Z-meter: Easy-to-use Application and Theory

Transcription

1 Z-meter: Esy-to-use Applcton nd heory G. Gromov, D. Kondrtev, A. ogov, L. Yershov M Ltd. 53 Lennskj prosp. Moscow 999 uss phone: fx: e-ml: rmtcom@dol.ru Abstrcts he pper s dvded nto two prts. he frst prt s n pplyng one. We present hndy, esy-to-operte userddressng Z-meter. he devce provdes mesurement of thermoelectrc (E modules prmeters: AC resstnce (, thermoelectrc fgure-of-mert (Z nd mxmum temperture dfference ( mx. he second prt s of theoretcl vlue. As rule, the devce exposure does not hppen to be delly nsulted nd vcuumlke. Consequently need to tke nto consderton het losses of vrous sorts. In ths prt we re to dscuss specfc formule for estmtng het-exchngng uncertntes nvolved by Z-meterng. All the expressons re explct On the bss of theoretcl estmtons t s dvsed nd relzed n Z-meter new vlbltes to mesure performnce prmeters of sngle stge E modules wth correctons fctors, s well s modules mounted nto pckges nd twostge modules. Introducton Applctons of thermoelectrcl (E modules re becomng wder from yer to yer. Hvng strted from commercl use mnly n consumer felds (E refrgertors, cool boxes nd so on now pplctons of E modules ncrese drmtclly n optoelectroncs, electroncs lser technque nd come from speclzed felds, such s mltry nd rspce, to commercl mss producton. In mny emergng pplctons E modules re crtcl components becuse they ffect the temperture of the whole devce, cn hve n effect on ts correct operton, nd mpct on the het dsspton. ht s why relblty requrements to E modules re very hgh nd re stll growng even f comprng wth consumer pplctons. ht s why severe test procedures (precse nd express re requred when specfc EC type needs to be used n expermentl nd serl producton. Any EC must provde hgh performnce nd long operton lfetme wthout flure. he suggested flure crter for relblty tests re the followng: - A drop n EC mxmum coolng cpcty ( mx below ts specfed rtng. Mesurements of Fgure-of-Mert Z s used here s mx f(z - An ncrese ( s usul vlue or hgher n EC resstnce. he reson of settng forwrd the two prmeters s due to the AC esstnce ( nd Fgure-of-Mert Z (nd, therefore, mx clculted bsed on the Z vlue beng very senstve to ltent defects or dmge of E modules. he slghtest chnge of these prmeters durng operton or storge could be the result of destructon of the E module. ht s why AC nd Z re very useful for control of E modules qulty nd relblty. Although there re lot of methods for mesurement of E modules prmeters,,3 only express methods re useful for certfctons nd mss producton qulty control. On the bss of Hrmn method 4 our compny M developed ts own seres of testng fcltes (Z-meters nd hs developed correspondng methods to exmne rnge of E modules, s well s modules mounted nto complete devces.. Clsscl evew of Hrmn Approch Ppers 4,5,6,7 descrbe nd develop n pproch for mesurng thermoelectrc (E propertes nd Fgure-of-Mert of Pelter modules. hs method ws frst suggested by.c. Hrmn 4 n 958 nd bers hs nme. A smll current I psses through the system genertng slght temperture dfferentl long the module pellets. By mesurng the Joule nd Seebeck voltge drops one cn fnd some thermoelectrc prmeters. Let us show t. If the Pelter effect results n the temperture grdent <, n the smplest cse the therml rte equtons for - stge EC cn be wrtten ths wy: I I k (, (. I I k ( here - cold sde temperture; - hot sde temperture; - ; k - pellet therml conductnce; - pellet electrcl resstnce; - pellets number; - mbent temperture; - het flux t the cold ( nd hot ( sdes. he energy dsspton should be smll but enough for Joule losses runwy. If the envronment by the hot nd cold sdes re the sme nd n smlr condtons, nd n cse cold nd hot res re equl, t s possble to dmt (. Summng up two equtons (. nd tkng nto ccount (. we derve: Z (, (.3 k the Fgure-of-Mert Z /k /κρ ( - Seebeck coeffcent; κ nd ρ - therml conductvty nd electrcl resstvty respectfully, - the verge smple temperture,, I, I - the devce current. If (. s justfed nd the current I s smll enough, we Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

2 cn ssume ξ nd ξ, nd the verge devce temperture pproxmtely equls the mbent temperture. Wth ths ssumpton nd n cse /k<< the mn Hrmn relton tkes the followng form: Z (.4 hs relton s commonly used n thermoelectrcty. However the requrement remns not cler. We wll dscuss t further. Mentme, wth the help of (. nd (.4 mx s estmted s mx Z (.5 Or, s relted to the mbent temperture Z ( mx (.6 Z mx, K K 33 K,3,4,5,6,7,8,9 3, 3, 3, Z, x -3 K - Fg... he outlook of Z- Meter he Z-Meter pckge s mde of lumnum lloy. he metl pckge plys the role of pssve thermostt for testng modules. emperture o s mesured wth bult-n dgtl thermometer wth ccurcy. С. Mesurement of AC resstnce nd Z prmeters re performed seprtely. he AC mesurement s mde frst. AC esstnce Mesurement Module s tested by AC current of smll mpltude. he AC s smulted wth the Commuttor (Fg..3, whch perodclly (wth duty crcle reverses crcut of reference current I m. E m I m EC Fg.. he plot mx vs Z In Fg.. the rnge of Z-vlues (pprox.5-3. commonly cheved by most of commercl E modules supplers s mrked. ht s why nyone cn fnd tht n stndrd specfctons of the sngle stge E modules mx flls wthn the rnge of K.. Z-Meter Arrngement nd Prncples of Operton he bove descrbed soluton for the Z prmeter requres ccurte mesurements of, nd. Addtonlly AC resstnce s requred for E module qulfcton s mentoned bove n Z-meter Outsde nd Insde For soluton of the tsk we developed seres of portble Z-Meters. he outlook of our Z-Meter s plced n Fg... E m / Fg..3 Smplfed Dgrm of AC Mesurement p t t t 3 t 4 t n - t n - t n n p n n n - p n n n Fg..4 me dgrm of AC mesurement In the no nput sgnl stte the output voltge of the Instrumentton Amplfer s equl to E m / (Fg..4. Durng AC resstnce mesurng the output voltge s smpled nd mesured by bt ADC every tme before I m current reversng. he smplng ponts re mrked s t n the fgure. he voltge drops p nd n correspondng to the postve nd negtve polrtes re used for E module resstnce ( clculton wth the help of the followng formul: n ( p n I m A V n I m - opertng current; p - voltge drop on E module t postve opertng current; n - voltge drop negtve (. Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

3 opertng current; A V - voltge gn of nstrumentton mplfer; n - totl number of smples per mesurement. An exmple of expermentl tme dgrm ((t nd (t s presented n Fg..7. Z nd mx mesurements he mesurement of Z nd mx s bsed on the Hrmn method ( At mesurement of nd prmeters the smll voltge E s ppled to module (Fg..4. he E voltge s dsconnected perodclly wth tme off suffcent to mesure voltge on module wth ADC. he s mesured durng off. Durng on perod the s mesured. Fnlly s clculted. E / m E E Im EC Fg..4 Smplfed Dgrm of nd mesurements o n o f f n n Fg..5 me dgrm of nd mesurements he followng formuls re used: n Em, (. A n n V Em, (.3 A n V, (.4 A V - voltge gn of nstrumentton mplfer, n - totl number of smples per mesurement. Correct vlue of (nd cn be mesured correctly only f module s n the stte of thermodynmc blnce,.e. f feedng energy s equl to tht dsspted. So the specl run-up phse should precede mesurng. Fg..6 llustrtes ths. Durng the run-up phse the vlues nd re beng stblzed. Durton of the phse s usully few seconds. Operton mode of Z-Meter contns lgorthm, whch llows to strt mesurements only fter stblzng of nd results. E E m /, mv o n o f f 3 - Fg..6 un-up phse dgrm tme, ms Fg..7 Expermentl tme dgrm (EC MC6-3- Correcton fctors Z-mesurements yeld some effectve Fgure-of-Mert Z eff, nd not the true Z-vlue /κρ, becuse non-zero therml het lod tkes plce due to rel r envronment, ctul current mpct nd desgn of the mesured module. 3. heoretcl Approch: -stge EC In the expermentl technque s descrbed bove, E module s exmned n the ctul rrngement. Some het exchnge wth mbent vcnty tkes plce, Joule hetng s not of zero vlue nd so on (Fg. 3.. So lot of correcton fctors need to be tken nto ccount to pply Hrmn s equton to obtn the true Z nd the correspondng mx. Fg. 3.. A scheme of therml exchnges to tke nto ccount Descrbed bove clsscl bss of Hrmn method leves certn mportnt questons beyond ts scope:. Wht s the requrement for usng the mbent temperture nd the verge temperture vlue? 3 Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

4 . Wht s the current nd, therefore, Joule hetng lmtton? 3. If the EC s not n vcuum, wht wy s rto (.4 modfed nd wht correctons re to be clculted? 4. Wht wy s rto (.4 trnsformed nd wht re the mens of llowng for symmetry, tht s for rel cse when (. s not true? Commonly the therml rte equtons for -stge EC must be wrtten the followng wy: I I k' ( /, (3. I I k' ( / s pellets number, а - therml conductnce from the outer cold sde, s therml conductnce from the outer hot sde (, k s effectve pellets therml conductnce llowng for the r nd electromgnetc feld between them. he term k ' descrbes therml conductnce normlzed to one pellet between the cold nd hot surfces: k ' k( bth, (3. b th Bcond Brd, (3.3 he B nd cond B re correctons for nter-pellet therml rd conductnce vlues through r therml conductvty nd rdton, respectvely: κ B r (, cond (3.4 κ β Here pellets fllng term s: s β, (3.5 S S s cold sde dmensons; S 3 B rd γ σ ( β, (3.6 k σ - Boltzmn constnt, γ - therml emssvty. As for (3.6 t cn only be regrded s rough estmte. We do not tke nto ccount r convecton between the pellets s Grsgof nd Prndtl crter show for ths cse 8 Solvng equtons (3. we fnd the followng: I I, k k (3.7 ( ( k ( k I I ( k, k (3.8 k I nd k I (3.9 rnsformng equtons (3.8 wth << k, << k nd k I <<, (3. we hve nd I k ( ( ( I k 4nk I I k k ( I (3. (3. Let us dscuss n wht wy Hrmn Z-mesurng nvolves the bove mentoned. Allowng for (3. we obtn the followng expressons for the thermoelectrc power nd voltge rto: ( I k ( I I k (3.3 I ( I k, (3.4 k ( or I ( I Z' k (, (3.5 Z. nlke equtons (. (.4 relton (3.4 k contns drectly the mbent temperture. If usng the verge temperture (see (.3 nd (3. we should hve llowed for the ddtonl term ~ /k chrcterzng het dsspton from the externl surfces. Formul (3.4 tkes ths term nto ccount utomtclly v, levng just the correctons dscussed below. So, the true Z ( /k could be defned s Z ( bth( br ba ( b, (3.6 I b - Correcton fctor to mbent temperture ( I b A - Correcton fctor becuse of ( k symmetry of het exchnge wth envronment; 3 b th Bcond Brd - Correcton fctor to pellet thermoconductvty due to ddtonl het flux from wrm to cold sde through the mbent (ccordng to (3.3; 4 Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

5 r 4 b r - Correcton fctor becuse of non-zero EC resstnce of E module wres EC (he totl voltge drop s sum of the drop EC t the module nd some ddtonl drop t contctng wres (r s ther resstnce, ' so ' I( EC r IEC ( br, br Due to the bove formulted correcton fctors equton (3.6 shows effect of ctul rrngement of Z-meterng technque. We cn nlyze the reltve shre of the correcton fctors n the resulted true Z tkng the exmple of stndrd seres of modules tht our compny supples. In cse of modules dfferng by number of pellets the sum of correctons fctors rses from bg modules to smll ones (Fg.3.. he bggest fctor s the resstvty of wres. For smll modules the role of testng envronment s qute mportnt. % % % % % % MC6-4-5 MC6-8-5 conductnce ssymetry MC6- -5 MC6-8-5 wre resstnce joule hetng MC6-3-5 MC6-6-5 Fg. 3. Correcton fctors nd Z eff for E modules ordered by number of pellet prs In cse of modules wth dfferent heght (pellet heght there s lso tendency of reducton of mbent fctor correctons from thck to thnner types (Fg Agn the bggest fctor s the resstvty of wres nd the smllest s rdton. % % % % % % MC6-8-5 MC6-8- conductnce ssymetry MC6-8- MC6-8-8 wre resstnce joule hetng MC6-8-6 MC6-8-5 Fg. 3.3 Correcton fctors nd Z eff for E modules ordered by pellet heght 3,,9,8,7,6,5,4,3,,, 3,,9,8,7,6,5,4,3,,, Z eff, K - Z eff, K - If comprng modules by pellet cross-secton the dependence s very slght (Fg And summry effect s wthn pprox of Z only. % % % % % % conductnce ssymetry wre resstnce joule hetng M3-8-3 M4-8-3 M5-8-3 M7-8-3 Fg. 3. Correcton fctors nd Z eff for E modules ordered by pellet cross-secton 4. Z-mesurng of EC mounted on the het snk In most pplctons E modules re mounted nto devces such s lser dodes, detectors nd so on. It s not possble nd not resonble to dsssembly the devce to exmne E module, but often the exmntons re requred, for nstnce, for qulty control of ssemblng procedures nd so on. hus more sutble wy s to exmne E module ssembled. Let us consder vlblty of the Hrmn method nd Z-meterng technque for ths prctclly mportnt pplcton. 3,,9,8,7,6,5,4,3,,, Z eff, K - Fg. 4.. A EC on the het snk One cn fnd tht f plcng n ssembly nto the Z- meter, some vlue wll be resulted. How s t correlte wth E module performnce nd s t possble to estmte true Z prmeter ths wy? Het snk mens notceble ncrese of het dsspton through the bsement. It must be tken nto ccount when estmtng the role of ths fctor n mesurement results. Equton (3.6 llows for het dsspton through the wrm sde of E wth correspondng terms (b A nd b. So the estmton of Z vlue of the ssembled E module s possble f tkng nto ccount therml propertes of the het snk. S k, s (4. L κ s - therml specfc conductvty of the het snk; S, 5 Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

6 L - surfce nd length of the het snk, correspondngly. In Fg we demonstrte the effect of het snk on the effectve Fgure-of-Mert mesured by the technque on the bss of equton 3.6 nd 4.. Ζeff, K,8,7,6,5,4,3, MC MC E module mounted onto heder E module free MC6-- 5 MC MC Fg. 4. Effectve Z eff of E modules free nd mounted one onto het snk module (Z.8x -3 K One cn see tht mountng of E module onto the het snk leds to decrese of the mesured Z eff n comprson wth the effectve Z eff of the E module n the free spce. In Fg. 4.4 we demonstrte expermentl results of mesurement of E modules before nd fter mountng. he results re n good correlton wth the bove theoretcl estmtons.,4 ( I k ( I k (4.3 Summng (4. nd (4.3 we come to: I (4.4 Z tht s we mnge to solve the problem vodng ny correctons chllenge.. It s possble to ntroduce some emprcl correcton fctor tht s certnly unque for concrete pckge nd rrngement of ssembly, lke s O stndrd types, for nstnce, or others. 3. he effectve prmeter Z eff drectly mesured wthout ny correctons cn be used s flure crteron for relblty tests of ssembles. 5. Z-mesurng of -stge EC If plcng two-stge E module nto the Z-Meter t s possble to mesure some vlue s could be done for sngle stge module. Z eff, x -3 K,3,, Before ssemblng Assembled Fg. 3.4 Effectve Z eff mesured before nd fter ssemblng of E modules (M3--5 onto O5 heders Fg. 5.. A vew of - stge EC I he postve result of the bove estmtons s tht the mesured Z eff for ssembly correltes wth the true Z performnce of E module. Of course, ssumptons mde n theoretcl pproch put mny lmttons n pplcton of Z-meterng technque for specfc pckges nd rrngements of mounted E modules. evertheless there re two wys to use the technque for exmnton of ssembled E modules:. One cn nlyze equtons 3.5 nd 3.6 nd fnd tht vergng of mesurng results of two cses wth chnge of the current polrty llows to exclude effect of the het snk on Z resulted. he second term n 3.4 nd 3.6 genertes certn correcton. It s remrkble however tht ths term s lner functon of the current. hen mrkng one of polrtes by (, nd the other by (- we hve: ( I k ( I (4. k Let us consder f ths rto correltes wth the true Z vlue of two-stge module nd whether t s possble to trnsform the correlton nto smlr Hrmn equton. In other words: s t possble to pply the Hrmn method to twostge E modules? A smplfed drwng of two-stge E module s plced t Fg. 5.. he generl formule for two-stge module cold nd hot sdes re: I I k' ( (, (5. I I k' ( (, nd - E module s cold sde, medum nd hot sde tempertures, respectvely. Snce A S nd ssumng the stge pellets number ~ S s the cold sde re of the correspondng S 6 Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

7 stge, we cn mke pproxmtons A const (5. s β const S (5.3 kng (5. nd (5.3 nd settng k ' k' k' we modfy (5. the followng wy: I I k'( A( I I k'( A( (5.4 Summng up equtons n (5 we derve: I ( k' A, (5.5 s the verge module temperture. Solvng the followng set of equtons I ( k' A I, (5.6 we obtn the followng Z ( bth( br. (5.7 Here b B B A ( B A (5.8 th cond he prmeters ( ( conv conv rd rd B, B, B re descrbed bove cond conv rd l A conv (5.9 κβ γ 3 A rd σ l (5. κβ Equton (5.7 s rther smlr to (.4 nd (3.8. It proves tht we cn pply the Hrmn method to -stge EC meetng requrements (5. nd (5.3. Of course, the equton for estmton of mx for sngle stge modules (.5 s not vld here. But knowng the Z-vlue we cn evlute mx fndng the mxmum of the followng functon: x ( x Z( x (( ξ x ξ ( x x x ( ξ Z Z( x hus the Hrmn method could be used for estmton of two-stge E modules. In Fg we demonstrted clculted results nd tkng nto ccount bove dvsed correctons to estmte Z vlue of two stge modules bsng on the dt mesured by the Z-meter. % % % % MC MC6-- 5 MC conductvty convecton rdton wre resstnce MC6-43- MC Fg. 5. Correcton fctors for MC6-XXX-5 EC types % % % MC MC6-39- MC6-39- MC conductvty convecton rdton wre resstnce MC MC Fg. 5.3 Correcton fctors for MC-39-XX EC types,8,7,6,5,4,3,,8,7,6,5,4,3, Z eff, x -3 K - Z eff, x -3 K - 7 Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,

8 % % % % MC- 9-5 MC- 5-5 MC- 9-5 MC conductvty convecton rdton wre resstnce MC- 4-5 MC Fg. 5.4 Correcton fctors for two stge EC types of MC seres,8,7,6,5,4,3, Z eff, x -3 K - For some types of E modules, prtculrly wth low resstnce, the wres prt s qute lrge nd must be tken nto ccount. 7. Concluson here were dvsed new seres of portble Z-meters sutble for precse exmnton of Z nd AC prmeters of E modules, whch s very mportnt for certfcton, qulty control nd flure montorng. Detled theoretcl estmtons confrm tht pplcton of Z-technque could be brodened from clsscl mesurng of sngle stge E modules to two stge ones nd lso for E modules mounted nto devce housng. ew Z-meter technque pplctons re very mportnt for end-used prctce s well s could be useful for E modules mnufcturng process. 6. AC esstnce Mesurement he AC resstnce of E module s s mentoned bove one of the mportnt qulty control prmeters of E module. he method of mesurng of the AC s qute smple t s necessry to mesure precsely resstnce of E t AC current. Wthn Z-meter technque bsed on the Hrmn method t s possble to mke the mesurements durng Z meterng. As Z-meterng voltge drop s obtned, AC only requres to fnd the E module current ddtonlly. In our Z-meter technque we prefer nother known method of seprte mesurement of E module resstnce t precsely fxed AC current. here s the reson to use n ndependent method of AC resstnce mesurement. If to use Z technque then both resulted prmeters Z nd AC become drectly coupled. Accurcy of the resulted AC resstnce depends on the ccurcy of Z exmnton (ccurcy of nd. I.e.: δ δ δ 3, (6. - ccurcy of AC mesurement; δ ccurcy of voltge drop mesurement. Fctor 3 (three tkes plce s for AC exmnton t s requred to mesure, nd I m. Independent technques provde more ccurte result, s: δ δ, (6. Where fctor s due to requrements to mesure both negtve nd postve voltge drops t fxed current. Fnlly t s necessry to note tht n ny cse the resulted AC resstnce s sum of the ctul resstnce on E module nd some resstnce of contctng wres. EC r (6.3 Acknowledgements he uthors would lke to thnk M representtves of mnufcturng nd development group V. Volodn nd A. kolev, nd ll the M tem who hve been nvolved n work. We re lso grteful to our prtner Dr. V.A. Semenouk for collborton. Bblogrphy Duphnee.M., Mooser E. Apprtus for Mesurng esstvty nd Hll Coeffcent of Semconductors// ev. Sc. Instrum., 6, 66, 955. Hrmn.C. Mesurement of Pertnent thermoelectrc Propertes. //hermoelectrc Mterls nd Devces. Cdoff I.B., Mller E., enhold, 967, chp.6. 3 Busch G, Stegmeer E.F. herml nd electrcl Conductvtes, Hll Effect nd hermoelectrc power of InSb//Helv.Phs. Act, 34,, C. Hrmn, J.H. Chn, M.J. Logn. Mesurement of herml Conductvty by tlzton of the Pelter Effect// J.Appl. Phys., V. 3, 35, V.P.Bbn,S.M.Gorodetsky. hermoelectrc modules qulty testng by mnufcturer. Proc. XIV Int. Conf. on hermoelectrcs, June 7-3, St. Petersburg, uss, 995,pp J. Bust. A new method for estng hermoelectrc mterls nd Devces/Proc.XI Int. Conf. on hermoelectrcs. October 7-9,99,Arlngton,X,SA. 7 S.Gorodetsky,.J.Bust, P.G.Lu. Qulty testng of wostge hermoelectrc Cscdes. Proc. IC 97, August 6-9, 997.pp H.J.Goldsmd. Electronc efrgerton. Pon. London, Dulnev G.. herml exchnge n the rdoelectrcl devces//lenngrd, 963, p Proceedngs. Sxth Europen Workshop on hermoelectrcty of the Europen hermoelectrc Socety Freburg m Bresgu, September -,