handbook of modern sensors

464 16 Temperature Sensors
Usually, RTDs are calibrated at standard points which can be reproduced in a
laboratory with high accuracy (Table 16.1). Calibrating at these points allows for the
precise determination of approximation constants α and δ.
Typical tolerances for the wire-wound RTDs is ±10 m, which corresponds to
about ±0.025 ◦ C. Giving high requirements to accuracy, packaging isolation of the
device should be seriously considered. This is especially true at higher temperatures,
at which the resistance of isolators may drop significantly. For instance, a 10-M
shunt resistor at 550 ◦ C results in a resistive error of about 3 m, which corresponds
to temperature error of −0.0075 ◦ C.
16.1.2 Silicon Resistive Sensors
Conductive properties of bulk silicon have been successfully implemented for the
fabrication of temperature sensors with positive temperature coefficient (PTC) characteristics.
Currently, silicon resistive sensors are often incorporated into the micromachined
structures for temperature compensation or direct temperature measurement.
There are also the discrete silicon sensors (e.g., the so-called KTY temperature
detectors manufactured by Philips). These sensors have reasonably good linearity
(which can be improved by the use of simple compensating circuits) and high longterm
stability (typically, ±0.05K per year). The PTC makes them inherently safe for
operation in heating systems:Amoderate overheating (below 200 ◦ C) results in RTD’s
resistance increase and self-protection.
Pure silicon, either polysilicon or single-crystal silicon, intrinsically has a negative
temperature coefficient of resistance (NTC) (Fig. 18.1B of Chapter 18). However,
when it is doped with an n-type impurity, in a certain temperature range its temperature
coefficient becomes positive (Fig. 16.4). This is a result of the fall in the charge carrier
mobility at lower temperatures. At higher temperatures, the number n of free charge
carriers increases due to the number n i of spontaneously generated charge carriers, and
the intrinsic semiconductor properties of silicon predominate. Thus, at temperatures
below 200 ◦ C, the resistivity ρ has a PTC; however, above 200 ◦ C, it becomes negative.
The basic KTY sensor consists of an n-type silicon cell having approximate
dimensions of 500 × 500 × 240 µm, metallized on one side and having contact areas
on the other side. This produces an effect of resistance “spreading,” which causes
a conical current distribution through the crystal, significantly reducing the sensor’s
dependence on manufacturing tolerances. A KTY sensor may be somewhat sensitive
to current direction, especially at larger currents and higher temperatures. To alleviate
this problem, a serially opposite design is employed where two of the sensors are
connected with opposite polarities to form a dual sensor. These sensors are especially
useful for automotive applications.
The typical sensitivity of a PTC silicon sensor is on the order of 0.7%/ ◦ C; that
is, its resistance changes by 0.7% per every degree Celsius. As for any other sensor
with a mild nonlinearity, the KTY sensor transfer function may be approximated by
a second-order polynomial:
R T = R 0 [1 + A(T − T 0 ) + B(T − T 0 ) 2 ], (16.14)