# Piezoresistive effect

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The piezoresistive effect describes change in the electrical resistivity of a semiconductor when mechanical stress is applied. In contrast to the piezoelectric effect, the piezoresistive effect only causes a change in electrical resistance, not in electric potential.

## History

The change of electrical resistance in metal devices due to an applied mechanical load was first discovered in 1856 by Lord Kelvin. With single crystal silicon becoming the material of choice for the design of analog and digital circuits, the large piezoresistive effect in silicon and germanium was first discovered in 1954 (Smith 1954).

## Mechanism

In semiconductors, changes in inter-atomic spacing resulting from strain affects the bandgaps making it easier (or harder depending on the material and strain) for electrons to be raised into the conduction band. This results in a change in resistivity of the semiconductor. Piezoresistivity is defined by

$\rho_\sigma = \frac{\left(\frac{\partial\rho}{\rho}\right)}{\varepsilon}$

Where

∂ρ = Change in resistivity
ρ = Original resistivity
ε = Strains

Piezoresistivity has a much greater effect on resistance than a simple change in geometry and so a semiconductor can be used to create a much more sensitive strain gauge, though they are generally also more sensitive to environmental conditions (esp. temperature).

### Resistance change in metals

The resistance change in metals is only due to the change of geometry resulting from applied mechanical stress[1]:p.208 and can be calculated using the simple resistance equation derived from Changes in geometry resulting from applied mechanical stress affect the resistances of metals, which can be calculated using the simple resistance equation derived from ohm's law;

$R = \rho\frac{\ell}{A} \,$

where

$\ell$ Conductor length [m]
A Cross-sectional area of the current flow [m²][1]:p.207

### Piezoresistive effect in semiconductors

The piezoresistive effect of semiconductor materials can be several orders of magnitudes larger than the geometrical effect in metals and is present in materials like germanium, polycrystalline silicon, amorphous silicon, silicon carbide, and single crystal silicon.

#### Piezoresistive effect in silicon

The resistance of silicon changes not only due to the stress dependent change of geometry, but also due to the stress dependent resistivity of the material. This results in gauge factors to orders of magnitudes larger than those observed in metals (Smith 1954). The resistance of n-conducting silicon mainly changes due to a shift of the three different conducting valley pairs. The shifting causes a redistribution of the carriers between valleys with different mobilities. This results in varying mobilities dependent on the direction of current flow. A minor effect is due to the effective mass change related to changing shapes of the valleys. In p-conducting silicon the phenomena are more complex and also result in mass changes and hole transfer.

## Piezoresistive silicon devices

The piezoresistive effect of semiconductors has been used for sensor devices employing all kinds of semiconductor materials such as germanium, polycrystalline silicon, amorphous silicon, and single crystal silicon. Since silicon is today the material of choice for integrated digital and analog circuits the use of piezoresistive silicon devices has been of great interest. It enables the easy integration of stress sensors with Bipolar and CMOS circuits.

This has enabled a wide range of products using the piezoresistive effect. Many commercial devices such as pressure sensors and acceleration sensors employ the piezoresistive effect in silicon. But due to its magnitude the piezoresistive effect in silicon has also attracted the attention of research and development for all other devices using single crystal silicon. Semiconductor Hall sensors, for example, were capable of achieving their current precision only after employing methods which eliminate signal contributions due the applied mechanical stress.

### Piezoresistors

Piezoresistors are resistors made from a piezoresistive material and are usually used for measurement of mechanical stress. They are the simplest form of piezoresistive devices.

#### Fabrication

Piezoresistors can be fabricated using wide variety of piezoresistive materials. The simplest form of piezoresistive silicon sensors are diffused resistors. Piezoresistors consist of a simple two contact diffused n- or p-wells within a p- or n-substrate. As the typical square resistances of these devices are in the range of several hundred ohms, additional p+ or n+ plus diffusions are necessary to facilitate ohmic contacts to the device.

Schematic cross-section of the basic elements of a silicon n-well piezoresistor.

#### Physics of operation

For typical stress values in the MPa range the stress dependent voltage drop along the resistor Vr, can be considered to be linear. A piezoresistor aligned with the x-axis as shown in the figure may be described by

$\ V_r = R_0 I[1 + \pi _L \sigma _{xx} + \pi _T (\sigma _{yy} + \sigma _{zz} )]$

where $R_0$, I, $\pi _T$, $\pi _L$, and $\sigma _{ij}$ denote the stress free resistance, the applied current, the transverse and longitudinal piezoresistive coefficients, and the three tensile stress components, respectively. The piezoresistive coefficients vary significantly with the sensor orientation with respect to the crystallographic axes and with the doping profile. Despite the fairly large stress sensitivity of simple resistors, they are preferably used in more complex configurations eliminating certain cross sensitivities and drawbacks. Piezoresistors have the disadvantage of being highly sensitive to temperature changes while featuring comparatively small relative stress dependent signal amplitude changes.

Advanced stress sensors derived from piezoresistors are Wheatstone bridges, transducers, and picture frame sensors.

### Other piezoresistive devices

In silicon the piezoresistive effect is used in piezoresistors, transducers, piezo-FETS, solid state accelerometers and bipolar transistors.

## References

1. ^ a b Liu, Chang (2006). [www.mech.northwestern.edu/FOM/LiuCh06v3_072505.pdf "Piezoresistive Sensors"] Check |url= scheme (help). Foundations of MEMS. Upper Saddle River, NG: Prentice Hall. ISBN 0131472860. Retrieved 3 March 2013.
• Y. Kanda, "Piezoresistance Effect of Silicon," Sens. Actuators, vol. A28, no. 2, pp. 83–91, 1991.
• S. Middelhoek and S. A. Audet, Silicon Sensors, Delft, The Netherlands: Delft University Press, 1994.
• A. L. Window, Strain Gauge Technology, 2nd ed, London, England: Elsevier Applied Science, 1992.
• C. S. Smith, "Piezoresistance Effect in Germanium and Silicon," Phys. Rev., vol. 94, no. 1, pp. 42–49, 1954.
• S. M. Sze, Semiconductor Sensors, New York: Wiley, 1994.
• A. A. Barlian, W.-T. Park, J. R. Mallon, A. J. Rastegar, and B. L. Pruitt, "Review: Semiconductor Piezoresistance for Microsystems," Proc. IEEE, vol. 97, no. 3, pp. 513–552, 2009.