Design and Modeling of Nanodevices Compact Modeling of Nano MOSFETs

Transcription

1 : Design and Modeling of Nanodevices Design and Modeling of Nanodevices Compact Modeling of Nano MOSFETs Dr Zhou Xing Office: S1-B1c-95 Phone: Web: X. ZHOU 1 18

2 Top-down vs Bottom-up sand Lithography Top-down History: ICs have been designed by SPICE using BSIM over the past 3 years. 1 m 1 m 1 m 1 nm 1 nm 1 nm BSIM/SPICE for IC designs ~3yrs Minimum Feature Size Microelectronics SPICE models TG NW EDA tools for nanodevice ~yrs Nanoelectronics CNT Mol.Ele. Single atom 1 pm Motivation: New models for future nano-devices at the atomic scale. Bottom-up device Assembly X. ZHOU 18

3 Moore s Law Compact Model Parameters Chip complexity will double about every 18 months. M. Chan, et al., Microelectronics Reliability, vol. 43, pp , 3. A disturbing version of Moore s law the number of compact-model parameters doubles about every decade (as a result of evolutionary development) X. ZHOU 3 18

4 Approaches to Analyzing Microelectronic Systems X. ZHOU 4 18

5 Process Device Circuit Block System Block Gate Circuit Interconnect Analog and Digital Subcircuit expansion acceleration Motivation Compact multi-level technology/transistor/ subsystem modeling System performance Centered at transistor-level compact model Transistor optimization Device Process Parameter extraction Process/structural variations Technology development Process effects on device/circuit X. ZHOU 5 18

6 Paradigm Shift in IC Chip Design and Manufacturing ertically -integrated giant semiconductor manufacturers Horizontally -strong foundries and fabless design houses IC Chip Manufacturer Design Fab Fabless Design House Wafer Fab Foundry CAD EDA endor X. ZHOU 6 18

7 Design Fabrication Paradigm: Ideality & Reality Design House Ideality EDA endor Reality SPICE Wafer Fab Circuit designer CAD developer CM Process engineer Model developer X. ZHOU 7 18

8 Model Developer s Dilemma Design House I won t use it unless it s been implemented in my SPICE simulator Circuit designer Do you want to try my new model? EDA endor I won t code it unless fab can provide data and model CAD developer CM Can you implement my new model? 1 3 Model developer Wafer Fab I won t extract your model unless my customer (designer) wants it Process engineer Will you support my new model? X. ZHOU 8 18

9 Models and Modeling Groups NGSOI/MG Model BSIM EK HiSIM ULTRA-SOI/MG ACM Xsim Technology-dependent predictive model DG/MG SiNW/CNT PCMOS ISNE III-/Si X. ZHOU 9 18

10 Accuracy Speed Tradeoff: History & Future Accuracy & Speed (No demand for 3+ yrs) (High demand for analog) PSP M11 HiS SP Central concern for CM: accuracy speed tradeoff Determined by demand/supply M9 P S M1 M M3 B1 B B3 t -based s -based Q i -based EK ACM B4 U (Not as slow with HPC) SPP B5 X Iterative: can be costly for digital 1 Future: how to tradeoff? Scalable (non-binnable): accuracy over geometry Single-piece across all regions Selectable accuracy within the same core model Extension to non-bulk FETs Time X. ZHOU 1 18

11 Role of Compact Model (Courtesy: M. Chan) Ultimate goal: towards accuracy and simplicity X. ZHOU 11 18

12 SPICE Circuit Simulation: (Modified) Nodal Analysis KL/KCL: I R R R R R R3 DC: R1 R R 1 I R R R 3 Transient: companion 1 1 C1 1 C1 R R h R h I i 1 1 C1 1 C1 1 1 C i 1 C i 1 C R h R R h 3 AC: jc jc 1 1 j R1 R R 1 Ie jc1 jc 1 R R R 3 f(x) I I e nv th 1 x x x 3 1 x Nonlinear: N R iteration x x x n1 n f f ' x x n n X. ZHOU 1 18

13 What Is a Model, and Modeling? John von Neumann The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work. A model is a mental image of reality One can have many different images of the same reality. Correct physical approximations and correct mathematical formulations to emulate ideal device physical behaviors and corroborate with real device characteristics. What does compact mean? What is physical of a model? X. ZHOU 13 18

14 Perspective: Compact Modeling for Circuit Simulation Monte Carlo: (6-D, t) I D (k,r,t) t I D () = I ds + I b + I g S G I g D I D Compact: (-D, t) I = Qv Q C ij = Q i / j r I ds Ib G ij = I i / j Q + Q(t) SPICE (nodal analysis) k B Age Numerical: (3-D, t) I D (r,t,) mental image t r(x,y,z) L,W,(Z) DC (n sets = unphysical ) T g, d, b, s f, (t) X. ZHOU 14 18

15 Ideal vs Real MOSFET To Be Modeled But we need to model this This is what the core model deals with. (R. Rios, WCM5) X. ZHOU 15 18

16 Binning vs Meshing Binning = piece-wise (in geometry) Infinite number of bins = single-device model = nonscalable (= unphysical?) Key difference: binnable (transistor-based) vs non-binnable (technology-based) model Binnable model: parameters extracted by fitting electrical data at fixed geometry Non-binnable model: parameters extracted by fitting data over geometry at fixed bias Compare: Meshing necessary? and physical? Numerical: meshing t Compact: binning N Homogeneous: Meshing unnecessary, 1 mesh n mesh ( s -model numerical) 1 bin n bin N(x,y) Inhomogeneous: Meshing necessary, and physical ( s -model less physical ) Necessary and physical for non-binnable model Binnable model: n sets = unphysical L X. ZHOU 16 18

17 MOSFET Compact Models: History and Future Classical bulk-cmos ~4 yrs Poisson + GCA Sah Pao (input) oltage Equation Pao Sah (output) Current Equation Q b linearization Charge Sheet Model (Q sc =Q b +Q i ) t -based Q i linearization Iterative / explicit Q i -based s -based Non-classical CMOS SOI Partially-Depleted (PD) Bulk oltage/current Equations, CSM nontrivial Fully-Depleted (FD), Ultra-Thin Body (UTB) Non-Charge-Sheet MG New oltage/current Equations Body Contact/Floating Body Symmetric/Asymmetric Double Gate (s-dg/a-dg) Tri-gate, GAA, Schottky-barrier, DSS, TFET, X. ZHOU 17 18

18 Conceptual Core Bulk-MOS at arious Body Doping G N A (cm 3 ) S L g D s s n + n + N sd T ox s o d N g d X j Bulk FinFET/SiNW (unintentional doped) C) Intrinsic (7 C) o X dm (m) (N A = N D = : undoped = pure Si) T Si Bulk: T Si >> X dm, with B : o = b = B SOI: T Si > X dm, without B : o floating o b B N A N D DG/GAA: T Si /R << X dm : volume inversion ( o : virtual electrode ) X. ZHOU 18 18

19 Need for an Extendable Core Model for Future Generation S Pao Sah G I ds D I D S t -based models History has witnessed generations of MOS models and efforts required from one generation to the next Need for a core model extendable to future generations, and with less duplicating efforts G (B) D I D Q i -based models S s -based models G D I D S G1 Time HEMT leveraging on MOS models MG/FinFET is just a special case D I D B Sub Sub G Bulk PD-SOI FD-UTB/SOI DG/GAA/SB/DSS X. ZHOU 19 18

20 Seamless Transformation and Unification of MOSFETs (a) g (b) g b (c) g ' b oxf t oxf s t Si s d s d s d b b oxb t oxb t Si t oxb = t oxf a-dg (f) b PD-SOI g ' b = b = b FD-UTB/SOI t oxb ' = (e) g (d) b = g g ' = s = b s d s d s d t Si 'Bulk-UTB' half s-dg g s-dg b PD-SOI FD-UTB/SOI a-dg s-dg UTB Bulk Bulk X. ZHOU 18

21 The Generic SOI/DG/GAA MOSFET Zero-field potential: o [ o' (X o ) = ] Imref-split: cr = Fn Fp = c r r = b (BC: body-contacted) r = min = min( s, d ) ( FB : w/o BC) Bulk: special case of s-dg SOI: special case of ia-dg Common/symmetric-DG [GAA] g1 = g = g : two gates with one bias C ox1 = C ox : s-dg (X o = T Si /; [R]) Full-depletion: FD = g (X d =T Si /) C ox1 C ox : ca-dg (X o < T Si ) Independent/asymmetric-DG g1 g : ia-dg, biased independently Zero-field location may be outside body Consider two independent gates; linked through full-depletion condition: X d1 + X d = T Si GAA SOI ia-dg ca-dg s-dg bulk Unification of MOS X. ZHOU 1 18

22 Generic Double-Gate MOSFET with Any Body Doping S n + x r T ox1 R X o1 ( g1 ) L g p1 s1 o1 G1 N g1 ( ox1 ) o1 = o = r = (at gi = FBi, s = d =) D n + y N A (cm 3 ) Bulk FinFET/SiNW (unintentional doped) C) Intrinsic doping (7 C) (< 6 m) X dm (m) (N A = N D = : undoped = pure Si) X o ( g ) o Bulk: T Si >> X dm, with BC: o = b = B T Si x 1 T ox s G N g p ( ox ) N sd y SOI: T Si > X dm, without BC: o floating DG/GAA: T Si /R << X dm : volume inversion ( o : virtual electrode ) X. ZHOU 18

23 PD/FD at arious Body Doping/Thickness L g G S = D = G S = D = n + T ox o X dm o s N g PD n + y T Si n + n + o X dm s FD T Si o o = r G = FB, S = D = 1 14 G S = D = T Si N A N D (cm 3 ) K ox s N sd n + n + o PD T X dm Si o FD s x G X. ZHOU 3 18

24 Dynamic Depletion (DD) at arious Body Thickness S = L g G D = DD S = G D = DD n + T ox X dm,s s N g n + y T Si n + n + X dm,c s FD X dm,d T Si o PD S = G D = DD T Si N A N D (1 17 cm 3 ) K ox s N sd n + T Si X dm,s s DD X dm,d n + x G X. ZHOU 4 18

25 Symmetric Charge Linearization Symmetric bulk/inversion charge linearization dqi Q y Q C q A i i s s ox i b s s ss ds I q Av q Av ds i b th s i b th ds, eff W L eff Cox eff eff, s eff, d s 1 s Long-channel symmetric current model sc, F cb vth v e C ox eff, c 1 Lc, eff b LEsat, c gt, c sc, b th sc, b W L 1 gt gt, s gt, d q i gb FB s s b 1 s s, s s, d A b 1,, ds s eff ds d eff,, s sd ss F db F sb ds,, ;, ; ', c s d c d s ceff, c csat, cc', sat cs, d d, eff s, eff ds, eff E C n ox b eff gt s b Si n s b LE gt, s sat, s ds, sat d, sat s gt, s Ab, slesat, s Ab, svth LE gt, d sat, d sd, sat s, sat d gt, d Ab, d LEsat, d Ab, dvth E sat, c v sat, c X. ZHOU 5 18

26 Symmetric Linearization of Bulk-Charge Factor for DD PD FD DD Due to the use of ds and f ( gf ), no singularity occurs at flatband X. ZHOU 6 18

27 The Poisson Boltzmann Equation and Solution X. ZHOU 7 18

28 The Complete ( Sah Pao ) oltage Equation X. ZHOU 8 18

29 Drain Current: Pao Sah Double Integral J x, y qn E qd n y ny n y n kt n qnn y qn y kt n qnn ln y q ni qnnfn y qn d dy n cb d t cb Si Ids yw qnx, y n x, ydx dy W y Q y d dy const. J qn d dx nx n cb s i cb Ey D n v y kt q ln n n Fn th i Fcb vth dx s n, cb qn s A e Qiyq nx, ydxq, n cb d q d d 1 s d E, F cb vth x cb qn A Si ve th 1 Fcb vth vth th e v v th e e qn F cb qn A Ex x, ysgn 1 vth 1 sgn A Si, Si s ti ti,,, y n x y n x y dx n x y dx db sb db y Q y d Q y d s i cb i cb sb A Ex n N e x n y y cb Fn F F cb v th W db W db s e ds i cb ox 1 cb L sb L sb Fcb v th ve th v F cb th I Q d C dd,, F F cb di cb ve th v F cb th X. ZHOU 9 18

30 CSM: Charge-Sheet Model vth, s 1, qn, dx N p qn e Q y q N p dx q N p d q d d s A cb A b A A s d E x cb F A Si cb Depletion approximation (n = p = ; also N D = ): qn 1 Q y d C y s A, b ox s s qn A Si Potential/charge balance: Q y C y Q g ox gb FB s ox Qi Qb Qox Qg Charge-sheet model (CSM): Qi y Qg y Qox Qb y Cox gb FB s y s y Sah Pao ( S P ) voltage equation ( s > 3v th ): sy F cb y vth gb FB s y s y vthe gb FB s y gb FB s s dcb y 1v th ds y y i y Cox vc Q th ox vc th ox C ox Qiy Qi y Qb y Qi y Qb y CSM dq i d s d s Cox d s C ox Cox 1 dy dy dy Q s b dy I y W y Q y ds s i drift s i s th diff dcb y ds d dy ds W yq y W yv dy I y I y s dq i y dy X. ZHOU 3 18

31 Drain Current Model: s -based vs Q i -based W L d I Q d s cb ds i s s L s ds s I W Q db i Qid cb ds Qi dcb L Ids Qi dqi sb L Q is dqi W d CSM: Q C i ox gb FB s s S P: 3v s th y y v e gb FB s s th y y v s F cb th q Q C v i i ox th q Q C v b b ox th s I dqi ds Idrift I Idiff y Ws yv UCCM: diff th dy q v i q i gb vfb d s W sl I ln vcb n1 drift y Ws y Qi y I n q n dy diff vth dqi q nq L v s W sl W 1 1 Idrift Qd i s L Cox v th sl s sl s s L From S P: W 1 3 3, Cox gb FB sl s sl s sl s L 3 L, L y q q q q q ln v v v i i b i b gb fb F cb Q i linearization v v gb gb th v v FB FB th s s cb sb sl s cb db th X. ZHOU 31 18

32 Q i -based Current Model CSM / S P: Q C C i ox gb FB s ox s s y Fcb y vth ox s th ox s C v e C Q i linearization: dqi nc q dy d cb Ids y WsQi dy ox ds dy CSM / D+D: d v dq s th i WsQi dy Q i dy i qn n C s q ox s sa n 1C C 1 v th dqi WsQi nc q ox Q i dy q b ox Qip Qi s p C, Q y q n x y dx qn y s b Cox nc sa UCCM: 1 th q ox i W W d I Q d Q dq v Q db Qid cb ds i cb i i L sb L Q is dqi I W Q 1 v dq Qid th ds i i L Qis nqcox Q i W Q Q W v Q Q L n C L I I I ds drift diff id is q ox dqi d Qip Q i Q i v ln nc q ox Q ip cb th p cb th id is I I I ds f r q Q C v s is ox th q Q C v d id ox th I C W v q q q q s d ds ox th s d L nq I ds q s q d qs qd I s n q n q From UCCM: I v, C W L s n th n ox X. ZHOU 3 18

33 t -based Model: Linear (Drift) Current Source-referenced threshold condition ( pinned surface potential): y y y y y, s s cb F sb cb ds s F Bulk-charge linearization: y Q C C y b ox s ox F sb Cox F sb F Q C Q i ox gb FB s b sb y Cox gb FB F sb y F sb F C ox gs t A b y Linear (drift) current: ( gs > t ) Threshold voltage: Bulk-charge factor: sb t FB F F sb A b 1 1 (For fixed bulk-charge: A b = 1),, I y W Q y d dy WQ y v v E E d dy d dy ds s i s i s y y s W ds W 1 I I Q d C A L L ds drift i ox gs t b ds ds F sb X. ZHOU 33 18

34 t -based Model: Subthreshold (Diffusion) Current Q Subthreshold surface potential: C b ox dd Q C gb FB dd b ox CSM / S P: s y dd 4 dd gb FB dd F cb y vth i ox dd th b Q C v e Q v Q C 1 e C th dd F cb vth i ox dd ox dd dd vth dd F cb v th Cox dd 1 e Cox dd dd vth dd F cb vth Cox e dd Subthreshold (diffusion) current: ( gs < t ), 1.5 ' ' t t off s F sb Q C d W L Q I id v dq v Q Q is ds th i th id is Q Q Q Q Q W L is i id i cb sb cb db W Ids Cdvth e 1 e L dd C q N X dd F sb vth ds vth ox Si A Si Qb dd Q dd Q b dd b s dd s b s d gb FB dd dd s Cox Cox n dd F sb gs t s -based dd C s F sb ' W Cd Ids Idiff Cox vth e e L C ox dm X ' ' gs t nv th ds th 1 v dm Qb dd C n1 Cd Cox 1 F d sb Si dd qn A X. ZHOU 34 18

35 elocity Saturation and Saturation Current v ertical-field mobility (empirical) Qi Coxgs t Qb Coxt v sat E eff Qb Qi Si n Piecewise model 1 E Bulk-Si eff E crit gs t ne 6T E E n property (.5) ox sat Saturation field v 1 EEsat n E sat v sa t vsat E Esat v E sat Esat sat 1 Esat Esat n Saturation current CSM: Lateral-field mobility Idsat WvsatQsat WvsatCox gs t A b dsat n 1 eff Ab 1 1 ds EsatLeff F sb EsatLeff gs t (1)( dsat ) = (): dsat Linear current gs t AbEsatLeff (3) (): W 1 I C A L ds eff ox gs t b ds ds ~1 7 cm/s (1) gs t Idsat WvsatCox gs t A b E sat L eff L (Amplitude) gs () (3) Linear! E Qi Cox gs t A b y t X. ZHOU 35 18

36 Charge-Sharing Model: t Roll-Off Charge-sharing model ( triangle ) Without charge-sharing Q C t FB bm ox F With charge-sharing Q C ' ' t FB ox F bm ' t t t 1 C Q C L bm qn AX dm X dm Si F sbtox T L L X t ' Q Q Q X bm bm bm dm ox ox eff ox ox eff ox g j t C ox ox Tox Qbm qnaxdm X qn dm Si F sb A Short-channel effect (SCE): t roll-off (L eff ) ds L g L L X eff g j T ox X j n + X. ZHOU s o Total bulk charge: X dm Bulk charge per unit area: W o L g Q' b Q b o g b L eff Simple Triangle Model n + d Charge shared by the gate/drain o Q qn W L X X ' B A eff d d Q qn W L X B A eff d ' ' Qb QB X 1 Q Q L b B eff d N sd

37 Charge-Sharing Model: t DIBL Charge-sharing model ( trapezoidal ) Source-end (linear): ( ds = d ) Drain-end (saturation): ( ds = dd ) Average depletion width: (any ds ) X X, qn dm dm s Si F sb A X dm, s dm, d qn Si A X, qn dm d Si F db A X s F sb d F db DIBL: Drain-Induced Barrier Lowering L L L DIBL g t g ts g db sb ds Trapezoidal area = box t s o T ox X j n + ' Q qn b A XdmLeff t t ts X dm,s Dynamic depletion (DD) W qn A ts b, ds T L o L g Q' b Q b o g b L eff X dm,d n + d o Charge shared by the drain y L g N sd X F sb dm T s d F db Si ox L X ox ox eff ox g d j ~ 6 /.7 / d. ts DIBL t FB F F sb t t t ds ts t t ds d dd X. ZHOU 37 18

38 Reverse Short-Channel Effect: t Roll-Up & Halo Empirical RSCE model ( halo ) N eff N Halo pile-up: () N pile A N N pile cosh L l Halo lateral spread: () A Replacing all previous N A by N eff eff.5 l F sb F kt qln N A ni Halo N eff s o T ox X j n + X dm,s W o Q b N A o g d L g o L eff y n + N sd X dm,d Q' b b Gaussian halo model p N y N e pile yl l t Reverse SCE: Halo Halo dose, tilt, energy y t L g N eff L eff N y dy N L l l erf l l l p pile eff N A erf Leff Le ff X. ZHOU 38 18

39 Summary of Important (Simple) Equations Effective body doping and related equations Halo doping F vth ln N A ni Physical quantities L N N l.5 eff Lg d X N pile eff N A A N pile cosh L l Neff q SiNeff F vthln ni Cox Threshold voltage Long-channel (1D theoretical model) eff F sb t gs FB F F sb s F sb Any channel-length and body/drain-bias v th kt C T ox ox ox Q C E qn C C FB MS ox ox M g F ss ox X d Si dm X dm Si F s b qn eff ox ox o n 1 Cd Cox SiTox tsb, ds t t tneff, Tox F sb F sb ox q.59 s d ds L g d X j Linear t : Saturation ts : Si Si o (Physical constants) Physical parameters: L, T, X,, N, T g ox j M ss t t t ds d j sb ts t t ds dd sb X. ZHOU 39 18

40 Summary of Important (Simple) Equations Drain current Bulk-charge factor 1 Ab 1 F sb Linear W 1 Idlin gs, s b, eff Cox gs t Ab L Saturation I dsat gs, s, ds Subthreshold b ds ds ds eff Wv sat Fitting parameters: C ox gs gs t A E t b sat W I C v e e L eff gs t eff ertical-field N 6T A,,, d, s/ d ox v E sat n vsat,, Ecrit,, sat 1 Eeff Ecrit n X. ZHOU 4 18 gs t nvth ds vth dsub gs, sb, ds n d th 1 Leff (TCAD: W = 1 m) E I I I I dsat dsat dlin gs,,,, d dlin dd ds I I gs dd,,,, dd ds dsub gs d dsubs gs,,,, dd Mobility Lateral-field eff 1 ds Drive current I on : I I n E L sat eff dd,, d on dsat d Leakage current I off : I I,, off dsub dd