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66
F~JNL~AMENTALS OF' THE:RMC>ME:TRY
PART VI
THE:RMISTC>R THERMC>ME:TE:RS
by Henry E. Sostmann
and Philip D. Mets
ABSTRACT
Thermistors are a useful and important class of electrical ther-
mometer, with a transfer function of resistance versus temperature. The
resistance-temperature relationship is usually highly non-linear, and
much effort has been given to the invention of linearizing circuitry. In
the most commonly used types, the coefficient of resistance change is
negative; that is, higher temperatures result in higher conduction (lower
resistance). (We will ignore positive temperature coefficient thermistors,
which have little metrological signifigance). Quality of performance varies
widely, in terms of interchangeability, stability, temperature range, and
other characteristics. Consideration here will be given only to classes of
thermistor which are of interest to the metrologist, but it is worth
mentioning that there is a very large number of cruder types, and the
number of thermistors produced by all producers in a given year is
perhaps in the millions. We will also not consider here, except in a
discussion of applications, the many configurations of sheathed,
encapsulated, etc., thermistor temperature probes which are available in
the marketplace.
THEORY OF OPERATION
Figure 1 illustrates the property of intrinsic conductivity in a
semiconducting solid. In the vicinity of 0 K, all electrons are captured
in the valence band, and the conduction band is empty. With increasing
temperature, electron movement into the conduction band increases,
leaving holes in the valence band. The equilibrium is dynamic, with free
Vacant conduction band
I
E Forbidden band Eg ---Fermi Limit
,, ,
.,,;;;;,,,,,/,/,/ll,,,~~~~~~~~~~:~:~~;:;;
`:$$S:;<;Z Filled valence band :;;$:.
:;I'::;:::,,,,,,,,~-~~;;;;;;;;,;;;;i;;:::;
Fig 1: Band scheme for intrinsic conductivity. From Kjttel,
Introduction to Solid State Physics, Wiley, N. Y, ,956, 348
67
electrons in the conductance band recombining with holes in the valence
band, and electrons in the valence band excited to the conduction
band.The increase in electron mobility (therefore conductance) with
increasing temperature accounts for the positive conductance, or
negative temperature-resistance, characteristic.
Early experimental work with thermistors used the electronic
properties of "pure" materials; germanium, silicon, diamond. I place
"pure" in quotation marks, because even minute concentrations of impu-
rities can alter the properties of the thermistor by acting as electron
donors or acceptors; an activity which may be partial or complete de-
pending upon temperature. The most common effect of dopants in pure
materials is to decrease the temperature coefficient of resistance.
COMMERCIAL THERMISTORS; MATERIALS AND FABRICATION
Pure materials are seldom used in commercially distributed ther-
mistors, which are extrinsic devices. The usual materials are metal ox-
ides, or complex oxide systems such as spinels. In these compounds de-
fective crystal structures, and the mutual reactions of the constituents,
abetted by heat applied in fabrication and/or in use, can play a signifi-
cant role in the conductance mechanism.
Typical materials are oxides of manganese, nickel, cobalt, copper,
iron and titanium. Any of these individual materials may be doped with
others to obtain a variety of temperature-resistance characteristics. The
powdered materials are combined, ground together in ball milla (which
may add their own contribution of impurity), constituted to pasty form
with organic liquids (for bead thermistors) or with binders, such as
acrylic (for disc thermistors), dried into beads or punched into disks,
and sintered to form a physically relatively stable material.
From this description, it will be evident that the thermistor mate-
rial is physically, chemically and electronically an extremely complex
system, whose properties continue to defy exact description, and in gen-
eral the manufacturer makes no attempt to gauge or control its proper-
ties by theoretical analysis. Practical production of useful thermistors
depends upon a great deal of experience, adjustments in mix and fabri-
cation, the rejection of some fraction of batches produced on the basis
of post-production test (fortunately at this point the costs of scrap are
small), and some luck and black art. One prominent producer of premium
thermistors routinely loses the touch about a month out of the year
(and we well remember the panics which ensue) until the process
mysteriously corrects itself.
68
Fortunately, lot characteristic analysis at this point lends itself
well to the techniques of statistical analysis.
CLASSIFICATION - DISKS AND BEADS
While any sort of classification in so broad a range of devices is
chancy, we will separate metrology-quality thermistors into two cate-
gories, disks and beads. These two types have, in general, differing
methods of production and different characteristics.
The process of making disk thermistors is illustrated in Fig. 2.
Fig 2: Steps in the manufacture of a disk thermistor. A, ball-
milled powder; B, pressed disk; C, sintered disk; D, silvered
disk; E, edge-ground disk; F, lead wires attached; G, epoxy-coated
(courtesy YSI Inc.)
In 2A, a metal oxide, for example manganese oxide, has been com-
bined with a suitable dopant, for example nickel oxide, and the materials
have been ground together to a fine powder of specific mesh size in a
ball mill . Some acrylic has been added to the mix to make it somewhat
self-adherent.
2B, the powder
In has been compacted into a fragile disk. The di-
mensions of the disk may vary with manufacturer and type, but the or-
der of magnitude is 2.5 mm diameter by 0.5 mm thick.
In 2C, the disk has been sintered by exposure to heat, usually
above 1OOO'C. The rate at which the boat of disks (perhaps several
thousand at once) is inserted into the furnace, the location in the fur-
nace zone, the dwell time at temperature, the atmosphere of the furnace
(and perhaps its state of contamination from previous batches or other
sources), the rate of cool-down or withdrawal, are all part of the manu-
facturer's arcane science; usually the same procedure produces the same
results, and occasionally it doesn't. However , at this point, samples can
69
be taken from the batch and checked, principally for consistency of
dR/dt. No later process can modify the slope, if it is wrong at this
stage; the batch must be scrapped, and another try made, with modifi-
cations of technique and appropriate incantations.
In 2D, the disk has been coated with a silver frit and the frit
fired in place. The purpose of the frit is to permit attachment of lead
wires by soldering or pressure bonding. The silver, it will be noted, is
applied overall, and tends to coat the cylindrical as well as the plane
surfaces of the disk (a direct electrical short), and so in 2E the edges
must be ground free of silver.
It is at this point that disk thermistors can be given their most
important characteristic: that is, interchangeability of units with respect
to Ro and Rt Assuming that the proper slope characteristic has been
achieved in previous steps, the individual disks are clamped in a fixture
immersed in a temperature bath (often at 25-C) and material is removed
from one edge by fine grinding, while the resistance is monitored in
comparison with a standard thermistor at the same temperature. Ther-
mistors can thus be made interchangeable to !zO.l'C, s.O5'C, or some
similar desirable level.
In 2F, lead wires are attached by some commonplace means. One
means is to dip-solder them. Since soldering heat has been applied, it is
prudent to evaluate the batch again after lead attachment. Other meth-
ods involve conductive adhesives, various forms of spot-welding, and
compression bonds.
Soldering is usually accomplished with a lead-tin solder alloy al-
ready partially saturated with silver to avoid scavenging the silver
coating. The phenomenon of scavenging results from the solubility of
silver in tin, which increases with temperature, and scavenges the silver
coating from the substrate. Excess silver in the alloy is equally to be
avoided. (The phenomenon of scavenging can also be observed with
gold) 111.
In 2G, a protective epoxy coating has been applied, usually with
color-coding to indicate the dR/dT type of thermistor. It is then the
custom of at least one manufacturer to evaluate the product, on a 100%
basis, at 3 temperatures not including 25'C. In this manner, thermistors
are produced with close zero and slope conformity, in a wide range of
base resistances. Commercial thermistors are available with 25-C re-
sistance of lOOQ, 300'52, 100051 . . . 1 MQ. Fig. 3 shows the relative ratios
Rt/R25 for several of the common types.
70
For comparison, the Rt/Ro
curve of a platinum resistance
thermometer is also shown. At
this scale, these curves must
be taken to be illustrative
rather than quantitative.
Here is evident one of the
great strengths of thermis-
tors: a large change in resis-
tance is realised for a rela-
tively small change in temper-
ature over the portion of its
curve where it is most sensi-
tive.
-80 0 80 120 140 The change in resistance of a
'C thermistor is about 4X of the
immediate resistance per 1 `C
Fig 3: Rt/R(25) for several common
change, while the change in
thermistor types. I q lOOQ, II =
22528. IOKP. IOOKQ, III = IMP at resistance of a platinum re-
25-C. IV q Rt/Ro for a platinum sistance thermometer is about
resistance thermome'ter. 0.4% per `C of the resistance
at 0-C.
The process of manufacturing bead thermistors is illustrated in
Fig. 4.
The process of compounding the powder is essentially as in 2A for
disks, The powder is compounded usually not with an acrylic binder but
with some volatile organic, to produce a manageable slurry,
In Fig 4, lead wires, of a material which will tolerate the sintering
temperature, are held in slight tension and parallel to each other at a
distance which is dictated by the desired siee of the bead. Slurry'is
lead
- wires 7 ?,- slurry beads
a I I
a
cut (a) cut (b)
Fig 4: Manufacture of bead thermistors. The process is de-
scribed in the text. The l.ead wires may be cut in several
styles (a), (b).
71
apphed between the lead wires. The system is then dried and sintered,
in a controlled atmosphere, at a temperature which will result in suffi-
cient density to hold the thermistor material and the lead wires to-
gether. The bead and the adjacent wires are then cut into a desired
lead configuration, and the surface of the bead and a short length of
the emergent wires are coated with a thin glass film (alternatively,
sealed within the tip of a thin-walled glass tube) for mechanical secu-
rity.
The various forms of bead which can be made by this process of-
ten result in a sensitive element smaller than possible in disc produc-
tion; but as a generality, beads cannot be made to close tempera-
ture/resistance tolerances (interchangeable) and can satisfy such re-
quirements only by test and selection after fabrication, or by a network
of pads and shunts (which reduce sensitivity). Typical unit-to-unit
interchangeability for bead thermistors is ?20%.
Other forms of thermistor are common. These are short rods,
flakes and chips (of small mass but larger area, suitable, e.g., for in-
frared detectors), washers and films. Thermistors have been formed in
place by vapor deposition; such forms will not be considered here, since
their metrology applications are limited (but films have been used in
low-mass sensitive bolometers).
TH,E CHOICE - DISKS OR BEADS?
The better choice is based upon the application and the properties
required from the sensor. However all choices involve trade-offs; for ex-
ample, a bead thermistor, which might be chosen because it is very
small, will not satisfy a requirement for interchangeability, and will have
a lower dissipation constant (higher self-heat), than a disk. Table 1 will
attempt to summarise salient considerations.
I: Size. Often an advantage of thermistor temperature sensors is
the small size of the sensitive element; its ability to make a spot mea-
surement. Bead thermistors can be made much smaller than discs.
2: Stability. Legend has it that bead thermistors are more stable
than disk thermistors, and early experience seems to confirm this [Zl.
The explanation for this superior stability is probably the result of the
customary glass encapsulation of bead thermistors, which has the fol-
lowing consequences:
(a) The semiconductor bead and its lead attachments are an her-
metically sealed system, preventing oxidation of the attachment contact.
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CATALOGS
TIIRRHOWITRICS, RIGEYAYKDISON, JERSEY
808OS I, NBU 08817,(201)-287-2870
?SI INC, BRANNOW YKLLOY
LANK, SPRINGS, 45387,
OH0 (513)-767-7241
73
There is reason to believe that some of the shift in epoxy-coated ther-
mistors, after exposure to temperature at their upper rated limit, is due
to deterioration of the contact between the thermistor surface and the
contact frit.
(b) The semiconductor is constrained by the shrinkage of the
glass coating, binding the grains more tightly together.
In the early days of radio, microphones were made with a carbon
element. Sound pressures reoriented the contact boundaries of the car-
bon granules, altering the bulk resistance of the element. It is possible
to find in this an analogue of the thermistor. A structure which physical
constrains the grains into a constant-contact mass would produce a less
sensitive microphone, and a more stable thermistor.
Recently (perhaps 10 years ago) one manufacturer of disk ther-
mistors began manufacturing interchangeable sensors in which, after
grinding to 25 `C interchangeability, the assembly was glass-coated.
These units have been shown to approach the stability of the best
beads and offer the advantage of interchangeability, which beads do
not.
Stability of any thermistor depends upon the maximum temperature
to which the sensor is exposed. Reported stability for glass-coated disks
is shown in Table 2.
TABLE 2
OP TEMP* 1 MONTH 10 MONTH 100 MONTH
25-C to.01 `C (0.01 `C
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