III.5. THE THERMISTOR
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1 III.5. H HRMISOR 1. Wor uros o cc t law dscribig t tratur ddc of t lctrical rsistac of sicoductor atrials ad to valuat tir ga.. ory Quatu caics stats tat isolatd icrosysts (lctros, olculs, ios) av oly discrt rgy sctra aog wic trasitios ar ossibl. rasitios to igr rgy lvls rquir rgy absortio fro t surroudig dia, ad tos to lowr rgtic lvls occur wit rgy issio. As t ubr of atos icrass, sultary itractios, wic subsqutly occur, lad to t slittig of t iitial rgy lvls, t cosquc big a orous ubr of suc lvls, groud i sts, calld rittd rgy bads. y ar saratd by doais witout rgy lvls, calld forbidd rgy bads. widt of a forbidd bad is calld ga. Out of ts allowd bads, two bads ar of articular itrst, aly t valc bad ad t coductio bad. y ar saratd by a ga g c v, wr c ad v ar t botto of t coductio bad ad t to of t valc bad rgis, rsctivly. lctros fro t valc bad cotribut to t ato bodig. s lctros ar tid u, aig ty ar locatd i t igborood of a ato, ot avig oug rgy to lav it. If ty soow gt t cssary rgy, ty ca bco fr lctros, abl to ov ad, 149
2 rgtically saig, blog to t coductio bad. As o ca s fro Figur 1, t rgy surlus sould xcd g. Figur 1. If t valc (coductio) bad is artially filld at absolut zro tratur, all t lctros ar arly fr ad t substac is a tal. If g is vry sall, t trasfr ca asily ta lac ad t substac as a larg aout of coductio lctros. is id of substacs is calld a sital. ot tals ad sitals ar coductors. Covrsly, w g is vry grat, t trasitio is uc lss robabl ad t substac is oor i coductio lctros. currt is vaisigly sall; tus it is a lctric isulator. tw ts two xtrs ar t sicoductors. It is obvious tat t ga is of grat iortac for alicatios. Actually, t goal of tis xrit is valuatig g for sicoductors. For t ur or waly dod sicoductor atrials, at traturs ifrior to so udrds of Clsius dgrs, t Fri lvl is situatd i t forbidd bad, far fro bot t valc ad coductio bads. 150
3 151 For 0, t tral agitatio will grat a coctratio of fr lctros (quotd ) i t coductio bad, wil i t valc bad will aar ols wit a coctratio. If t sicoductor is ur (itrisic), i. xrssios of t two carrir coctratios rsult fro t tory of t rgy bads i sicoductor atrials: F c x 3/, (1) v F x 3/, () wr ad ar t lctro ad ol ffctiv asss, is t oltza costat, is t sicoductor tratur, ħ is t Plac costat, ad F is t Fri lvl rgy. Maig t roduct of t xrssios (1) ad () w obtai: v c x 4 3. (3) As i, o ca ifr tat t carrir coctratio i itrisic sicoductors is: g i x 3. (4) lctric coductivity of a sicoductor is: ( ) µ + µ ρ σ 1. (5) obilitis µ µ, big ractically iddt of t tratur, it rsults tat:
4 σ 3/ x g, (6) 3/ g ρ x. (7) sicoductor rsistac will t b b: 3 g R C x ad its tratur ddc is sow i Figur. (8) Figur. Alyig t logarit to quatio (8), o obtais: log ( R 3/ ) g C' +. (9) 3. xrital st-u sicoductor usd i t xrit is a trasducr calld tristor. ristors ar sicoductor circuit lts, scially dsigd ad usd for t tratur ddc of tir rsistac. y ar aufacturd fro a ixtur of tallic oxids (of Cu, F, Cr, tc.), tat ar groud ad rssd togtr wit a orgaic bidr ad t 15
5 rocssd. ir sa is usually tat of a ill (a), arl (b), or stic (c). ristors ar sall i siz ad ar caractrizd by sturdiss, stability of tir fuctioal aratrs, ad low rics. ir ai uss i ractic ar to asur ad adjust t tratur i iaccssibl lacs, ad to cosat ad stabiliz t variatio of otr dvics aratrs (. g. t voltag). Figur 3. xrital st u is sow i Figur 4 ad it icluds a lctrical furac (1) usd to at t tristor, a otr () usd to asur t tristor rsistac, ad a lctrical trasforr (3) usd to fd t otr. furac as grat tral irtia, so tat altoug it is ot owrd troug a rostat but dirctly fro t lug, t tratur icrass slowly. caus of tis fact t usag of a trostat is o logr cssary, allowig us to assu tat ac rsistac asurt is rford i quasistatic coditios. trotr ad t tristor ar attacd o t furac lid. tristor as two jacs, wic ar coctd to t otr by two isolatd coductors. otr is built usig a Watsto bridg. It as a galvaotr (6) as zro istrut, a switc (7) tat cags t rags, idicatig t ultilicatio factor, ad a variabl rsistac (8) wit a scal ad a rur. A switc (9) i t owr sourc circuit allows t otr to b fd oly durig t radigs. So otrs av a built-i butto, wic rlacs t traditioal switc. I so otr st-us, t Watsto bridg otrs ar rlacd by sil otrs (atrs wit a rvrsd scal). 153
6 Figur Worig rocdur W cc t coctios fro t tristor to t otr ad t trasforr. first asurt of t tristor rsistac is rford udr a rofssor survy. rur of t variabl rsistac is st to t iiu ositio ad t switc of t ultilicatio factor to axiu. t butto (switc) ust b brifly rssd to obsrv t dirctio of t galvaotr ad dviatio. w ust ass to t ifrior ultilicatio factor, quotig agai t ad dviatio. oratio is ratd util t dirctio of t ad dviatio is cagd. t butto ust b rssd ratly, turig t rur, util t galvaotr ad racs zro. Aftr tat t butto is rlasd. tristor rsistac is qual to t valu idicatd by t rur ultilid by t ultilicatio factor. At tat ot t tratur is also rad. If t otr is of t atr ty, t radigs ar ad dirctly. Du to t diffrt at caacitis, t trotr ad tristor traturs ar ot qual. o corrct t discracy, t asurts ar rford durig bot t atig ad t coolig of t tristor ad t a valu of t rsistac is valuatd for ac tratur. 154
7 rsults ar writt i abl 1: abl 1 R (Ω) t ( o C) (K) 1/ (K -1 ) log(r 3/ ) atig coolig a furac is luggd (or switcd o). As t tratur icrass, w rsistac asurts ar rford, witout ccig agai diffrt ultilir factors. tratur is rad idiatly aftr t ad is brougt to zro. tratur itrval btw two radigs is 5 o C ad t fial tratur ust ot xcd 100 o C. At t d of t atig t furac is uluggd (or switcd off), ad o rats t asurts durig t coolig, at t sa tratur valus. 5. xrital data rocssig 3 Usig t data fro t tabl w draw t log( R ) f ( 1 ) caractristic. tw t xrital oits fro t caractristic, a itrolatio straigt li is draw. Fro quatio (9), t li slo is g. g ust b coutd i lctro volts ( V/K). 6. Qustios 1. Wat is a tristor ad wy it is or ssitiv to t tratur variatio ta a tal?. Wic is t fillig of t rgy lvls fro t coductio ad valc bads for a sicoductor at 0 K ad 0 K? 155
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