pn-Junction as Temperature Sensor

A pn-junction (i.e. a diode) can be used as a simple and easy to use temperature sensor. According to the diode equation

I_D ... diode current
I_s ... saturation current
e .... Euler's constant (2.71828...)
q .... charge of electron (1.610^-19 As)
V .... voltage across the diode
N .... "non-ideality" coefficient (typ. between 1 and 2)
k .... Boltzmann's constant (1.3810^-23)
T .... junction temperature in Kelvin

the current through the diode depends on the Voltage V_D applied to the diode and its temperature. If you keep the current through the diode constant, the voltage decreases with increasing temperature. Assuming a current of 10 mA through the diode we can insert all known values into the diode equation and calculate the change of the voltage if the temperature changes by 1K:

Applying the logarithm to both sides and assuming a "non-ideality factor" of N=1 we get:

This means that the voltage across a forward biased diode decreases by approx. 2 mV/K. Please note that the characteristic curve of the temperature dependence of the diode voltage is strictly linear, so that the calibration of a diode temperature sensor is straightforward and simple.