Force-sensing resistor
A force-sensing resistor is a material whose
History
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 received the prestigious International IR 100 award for developing the FSR. In 2001 Eventoff founded a new company, Sensitronics,[3] that he currently runs.[4]
Properties
Force-sensing resistors consist of a
Operation principle of FSRs
There are two major operation principles in force-sensing resistors:
To date, no comprehensive model is 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 based on percolation exhibits a positive coefficient of pressure, and therefore, an increment in the applied pressure causes an increment in the
where matches for a prefactor depending on the transport properties of the conductive polymer, and is the critical conductivity exponent.[15] Under 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
The quantum tunneling operation implies that the average inter-particle separation is reduced when the conductive polymer is subjected to mechanical stress; such a reduction in causes a probability increment for particle transmission according to the equations for a rectangular potential barrier.[19] Similarly, the contact resistance is reduced amid larger applied forces. To operate based on quantum tunneling, particle concentration in the conductive polymer must be held below the percolation threshold .[6]
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 in the equations for a rectangular potential barrier, the Simmons' equations are piecewise regarding the magnitude of , i.e., different expressions are stated depending on and the height of the rectangular potential barrier . The simplest Simmons' equation [22] relates with , when as next:
where is in units of electron volt, , are the electron's mass and charge respectively, and is the Planck constant. The low voltage equation of the Simmons' model [22] is fundamental for modeling the current conduction of FSRs. The most widely accepted model for tunneling conduction has been proposed by Zhang et al.[23] based on such equation. By re-arranging the equation above, 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 ,the filler volume fraction and particle diameter :
Similarly, the following relationship can be stated between the inter-particle separation and stress
where is the Young's modulus of the conductive polymer. Finally, by combining all the equations above, the Zhang's model [23] is obtained as next:
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 externally 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:
where is the resistance of the conductive nano-particles and , are experimentally determined factors that depend on the interface material between the conductive polymer and the electrode. Finally the expressions relating sensor current with are piecewise functions just as the Simmons equations [22] are:
When
When
When
In the equations above, the effective area for tunneling conduction is stated as an increasing function dependent on the applied stress , and on 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
Uses
Force-sensing resistors are commonly used to create pressure-sensing "buttons" and have applications in many fields, including
See also
- Velostat – used to make hobbyist sensors
References
- ^ FSR Definitions
- ^ "Interlink Electronics".
- ^ Physics and Radio-Electronics. "Force Sensitive Resistor".
- ^ Sensitronics
- ^ "Tactile Sensors". Archived from the original on April 24, 2001.
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- ^ Tekscan, Inc. "FlexiForce, Standard Force \& Load Sensors Model A201. Datasheet" (PDF).
- ^ Interlink Electronics. "FSR400 Series Datasheet" (PDF).
- ^ Peratech, Inc. "QTC SP200 Series Datasheet. Single Point Sensors" (PDF).
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