeESD
Online tutorial on how to find resistance and resistivity of a conductor
Online tutorial on how to find resistance and resistivity of a conductor
Published: 2012/05/02
Channel: techtrainingonline
Digital Surface Resistance Meter Kit
Digital Surface Resistance Meter Kit
Published: 2017/01/30
Channel: DescoESDControl
Sheet Music: La Resistance (Instrumental)
Sheet Music: La Resistance (Instrumental)
Published: 2010/07/30
Channel: RobertTheBruce111
SRM100Kit - Surface resistance checker kit
SRM100Kit - Surface resistance checker kit
Published: 2013/01/02
Channel: BondlineESDProducts
March of the Resistance (Star Wars: The Force Awakens) Williams/Lavender
March of the Resistance (Star Wars: The Force Awakens) Williams/Lavender
Published: 2016/02/01
Channel: Hal Leonard Orchestra
Vermason Surface Resistance Checker
Vermason Surface Resistance Checker
Published: 2016/05/11
Channel: DescoEuropeESD
Surface Resistivity
Surface Resistivity
Published: 2015/06/22
Channel: Louisiana Transportation Research Center
Orion Jewelry Welders - Resistance Welding Sheet Stock
Orion Jewelry Welders - Resistance Welding Sheet Stock
Published: 2009/07/31
Channel: Sunstone Welders
NC-80MAP
NC-80MAP
Published: 2014/12/02
Channel: Napson Resistivity measurement
Resistor Review Problems
Resistor Review Problems
Published: 2012/05/07
Channel: booksofscience
Vermason Analogue Surface Resistance Tester
Vermason Analogue Surface Resistance Tester
Published: 2016/06/21
Channel: DescoEuropeESD
The Equation for the Resistance of a Wire
The Equation for the Resistance of a Wire
Published: 2015/07/13
Channel: Jennifer Cash
March of the Resistance (from "Star Wars: The Force Awakens") Trumpet Cover
March of the Resistance (from "Star Wars: The Force Awakens") Trumpet Cover
Published: 2016/07/22
Channel: The Trumpet Man
Surface Resistance Measurements per ANSI/ESD S11.11
Surface Resistance Measurements per ANSI/ESD S11.11
Published: 2009/11/12
Channel: Prostat
RT-70V / RG-7
RT-70V / RG-7
Published: 2014/10/22
Channel: Napson Resistivity measurement
March of the Resistance
March of the Resistance
Published: 2016/07/07
Channel: Steve Squirrel
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WIKIPEDIA ARTICLE

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Resistor based on the sheet resistance of carbon film

Sheet resistance is a measure of resistance of thin films that are nominally 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 regions (e.g., silicon or polysilicon), and the resistors that are screen printed onto the substrates of thick-film hybrid microcircuits.

The utility of sheet resistance as opposed to resistance or resistivity is that it is directly measured using a four-terminal sensing 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[edit]

Geometry for defining resistivity (left) and sheet resistance (right). In both cases, the current is parallel to the direction of the double-arrow near the letter L.

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 can be written as

where is the resistivity, is the cross-sectional area, and 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·cm) can be calculated by multiplying the sheet resistance by the film thickness in cm:

Units[edit]

Sheet resistance is a special case of resistivity for a uniform sheet thickness. Commonly, resistivity (also known as bulk resistance, specific electrical resistance, or volume resistivity) is in units of Ω·m, which is more completely stated in units of Ω·m2/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 ohms. 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[edit]

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[edit]

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 is applied to two probes, and the potential on the other two probes is measured with a high-impedance voltmeter. 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.

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.

Inductive measurement is used as well. This method measures the shielding effect created by eddy currents. 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.[1]

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[edit]

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[edit]

References[edit]


General references[edit]

  • Van Zant, Peter (2000). Microchip Fabrication. New York: McGraw-Hill. pp. 431–2. ISBN 0-07-135636-3. 
  • Jaeger, Richard C. (2002). Introduction to Microelectronic Fabrication (2nd ed.). New Jersey: Prentice Hall. pp. 81–88. ISBN 0-201-44494-1. 
  • Schroder, Dieter K. (1998). Semiconductor Material and Device Characterization. New York: J Wiley & Sons. pp. 1–55. ISBN 0-471-24139-3. 

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