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# 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:

$V_{BE}=V_{G0}(1-{T/T_0})+V_{BE0}(T/T_0)+(nKT/q)\ln(T_0/T)+(KT/q)\ln(IC/IC_0) \,$

where

T = temperature in kelvins
VG0 = bandgap voltage at absolute zero
VBE0 = bandgap voltage at temperature T0 and current IC0
K = Boltzmann's constant
q = charge on an electron
n = a device-dependent constant

By comparing the bandgap voltages at two different currents, IC1 and IC2, many of the variables in the above equation can be eliminated, resulting in the relationship:

$\Delta V_{BE}=(KT/q)\ln(IC_1/IC_2) \,$

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