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 B E = V G 0 (1 - T / T 0) + V B E 0 (T / T 0) + (n K T / q)ln(T 0 / T) + (K T / q)ln(I C / I C 0)

where

T = temperature in kelvins

V_G0 = bandgap voltage at absolute zero

V_BE0 = 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:

Δ V B E = (K T / q)ln(I C 1 / I C 2)

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, more exotic materials such as silicon carbide can be used instead of silicon.