Force-sensing resistor
`
`A force-sensing resistor is a material whose resistance changes when a force, pressure or mechanical stress is applied. They are also known as "force-
`sensitive resistor" and are sometimes referred to by the initialism "FSR".[1]
`
`Contents
`History
`Properties
`Operation Principle of FSRs
`Percolation in FSRs
`Quantum tunneling in FSRs
`Current research trends in FSRs
`Uses
`See also
`References
`
`History
`
`FSR usage
`
`The technology of force-sensing resistors was invented and patented in 1977 by Franklin Eventoff. In 1985 Eventoff founded Interlink Electronics,[2] a
`company based on his force-sensing-resistor (FSR). In 1987, Eventoff was the recipient of the prestigious international IR 100 award for the development of
`the FSR. In 2001 Eventoff founded a new company, Sensitronics,[3] that he currently runs.[4]
`Properties
`
`Force-sensing resistors consist of a conductive polymer, which changes resistance in a predictable manner following application of force to its surface.[5] They
`are normally supplied as a polymer sheet or ink that can be applied by screen printing. The sensing film consists of both electrically conducting and non-
`conducting particles suspended in matrix. The particles are sub-micrometre sizes, and are formulated to reduce the temperature dependence, improve
`mechanical properties and increase surface durability. Applying a force to the surface of the sensing film causes particles to touch the conducting electrodes,
`changing the resistance of the film. As with all resistive based sensors, force-sensing resistors require a relatively simple interface and can operate
`satisfactorily in moderately hostile environments. Compared to other force sensors, the advantages of FSRs are their size (thickness typically less than
`0.5 mm), low cost and good shock resistance. A disadvantage is their low precision: measurement results may differ 10% and more. Force-sensing capacitors
`offer superior sensitivity and long term stability, but require more complicated drive electronics.
`Operation Principle of FSRs
`
`There are two major operation principles in Force-sensing resistors: percolation and quantum tunneling. Although both phenomena actually occur
`simultaneously in the conductive polymer, one phenomenon dominates over the other depending on particle concentration.[6] Particle concentration is also
`.[7] More recently, new mechanistic explanations have been established to explain the performance of
`referred in literature as the filler volume fraction
`force-sensing resistors; these are based on the property of contact resistance
` occurring between the sensor electrodes and the conductive polymer.
`Specifically the force induced transition from Sharvin contacts to conventional Holm contacts.[8] The contact resistance,
`, plays an important role in the
`current conduction of force-sensing resistors in a twofold manner. First, for a given applied stress
`, or force
`, a plastic deformation occurs between the
`sensor electrodes and the polymer particles thus reducing the contact resistance.[9][10] Second, the uneven polymer surface is flattened when subjected to
`.[10] At a
`incremental forces, and therefore, more contact paths are created; this causes an increment in the effective Area for current conduction
`macroscopic scale, the polymer surface is smooth. However, under a Scanning electron microscope, the conductive polymer is irregular due to agglomerations
`of the polymeric binder.[11]
`
`Up to date, there is not a comprehensive model capable of predicting all the non-linearities observed in force-sensing resistors. The multiple phenomena
`occurring in the conductive polymer turn out to be too complex such to embrace them all simultaneously; this condition is typical of systems encompassed
`within Condensed matter physics. However, in most cases, the experimental behavior of force-sensing resistors can be grossly approximated to either the
`percolation theory or to the equations governing quantum tunneling through a Rectangular potential barrier.
`
`Percolation in FSRs
`
`The percolation phenomenon dominates in the conductive polymer when the particle concentration is above the percolation threshold
`. A force-sensing
`resistor operating on the basis of percolation exhibits a positive coefficient of pressure, and therefore, an increment in the applied pressure causes an
`,[12][13] For a given applied stress
` of the conductive polymer can be computed from:[14]
`increment in the electrical resistance
`, the electrical resistivity
`
` is the critical conductivity exponent.[15] Under
` matches for a prefactor depending on the transport properties of the conductive polymer and
`where
`percolation regime, the particles are separated from each other when mechanical stress is applied, this causes a net increment in the device's resistance.
`
`Quantum tunneling in FSRs
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`

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`Quantum tunneling is the most common operation mode of force-sensing resistors. A conductive polymer operating on the basis of quantum tunneling
`. Commercial FSRs such as the FlexiForce,[16] Interlink [17] and Peratech [18] sensors operate
`exhibits a resistance decrement for incremental values of stress
`on the basis of quantum tunneling. The Peratech sensors are also referred to in the literature as Quantum tunnelling composite.
`
`The quantum tunneling operation implies that the average inter-particle separation
` is reduced when the conductive polymer is subjected to mechanical
` causes a probability increment for particle transmission according to the equations for a Rectangular potential barrier.[19]
`stress, such a reduction in
`Similarly, the Contact Resistance
` is reduced amid larger applied forces. In order to operate on the basis of Quantum tunneling, particle concentration in
`.[6]
`the conductive polymer must be held below the percolation threshold
`
`Several authors have developed theoretical models for the quantum tunneling conduction of FSRs,[20][21] some of the models rely upon the equations for
`particle transmission across a Rectangular potential barrier. However, the practical usage of such equations is limited because they are stated in terms of
`Electron Energy
` that follows a Fermi Dirac probability Distribution, i.e. electron energy is not a priori determined or can not be set by the final user. The
`analytical derivation of the equations for a Rectangular potential barrier including the Fermi Dirac distribution was found in the 60`s by Simmons.[22] Such
`equations relate the Current density
` with the external applied voltage across the sensor
`. However,
` is not straightforward measurable in practice, so the
`transformation
` is usually applied in literature when dealing with FSRs.
`
`Just as the in the equations for a Rectangular potential barrier, the Simmons' equations are piecewise in regard to the magnitude of
`. The simplest Simmons' equation [22] relates
`expressions are stated depending on
` and on the height of the rectangular potential barrier
` as next:
`
`, i.e. different
` with
`, when
`
` is the Planck constant. The low voltage equation of the
` are the electron's mass and charge respectively, and
`,
` is in units of electron Volt,
`where
`Simmons' model [22] is fundamental for modeling the current conduction of FSRs. In fact, the most widely accepted model for tunneling conduction has been
`proposed by Zhang et al.[23] on the basis of such equation. By re-arranging the aforesaid equation, it is possible to obtain an expression for the conductive
`polymer resistance
`, where
` is given by the quotient
` according to the Ohm's law:
`
`When the conductive polymer is fully unloaded, the following relationship can be stated between the inter-particle separation at rest state
`fraction
` and particle diameter
`:
`
`,the filler volume
`
`Similarly, the following relationship can be stated between the inter-particle separation
`
` and stress
`
`where
`next:
`
` is the Young's modulus of the conductive polymer. Finally, by combining all the aforementioned equations, the Zhang's model [23] is obtained as
`
`Although the model from Zhang et al. has been widely accepted by many authors,[11][9] it has been unable to predict some experimental observations reported
`in force-sensing resistors. Probably, the most challenging phenomenon to predict is sensitivity degradation. When subjected to dynamic loading, some force-
`sensing resistors exhibit degradation in sensitivity.[24][25] Up to date, a physical explanation for such a phenomenon has not been provided, but experimental
`observations and more complex modeling from some authors have demonstrated that sensitivity degradation is a voltage-related phenomenon that can be
`avoided by choosing an appropriate driving voltage in the experimental set-up.[26]
`
`The model proposed by Paredes-Madrid et al.[10] uses the entire set of Simmons' Equations [22] and embraces the contact resistance within the model; this
`implies that the external applied voltage to the sensor
` is split between the tunneling voltage
` and the voltage drop across the contact resistance
`as next:
`
`By replacing sensor current
`
` in the above expression,
`
` can be stated as a function of the contact resistance
`
` and
`
` as next:
`
`and the contact resistance
`
` is given by:
`
` are experimentally determined factors that depend on the interface material between
`,
` is the resistance of the conductive nano-particles and
`where
`the conductive polymer and the electrode. Finally the expressions relating sensor current
` with
` are piecewise functions just as the Simmons equations
`[22] are:
`
`When
`
`Samsung Electronics Co. Ltd. et al v. Neodron Ltd
`Exhibit 2008
`IPR2020-00308
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`

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`When
`
`When
`
`, and on
` is stated as an increasing function dependent on the applied stress
`In the aforesaid equations, the effective area for tunneling conduction
`coefficients
`,
`,
` to be experimentally determined. This formulation accounts for the increment in the number of conduction paths with stress:
`
`Current research trends in FSRs
`
`Although the above model [10] is unable to describe the undesired phenomenon of sensitivity degradation, the inclusion of rheological models has predicted
`that drift can be reduced by choosing an appropriate sourcing voltage; this statement has been supported by experimental observations.[26] Another approach
`to reduce drift is to employ Non-aligned electrodes so that the effects of polymer creep are minimized.[27] There is currently a great effort placed on
`improving the performance of FSRs with multiple different approaches: in-depth modeling of such devices in order to choose the most adequate driving
`circuit,[26] changing the electrode configuration to minimize drift and/or hysteresis,[27] investigating on new materials type such as carbon nanotubes,[28] or
`solutions combining the aforesaid methods.
`Uses
`
`Force-sensing resistors are commonly used to create pressure-sensing "buttons" and have applications in many fields, including musical instruments, car
`occupancy sensors, artificial limbs, Foot pronation systems and portable electronics. They are also used in Mixed or Augmented Reality systems[29] as well as
`to enhance mobile interaction.[30][31]
`
`See also
`Velostat - used to make hobbyist sensors
`References
`
`1. FSR Definitions (http://acronyms.thefreedictionary.com/FSR)
`2. "Interlink Electronics" (https://www.interlinkelectronics.com/).
`3. Physics and Radio-Electronics. "Force Sensitive Resistor" (http://www.ph
`ysics-and-radio-electronics.com/electronic-devices-and-circuits/passive-c
`omponents/resistors/forcesensitiveresistor.html).
`4. Sensitronics (http://www.sensitronics.com/about_us.htm)
`5. Tactile Sensors (http://www.soton.ac.uk/~rmc1/robotics/artactile.htm)
`6. Stassi, S; Cauda, V; Canavese, G; Pirri, C (March 14, 2014). "Flexible
`Tactile Sensing Based on Piezoresistive Composites: A Review" (https://
`www.ncbi.nlm.nih.gov/pmc/articles/PMC4003994). Sensors. 14 (3): 5296–
`5332. doi:10.3390/s140305296 (https://doi.org/10.3390%2Fs140305296).
`PMC 4003994 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4003994).
`PMID 24638126 (https://pubmed.ncbi.nlm.nih.gov/24638126).
`7. Bloor, D; Donnelly, K; Hands, P; Laughlin, P; Lussey, D (August 5, 2005).
`"A metal-polymer composite with unusual properties" (https://www.pure.e
`d.ac.uk/ws/files/4945595/2005_JPhysD_preprint_Metal_polymer_compos
`ite_with_unusual_properties.pdf) (PDF). Journal of Physics D. 38 (16):
`2851. Bibcode:2005JPhD...38.2851B (https://ui.adsabs.harvard.edu/abs/
`2005JPhD...38.2851B). doi:10.1088/0022-3727/38/16/018 (https://doi.org/
`10.1088%2F0022-3727%2F38%2F16%2F018).
`8. Mikrajuddin, A; Shi, F; Kim, H; Okuyama, K (April 24, 2000). "Size-
`dependent electrical constriction resistance for contacts of arbitrary size:
`from Sharvin to Holm limits". Materials Science in Semiconductor
`Processing. 2 (4): 321–327. doi:10.1016/S1369-8001(99)00036-0 (https://
`doi.org/10.1016%2FS1369-8001%2899%2900036-0).
`
`9. Kalantari, M; Dargahi, J; Kovecses, J; Mardasi, M; Nouri, S (2012). "A
`New Approach for Modeling Piezoresistive Force Sensors Based on
`Semiconductive Polymer Composites" (https://spectrum.library.concordia.
`ca/974523/1/Masoud_Kalantari_Final_Version.pdf) (PDF). IEEE/ASME
`Transactions on Mechatronics. 17 (3): 572–581.
`doi:10.1109/TMECH.2011.2108664 (https://doi.org/10.1109%2FTMECH.2
`011.2108664).
`10. Paredes-Madrid, L; Palacio, C; Matute, A; Parra, C (September 14,
`2017). "Underlying Physics of Conductive Polymer Composites and Force
`Sensing Resistors (FSRs) under Static Loading Conditions" (https://www.
`ncbi.nlm.nih.gov/pmc/articles/PMC5621037). Sensors. 17 (9): 2108.
`doi:10.3390/s17092108 (https://doi.org/10.3390%2Fs17092108).
`PMC 5621037 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5621037).
`PMID 28906467 (https://pubmed.ncbi.nlm.nih.gov/28906467).
`11. Wang, L; Ding, T; Wang, P (June 30, 2009). "Influence of carbon black
`concentration on piezoresistivity for carbon-black-filled silicone rubber
`composite". Carbon. 47 (14): 3151–3157.
`doi:10.1016/j.carbon.2009.06.050 (https://doi.org/10.1016%2Fj.carbon.20
`09.06.050).
`12. Knite, M; Teteris, V; Kiploka, A; Kaupuzs, J (August 15, 2003).
`"Polyisoprene-carbon black nanocomposites as tensile strain and
`pressure sensor materials". Sensors and Actuators A: Physical. 110 (1–
`3): 142–149. doi:10.1016/j.sna.2003.08.006 (https://doi.org/10.1016%2Fj.
`sna.2003.08.006).
`13. Yi, H; Dongrui, W; Xiao-Man, Z; Hang, Z; Jun-Wei, Z; Zhi-Min, D (October
`24, 2012). "Positive piezoresistive behavior of electrically conductive
`alkyl-functionalized graphene/polydimethylsilicone nanocomposites". J.
`Mater. Chem. C. 1 (3): 515–521. doi:10.1039/C2TC00114D (https://doi.or
`g/10.1039%2FC2TC00114D).
`
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`Exhibit 2008
`IPR2020-00308
`
`

`

`14. Basta, M; Picciarelli, V; Stella, R (October 1, 1993). "An introduction to
`percolation". European Journal of Physics. 15 (3): 97–101.
`Bibcode:1994EJPh...15...97B (https://ui.adsabs.harvard.edu/abs/1994EJ
`Ph...15...97B). doi:10.1088/0143-0807/15/3/001 (https://doi.org/10.1088%
`2F0143-0807%2F15%2F3%2F001).
`15. Zhou, J; Song, Y; Zheng, Q; Wu, Q; Zhang, M (February 2, 2008).
`"Percolation transition and hydrostatic piezoresistance for carbon black
`filled poly(methylvinylsilioaxne) vulcanizates". Carbon. 46 (4): 679–691.
`doi:10.1016/j.carbon.2008.01.028 (https://doi.org/10.1016%2Fj.carbon.20
`08.01.028).
`16. Tekscan, Inc. "FlexiForce, Standard Force \& Load Sensors Model A201.
`Datasheet" (https://www.tekscan.com/sites/default/files/resources/FLX-A2
`01-A.pdf) (PDF).
`17. Interlink Electronics. "FSR400 Series Datasheet" (http://www.interlinkelect
`ronics.com/datasheets/Datasheet_FSR.pdf) (PDF).
`18. Peratech, Inc. "QTC SP200 Series Datasheet. Single Point Sensors" (http
`s://www.peratech.com/assets/uploads/datasheets/Peratech-QTC-DataSh
`eet-SP200-Series-Nov15.pdf) (PDF).
`19. Canavese, G; Stassi, S; Fallauto, C; Corbellini, S; Cauda, V (June 23,
`2013). "Piezoresistive flexible composite for robotic tactile applications".
`Sensors and Actuators A: Physical. 208: 1–9.
`doi:10.1016/j.sna.2013.11.018 (https://doi.org/10.1016%2Fj.sna.2013.11.
`018).
`20. Li, C; Thostenson, E; Chou, T-W (November 29, 2007). "Dominant role of
`tunneling resistance in the electrical conductivity of carbon nanotube–
`based composites". Applied Physics Letters. 91 (22): 223114.
`Bibcode:2007ApPhL..91v3114L (https://ui.adsabs.harvard.edu/abs/2007A
`pPhL..91v3114L). doi:10.1063/1.2819690 (https://doi.org/10.1063%2F1.2
`819690).
`21. Lantada, A; Lafont, P; Muñoz, J; Munoz-Guijosa, J; Echavarri, J
`(September 16, 2010). "Quantum tunnelling composites: Characterisation
`and modelling to promote their applications as sensors". Sensors and
`Actuators A: Physical. 164 (1–2): 46–57. doi:10.1016/j.sna.2010.09.002
`(https://doi.org/10.1016%2Fj.sna.2010.09.002).
`22. Simmons, J (1963). "Electrical tunnel effect between dissimilar electrodes
`separated by a thin insulating Film". Journal of Applied Physics. 34 (9):
`2581–2590. Bibcode:1963JAP....34.2581S (https://ui.adsabs.harvard.edu/
`abs/1963JAP....34.2581S). doi:10.1063/1.1729774 (https://doi.org/10.106
`3%2F1.1729774).
`23. Xiang-Wu, Z; Yi, P; Qiang, Z; Xiao-Su, Y (September 8, 2000). "Time
`dependence of piezoresistance for the conductor-filled polymer
`composites". Journal of Polymer Science Part B: Polymer Physics. 38
`(21): 2739–2749. Bibcode:2000JPoSB..38.2739Z (https://ui.adsabs.harva
`rd.edu/abs/2000JPoSB..38.2739Z). doi:10.1002/1099-
`0488(20001101)38:21<2739::AID-POLB40>3.0.CO;2-O (https://doi.org/1
`0.1002%2F1099-0488%2820001101%2938%3A21%3C2739%3A%3AAI
`D-POLB40%3E3.0.CO%3B2-O).
`
`24. Lebosse, C; Renaud, P; Bayle, B; Mathelin, M (2011). "Modeling and
`Evaluation of Low-Cost Force Sensors". IEEE Transactions on Robotics.
`27 (4): 815–822. doi:10.1109/TRO.2011.2119850 (https://doi.org/10.110
`9%2FTRO.2011.2119850).
`25. Lin, L; Liu, S; Zhang, Q; Li, X; Ji, M; Deng, H; Fu, Q (2013). "Towards
`Tunable Sensitivity of Electrical Property to Strain for Conductive Polymer
`Composites Based on Thermoplastic Elastomer". ACS Applied Materials
`& Interfaces. 5 (12): 5815–5824. doi:10.1021/am401402x (https://doi.org/
`10.1021%2Fam401402x).
`26. Paredes-Madrid, L; Matute, A; Bareño, J; Parra, C; Gutierrez, E
`(November 21, 2017). "Underlying Physics of Conductive Polymer
`Composites and Force Sensing Resistors (FSRs). A Study on Creep
`Response and Dynamic Loading" (https://www.ncbi.nlm.nih.gov/pmc/articl
`es/PMC5706281). Materials. 10 (11): 1334.
`Bibcode:2017Mate...10.1334P (https://ui.adsabs.harvard.edu/abs/2017M
`ate...10.1334P). doi:10.3390/ma10111334 (https://doi.org/10.3390%2Fma
`10111334). PMC 5706281 (https://www.ncbi.nlm.nih.gov/pmc/articles/PM
`C5706281). PMID 29160834
`(https://pubmed.ncbi.nlm.nih.gov/29160834).
`27. Wang, L; Han, Y; Wu, C; Huang, Y (June 7, 2013). "A solution to reduce
`the time dependence of the output resistance of a viscoelastic and
`piezoresistive element". Smart Materials and Structures. 22 (7): 075021.
`Bibcode:2013SMaS...22g5021W (https://ui.adsabs.harvard.edu/abs/2013
`SMaS...22g5021W). doi:10.1088/0964-1726/22/7/075021 (https://doi.org/
`10.1088%2F0964-1726%2F22%2F7%2F075021).
`28. Cao, X; Wei, X; Li, G; Hu, C; Dai, K (March 10, 2017). "Strain sensing
`behaviors of epoxy nanocomposites with carbon nanotubes under cyclic
`deformation". Polymer. 112: 1–9. doi:10.1016/j.polymer.2017.01.068 (http
`s://doi.org/10.1016%2Fj.polymer.2017.01.068).
`29. Issartel, Paul; Besancon, Lonni; Isenberg, Tobias; Ammi, Mehdi (2016). A
`Tangible Volume for Portable 3D Interaction (https://hal.inria.fr/hal-014235
`33/document). IEEE. arXiv:1603.02642
`(https://arxiv.org/abs/1603.02642). doi:10.1109/ismar-adjunct.2016.0079
`(https://doi.org/10.1109%2Fismar-adjunct.2016.0079). ISBN 978-1-5090-
`3740-7.
`30. Besançon, Lonni; Ammi, Mehdi; Isenberg, Tobias (2017). Pressure-Based
`Gain Factor Control for Mobile 3D Interaction using Locally-Coupled
`Devices (https://hal.inria.fr/hal-01436172/document). New York, New
`York, USA: ACM Press. doi:10.1145/3025453.3025890 (https://doi.org/10.
`1145%2F3025453.3025890). ISBN 978-1-4503-4655-9.
`31. McLachlan, Ross; Brewster, Stephen (2015). Bimanual Input for Tablet
`Devices with Pressure and Multi-Touch Gestures. New York, New York,
`USA: ACM Press. doi:10.1145/2785830.2785878 (https://doi.org/10.114
`5%2F2785830.2785878). ISBN 978-1-4503-3652-9.
`
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`
`Samsung Electronics Co. Ltd. et al v. Neodron Ltd
`Exhibit 2008
`IPR2020-00308
`
`