NTHU ESS5850 Micro System Design F. G. Tseng Fall/2016, 7-2, p1. Lecture 7-2 MOSIS/SCNA Design Example- Piezoresistive type Accelerometer II

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1 F. G. Tsng Fall/016, 7-, p1 ctur 7- MOSIS/SCNA Dsign Exampl-!! Pizorsistivity Pizorsistiv typ Acclromtr II a Considr a conductiv lock of dimnsion a as shown in th figur. If a currnt is passd through th lock paralll to th dirction, th rsistanc of th lock is givn y ρ a 0 (7-1- whr ρ is th rsistivity of th lock matrial. Whn an inward forc F is applid against th two nds of th lock, this gnrats a strss σ F /, and th lock dforms. Th amount of dformation is a function of th Young s modulus E and th Poisson s ratio ν of th matrial. Th chang in dimnsions of th lock ar givn y σ σνa σν Δ ε Δa ενa Δ εν (7-1- E E E This dimnsion chang rsults in a nw valu for th rsistanc: 4 ρ(1 ε (1 + εν a(1 + εν ε [1 (1 + ν ε] 0 (7-1-5

2 F. G. Tsng Fall/016, 7-, p Th gag factor G gaug is dfind to th chang in rsistanc pr chang in strain: Δ / G guag 0 ε (7-1-6 Th gaug factor from Eqn. (7-1-5 is G1+ν. Th Poisson s ratio for most matrials is roughly 0., giving a typical gaug factor for most conductors of G gaug 1.6..g. a 1% strain will rsult in a 1.6% chang in rsistanc. In addition to this shap-asd chang in rsistanc, som matrials xhiit a sustantial chang in rsistanc du to a strain-inducd chang in th rsistivity of th matrial. This is known as th pizorsistiv ffct, and is particularly apparnt in silicon crystals, whr th gaug factor du to pizorsistivity can as larg as 00 in magnitud. Th gaug factors of n-typ and p-typ silicon hav opposit sign, with n-typ ing ngativ. Du to a varity of ffcts, th gaug factor of polysilicon films is typically an ordr of magnitud lowr than singl crystal films, with typical valus of 0 to 0 for p-typ silicon, and 15 to 5 for n-typ. Th avrag strain for finit lngth of pizorsistiv matrial sitting on top of th am, xtnding a lngth g from th as of th am. Th strain varis linarly along th am, and is zro at th tip and maximum at th as, so th avrag stain in th pizorsistor is givn y: ε av g ( 1 ε max (7-1-7 Comining Eqn. 7-1-, 6, 7, w can hav

3 F. G. Tsng Fall/016, 7-, p Δ G gaug (1 g ya (7-1-8 p!! Maximum dflction Y( θ( p From Eqn , th dflction of a cantilvr am: 1 Fx y ( x [ ( x + EI 6 M 0x ] whr F and M ar th forc and momnt applid to th am. In th aov cas, Fma, and MF p / 1 F M F p y ( [ + ] [ + ] (7-1-9 EI EI 4 Th tip of th proof mass dflcts an additional amount dtrmind y th angl of th tip of th support am (assum th proof mass is a rigid ody without any dflction undr th acclration forc F p θ ( [ + ] (7-1-0 EI Th dflction of th tip of th proof mass is (7-1-1

4 F. G. Tsng Fall/016, 7-, p4!! sonant frquncy From th analysis of th dynamic of th am, th natural frquncy is ω n Ea p K 4 (7-1- m W tρ!! sponsivity sponsivity input output signal physical quantity acclrom tr output input Voltag acclration V +Δ V + V - +Δ From th aov Whatston ridg

5 F. G. Tsng Fall/016, 7-, p5 ΔV V + V + Δ V + Δ V + Δ Δ V + Δ Δ V (7-1- From Eqn. (7-1-6 Δ g Ggaugε Ggaug(1 ε max g zm max Ggaug(1 EI p z[( maac ( + g G (1 gaug a E( 1 ] (7-1-4 Comin Eqns and 4, w can hav acc ΔV a acc ac 6V G V G gaug gaug (1 g z ( tw Ea p z( tw ρ p ρ( Ea p + (7-1-4!! Nois Thr ar svral sourcs of nois in this dvic. 1.! Johnson Nois:

6 F. G. Tsng Fall/016, 7-, p6 Th rsistors in th Whatston ridg ach contriut nois powr of 4kT pr Hrtz of andwidth. Johnson nois coms from thrmal agitation of lctrons within a rsistanc, and it sts a lowr limit on th nois prsnt in a circuit. Th corrsponding ffctiv voltag nois is rlatd to powr y th usual rlationship: Powr v n /, or v n 4 ktδf (7-1-5 Whr Δf is th andwidth of intrst. Johnson nois is also rfrrd to as thrmal nois, rsistanc nois or whit nois. It is indpndnt of th composition of th rsistanc, and th frquncy distriution of thrmal nois powr is uniform. Th instantanous amplitud for thrmal nois has a Gaussian, or normal, distriution. Th avrag is zro and th MS valu is givn aov. Th thrmal nois gnratd y any aritrary connction of passiv lmnts is qual to th thrmal nois that would gnratd y a rsistanc qual to th ral part of th quivalnt ntwork impdanc..! TNEA (Thrmal nois-quivalnt acclration: Th spring/mass systm of th cantilvr contriuts its own nois to th systm, with a nois powr of kt/ in ach mod of viration. This lads to an ffctiv MS dflction of 1 1 Kx n kt (7-1-6

7 F. G. Tsng Fall/016, 7-, p7 which yilds an quivalnt MS acclration of 4kTω a n 0 (7-1-7 MQ whr ω 0 is th natur frquncy, M is th mass, K is th spring constant, and systm. ω M Q 0 is th quality factor of th spring c k is Boltzmann s constant (1.8 - jouls/ K.!! Snsitivity In ordr to compar th rlativ importanc of ths nois sourcs, it is usful to mov thm from thir sourc to som common location in th signal lock diagram. Typically this is th input to th lctronic amplifir, or th ral input (such as acclration. In this way w can rally compar th ffcts from diffrnt nois sourcs. For xampl, w can mov all aov noiss to th input, y which w can hav thm as nois quivalnt acclration. Hr th nois quivalnt acclration is th snsitivity of th systm, i.., th minimum input signal w can dtct.!! Dynamic rang 1. Uppr limit: Strain limits For most of th micro-mchanical matrials, th fractur strain is roughly 1%. W nd to transfr th strain limit into quivalnt acclration. From Eqn

8 F. G. Tsng Fall/016, 7-, p8 zm ε frac (0, z EI p z[( mauppr ( a E( 1 + ] a uppr a ε(0, a E( 1 a p [( m( + ] ( owr limit: Snsitivity Hr is th nois quivalnt acclration.!! Tmpratur dpndncy TC (Tmpratur Cofficint of sistanc 1.! Mtal: ρ ρ0[ 1+ α( T T0 ] Matrial sistivity: ρ 10-8 TC: α (10 - K Ωm Aluminum.65.9 Coppr Nickl Platinum Gold.4.4 Tal adoptd from J. Fradn[1].

9 F. G. Tsng Fall/016, 7-, p9. Silicon: vry snsitivity to purity

10 F. G. Tsng Fall/016, 7-, p10.! How to compnsat tmp. ffct? a.! Cancl out through rfrnc or symmtry dsign..!fdack control through adjustal gain from tmp snsor c.! Softwar adjustmnt!! ong trm staility 1.!Opration iftim?.!on shlf lif?.!ong-trm drift? frnc: 1.! Jaco Fradn, AIP Handook of Modrn snsors, Physics, Dsigns and Applications, Amrican Institut of Physics, 199..! Hnry W. Ott, Nois duction Tchniqus in Elctronic Systms, scond dition, John Wily & Sons, Inc., ! Jams M. Gr and Stphn P. Timoshnko, Mchanics of Matrials, fourth dition, PWS pulishing company, ! Smiconductor Snsors, S.M. Sz, Wily Intr. Scinc, 1994.