Topics in..
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Chemical Instrumentation
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Edited by GALEN W. EWING, S e t m Hall University, So. Orange, N. J. 07079 These articles, most of which are to be contributed by guest authors, are intended to serve the readeTs of this JOURNAL by calling attention to new developments i n the theoy, design, or availability of chemical laboratory instwmeninlim, or by presenting useful insights and explanations of topics that are of practical importance to those who use, or teach the use of, modern instrumentatim and instrumental techniques.
XXXIV. Theory and Applications E. A. BOUCHER, Deportment o f Physic01 Chemistry, The University, Bristol, England. INTRODUCTION .4 thermistor (thermally sensitive resis-
is their large negative coefficient of resirt m c e change with temperature. The properties of semiconductors. rouoled with
rimetry, pressure gauges, flow meters, hygrometers, gas analyzers and thermametric titratom, as well ai in electronic instruments when they are employed, for example, in power level control, it) power measurement, and for automatic gain c o w trol iu amplifiers. The purpose of this article is tu examine critically the oharaeteristici of thermistors and to offer an introdnotion to applications of interest t,o the chemist. To do this it is first de~irsbleto have a working knowledge oi the underlying theory of semieond u d o m .4n indication is the,, given of how thermistors are made. This is followed hy a discussion of the characteristics of thermistot.~upon which the applications depend.
germanium, selenium and tellurium, compounds of the type GaA8, spinels, m e h l oxides, and certain organic compounds. Mixtures of metal oxides (including those of manganese, niokel, cobalt, copper, tungsten, titanium, chromium, and vanadium) are the most common semiconductors used in thermistor man,&wture. Semiconduct,ing materials are also used in t,rensist,ors, rectifiers, modulators, detectom, and photocells. An introduction to these devices can he obtained from general books on electroniw (1, $2).
Metals and Insulators
To understand the nature of semiconductivity, it is convenient to consider fixst the eleetricd properties of metals and insulators on the basis of the hand theory. I>et,ailsof the band theory can he obtained from books on t,he solid fitate, e.g., Kittel (S), although t,he t,reatment in Moore's textbook (4) provides suflicient basis for discussion. I t mnst be emohasised. since it is not obvious from the elementary treatment given here, that the development of qusntum mechanics was essential t,o an explanation of the behavior of solids-in particular semicondoebars-in the presence of an applied electric field. The electrons in a single isolated atom of THEORY OF SEMICONDUCTORS a metal are confined to discrek energy At mom temperature, semiconduct~o~~s levels or atomic orbitals. An ideal piece of metal can be considered l o he an ordered have specific resistances in t,he range 1I1Fz r2nq of n l d e i ill a sea of electrons. Pauli's t,o 10' ohm cm, which is intermediate hetweeu conductors ohm em) and ksulators (>lO1' ohm cm), and, wit,h rare exceptions, they have negative* temperature coeflicients of resistance (3-57, per deg C is not uncommon). Semicondurtivity i~ displayed by a variety of substanres, iueluding elements such as silicon,
' Sir Charles Goodeve, Brit,ish Iron and Steel Res. Assoc., is credited with the ~.enmrk that semiconductors are feminine, . .became their resistance derremes as they warm up!'' [See Ameriran S~.im/ist, p. 440A (Dee. 196i)l.
".
Ernest A. Baucher was gradwnted fl.orn ihe University of Wales and obtained I Ph.1). degree from the University of Brist,ol. An kssociade Axember of the Royal Institute of Chemistry, and I Member of Sigma Xi, Dr. Boucher was Research Associate a t Lehigh University during 196546, and joined the staff of the University of Bristal ~nJanuary, 1967.
~~~
~
~~~
exclusion principle permits only two electrons in a given energy level. Thus, an energy level of an isolated atom becomes in the solid, a. very large nnmher of closely spaced energy levels forming a. band. Eaoh energy level in the lower bands will be doubly occupied and so these bands will be completely filled. The electrons in these hands will not be able to move under the influence of an applied electric field and will not contribute to the conductivity of the metal. The upper hand of a metal will not be completely occupied, or will overlap with the next empty band, as depicted in Figure la. When an electric field is applied, electrons near the tap of the filled zone can readily move into unoccupied levels where they are free to move throughout the solid. (Continued a page A936) Donor
level
Figure 1. Bond Model Depictions of (01 metal, Ib) insulator, Ic) intrinsic remiconductor, Id1 n-type remicanductor and lel p-type remiconductor.
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Chemical instrumentation The axductivity of a snhatanae is a mrwsure of the prodnct of the rntmher of n w rent carriers (in this ease elealmni) and their mobility. I n a perfectly wdered ideal metallic crystal, the electrow wm~ld be completely free to move and thr w.;is tance would be zero. In a real solid, :L large contribution to the resistance (i.c.. obstruction of current carriers) comes from thermal motion of the atomic nuclei. In a metal the number of current carriers is very large (approx. 1021/cm3) mtd is virtually independent, of bemperatwe. The mobility of the electrons decreases as the temperature increases, producing xu increme in resist,anee. The variation in resistance wit,h temperatore of plalinwn and of a t,ypical ihermistor are shown in Figure 2.
Figure 2. Variation of Rerirtonce with Temperature for Plotinurn and a T y p i m l Thermistor.
Insulators are characterized by having completely filled lower hands and a large energy gap between the highest filled and the lowest empty band, a3 represented in Figure l b .
Intrinsic Semiconductors Pure materids exhibiting semieonductiviiy are termed intrinsic semicondocto~.s, of which silicon and germanium are the most common and the best ,mdel.stoud. An intrinsic semiconductor would, at ahsalute zero, possess a filled valence hand separated by only a small energy gap from a vacant conduction band. As the temperature is raised, a numher of electrons are thermally excited from the valence band, leaving an eqrtd number of hales (Fig. le). Both the electrons and the positive holes act as c~lrrentcarriers by moving in opposil,e directions when an electric field is applied. As bhe tempemture increases, the numher of current carriers increases and outweighs t.he decrease in mobilit,y due to thermal vibrations of the nuclei, so that the conductivity inrreases. Application of Fermi-IXrae st,atistirs gives the t,emperature dependence of the number of electrons n- exoiled from the valence hand t.n the crmdocl.ion hand as (5), n- a T'h exp[-AElliT] (I) (Conlinued on page A 9 5 8
A936 /
Journol of Chemicol Educofion
Chemical Instrumentation where AR is one half of the energy gap belweet~ tlrr I ~ a n d ~The . temperature depmden~.eof m ~ ~ ~ ecmrier u l . mobility, considered ;LS prirrmrily due to lattice soatl,ering, is proportiond to 1'-'b. The reriafanee c m then be expected to h e y the :tpp'.mirnak i.elitt,iomhip:
R
=
A exp[+AE/kT]
(2 )
Equation (2) is obeyed by actual intrin.iic semiconduolm.~ only over a limited tempel.at~rre range, as sham-n in Figure 3. ( h n ~ a n i u mHMI silicon do not show inI.rinsic sernico~~~h~otivity a t low temperat.ures, hut uevertheless semieonductivit,y i~lvarial,l.ypwsist.s owing to the presence
Figure 3. Showing Silican Doped with Phapharvr Behaving ar on Intrinsic Semiconductor a t High Temperature. and or an impurity (".type) Semiconductor ot Low Temperatures (Lineor Portions Indicate Applicabilily of Equation 2) after Friedberg 15L
Impurity Semiconduc~ors The t,hewy oi impurit,~semicondwt,ors can be readily explained using germanium as the horl lat,tirz. The same general scheme is applicable to more complex s y s terns, some of which are however not completely inlderstood. In Figure 4a, a few t,elravsle~tlat,oms, iu this case germanium, have been replaced by a n equal number of penbavalenl, arsenic atoms; the arsenic nboms baking up pusition% in the lattice (dismond stnkebure) originally occupied by germanium atoms. Each arsenic atom has a. loonely bound electron attached to it which can be readily promoted to the conduct,ion band by am itmount of energy, ED, in Figure I d . AILelectron when bound to an amenio atom is said to be in a donor level. The cument carriers in this case are electrons and the semiconductivity exhibited ia termed n-type. When a few atoms in s. germanium I& $,iceare replaced by t,rivalent atoms, such as indium in Figure 4b, the impurity atoms provide empty levels (acceptor levels in Figwe l e ) just above the valence hand, into which eleot,rons e m be promoted. The promotnl eleot~~~ons leave behind poxi-
A938
journal of Chemical Educdion
Chemical instrumentation
II ll n II II =M=M=M=M=M= II 11 11 II II =M=M-M=M=M= II II U II II =M=Y=M=M=M= II II I1 II II =MeM=M=y=M= II II II II II @
b Figure 4a. Conduction b y Donor Electrons e, produced b y Impurity X from Group V in o Lonice of Group iV Element M, e.g. M = Ge, X = As. Figure 4b. Conduction due to Positive Holes xherea Group Ill Impurity, Y, hor Accepted Electrons in o Group IV Element[Lanice, e.g. M = Ge, Y = In.
+
live holes which ael H..c ~ r r r e ~ewriws ~t n ~ d the semiconductor is termed p-lype. Generally hoth accept,or and domx levels will owor in a snmiw,nd~talor, although one will usually dominate t,he conductivily at a given, t.emperst,twe. The general scheme jwf. deacrihed is followed hy semicondwt~oi~sof the t,yye (:%As. Suhstit,ut.ion of a (:l.oup BI elemeut for arsenic pmdrmes donors, whereas suhstitut,ion of a Group I1 element for gallimn yields acceptor levels.
Metal Oxides Transition metal uxides, fur e x n q d r NiO rtnd CulO, hemme semiconductors of the so called "controlled valence" type hg impurity suhst~itntion. If, for example, x small numher of munovalent. lithium ions replaces an equal number of niekel ions in nickel oxide, anequal number of remshling nickel ion8 will he oxidized from the dito the tri-valent state. Elecfmns can now move under an applied electric field from divalent to trivalent nickel ions. Metal oxides can also h o w semicoudnctivity if they depart, from atoichiometry. There ase four principal ways in w h i d ~ nonstoiohiometr?i can lead t,o semieondncting hehsvinr (8). In Type I, anion vacmcies itre present,, that in, the met,al is in excess, while in Type 11, the metal is in excess due to cations in interst.it,ialpositions. I n hoth cases the crystd is kept elect,ricslly neutral (by electlms t,rapped in (.heviciw
(Continued nn pngs A.94Z)
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A939
Chemical instrumentation ity of the vaoanoies and interstitial cations respectively). Such solids will exhibit semiconductivit,y if these trapped electrons can be liberated by thermal energy. In Types 111 and IV, the anions are in excess due to the presence of interstitial anions and of cation vacancies respectively. Electrical nentralitv is now maintained hv be a. semiconductor. The electronic conductivity shown by nonstoiehiometric metal oxides is therefore classified into n-type or p-type. The conduetivi1,y will increase with temperature in s. similar manner to that of intrinsic semiconductors discussed above.
in terms of t,he outline given above, albhough the general scheme remains the same. The conducting properties of the materials are greally influenced by grain boundaries and by the nature of the surface of the material. The band levels a t the fiurfaee differ from those in the hulk solid (7), and are aNeoted by adsorption of gmes and vapurs of which water vapor is commoll.
M A N U F A C T U R E O F THERMISTORS The 8cmicondooting materials used in the mnnufileture of thermistors are generally either mixtures of transitim mebd oxides, or of spinels, e.g., MgCr01 and .MgALOr. These snbstances are least send i v e to changes in impurity content,. Thermistors can be obtained in five ba.ic shapes, rods, discs, headn, washers, and flakes. The manufacturing procedure most often used is to make a homogeneous mixture of the powdered constituents, often with an organic hinder. The mixture is molded and fired so as to cause sintering or even melting. I t is necessary in some cases to control the rate of heating, the maximum temperature reached, the length of firing, and the atmosphere, in order t,o obtain reproducible products. After firing, metal contacts are made, ming metal pastes a'. by spraying metal to whioh conducting w'res can be soldered. The head type of thermistor is perhaps of most interest to the chemist. These
he semiconductor meteri& in the jig. form of a slurry, is applied at intervals along the wires, a5 shown in Figure 5. The slurry is dried and sintered, and then the leads are cut to give individual t h e r m ist,ors. To protect this type of thermistor from moisture and other contaminants, which could affect i k stability, the bead is placed in a glass envelope which can be in direel o n t a c t with the bead, can be evacuated, or can be filled with a dry gas. Thermistors covering a wide range of specific resistances and temperature eneflicients can be made by variation of the composition of the starting mixture. A (Continued on page A944)
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Chemical Instrumentation
Figure 5.
Mmufocture of Beod Thermistors for Rring b. Beod fired and detached.
o. Semiconductor piaced an wirer
wide range of electrical characteristics (discussed in the next section), necessary for different applications, can be achieved wit,h thermistors of various sizes and forms.
CHARACTERISTICS OF THERMISTORS The most obvious characteristic of thermistors which is exploited in applications is the large variat,ion of resistance with temperature. The purpose of this section is to show the importance of other (often olosely related) factors which must be considered when designing and operatr ing thermistor devices.
Variation of Resistance with Temperature, and of Current with Applied Voltage The large deorease in resistance with increase in temperature, as shown in Figure 3, can be described, a t least for intrinsic semiconductors, by eqn. (2). For actual thermistors it is convenient to determine the resist,ance Ro at 298-K in such a manner that the current flowing causes negligible self-heating of the thermistor. The resistance R of the thermistor a t temperature T0K can then be represented hy,
Roexp [B(lK
- l/298)1
temperatnre is defined as,
and may be of the order of -3 to -5% per deg K compared with +0.35% per deg K far platinum. Except when the current flowing is very small, the magnitude of the current for a given applied voltage will be dominated by the R-T relationship, since the thermistor will experience self heating. It is import,ant to note that o is temperature dependent. (B also is slightly dependent on temperature.) Consider a thermistor suspended in still air. When the current flowing is very small, that is, when there is no self heating, the thermistor will obey Ohm's law. When the current is increased, the t,hermistor temperature will rise above ambient and t,he resistsnce will decrease. The volt,age will be less than it wodd have been had the resistance not changed. In fact, the voltage V across a thermistor reaches x maximom value as the cnrrent I increases. The variation of voltage with
(Continued on page AB48)
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Journol of Chernicol Education
Chemical Instrumentation current, typical of Lhermistors, is conveniently rept.esenled as log V plotted against. log I as in Fignre 6 , which is adapted from Derker, Green, and Pearson (9). The tempe~.atme.=on the ewves represent the diflerenee between the thermi d o r and amhietlt t,emperatwes. On such a plot, lines of positive unit slope
Figure 6.
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repvesent constm! resistance, and lines of negative unit slope represent e a n s h n t power.
Characteristic Quantities of a Thermistor I n addition t,o the R-T relation and the
V-I relation, a particular thermifit,or is characterized by its heat capacity (which depends upon its size and amposition),
Plot of log V against log I for
Journal of Chemical Edumfion
0
Typical Thermistor.
its dissipation constant, power sensitivit,y, time constant,, and by the maximum power xhieh it, can t,alerste ensuring good stittility and long life. (i) The disnipat,iau eowtant C specifies the ammuit of powel. dissipated (in watts) per degree of thermistor temperature ( T - T.) deg C above that of the smroundings. The dissipation constaut depends upon the natwe of the surrounding medium, and upon thermal conduct,ion along t,he supports (oflen the l e d wires). Change in the dissipation crmstant can be hvought ahont n o t only h:- changing t,he medium, but also h y rhsuging, for example, the rate of rtirring of smbient liquid or the rale of cireulstiorr of n ease011s mediom. The effect of a change in C ltpon the log V against log I plot is shown in Figure 7 (9). For s point on the V-1 curve V I I = R, and 1' X I = IT,' the liumber of watts dissipated. The hemperat,ure of the thermistor e m now be read from t,he R-T cnrve. A plot of power dissipnt,ed against T can be constructed which allows C = Tf/(T - T,) t o be ealculated. The dependence of C upon ambient gas velocity, gas pressure, and the nature of the gay, forms t,he baais of ?he applicat,ion of t,hermistor in anemometers, mnnomcters, and gas m a l y z e ~respectively. .~ (ii) The power sensitivity, which depends upon the same f a c t o t ~as t,he dissipation constant., is defined as t,he power which most be dissipated in order to rerh~cethe resistance by 1%. The value of the power sensitivity is given by CIlOOa.
(Contineed a page .Uf50)
Chemical Instrumentation
e r n x s the themistor (determined with a dl ctwent Rowing) is recorded a f~wcl,im of tinrc, the variation of bernpera-
Current nA Figure
7. Effect of Chmge in C upon Variation of log V with log I.
(iii) The h e aonsliml,, r ser, is an i m p ~ t a u factor t it, rlwign n,widn.nt.iol~s, The fndors diso!t.;sed Y O far have all referred bo steady-stale nonditionr, wherr varinhles nwlr as lemper.ntto.e, rwrent, and powev dissipalic,~~have r e a d 11, vary with h e . I t is twefltl to know, in sddit,ion, {.he rate at, whirh t.he thezmiat,c,r resiat,ance will change fat. s given change it, srnhienl, tempwxl\lre. Suppose H, t.hermirtor is in a steady-state rmrrlition with a relativelv lame current
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Journal of Chemical Educofion
bore (as T - T , , ) with time can be calcrllat,ed. If t,he heat capacity of the thermistm is H, and ii At is an increment of time, st,wting nt 1 = O when the current is cut. r,R, t,he nmotmt of power dissipated in Al see will be C ( T T.)Al joules. Uuling this time interval the t,hermist,or temperaI !we will dewease AT such that,:
-
-HAT
""
=
C(T - T , ) X
(5)
Chemical Instrumentation
Type of Thermistor
Integratim of eqn (6) given: T - T,
=
(Ti
- T,)
exp(-117)
Table I.
ii)
where a t 1 = 0, T = Tiand t,herefore r = H/C. The slope of a plot of log ( T - T.) against time 1 is (-1/2.3037). A representative plot is shown in Figure 8. An nltemative way of thinking of the time constant is as the t,ime taken for -log,[(T-T.)/(Ti - To)], ahhined from eqn. (7), to hecome rmit,y, or for ( T - T,)
Typical Characteristic Quantities for Three Types of Thermistor (data supplied by Fenwsl Electronics Inc.) Rars
a
% per deg C
Mini-probe* head in glms 100 to 100kR - 3 . 2 to -4.6
Disc of hare material 0.4 in diam e.g., LBYU2
18.6Q
-3.9
Bead type for gas analyzelr e . ~ .GI12 ,
2000n
-3.4
(Ti - T,) to equal ( l / e ) ( = 0.37). The time constant can thas he defined as the time taken for the t,hermistor tempersture to dmp Lo 63y0 of its initial value above amhient [(Ti - T)/(T; - T.) = 0.631. It can be seen from ihe above equation; that t,he t,ime cons1,anL depends upon the heat capacity of the thermistor and upon it,sdissipat,ion constant. The temperattwe dependence of H and C has been neglected in the discussion of thermistor properties. .4 few representative values of a, C, and rare given in Table I.
Thermistor Stability
Figure 8. Plotof log IT - T.I Slope of which is -112.303r.
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ogainrt time, the
Journal of Chemiml Educafion
Thermistors have had a reputation fov being unstable, which was to some exbent just,ified, following their commercial production in the early forties. The situation
T
sec
C mw per deg C
16 in still air 0.7 in still air 0.8 in still wster and 3.8 in still and 0.16 in water moving wster
26 in still air
1
6 in still air
0.16
ha3 changed considerably with the introduction of more satisfactory methods of attaching t,he lead wires, and by preaging of thermistors by the manufacturers. No doubt the st,ringent requirements set for components uned in space exploration have induced manufsct,~lrersto improve their products. Thermistors are sensitive to light, since it is possihle far photons to supply sfieient energy t,o promote electrons into upper hands. (The frequency a t which hv is just sufficient t,o promote electrons corresponds to the edge of t,he absorption spectrum of t,he semiconductor.) I t is advisable to probect thermistors from mechanical shock, sinoe this can impair their shbility (10). The maximum power rating of thermisbors, which is usoally specified by t,he (Continued on page A9.54)
Chemical Instrumentation mannfaetwws, has already been mentioned. The w e of too large a cnrrenl, will cause the thermislov to be unstable, and it ha? heeo suggested t,hat maximwn stability is enawed by keeping t,he current well below the specified rnaximmn value (10). \'cry little has heen rcptrrted in the scientifir literat,ure mgarding thermist,or stability, and few get~el.alinatL,nseourerlting all types of p1vduc1 8.1% possible. A precaul,io~ which is rewmmended, espeeidly if not cnl.~ried
