Reaction rate

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:

$V_{BE}=V_{G0}(1-\frac{T}{T_0})+V_{BE0}\left(\frac{T}{T_0}\right)+\left(\frac{nKT}{q}\right)\ln \left(\frac{T_0}{T}\right)+\left(\frac{KT}{q}\right)\ln \left(\frac{I_C}{I_{C0}}\right)$

where

T = temperature in kelvin

T₀ = reference temperature

V_G0 = bandgap voltage at absolute zero

V_BE0 = bandgap voltage at temperature T₀ and current I_C0

K = Boltzmann's constant

q = charge on an electron

n = a device-dependent constant

File:Bandgap-reference.svg

Circuit of a Brokaw bandgap reference

By comparing the bandgap voltages at two different currents, I_C1 and I_C2, many of the variables in the above equation can be eliminated, resulting in the relationship:

$\mathrm{\Delta }{V}_{BE}=\frac{KT}{q}\cdot \ln \left(\frac{I_{C1}}{I_{C2}}\right)$

A circuit that forces I_C1 and I_C2 to have a fixed N:1 ratio, gives the relationship:

$\mathrm{\Delta }{V}_{BE}=\frac{KT}{q}\cdot \ln \left(N\right)$

An electronic circuit, such as the Brokaw bandgap reference, that measures ΔV_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 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).

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

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External links

• Temperature Sensing Theory and Practical Techniques, Analog Devices
• Precision Monolithic Temperature Sensors, National Semiconductor