Silicon bandgap temperature sensor

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:

$V_{BE}=V_{G0}\left(1-{\frac {T}{T_{0}}}\right)+V_{BE0}\left({\frac {T}{T_{0}}}\right)+\left({\frac {nKT}{q}}\right)\ln \left({\frac {T_{0}}{T}}\right)+\left({\frac {KT}{q}}\right)\ln \left({\frac {I_{C}}{I_{C0}}}\right)\,$

where

T = temperature in kelvins

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

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:

$\Delta V_{BE}={\frac {KT}{q}}\cdot \ln \left({\frac {I_{C1}}{I_{C2}}}\right)\,$

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.

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

• R. J. Widlar (1967). "An exact expression for the thermal variation of the emitter base voltage of bi-polar transistors". Proceedings of the IEEE. 55 (1): 96–97. doi:10.1109/PROC.1967.5396. {{cite journal}}: Unknown parameter |month= ignored (help)

External links

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