handbook of modern sensors

16.3 Semiconductor P-N Junction Sensors 489
Fig. 16.20. Forward-biased p-n junction temperature sensors: (A) diode; (B) diode-connected
transistor.
where E g is the energy band gap for silicon at 0 K (absolute zero), q is the charge of
an electron, and K is a temperature-independent constant. It follows from Eq. (16.46)
that when the junction is operated under constant-current conditions, the voltage is
linearly related to the temperature and the slope is given by
b = dV
dT − 2k (ln K − ln I). (16.47)
q
Typically, for a silicon junction operating at 10 µA, the slope (sensitivity) is approximately
−2.3 mV/ ◦ C and it drops to about −2.0 mV/ ◦ C for a 1-mA current. Any
diode or junction transistor can be used as a temperature sensor. A practical circuit
for the transistor used as a temperature sensor is shown in Fig. 16.19B. A voltage
source E and a stable resistor R is used instead of a current source. Current though
the transistor is determined as
I = E − V
R . (16.48)
It is recommended to use current on the order of I = 100 µA; therefore for E = 5
V and V ≈ 0.6 V, the resistance R = (E − V )/I = 44 k. When the temperature increases,
the voltage V drops, which results in a minute increase in current I.According
to Eq. (16.47), this causes some reduction in sensitivity which, in turn, is manifested
as nonlinearity. However, the nonlinearity may be either small enough for a particular
application or it can be taken care of during the signal processing. This makes a
transistor (diode) temperature sensor a very attractive device for many applications,
due to its simplicity and very low cost. Figure 16.21 shows an error curve for the
temperature sensors made with the PN100 transistor operating at 100 µA. It is seen
that the error is quite small, and for many practical purposes, no linearity correction
is required.
A diode sensor can be formed in a silicon substrate in many monolithic sensors
which require temperature compensation. For instance, it can be diffused into a mi-