Design Issues for Low Power Integrated Thermal Flow Sensors with Ultra-Wide Dynamic Range and Low Insertion Loss

Transcription

1 Mcromachnes 01, 3, ; do: /m30095 Artcle OPEN ACCESS mcromachnes ISSN X Desgn Issues for Low Power Integrated Thermal Flow Sensors wth Ultra-Wde Dynamc Range and Low Inserton Loss Paolo Brusch 1, * and Massmo Potto 1 Dpartmento d Ingegnera dell Informazone, Unversty of Psa, va G. Caruso 16, I-561 Psa, Italy Isttuto d Elettronca e d Ingegnera dell Informazone e delle Telecomuncazon, Psa, CNR, va G. Caruso 16, I-561 Psa, Italy; E-Mal: massmo.potto@et.cnr.t * Author to whom correspondence should be addressed; E-Mal: p.brusch@et.unp.t; Tel.: ; Fax: Receved: 7 February 01; n revsed form: 7 March 01 / Accepted: 5 Aprl 01 / Publshed: 10 Aprl 01 Abstract: Flow sensors are the key elements n most systems for montorng and controllng flud flows. Wth the ntroducton of MEMS thermal flow sensors, unprecedented performances, such as ultra wde measurement ranges, low power consumptons and extreme mnaturzaton, have been acheved, although several crtcal ssues have stll to be solved. In ths work, a systematc approach to the desgn of ntegrated thermal flow sensors, wth specfcaton of resoluton, dynamc range, power consumpton and pressure nserton loss s proposed. All the crtcal components of the sensors, namely thermal mcrostructure, package and read-out nterface are examned, showng ther mpact on the sensor performance and ndcatng effectve optmzaton strateges. The proposed desgn procedures are supported by experments performed usng a recently developed test chp, ncludng several dfferent sensng structures and a flexble electronc nterface. Keywords: thermal flow sensors; devce optmzaton; MEMS; mult heater; senstvty; resoluton 1. Introducton An accurate measurement of gas flow s requred n many applcatons, ncludng ndustral processes control, nternal combuston engnes optmzaton, montorng of gas dstrbuton lnes,

2 Mcromachnes 01, 3 96 control of ventlaton and ar-condtonng systems and montorng of patent breathng. The ntroducton of MEMS (Mcro-Electro-Mechancal Systems) technology allowed the fabrcaton of mnaturzed flow sensors wth unprecedented performance n terms of spatal resoluton, response tmes, senstvtes, measurement range and power consumpton. Integrated flow sensors have been largely nvestgated n last decades and lterature revews can be found n [1 6]. The wde majorty of the proposed devces are based on a thermal prncple. Ths s manly due to ther sutablty to be ntegrated on slcon chps usng standard mcroelectronc processes, makng them deal canddates for the fabrcaton of ntegrated smart sensors. Accordng to the operatng prncple, thermal flow sensors can be dvded nto three man categores, namely hot-wre sensors, calormetrc sensors and tme-of-flght sensors. Hot-wre sensors are based on the heat loss of a heater exposed to the flud and the output sgnal s the heater temperature (constant power anemometry) or the heater power needed to stablze the heater temperature (constant temperature anemometry). Calormetrc sensors measures the dfference between the downstream and upstream heat fluxes stemmng from one or more heaters exposed to the flow. Tme-of-flght sensors measure the tme that elapses between a heat pulse appled to the heater and the pulse detecton by a downstream temperature probe. Sensors based on a combnaton of multple prncples for extendng the operatng range have been proposed [7,8]. Calormetrc sensors are the sensors of choce when superor performance n terms of resoluton, lnearty and offset are requred. These propertes, partly due to ther dfferental structure, are fundamental n applcatons nvolvng the measure and control of very low flow rates. Ths s the case, for example, of gas dstrbuton lnes n semconductor manufacturng equpments [9], fuel/ar mxng system n car engnes [10] and propellant feed system n thrusters on board satelltes [11,1]. Recently, very senstve ntegrated flow sensors have been proposed for the development of a drectonal wnd sensor, wth robustness, power consumpton and mnaturzaton characterstcs sutable for applcaton n wreless sensor networks [13]. Although dfferental temperature flow sensors have been wdely nvestgated [1 6], very few works have been devoted to fnd the mpact of the sensor structure and dmensons on the key fgures of mert of the devces [14 0]. Flud dynamc smulatons provde useful ndcatons on partcular aspects of the sensor operaton, but are unable to embrace the whole transducton process, nvolvng dfferent physcal domans that altogether contrbute to the sensor performance. Studes based only on thermal and flud-dynamc smulatons generally lack a framework capable of organzng the smulated results nto smple and general desgn formulas. As a result, the constrants and drawbacks that lmt the effectveness of the varous desgn parameters are often overlooked, together wth the connectons to real fgures of mert, such as resoluton, dynamc range and power consumpton. In fact, talorng a flow sensor for a real applcaton s a process that should necessarly nvolve several dfferent parameters, ncludng: () nose and offset from ether the sensor or the amplfer; () pressure drop (head loss) ntroduced by the nserton of the sensor n the fludc system; () correlaton between the sensor characterstcs and the readout nterface specfcatons (.e., power consumpton). In ths work, a systematc approach for the desgn of ntegrated calormetrc flow sensors, takng nto account all the crtcal components of the devces, namely thermal mcrostructure, package and read-out nterface, s proposed. Some desgn strateges for the devce optmzaton are analytcally extrapolated startng from a smplfed model of the sensors and are expermentally verfed by means

3 Mcromachnes 01, 3 97 of a recently developed test chp, ncludng several dfferent sensng structures and a flexble electronc nterface [1].. Desgn Parameters and Optmzaton.1. Descrpton of the Sensor Structure and Man Performance Parameters The general structure of the flow sensors analyzed n ths work s shown n Fgure 1(a). Two temperature sensors (thermoples) are placed on cantlevers suspended over a cavty etched nto the substrate n order to provde thermal nsulaton. The thermoples are composed of N T thermocouples wth the hot and cold junctons placed on the cantlever tp and the substrate, respectvely. A varable number of heaters are placed n the space between the thermoples. The heaters are deposted over thermally nsulatng membranes (rectangular), anchored to the cavty edges through a seres of arms. The partcular shape of the suspendng arms s dctated by the propertes of the wet ansotropc etch used to open the cavty. The consderatons made n ths paper can be easly extended to dfferent sensor layouts. The basc operatng prncple of the sensor s smple: as the flow progressvely ncreases, heat transfer n the downwnd drecton ncreases as well, producng a temperature dfference that s sensed by the thermoples. The typcal confguraton ncludes a sngle heater whereas mult-heater structures can be used to perform partcular functons [17, 4] or smply extend the effectve heater area wth no adverse consequences on the etchng tme requred to release the suspendng membranes. Fgure 1. (a) Schematc vew of a thermal flow sensor, based on a calormeter type confguraton wth the man dmensons ndcated; (b) Representaton of the flow channel. N H heaters suspendng arm heater thermople 1 heater connecton heater thermople Flow Flow channel L S L C L G L GH W (a) L H cavty NT thermocouples W CH (b) L sensng structure H Possble alternatves to the structure shown n Fgure 1(a) are often used. A smple modfcaton s the replacement of the thermoples wth resstve temperature detectors (RTD) [14,17,4], wth the drawback of an addtonal offset term derved from resstor msmatch. Another varant that adds robustness to the devce, but requres front-to-back algnment equpments and sgnfcantly longer etchng tmes, s the placement of all sensor elements on a sngle closed membrane [5]. The devces are placed nto channels where they are drectly exposed to the flow. The shape of the flow channels s shown n Fgure 1(b) wth the most relevant dmensons ndcated.

4 Mcromachnes 01, 3 98 Several phenomena, regardng the flud-dynamc, thermal and electrcal domans, are nvolved n the operatng prncple of a flow sensor. In order to smplfy the analyss, t s useful to ntroduce a block dagram such as Fgure (a), representng the successve conversons of the orgnal quantty (flow rate) resultng n the output voltage. The amplfer (A), used to read the output voltage, s also ncluded, snce t contrbutes to the overall devce accuracy. Flud-dynamc and thermal mechansms are confned to block h, whch converts the volumetrc flow rate Q nto a temperature dfference ΔT S usng the heatng power P H (total power delvered to the heaters). Fgure. (a) Sgnal flow path representaton of the transducton mechansm, wth the man non-dealtes ndcated; (b) Effect of the offset and nose on the sensor detecton lmt. Q meas s the flow sensor readng under stll flud condtons. v ns v na Q meas Q (flow) h ΔT S v out A Avout Q O Q np-p Q mn (a) P H k tp sensor v os v oa nterface (b) tme The thermoples, represented by the multplcaton of the constant k tp, convert the temperature dfference nto the output voltage. Note that ΔT S s consdered free of random phenomena such as offset and nose, whch are taken nto account wth the terms V ns and V OS (sensor nose and offset voltage), added to the output voltage. The sensor nose s manly thermal nose from the thermople resstance, whle the sensor offset s domnated by geometrcal asymmetres of the sensor structure, producng a temperature dfference even at zero flow rate. Fnally, a nose and offset contrbuton comes also from the amplfer, as represented n the fgure. Several parameters are used to specfy the performance of a flow sensor. These parameters are strctly correlated and, generally, t s meanngless to boost a sngle characterstc (e.g., hgh senstvty) wthout clearly ndcatng at whch cost t has been acheved. Some of the most mportant performance parameters are lsted below. (a) Senstvty, defned as S = dv out /dq. The senstvty depends generally on the nput flow rate, although dfferental calormeters exhbt a nearly lnear behavor at small flow rates, where a constant senstvty S(0) can be used. The senstvty alone s not a real fgure of mert, but t s a fundamental parameter for the desgn of the nterface and, together wth other parameters, contrbutes to the resoluton and detecton lmt, defned below. (b) Resoluton, defned as the mnmum varaton of the nput flow that can be detected. The resoluton s expressed n terms of the equvalent nose flow rate, Q np p = v np p /S, where v np p s the peak to peak ampltude of the total output nose voltage. (c) Offset flow rate, defned as Q O = v O /S(0), where v O s the total offset voltage. The offset flow rate concdes wth the readng of the flow sensor when the flud velocty s zero.

5 Mcromachnes 01, 3 99 (d) Detecton lmt Q mn, defned as the mnmum (unsgned) flow value that can be relably detected by the flow sensor. Ths parameter s partcularly mportant for leakage sensors, whch should be able to determne f very small flow rates are present. Fgure (b) shows a sketched tme dagram of the flow sensor readngs n condtons of zero flow. If calbraton of the offset s not performed, Q 0 s an unknown quantty and we only have statstcal nformaton about t,.e., we can presume that t falls between Q 0max and Q 0max, where Q 0max s the maxmum offset for that knd of sensor. It s apparent that, n ths case, f a readng s wthn Q 0max Q np p / and Q 0max + Q np p /, t s not possble to determne whether a flow rate s present or Q = 0 and the measurement s smply the result of a possble combnaton of offset and nose. Therefore, n the case of no offset calbraton, the detecton lmt s Q mn = Q Omax + Q np p /. Even f an offset calbraton procedure s appled, a resdual offset wll stll be present. The detecton lmt concdes wth the theoretcal lmt Q np p / only f the resdual offset s neglgble wth respect to nose. (e) Bandwdth, B, defned as the frequency range of the flow velocty n whch the sensor senstvty remans over nearly 70% of the value for constant flow. The sensor response tme s nversely proportonal to the bandwdth. Note that the ntrnsc bandwdth, due to the sensor thermal masses and resstances, can be further reduced n the nterface to lmt the nose and mprove resoluton. (f) Full scale flow rate, Q max. The response of thermal flow sensors tends to saturate at hgh flows, for the effect of several concomtant causes. As a result, the senstvty progressvely drops, degradng the resoluton. The maxmum value Q max can be conventonally set at the pont where the senstvty drops below a gven fracton of the ntal S(0) value. Response saturaton s manly due to flud-dynamcs and forced convecton mechansms that can be studed only by means of smulatons or experments. In ths work we wll provde some ndcatons based on tests performed on dfferent sensor confguratons. (g) Dynamc range, DR = Q max /Q np p. The DR concdes wth the number of dstnct flow levels that can be dstngushed by the flow sensor. Ths parameter s partcularly mportant for flow sensors used to measure large flow rates wth hgh resoluton. Hgh dynamc range flow sensors are requred n flow control unts desgned to delver precse flud flows to reacton chambers (as n semconductor processng equpments [9]) or onc thrusters for fne handlng of satellte atttude and orbtal parameters [11]. The DR of tradtonal macroscopc flow sensors s typcally lower than 10 whle t may exceed 10 3 n MEMS flow sensors. (h) Inserton loss, p loss, defned as the pressure drop across the sensor flow channel, measured at Q max. () Power consumpton P H. Ths s an extremely mportant parameter for battery powered applcatons... Lumped Element Model of the Transducton Prncple Analytcal soluton of the flud-dynamc and heat transfer equatons nvolved n the operaton of thermal flow sensors s feasble only for very smplfed cases, that are poorly related to the complex three dmensonal structures used n MEMS sensors. In ths sub-secton, a lumped element model for

6 Mcromachnes 01, the whole transducton process wll be ntroduced n order to provde some desgn ndcatons. The flud flow and the substrate wll be assumed to be at the same temperature of the surroundng envronment, ndcated wth T A (ambent temperature). The temperature dfference of the sensor elements wth respect to T A wll be ndcated as overheatng. The model s based on the hypothess that the relatonshp between overheatng and the heater powers s lnear (lnearty hypothess). Ths approxmaton derves from consderng that: () heat transfer s domnated by conducton and forced convecton; and that () the flud parameters are ndependent of temperature. Fgure 3. Vsual representaton of the symbols used to defne the lumped element model. -th heater k-th thermople flow P k, w T A ΔT H ΔT k, V k, P H T A Fgure 3 represents the nteracton of the -th heater wth the k-th thermople. The heater receves the power P H whle all the other heaters are not powered. The overheatng of the heater s gven by: ( th) Δ TH TH TA = RH PH (1) (th ) where R H s the total thermal resstance between the heater and the envronment. The fracton of the power P H, ndcated wth P k, that reaches hot junctons of the k-th thermople can be expressed as: Pk, = WΔTH g k, ( Q) () where g k, s a flow dependent couplng coeffcent. Wth Equaton () we have consdered that the lnear power densty across the devce wdth (W) s constant (-dmensonal approxmaton). Several geometrcal parameters of the sensng structure affect coeffcents g,k (Q), ncludng the depth of the nsulatng cavty underneath the sensor elements. The temperature overheatng of the thermople, ΔT k, s gven by: ( th) T k, TA ΔTk, = RC Pk, (3) (th ) where RC s the thermal resstance between the thermople hot junctons and the envronment. For the structure of Fgure 1(a) the thermal resstance s domnated by conducton through sold elements (cantlever), and s then gven by: ( th) 1 LC RC = keq tcw (4) where t c s the cantlever thckness and k eq the effectve conductvty that takes nto account the cantlever and the thermople materal [0]. Introducng parameters a k,, defned as: ΔTk, 1 LC ( th) ak, ( Q) = RH gk, ( Q) P k t (5) H eq C

7 Mcromachnes 01, It s possble to wrte the transducton law between power P H and voltage V k, : V k, = ktpak, PH (6) Usng the lnearty hypothess, we can consder that the total thermople voltage s the superposton of the effects of the N H heaters. Therefore: V = k a, P The output sgnal s the dfference V -V 1, resultng n: k tp k V = V V = k a a ) P out 1 tp H (, 1, The sensor senstvty can be calculated from Equaton (8) and wrtten n the followng compact form: H (7) (8) V S = Q out = k N H tp = 1 h ( Q) PH (9) where the coeffcents h are defned as follows: a, h = Q a1, Q (10) It s convenent to relate the powers P H of the ndvdual heaters to the total power P H, through a set of dmensonless parameters x, ndcated as power dstrbuton : N H P H = xph ; 0 x 1; x = 1 (11) Thus, Equaton (9) becomes: S = ktpheff PH wth heff = xh (1).3. Sensor Resoluton In order to calculate the equvalent nose flow t s necessary to estmate the total nose voltage v np p. The peak-to-peak nose can be derved from the rms value, consderng that, for Gaussan nose, t can be assumed that v np p = 4v nrms. Wth ths choce, the nose voltage exceeds the conventonal peak-to-peak value only for 4.6% of the observaton tme. The sensor nose s essentally thermal nose from the thermople resstance (R). Ths contrbuton s clearly ndependent of the amplfer nose. Wth these consderatons: = 1 ( 4kBTRB v ) v + np p = 4 na (13) where v na s the amplfer rms nput nose voltage, k B the Boltzmann constant, T the absolute temperature, B the sensor bandwdth, consdered concdent wth the equvalent nose bandwdth. Note that the thermople overheatng s generally lmted to a few Kelvn n ths type of sensors, so that we can assume that T concdes wth T A. In order to fnd the degrees of freedom on the sensor desgn that actually affect the resoluton, t s necessary to obtan an expresson for the thermople resstance.

8 Mcromachnes 01, 3 30 Fgure 4 shows a sngle thermocouple, formed by conductors A and B. The ptch, by whch the thermocouple are lned up over the cantlever, s ndcated wth W P = (W S + W T ), where W S s the mnmum spacng between two lnes, whle W T s the dmenson of a sngle conductor formng the thermocouple. For the sake of smplcty, we have consdered that the two materals A and B have dentcal sheet resstance R S, otherwse the mean sheet resstance can be used. Fgure 4. Dmensons used to descrbe the thermocouple geometry. W S juncton A B W T W P L T Consderng that the thermople spans the whole cantlever wdth, and neglectng the margn at the cantlever borders we get: W P = W/N T. The lne wdth W T s then gven by: W W = W W = N 1 P S T T WS N W The total sensor electrcal resstance, R, s the sum of the resstances of the two thermoples. Wth the above smplfcatons: T 1 (14) L 8 = T R 4 = SLT NT W N 1 S T R RS NT W W W (15) T where R S s the thermople layer sheet resstance, equal to the resstvty to thckness rato. The total thermople senstvty (k tp ) s smply gven by N T s AB, where s AB s the Seebeck coeffcent of the A-B couple. The spacng W S should be kept at the mnmum value allowed by the technology, W SMIN, n order to reduce the resstance, so that we assume W S = W SMIN. The W SMIN /W rato can be expressed n term of the maxmum number of thermocouples, N TMAX, gven by: N TMAX W W = = + (16) ( W + W ) W ( 1 W / W ) TMIN SMIN where W TMIN s the mnmum wdth of conductors A and B allowed by the technology. Generally, n mcroelectronc processes, W TMIN W SMIN, so that m = (1 + W TMIN /W SMIN ). Usng Equaton (16) and the above consderaton, the followng expresson can be derved: R SMIN 1 = TMIN L 8 T R 4 = S LT NT N 1 T R S NT wth m (17) WT W mntmax Substtuton of Equaton (17) n Equaton (13) yelds: 3kBTRS BLT vna Q np p = 4 f + wth 1< f < NT (18) W NT ( P h s ) ( N P h s ) H eff AB T where f NT = (1-N T /mn TMAX ) 1 s a factor that monotoncally ncreases wth N T. Now, let us make a few consderatons about the amplfer nose. The fact that the output sgnal of a flow sensor ncludes a DC H eff AB SMIN

9 Mcromachnes 01, component dctates the use of dynamc technques, such as chopper stablzaton or autozerong to cancel the amplfer offset and offset drft [6]. These technques also strongly reduce the low frequency (Flcker) components, so that the amplfer nose conssts only of thermal nose. For a gven amplfer topology t s possble to express the rms thermal nose as n [7]: v ( NEF ) U 4k TB B na = T I (19) A where U T s the thermal voltage (nearly 6 mv at 300 K), I A the total current absorbed by the amplfer and NEF (nose effcency factor) s a fgure of mert assocated to the amplfer archtecture..4. Offset Flow Rate Consderng the sensor and amplfer contrbuton to the total offset voltage t s possble to wrte: Q O vos + voa = (0) S(0) The second term can be made very small usng the mentoned dynamc approaches to cancel the amplfer offset. Such technques are neffectve wth respect to the sensor offset, whch consttutes the man contrbuton. The sensor offset can be calculated usng Equaton (8) n condton of zero flow [ a, ( 0) a1, (0 ] v = k ) P OS tp In practce, the majorty of flow sensors exhbt a thermople and heater arrangement that s symmetrc wth respect to a plane perpendcular to the flow drecton. Therefore, f the heaters are drven wth dentcal power, the v OS should be nomnally zero. Unavodable random asymmetres due to the fabrcaton process add errors to the a k, (0) terms n Equaton (1). Introducng the relatve errors e k, assocated to the quanttes a k,, t s possble to wrte the offset n the case of unform power dstrbuton (x = 1/N H ) as: [ e, a, ( 0) e1, a1, (0)] v = k P / N OS From the senstvty expresson Equaton (1), fnally we get: Q tp O = H [ e, a, ( 0) e1, a1, (0)] h where the amplfer offset has been neglected. Snce the entty of relatve errors s a technologcal parameter, the numerator s larger n sensors where the statc couplng coeffcents a k, (0) are larger. In turn, consderng Equaton (7), the larger the a k, (0) values, the larger the voltages V 1 and V, ndvdually produced by the two thermoples at zero flow (statc thermople voltages). On the other hand, the denomnator ncludes the dervatve of the a,k parameters wth respect to flow. In dervng Equaton (7), one fnds that the larger the a,k dervatves, the larger V 1 and V dervatves wth respect to flow. Then, as a general rule, n order to acheve a small offset, the thermople voltage should exhbt a small statc value and a large dervatve wth respect to flow rate. H H (1) () (3)

10 Mcromachnes 01, Inserton Loss vs. Senstvty The pressure drop across the flow channel sketched n Fgure 1(b) can be approxmated by the followng expresson [8]: L Q Δ p = ploss = 3μ D A (4) where a lamnar flow regme have been assumed, A s the channel cross sectonal area, µ the gas dynamc vscosty and D H the hydraulc dameter, defned as: WCH H DH = WCH + H (5) where W CH and H are the channel wdth and heght, respectvely, as shown n Fgure 1(b). Combnng Equatons (4) and (5) we get: H ( WCH + H ) 3 ( W H ) Δp = 8μ L Q (6) CH Equaton (6) states that reducng the channel cross secton (ether reducng W CH or H, or both) for a gven flow rate leads to an ncrease n pressure drop. Note that reducng the cross secton s the most commonly used method to ncrease the senstvty of flow sensors. Ths occurs through the sum of the a,k dervatves wth respect to flow, ncluded n the parameter h eff. In turn, these dervatves are proportonal to the flow dependent components of g,k terms,.e., to the forced convecton contrbuton to heat transfer from the heaters to the thermoples. Ths contrbuton s proportonal to the velocty gradent perpendcular to the sensor element surfaces []. Therefore: g FC k u Q, (7) y AH where y s a coordnate referred to an axs parallel to the channel dmenson H (see Fgure 1(b)) and FC g, k s the g,k component due to forced convecton. Note that the rghtmost proportonalty relatonshp n Equaton (7) s vald f the shape of the velocty dstrbuton does not change wth flow (e.g., remans parabolc for a lamnar regme). Consderng Equatons (5), (10) and (1) we fnally get: h 1 1 eff = AH WCH H (8) Equaton (8) shows that reducng the channel cross-secton, and n partcular the channel heght, s a very effectve way to mprove the sensor senstvty but at the cost of mproved pressure drop, as ponted out by Equaton (6)..6. Desgn Consderatons The expressons found so far do not allow ab-nto predcton of the sensor performances but should be complemented wth expermental data measured on test structures. It s beyond the am of ths work to examne all possble combnatons of desgn constrants, so that ths secton s lmted to a smple example where we wll suppose that parameters h have been measured on a prototype and that

11 Mcromachnes 01, the followng parameters are fxed: () bandwdth, dctated by the applcaton; () s AB, R S, t C, W S, W TMIN, dervng from the fabrcaton technology; () N H, dctated by the chosen sensor archtecture. As a desgn constrant we wll consder a target resoluton ndcated wth Q*. Note that, f we neglect the amplfer nose term n Equaton (18), we get the ntrnsc resoluton lmt of the sensor. At ths pont the desgner needs to mpose that: The followng desgn ndcatons are straghtforward: * 3 4 ( ) k BTRS BLT Q = f NT (9) W PH heff s AB (1) The sensor wdth W should be set at the maxmum allowed value, mposed by the fabrcaton process (etchng tmes) and by the channel wdth W CH. Increasng W CH to make room for a further W ncrease s neffectve, snce h eff proportonally decreases through Equaton (8). () The power P H should be set to the maxmum value, whch can be due ether to a power consumpton constrant or a relablty ssue, the latter dervng from the maxmum allowed heater temperature. (3) The effect of the thermople number s rather weak, snce t acts only on f NT, whch vares n a narrow nterval. From Equaton (17) the optmum stuaton seems to be represented by N T = 1. Nevertheless, we wll dscover later that such a choce can adversely affect the amplfer desgn and should generally be avoded. (4) If the above operatons are not suffcent to obtan the target resoluton, parameter h eff should be mproved. The relevant equatons are (5), (10) and (1). Improvement of the heater nsulaton (th ) ( R H ) s effectve only f the power constrant does not derve from relablty ssues, snce, n (th ) ths case, an ncrease of R H wth the maxmum allowed power appled would smply result n exceedng the maxmum heater temperature. Improvng the thermople nsulaton by ncreasng L C produces sgnfcant h eff mprovements when L C < L S, so that L T s not proportonally affected. Furthermore, L C s often lmted by the allowed etchng tmes and mechancal robustness. Thermople nsulaton can also be mproved by reducng the cantlever thckness t c, as clearly shown by Equaton (4). Usng the post-processng approach, ths parameter s determned by the delectrc thckness dervng from the orgnal process. Thckness reducton can be acheved n the post-processng phase by selectve etchng steps. The mnmum thckness value s fxed by structural ssues and by the necessty to mantan a suffcent margn wth respect to the thermople conductors, n order to prevent them from beng damaged by the etchng process. The last parameter to be taken nto account to mprove the senstvty s g,k / Q. Reducng the channel heght (H) s strongly effectve as shown by Equaton (8). However, the concomtant pressure drop ncrease, dervng from Equaton (6), should be carefully taken nto account. (5) If the prevous steps are successful, then t s necessary to desgn an amplfer wth an nput nose just low enough not to sgnfcantly change the acheved resoluton. To obtan that, the followng condton should be met: 4 na ( NT PH heff s AB ) v << Q* (30)

12 Mcromachnes 01, Equaton (19) states that, once an optmum amplfer topology has been chosen, the amplfer nose can be reduced only by ncreasng the absorbed current and, as a consequence, the amplfer power consumpton. The latter, gven by I A V DD, where V DD s the amplfer supply voltage, adds to the heater power P H, ncreasng the overall power consumpton of the system. As antcpated earler, t s generally convenent to renounce to the margnal advantage of the choce N T = 1 and adopt an N T number as close as possble to the maxmum value N TMAX. In ths way the nose constrant on the amplfer s relaxed, wth proportonal advantages n terms of power consumpton. 3. Expermental Results and Dscusson 3.1. Test Chp Archtecture and Technology In order to fnd addtonal nformaton about the desgn of thermal flow sensors, measurements have been performed on sample structures ncluded n a test chp. An optcal mcrograph of the latter s shown n Fgure 5(a), whle an enlargement of three dfferent sensor structures s shown n Fgure 5(b). The chp ncludes also a low nose chopper amplfer, properly desgned to ntroduce neglgble nose contrbutons wth respect to the thermople thermal nose. The amplfer can read the dfferental voltage (V out = V V 1 ) or the ndvdual thermople voltages V 1 and V. The electronc nterface ncludes also a drver for the sensor heaters. More detals on the nterface can be found n [1]. The sensng structures share a seres of common parameters, shown n Table 1, regardng ether the structure and channel dmensons. The dfferences between the devces are descrbed n next sub-secton. Fgure 5. (a) Optcal mcrograph of the test chp, ncludng the read-out electroncs and the flow sensors before the post-processng; (b) Magnfcaton of the sensng structures after post-processng, showng the three dfferent confguratons, namely the sngle heater, the double heater and the trple heater. Electroncs Sensors (a) (b) Table 1. Parameter values common to all sensng structures. The Seebeck coeffcent was measured wth a test structure on the chp. N T s AB L C L S L H L GH W L W CH µv/k 35 µm 90 µm 46 µm 71 µm 11 µm mm 0.5 mm The test chp has been desgned wth the BCD6s (Bpolar, CMOS, DMOS) process of STMcroelectroncs. The heaters are polyslcon resstors placed over suspended delectrc membranes whle the thermoples consst of N T = 10 n + poly/p + poly thermocouples wth the hot contacts at the

13 Mcromachnes 01, tp of a cantlever beam. Each thermople has an electrcal resstance of 50 kω. The thermal nsulaton of the heaters and the thermoples from the substrate has been obtaned applyng a post-processng technque based on front-sde bulk mcromachnng, as schematcally shown n Fgure 6. Fgure 6. Schematc vew of the post-processng: (a) passvaton openngs performed by the slcon foundry; (b) delectrc openngs by reactve on etchng (RIE); (c) slcon ansotropc etchng n TMAH soluton. Passvaton Openngs Delectrc Openngs Slcon Etchng Slcon Substrate Slcon Substrate Slcon Substrate Passvaton InterMetal SO BPSG Polyslcon Feld Oxde (a) (b) (c) In order to access the bulk slcon n selected areas of the chp, the delectrc layers have been selectvely removed from the front-sde. In partcular, the passvaton layer and a part of the nter-metal delectrc layers have been removed drectly by the slcon foundry at the end of the chp fabrcaton (Fgure 6(a)). Ths was obtaned explotng the same etchng step used by the foundry to open the passvaton layer over the pads [9]. Then, durng the post-processng phase, resdual delectrc layers have been completely removed by means of a photolthographc step followed by slcon doxde reactve on etchng (RIE) (Fgure 6(b)). A slcon ansotropc etch was then appled through the openngs, usng an aqueous soluton of TMAH wth slcc acd and ammonum persulfate [9] (Fgure 6(c)). An optcal mcrograph of the sensng structures after the slcon removal s shown n Fgure 5(b). The depth of the cavty was 80 µm for all devces used n ths work. Fgure 7. (a) Schematc vew and (b) photograph of the assembled devce. Conveyor Chp Gas n Gas out Cyanoacrylate (a) (b) After post-processng, the chps were glued to ceramc DIP8 cases by means of epoxy resn and wedge bondng was used to connect selected chp pads to the case pns. A recently proposed packagng technque [30] has been used to connect the ntegrated flow sensor to the gas lnes. Ths technque s based on a purposely bult poly-methyl-methacrylate (PMMA) conveyor whch s algned to the chp by means of a gude and s capable to convey multple flows to dfferent areas of the chp [31]. Trenches wth dfferent cross-secton dmensons have been mlled on the flat face of the conveyor by means of a precson computer controlled mllng machne (VHF CAM 100) and cyanocrylate glue has

14 Mcromachnes 01, been used to fx the conveyor to the chp surface, as schematcally shown n Fgure 7(a). In Fgure 7(b) a photograph of a devce after packagng s shown Measurements The frst set of measurements has been performed on the trple-heater sensor and was devoted to check the valdty of the lnearty hypothess. The responses to ntrogen flow have been measured delverng a constant power (1.5 mw) to one heater at a tme. The channel heght (H) s 0.5 mm. The other dmensons are specfed n table 1. The response of the three heaters H 1 3 s shown n Fgure 8. Clearly, only the case where the central heater (H ) s actvated produces an deally symmetrcal power dstrbuton, resultng n a relatvely low offset (30 µv), due only to random asymmetres, whle n the other two cases a large systematc offset s present. Fgure 8. Response to ntrogen flow rate of a trple heater sensor wth only one heater powered at a tme. The powered heater s ndcated n the plots V out (mv) H 1 V out (mv) H V out (mv) H Q (sccm) Q (sccm) Q (sccm) Fgure 9. (a) Measured (symbols) and calculated (lne) response of the trple heater sensor to a ntrogen flow wth all the heaters powered wth 1.5 mw; (b) Overheatng of the nd thermople wth respect to H 3 heater. 4 V out (mv) 0 measured calculated V,3 (mv) Q=0 sccm Q=0 sccm - (a) (b) Q (sccm) Power P 3 (mw) Fgure 9(a), shows the response to ntrogen flows when all the heaters are powered wth 1.5 mw. The sold symbols represent the result of an actual measurement, whle the lne has been obtaned by superposton of the three responses shown n Fgure 8. A good agreement, confrmng the valdty of

15 Mcromachnes 01, the lnearty hypothess, s vsble. To test also the supposed lnearty of the sensor element overheatng wth respect to the heater powers, we have measured the output voltage of the nd thermople (downstream thermople) as a functon of the power delvered to the H 3 (downstream heater). The measurements have been performed wth zero flow and 0 sccm and the results are shown n Fgure 9(b). In both cases an excellent lnearty can be observed. The second seres of experments, whch nvolved samples wth one, two and three heaters was devoted to test the effects of parameters change on the sensor resoluton and dynamc range. The resoluton s calculated consderng the thermal nose of the two thermoples over a bandwdth of 100 Hz (v np p = 1.6 µv) and the senstvty at zero flow rate, S(0), also reported n Table. Numercal dervaton of the sensor responses was used to calculate the senstvty. The full scale flow rate, Q max, was set at the pont the senstvty dropped below 50% of S(0). The results, all referrng to ntrogen flows, are summarzed n Table, where the parameters that dstngush the varous samples are also reported. Note that n the sngle heater samples (frst three lnes) metal nterconnectons (Alumnum) are used to access the heaters through the suspendng arms (heater connecton column). The other samples n the table use slcded polyslcon (S-Poly), provdng a low enough sheet resstance wth much less thermal conductvty than Alumnum. As a result, the heater thermal resstance s nearly 50% hgher for the samples usng slcded nterconnectons, wth a proportonal beneft n terms of h eff, and, consequently, low power performances. Table. Man parameters and performances of the sensors used n ths work. The sensor resoluton (Q np p ) has been estmated consderng a 100 Hz bandwdth. All fgures refer to ntrogen flows. Sensor parameters Sensor performance (P H = P H /N H = 1.5 mw) (th ) R H k tp h eff at Q = 0 V K (0) Q np p K/mW µv/sccm/mw mv sccm N H Heater H connecton mm L G µm S(0) µv/sccm Q max sccm DR 1 Metal Metal Metal S-poly S-poly S-poly S-poly The experments performed on sngle heater structures have been devoted to nvestgate the role of the heater-thermople gap, L G. The test chp ncludes sngle heater structures wth L G = 40, 60 and 80 µm. The measured sensor responses are shown n Fgure 10. Note that the curves are smlar, wth a zero flow senstvty that exhbt varatons less than 13%. Ths experment suggests that varaton of the thermople-heater gap n ths range does not consttute a vable method to mprove senstvty. Ths result s n contrast wth [15,16], where the senstvty was found to ncrease wth larger thermople-heater spacng. A possble reason s that n [15,16] all sensor elements were placed on a sngle membrane, so that the dstance between the heater and the thermople strongly affects the thermal nsulaton of the thermople. On the other hand, L G strongly affects the statc thermople voltage V K (0) that n Table ndcates the average value of V 1 (0) and V (0). Ths quantty s

16 Mcromachnes 01, sgnfcantly hgher for the smallest L G value, provng that the a k, (0) parameters are larger. Consderng that the senstvty (and then h eff ) does not change wth L G, a proportonally hgher sensor offset should be expected for the smallest L G value. A hgher offset s actually vsble n Fgure 10 for L G = 40 µm. Fgure 10. Response to a ntrogen flow of the three sngle heater structures, dfferng for the dmenson of the thermople-heater gap L G, ndcated n the fgure together wth the senstvty at zero flow. V out (mv) L G =80 μm S(0)=96 μv/sccm V out (mv) L G =60 μm S(0)=100 μv/sccm V out (mv) L G =40 μm S(0)=87 μv/sccm Q (sccm) Q (sccm) Q (sccm) The last seres of experments was devoted to nvestgate the effect of channel heght, H. The measurements, shown n Fgure 11, were performed on double-heater structures, wth both the heaters drven wth 1.5 mw. These curves clearly show the senstvty ncrease that can be obtaned by reducng the channel heght, as predcted by Equaton (8). The senstvty ncrease was obtaned at the cost of ncreased pressure drop, whch passed from 0.1 kpa at 100 sccm for the 0.5 mm channel to 0.4 kpa for the 0.5 mm channel, at the same condtons. The actual senstvty gan obtaned by halvng the channel heght s nearly 3, whle a factor of 4 was expected from Equaton (8). A not fully developed flow regme n the relatvely short channel can be a reasonable explanaton. Fgure 11. Responses of double heater structures to a ntrogen flow. The structures were packaged wth dfferent channel heghts, H, ndcated n the fgure for each curve. V out (mv) H= 0.5 mm H= 0.5 mm H= 1 mm Q (sccm)

17 Mcromachnes 01, As far as the dynamc range s concerned, all tested sensors feature DR value greater than 10 3, whch s an excellent result for ths knd of sensors. Consderng the sngle heater sensors, the effect of reducng the thermople-heater gap (L G ) produces an nterestng DR mprovement, due to hgher full scale flow rate. On the contrary, the resoluton ncrease obtaned reducng the channel heght s accompaned by a range (Q max ) reducton, resultng n a slght deteroraton of the DR. Fnally, t can be observed that ncreasng the number of heaters mproves the DR at the cost of ncreased power consumpton. All consderatons made n ths work on the sensor resoluton and DR are based on the hypothess that the only sgnfcant contrbuton to the overall nose s thermal nose of the thermople resstance. Ths hypothess s confrmed by recordng the sensor output sgnal, properly amplfed by the on-chp amplfer (gan = 30). Data dgtalzaton has been performed usng a 16 bt acquston system (Pco Technology Ltd, mod. ADC16) combned wth a program for spectral analyss. Fgure 1(a) shows the total nose voltage spectral densty of the sensor and the amplfer background nose. The latter was measured by substtutng the sensor wth a short crcut. Fgure 1. (a) Nose voltage spectral densty (total sensor nose) referred to the amplfer nput, measured on double heater samples wth a total heater power (PH) of.5 mw, kept n stll ntrogen. The heater power dstrbuton on the two heaters was slghtly unbalanced to compensate for the sensor offset. The amplfer background nose and deal thermople thermal nose are also ndcated; (b) Tme dagram of the total voltage nose, referred to the amplfer nput. Nose spectral densty (nv/sqrt(hz) Total sensor nose (μv) Frequency (Hz) Total sensor nose Thermople thermal nose (deal) Amplfer background nose 0 5 Tme (s) 10 (a) (b) The sensor s a double heater verson, wth 0.5 mm channel heght, mantaned n stll ntrogen (zero flow). Both quanttes are referred to the amplfer nput, as n the scheme of Fgure (a). A ffth order Butterworth low pass flter s nserted at the amplfer output port, to lmt the sgnal bandwdth and elmnate alasng phenomena. The actual frequency response of the flter has been expermentally determned and the result has been used to correct the measured spectra shown n Fgure 1(a), whch can be consdered free of flterng effects n the whole dsplayed frequency nterval. DC couplng s used n all measurements; spectra are averaged over 5 ndependent captures. The deal thermal nose

18 Mcromachnes 01, 3 31 densty (40 nv/sqrt(hz) of the total thermople resstance (R = 100 kω) s ndcated by the dashed lne. The results shown n Fgure 1(a) prove that the approxmaton of consderng only the thermal nose contrbuton s approprate, at least for the sensors used n ths work. Ths was confrmed also by measurement of the rms nose voltage, estmated by data recorded over ntervals of 1.6 s, wth a 100 Hz sgnal bandwdth. Fgure 1(b) shows a tme dagram of the sgnal measured from a double heater sample kept n stll ntrogen. The orgnal sensor offset (around 100 µv) was compensated by balancng the heater power as descrbed n [1]; a resdual offset of nearly 1.5 µv can be observed. The estmated rms nose voltage (.e., the sgnal standard devaton) was 0.41 µv, n good agreement wth the theoretcal 0.4 µv value calculated by consderng only thermal nose. 4. Conclusons A detaled lumped element model of ntegrated thermal flow sensors has been ntroduced. The man advantage of the model s the separaton of the transducton process nto dstnct phases, whch can be ndependently analyzed n order to fnd concse expressons to be used for global optmzaton of the devce. A lnearty hypothess, based on reasonable approxmatons and supported by expermental results, s used to analyze mult-heater sensors, whch have been recently proposed as an effectve method to cancel the sensor offset [3] and extend the operatng range [17,4]. The expressons derved from the proposed schematzaton nclude several sensor specfcatons and may consttute a framework for organzng new data obtaned wth further expermental nvestgatons or flud-dynamc smulatons. Applcaton to the optmzaton of the sensor resoluton provded gudelnes that should contrbute to reduce the number of desgn-fabrcaton-testng cycles necessary for meetng the target specfcatons. A lmtaton of the model s the presence of generc heat exchange terms g,k (Q) that, wth ther dervatves, determne the sensor senstvty. Indcatons about the senstvty dependence on parameters that have a drect effect on the g k factors, such as the flow channel heght and heater thermople gap, are extrapolated by the experments performed on the test chp. Acknowledgments The authors thank the R&D group of STMcroelectroncs, Cornaredo, Italy, for fabrcatng the chps used n the experments descrbed n ths work. References 1. Schabmueller, C.G.J. Flow sensors. In MEMS Mechancal Sensors; Beeby, S., Ensell, G., Kraft, M., Whte, N., Eds.; Artech House: Norwood, MA, USA, 004; pp Elwenspoek, M.; Wegernk, R. Mechancal Mcrosensors, 1st ed.; Sprnger-Verlag: Berln, Germany, 001; pp van Oudheusden, B.W. Slcon thermal flow sensors. Sens. Actuat. A: Phys. 199, 30, Nguyen, N.T. Mcromachned flow sensors A revew. Flow Meas. Instrum. 1997, 8, Baltes, H.; Paul, O.; Brand, O. Mcromachned thermally based CMOS mcrosensors. Proc. IEEE 1998, 86,

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20 Mcromachnes 01, Nguyen, N.T.; Dötzel, W. Asymmetrcal locatons of heaters and sensors relatve to each other usng heater arrays: A novel method for desgnng mult-range electrocalorc mass-flow sensors. Sens. Actuat. A 1997, 6, Moser, D.; Baltes, H. A hgh senstvty CMOS gas flow sensor on a thn delectrc membrane. Sens. Actuat. A 1993, 37 38, Enz, C.C.; Temes, G.C. Crcut technques for reducng the effects of op-amp mperfectons: Auotzerong, correlated double samplng, and chopper stablzaton. Proc. IEEE 1996, 84, Steyaert, M.S.J.; Sansen, W.M.C.; Zhongyuan, C. A mcropower low-nose monolthc nstrumentaton amplfer for medcal purposes. IEEE J. Sold-State Crcuts 1987, SC-, Bejan, A. Forced convecton: Internal flows. In Heat Transfer Handbook; Bejan, A., Kraus, A.D., Eds.; Wley: Hoboken, NJ, USA, 003; pp Brusch, P.; Potto, M.; Bacc, N. Postprocessng, readout and packagng methods for ntegrated gas flow sensors. Mcroelectron. J. 009, 40, Brusch, P.; Nurra, V.; Potto, M. A compact package for ntegrated slcon thermal gas flow meters. Mcrosyst. Technol. 008, 14, Brusch, P.; De, M.; Potto, M. A sngle chp, double channel thermal flow meter. Mcrosyst. Technol. 009, 15, by the authors; lcensee MDPI, Basel, Swtzerland. Ths artcle s an open access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense (