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The '''silicon bandgap temperature sensor''' is an extremely common form of temperature sensor ([[thermometer]]) used in electronic equipment.  Its main advantage is that it can be included in a silicon [[integrated circuit]] at very low cost.  The principle of the sensor is that the forward voltage of a [[silicon]] [[diode]] is temperature-dependent, according to the following equation:
:<math>V_{BE}=V_{G0}\left(1-{\frac{T}{T_0}}\right)+V_{BE0}\left(\frac{T}{T_0}\right)+
    \left(\frac{nKT}{q}\right)\ln\left(\frac{T_0}{T}\right)+
    \left(\frac{KT}{q}\right)\ln\left(\frac{I_C}{I_{C0}}\right) \,</math>
where
:''T'' = temperature in [[kelvin]]
:''T<sub>0</sub> = reference temperature
:''V''<sub>''G''0</sub> = [[bandgap]] voltage at [[absolute zero]]
:''V''<sub>''BE''0</sub> = bandgap voltage at temperature ''T''<sub>0</sub> and current ''I''<sub>C0</sub>
:''K'' = [[Boltzmann's constant]]
:''q'' = charge on an [[electron]]
:''n'' = a device-dependent constant


[[Image:Bandgap-reference.svg|thumb|Circuit of a [[Brokaw bandgap reference]]]]
By comparing the bandgap voltages at two different currents, ''I''<sub>C1</sub> and ''I''<sub>C2</sub>, many of the variables in the above equation can be eliminated, resulting in the relationship:
:<math>\Delta V_{BE}=\frac{KT}{q}\cdot\ln\left(\frac{I_{C1}}{I_{C2}}\right) \,</math>


A circuit that forces ''I''<sub>C1</sub> and ''I''<sub>C2</sub> to have a fixed N:1 ratio,<ref name="bryant">
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James Bryant.
[http://www.analog.com/static/imported-files/rarely_asked_questions/moreInfo_raq_gapTempSensors.html "IC Temperature Sensors"].
Analog Devices.
2008.
</ref>
gives the relationship:
:<math>\Delta V_{BE}=\frac{KT}{q}\cdot\ln\left(N\right) \,</math>
An electronic circuit, such as the [[Brokaw bandgap reference]], that measures Δ''V''<sub>''BE''</sub> can therefore be used to calculate the temperature of the diode.  The result remains valid up to about 200 °C to 250 °C, when leakage currents become large enough to corrupt the measurement.  Above these temperatures, materials such as [[silicon carbide]] can be used instead of silicon.
 
The voltage difference between two [[p–n junction|p-n junctions]] (e.g. [[diode]]s), operated at different current densities, is '''p'''roportional '''t'''o '''a'''bsolute '''t'''emperature (PTAT).
 
PTAT circuits using either BJT or CMOS transistors are widely used in temperature sensors (where we want the output to vary with temperature), and also in bandgap voltage references and other temperature-compensating circuits (where we want the same output at every temperature).<ref name="bryant"/><ref>
AL.AL, M. B. I. Reaz, S. M. A. Motakabber Mohd Alauddin Mohd Ali.
[http://www.waset.org/journals/waset/v64/v64-2.pdf "A Single-chip Proportional to Absolute Temperature Sensor Using CMOS Technology"].
2012.
</ref><ref>
C. Rossi, C. Galup-Montoro, and M. C. Schneider.
[http://iie.fing.edu.uy/investigacion/grupos/microele/papers/nsti07_ptat.pdf "PTAT Voltage Generator based on an MOS Voltage Divider"].
Nanotechnology Conference and Trade Show, Technical Proceedings, 2007.
</ref><ref>
Andre Luiz Aita and Cesar Ramos Rodrigues.
[http://cobre.eletrica.ufpr.br/chipin/sbcci/accepted/220.html "PTAT CMOS Current Sources Mismatch over Temperature"].
The 26th Symposium on Integrated Circuits and System Design (SBCCI 2013).
2013.
</ref>
 
If high precision is not required it is enough to bias a diode with any constant low current and use its −2 mV/˚C thermal coefficient for temperature calculation, however this requires calibration for each diode type. This method is common in monolithic temperature sensors.[citation required]
 
==References==
{{reflist}}
*{{cite journal | doi = 10.1109/PROC.1967.5396 | author = R. J. Widlar |title = An exact expression for the thermal variation of the emitter base voltage of bi-polar transistors|journal=Proceedings of the IEEE|volume=55|issue=1|pages=96–97|date=Jan 1967}}
 
== External links ==
 
* [http://www.analog.com/static/imported-files/application_notes/AN_892.pdf Temperature Sensing Theory and Practical Techniques], Analog Devices
* [http://www.national.com/an/AN/AN-460.pdf Precision Monolithic Temperature Sensors], National Semiconductor
 
[[Category:Thermometers]]

Revision as of 16:10, 2 March 2014


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