The silicon bandgap temperature sensor is an extremely common form of temperature sensor (
thermometer
A thermometer is a device that measures temperature or a temperature gradient (the degree of hotness or coldness of an object). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a mercury-in-glass 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
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ta ...
diode, which may be the base-emitter junction of a
bipolar junction transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipola ...
(BJT), is temperature-dependent, according to the following equation:
:
where
:''T'' = temperature in
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
s,
:''T''
0 = reference temperature,
:''V''
''G''0 =
bandgap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (i ...
voltage at
absolute zero,
:''V''
''BE''0 = junction voltage at temperature ''T''
0 and current ''I''
C0,
:''k'' =
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
,
:''q'' = charge on an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
,
:''n'' = a device-dependent constant.
By comparing the voltages of two junctions at the same temperature, but at two different currents, ''I''
C1 and ''I''
C2, many of the variables in the above equation can be eliminated, resulting in the relationship:
:
Note that the junction voltage is a function of current density, i.e. current/junction area, and a similar output voltage can be obtained by operating the two junctions at the same current, if one is of a different area to the other.
A circuit that forces ''I''
C1 and ''I''
C2 to have a fixed N:1 ratio,
[
James Bryant]
"IC Temperature Sensors"
.
Analog Devices.
2008.
gives the relationship:
:
An electronic circuit, such as the
Brokaw bandgap reference Brokaw bandgap reference is a voltage reference circuit widely used in integrated circuits, with an output voltage around 1.25 V with low temperature dependence. This particular circuit is one type of a bandgap voltage reference, named after Paul Br ...
, that measures Δ''V''
''BE'' 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
Silicon carbide (SiC), also known as carborundum (), is a hard chemical compound containing silicon and carbon. A semiconductor, it occurs in nature as the extremely rare mineral moissanite, but has been mass-produced as a powder and crystal s ...
can be used instead of silicon.
The voltage difference between two
p-n junctions (e.g.
diodes), operated at different current densities, is proportional to absolute temperature (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).
[
Andre Luiz Aita and Cesar Ramos Rodrigues]
"PTAT CMOS Current Sources Mismatch over Temperature"
The 26th Symposium on Integrated Circuits and System Design (SBCCI 2013).
2013.
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.
References
{{reflist
External links
Temperature Sensing Theory and Practical Techniques Analog Devices
Precision Monolithic Temperature Sensors TI (formerly National Semiconductor)
Thermometers