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5.2.1 Principles of operation Thermistors are non-linear Stanley, 1973, temperature dependent proms, 1962; Hyde,1971 resistors with a high resistance temperature coefficient.. In practic

Semiconductor Thermometers

Semiconductor thermometers (Sachse, 1975) are made from materials which are neither conductors nor insulators Research of the thermal properties of semiconductors was first reported by William Faraday in 1834 Their industrial production was started at the Bell Telephone Company and, simultaneously, at Osram in 1930 It is apparent from the work of many authors such as Sze (1969) and van der Ziel (1968), among others, that these materials may have an intrinsic, or pure form, a compound form or a doped form Compound and doped semiconductors are often called extrinsic semiconductors.

Thermometers of this type, which may use bulk material temperature dependencies or junction effect carrier density relations, may be classified by the number of electrodes and number of junctions possessed per sensor This ordering is based upon that used by Sze (1969) in the classification of semiconductor devices There are two main groups of semiconductor thermometers

" Bulk effect two-electrode sensors, which belong to the resistive group, possess no semiconductor junctions They are thermistors or silicon-RTDs, also called Silistors by Hyde (1971).

" Junction device sensors are either diodes with one junction and two terminals, transistors, with two junctions and three terminals, or integrated circuit sensors with multiple junctions and numbers ofterminals.

Semiconductors exhibit strong temperature dependent behaviour From fundamental physical considerations it can be shown that extrinsic semiconductors possess three main regions of temperature dependence.

In doped materials at temperatures below about 150 K, and particularly within the cryogenic range, there are practically no minority carriers as most material impurities are

`frozen out' The other two regions correspond to what may be called normal (200 K to

500 K) and intrinsic (above 600 K) ranges (van der Ziel, 1968; Sze, 1969) As these effects can be tightly controlled and predicted for doped materials their use in temperature measurement is inevitable In the temperature range between about 200 K and 500 K, where ,normal' semiconductor behaviour occurs, carrier mobility has a sensitivity to both doping and temperature which is well described by an empirically derived analytical expression (Arora et al., 1982) Bulk effect semiconductor temperature sensors arise from this

104 SEMICONDUCTOR THERMOMETERS

temperature dependence ofmobility as well as the temperature dependent density ofcarriers

in the bulk homogeneous regions of a material Junction and monolithic temperature sensorsdepend upon the relations between carriers across junctions for their temperature dependentbehaviour At temperatures above about 600 K extrinsic materials behave in a similarmanner to intrinsic materials

5.2.1 Principles of operation

Thermistors are non-linear (Stanley, 1973), temperature dependent (proms, 1962; Hyde,1971) resistors with a high resistance temperature coefficient In practice, only thermistorswith a negative temperature coefficient (NTC type) are used for temperature measurement.Thermistors having positive temperature coefficient (PTC type) are only used for the binarydetection ofa given temperature value

The production of thermistors, which is very complicated, uses ceramic manufacturingtechnology, consisting of high pressure forming and sintering at temperatures up to

1000 °C Although the process for the manufacture of both types is similar, they are madefrom different materials (Roess, 1984) PTC types have a fundamental composition basedupon barium titanate Mixtures of different powdered oxides of Mn, Fe, Ni, Cu, Ti, Zn and

Co are used to make NTC thermistors Their properties depend upon their heat treatmenttemperature and atmosphere, as well as on the manner in which they are subsequentlyannealed After the thermistor has been metal coated and trimmed to adjust its resistance, itsconnecting leads are then attached before encapsulation At 20 °C the resistance of athermistor may be in the range of some k(2 to about 40 MO

From the relations in van der Ziel (1968) and Sze (1969) for the density of electrons inn-type material and the relation for carrier mobility due to Arora et al., (1982), it can beshown (Becker et al., 1946) that the resistivity of n-type material is directly proportional toT-ce(k,IT) where c is a small valued constant, which may be positive or negative, and kI

is a material dependent constant Hyde (1971) has shown that the best fit to these basicrelations gives the commonly used approximation to the resistance versus temperaturecharacteristic of a thermistor in the form:

where T is the thermistor temperature in K, RTis the thermistor resistance at temperature T,R., is the limit value of RTas T -4 -, and B is a constant depending on the thermistormaterial, in K

Although attempts have been made to provide a better approximation (Bosson et al.,1950), the approximate form given in equation (5 1) will be used exclusively in this book

As the value, Rte, is impossible to determine, equation (5 1) can be expressed in terms of itsresistance, RTr at some reference temperature, Tr,usually 293 K, in the more readily useableform:

RT =RT eB[(IIT)-(IIT,))

(5 2) r

The other quantities in equation (5 2) are the same as in equation (5.1) Define thethermistor's resistance temperature coefficient as:

_ 1 dRT

aT

RT dTDifferentiating equation (5.2) and inserting the result together with the value of RT intoequation (5 3) leads to:

From equation (5 3a) it is evident that the absolute value ofaT , and the sensitivity of thethermistor both decrease with increasing measured temperature The coefficient, aTr , isusually expressed in%/K Using equation (5.3a) it is possible to represent equation (5 2) inanother frequently used form,

be varied between 10 f2cm and 105 f2cm with a corresponding increase in the B coefficientfrom 2580Kto 4600 K At the reference temperature of 293 K, the value of aT usuallylies between -2 %/K and -6 %/K As these normal NTC materials have phase transitionsabove 500 °C, they cannot be used in the manufacture devices for use above this range.However, rare earths may be used up to temperatures around 1500 °C

Figure 5.1 shows the ratio, RT/ RTr , as a function of temperature with the coefficient,

aT ,r as parameter at a reference temperature taken as T, = 293 K (20 °C) For comparativepurposes, the characteristic of a Pt-1000 RTD is also shown The voltage-currentcharacteristic of a thermistor is defined as the voltage drop across the thermistor expressed

as a function of the current flowing in it, with the ambient temperature of a givensurrounding medium as a parameter A typical voltage-current characteristic, for athermistor in still air at the ambient temperature, Oal, is shown in Figure 5 2 Thecharacteristics of the same thermistor in still water at the temperatures dal , 6a2 , 0a3 arealso shown in this figure Initially, the thermistor voltage drop is directly proportional to itscurrent With increasing current, the resulting self-heating of the thermistor is accompanied

by a commensurate decrease of its resistance, so causing the voltage versus currentcharacteristic to decrease On the V =J(1) curves, for each current value, the corresponding

0,01-20 0 20 40 60 80 100 120 140 160 180

TEMPERATURE 3 , °CFigure 5.1 Resistance, RT , of a temperature sensor at temperature, T to RT at 293 K (20 °C) versustemperature,

temperature increases, A61, 1102 063, are also indicated These values may be usedfor the estimation of self-heating errors

From Figure 5.2 it can be seen that the resistance of the thermistor decreases withincreasing ambient temperature, which is also the measured temperature, so that itscharacteristics are shifted downwards

Thermistors possess a heat dissipation constant, C, given in W/K, similarly defined asthe dissipation constant, A, for the RTD used in equation (4.10) The value of this heatdissipation constant depends on the medium surrounding the thermistor For example, in air

C has a value which is smaller than its value in water Consequently, at the same measuringcurrent, the errors due to self-heating are larger in air than in water In the same way as forthe RTD, C permits a similar determination of the permissible measuring current, IT,max,

of a thermistor of resistance, RT, for a given assumed self-heating error, OO,ax , as:

IT,max - D TmaxC (5.5)

TConversely, the self-heating error, O6, at the measuring current, IT, can be evaluated as:

e~AZ A-1, _0 -TEMPERATURE RISE

Numerical example

Calculate the permissible measuring current of a thermistor intended to measure air temperature in

a range from 0 to 100 °C The self-heating error should be kept below 0.5 °C In air the heatdissipation constant, C, has a value of0.8x10-3 W/K, while the thermistor resistance at 20 °C is

RT = 8.5 W Also, at this temperature of 20 °C (293 K) the resistance temperature coefficient,raTr , has a value of-4 %/K or-0.04 1/K

Solution:

From equation (5.4) at a temperature T= 373 K or 100 °C:

RT =RT er [aTrAT(TrIT)] = 8.5X 1032[-0.04x80x293/3733] = 688 52Inserting this value ofRT into equation (5.5) yields the maximum measuring current as:

3

_ OSX0.8X IT,max- 688 0.76X10-3 A

10-Only the initial, linear part of the voltage-current characteristic shown in Figure 5.3 isused for temperature measurement The static value of the resistance, RT, of a thermistor atthe given temperature, Dal , can be calculated, from the values of current and voltage in

Compared with metallic resistance detectors,NTCthermistors have the advantages:

" smaller detector dimensions,

" higher temperature sensitivity,

" higher detector resistance, which means that readings are less affected by the resistance

of the connecting leads,

" lower thermal inertia of the sensor,

" possibility of measuring smaller temperature differences,

The main disadvantages ofNTCthermistors are:

" non-linear resistance versus temperature characteristic,

" non-standardised characteristics,

" lower measuring temperature range,

" susceptibility to permanent decalibration at higher temperatures.

Thermistors of the PTC type, which may be used as binary temperature sensors are also produced in thin film technology (Morris and Filshie, 1982; Nagai et al., 1982) They are used to protect semiconductor devices and electrical machinery At preset temperatures , such as for example, 35, 55, 75, 95 °C, the resistance of these PTC thermistors may increase from about 100 0 to about 100 kf2 with increasing temperature.

Tolerances of the value of RTr for a given type of thermistor are usually around 5 % to

20 %, whereas tolerance for the constant, B, is around 5 % These large tolerances areregarded as the main disadvantage in thermistor applications Selected thermistors, dividedinto various groups of narrow tolerances, are available This ensures totalinterchangeability, with temperature errors kept below ±0.1 to ±0.2 °C (Omega EngineeringInc, USA, 1999; Cole-Parmer Instr Co., 1999) Their prices, are ofcourse, much higher.Beads are made by allowing evenly spaced minute droppings of oxide slurry to fall upontwo parallel stringed platinum alloy wires Owing to the high surface tension of the slurry,the drops maintain their ellipsoidal shape After drying, the drops are sintered attemperatures between 1100 °C and 1400 °C During the sintering process they shrink, soadhering to the wires with a well formed good electrical contact Subsequently, they are cut,

as shown in Figure 5 4(a), before being hermetically sealed with a glass or teflon layerwhich protects them from oxidation and environmental influences The wires have adiameter of about 0.0125 to 0.125 mm while the beads vary in diameter from about 0.1 to

2 mm (Sapoff, 1972; Weichert et al., 1976)

Disk thermistors are produced by pressing oxide powders under several tons ofpressure

in a round die After sintering they are covered by a silver layer to permit soldering of theterminal wire The thermistors, shown in Figure 5 4(e), which are wholly protected by anepoxy layer, have diameters from 1 to 10 mm and thicknesses ranging from 0.1 to 2 mm.Square plate thermistors, also called chip thermistors, have dimensions of 0.54.5 mm to3x3 mm and thicknesses of 0.025 to 0.05 mm Stable glass-covered disk thermistors, whoseindications do not change more than ±0 005 °C per year in the temperature range from -

80 °C to 200 °C, are also produced (Wise, 1992; Siwek et al., 1992)

Portable thermistor sensors, in the form of probes, with extendible coiled cables, areproduced for all types of likely applications such as in the temperature measurement of air,

(a) BEAD (b) GLASS OR PLASTIC (c) ROD

liquids, surfaces of solids, meat, fruit and chemicals More specialised areas of applicationare in biology and medicine In the medical field, thermistor probes are disposed of afteronly one use to avoid the possibility of cross-contamination This is not unreasonable asthey are comparatively inexpensive Their 90 % rise time is about 1 to 3 s.

Stationary thermistor sensors are used in the temperature measurement of extruders,storage tanks and containers, in chemical apparatus and in grain silos as 3 to 6 sensor sets.Long time instability ofthermistors, which is mainly attributed to their resistance values,

is caused by lattice structure changes due to oxidation and thermal tensions or by changes inthe resistance ofthe metallized contact This last cause seems to be the most important Themost stable types are glass-covered bead thermistors, whose resistance does not changemore than 0.05 to 0.25 % per year, as compared with 0.5 to 3 % per year for disk and rodthermistors These resistance changes are usually easily compensated for in the measuringcircuits by periodic calibration checks

In most cases thermistors are used with a protective sheath

Thermistors, which are generally supplied with their indicating meters by the samemanufacturer, have many applications Their large signal, high sensitivity, small dimensionsand the possibility of applying long connecting leads make them especially appropriate inalmost all applications within their somewhat limited temperature range between about-50 °C to about 300 °C Thermistors are frequently used in the physical and biological fieldssuch as in the food industry or in medicine as detailed by Sapoff (1972) Other importantareas of application are in air and liquid temperature measurement as well as in thetemperature measurement of small electronic elements and machine parts

5.2.3 Correction and linearisation of thermistor characteristics

There are two main methods of guaranteeing the interchangeability of thermistor sensors

" Production control methods allow the selection and division of thermistors into groupswith a small scattering of the thermistor characteristics Subsequently they may beseparated into components with narrow temperature tolerances This may be either over arange of temperatures or at a single temperature Tolerances may be, for example,

±0.05 °C, ±0.1 °C, ±0.2 °C and ±1 °C which are marked on the component by a colourcode (Sierracin/Western Thermistors, Oceanside, USA)

" Array configuration methods employ the ideas associated with other resistancemanufacturing techniques (Connolly, 1982; Costlow, 1983) Thus it is possible to correctand linearise the thermistor characteristics using a computer program to calculate theresistor values based upon the measured thermistor characteristics at three giventemperatures Such a procedure is carried out during production

The non-linear resistance versus temperature characteristic is regarded as the maindisadvantage of thermistors This functional dependence, as given by equation (5 1), results

in decreased thermistor sensitivity at higher temperatures

Linearisation may use analogue linearising circuits or it may be digital (McGhee, 1989).The digital approach uses a number of different circuits

Analogue linearisation is mainly based upon the most convenient and classical methodgiven by Beakley (1951) and Hyde (1971) similar to those shown in Figure 5 5 For

30 mV/K, which is many times greater than that of a thermocouple For multi-pointtemperature measurement, one resistor set can be used for many thermistor assemblies Inthe circuit, given in Figure 5.5(a), both positive or negative slope output voltage signals arepossible Player (1986) describes an extension of this technique to give a wide rangethermistor thermometer In every 10°C sub-range the compensating network of thethermistor is changed As thermistor characteristics are exponentially deterministic, alogarithmic amplifier may be used for linearising purposes (Patranabis et al., 1988).

Digital linearisation methods fall into various main groups A general method applyingone-, two- and three-point digital methods to a number of electrical output temperaturesensors, including thermistors, is considered by Bolk (1985) The technique of using ananalogue-to-digital converter described by Iglesias and Iglesias (1988) may be adapted tosuit thermistors

A final group of methods uses post-conversion techniques based upon a ROM lookuptable/software routine (Brignell, 1985)

5.2 4 Measuring circuits

The common forms of thermistor thermometer measuring circuits are deflection type bridgecircuits, like that shown in Figure 5 6 The bridge energy source may be a battery cell or arectified supply voltage To ensure that the supplying voltage remains constant, astandardising resistor, Rs, is provided In the position 'O' of the switch, S, where RStemporarily replaces the thermistor, RT, the value of Ra is adjusted in such a way that thereadings of the meter, M, are brought to a marked scale position This is not necessary when

a stabilised voltage source is used Measuring temperatures ranges of 30 to 50 °C mayeasily be achieved The whole measuring range is divided into several selectable sub-ranges Most producers now supply thermistor thermometers in deflection type bridgecircuits with an IC output amplifier guaranteeing a precision of 0.5 to 1 0 °C More

generally, digital indicating instruments are used.

An example of a digital meter based on a bridge circuit with an A/D transmitter is theOmega Thermistor Thermometer This meter, of dimensions 178x84x46 mm, whichcontains a digital 100-section linearisation circuit, is intended for use with a 6800thermistor The same meter, which can also be used for thermocouples and RTDs, is fedfrom a 9V alkaline battery, giving an operational life of 1200 hrs The temperature range is

20 to 120 °C, depending on the thermistor type used, with a precision better than ±2 OC andindications updated every 0.5 s

For lower measurement precision, the simpleseries connected thermistor thermometers,shown in Figure 5 7, are also used They comprise a current limiting resistor, R1, and amicroammeter, M, graduated in temperature degrees A standardising resistor, RS, andswitch, S, are also provided The permissible measuring current ofthe thermistor should notexceed the value calculated using equation (5.5)

Sengupta (1988) describes a pulse generator whose frequency is related to the resistance

of the thermistor The principle of operation of the basic circuit, shown in Figure 5 8, isbased upon temperature to frequency conversion The frequency of the square wave outputsignal is:

2R'Cln(1 + 2R2/ R1)Since the resistance versus temperature characteristic of the thermistor has an exponentialform, replacing R2 by the thermistor resistance allows cancellation of the exponential

VOLTAGE SETTING E

RQ

<R3

Rp 'C

Figure 5.6 Deflection type bridge circuit for Figure 5.7 Series connected thermistor