ASYMMETRICAL DOUBLE GATE (ADG) MOSFETs COMPACT MODELING. M. Reyboz, O. Rozeau, T. Poiroux, P. Martin

Transcription

1 ASYMMETRICAL DOUBLE GATE (ADG) MOSFETs COMPACT MODELING M. Reyboz, O. Rozeau, T. Poiroux, P. Martin

2 005 OUTLINE I INTRODUCTION II ADG ARCHITECTURE III MODELING DIFFICULTIES I DIFFERENT WAYS OF MODELING IMPLICIT ANALYTICAL MODEL: ITERATIE RESOLUTION I EXPLICIT ANALYTICAL MODEL: FULLY ANALYTICAL EXPRESSIONS II CONCLUSION

3 005 INTRODUCTION GENERAL CONTEXT WHY ARE WE INTERESTED IN MODELING ADG MOSFETs? New Devices classical CMOS technologies + forecasts of the ROADMAP =?? New devices: GAA, FinFET, SON & planar DG ADG MOSFET PD SOI CMOS FD SOI CMOS Bulk CMOS New devices 90 nm 65 nm 45 nm nm Excellent channel control Design flexibility with a second gate independently driven Model: to take advantage of this new device designers need a model Compact Model: to design new circuits 3

4 005 ADG ARCHITECTURE DIFFERENCES BETWEEN SYMMETRICAL (SDG) AND ASYMMETRICAL (ADG) DG MOSFETs g Source Front gate Channel Back gate Drain PICTURE: ADG MOSFET M.inet et al, SSDM 004 nm node O x Front gate T ox Source Silicon film Drain T si Front oxide Back oxide Back gate g T ox SCHEMATIC: DG MOSFET L y The asymmetry of the structure:! gate oxide thicknesses! gate voltages! or/and gate work functions 4

5 005 MODELING DIFFICULTIES BASIC EQUATIONS OF ADG E s I ds GAUSS THEOREM Q inv = ε ( E E ) si s s DRAIN CURRENT W = µ L POISSON EQUATION & ITS FIRTS INTEGRATION d ψ q n =. dx ε. q. u t. n ψ i s φ imref E = s exp exp ε si u t s d Q inv dφ si imref E BOUNDARY CONDITIONS c ox E s = ( g ψ s ) ε si c ox s = ( g ψ s ε si ψ s u t φ imref ) to calculate physical I ds, unknowns are ψ s and ψ s 5

6 005 MODELING DIFFICULTIES MATHEMATICAL DIFFICULTIES ASYMMETRY Not always a minimum of potential in the silicon film: CASES Band diagrams Ψ s Ψ s Ψs i Ψ s Ψ s Ψ s Ψ s Ψ s E fermi ψ min ψ min FIRST DIFFICULTY DEFINE CASES AND THEN UNIFY THEM 6

7 005 MODELING DIFFICULTIES MATHEMATICAL DIFFICULTIES SECOND DIFFICULTY NO EXACT SOLUTIONS OF ψ s AND ψ s OPTIONS FLOATING NODE RESOLUTION 4 unknown parameters, ψ ssource, ψ sdrain & ψ ssource, ψ sdrain MAKE PHYSICAL ASSUMPTIONS Simplifications of Poisson equation 7

8 005 DIFFERENT KINDS OF MODELS DIFFERENT WAYS OF MODELING! st OPTION: IMPLICIT ANALYTICAL RESOLUTION Use of floating nodes or iterative resolutions to solve Poisson s equation.! nd OPTION: EXPLICIT ANALYTICAL RESOLUTION Poisson s equation is solved with physical approximations allow to get explicit formulations of electrical parameters fully analytical model. Charge-based model th -based model 8

9 005 IMPLICIT ANALYTICAL MODELING MAIN ACTORS: 3 teams Y. Taur (USA, University of California): mainly for SDG MOSFET M. Chan (Hong Kong University of Science & Technology): ADG MOSFET T. Nakagawa (Japan, AIST): ADG MOSFET!Y. Taur, Analytical Solutions of Charge and Capacitance in Symmetric and Asymmetric DG MOSFET, IEEE Trans. Electron Devices, vol.48, n, Dec. 00.!M. Chan, Quasi-D Compact Modeling for DG MOSFET, NSTI Nanotech, vol., pp.08-3, 004.!Nakagawa et al., Improved Compact Modeling for Four-Terminal DG MOSFETs, NSTI Nanotech,

10 005 IMPLICIT ANALYTICAL MODELING WHY? COMPLEXITY of basic equations MANY ADANTAGES No problem to unify the different operating modes ACCURACY because it keeps all basic equations without any (or with few) simplification PREDICTIITY because basic equations could be solved for all materials and geometrical parameters 0

11 005 IMPLICIT ANALYTICAL MODELING PRINCIPLE OF FLOATING NODE SOLUTION (Taur model) different modes UNKNOWNS + Minimum of potential Unknowns: ψ 0 and x 0 No minimum of potential Unknowns: ψ S & ψ S SOURCE & DRAIN SIDE 4 FLOATING NODES for each case Each mode should be NUMERICALLY solved thanks to BOUNDARY CONDITIONS.

12 005 IMPLICIT ANALYTICAL MODELING PRINCIPLE OF FLOATING NODE SOLUTION (Taur model) DRAIN CURRENT I ds I ds W = µ L s d Q inv dφ NUMERICALLY imref I ds = α. Q inv inv ANALYTICALLY (EK METHOD) Q d s Not really true for ADG because of interface coupling: need a unification

13 005 IMPLICIT ANALYTICAL MODELING PRINCIPLE OF FLOATING NODE SOLUTION (Taur model) Symmetrical case: eriloga + Eldo simulator SDG : L=0.5µm, W=.0µm, Tsi=0.0nm, Tox=.nm Drain current (µa).0 ds =5m Gate oltage () Transconductance (µs) Drain current (ma) gs =0.6 to Gate oltage () (µs) Transconductance Asymmetrical case: eriloga + Eldo simulator Currently: convergence problem 3

14 005 IMPLICIT ANALYTICAL MODELING LIMITS: - Convergence problems because of the 4 floating nodes. - Simulation time. For that, we choose to developp an explicit analytical model with only floating node: T 4

15 005 EXPLICIT ANALYTICAL MODELING MAIN ACTORS: teams J. G. FOSSUM (USA, University of Florida) G. Pei (USA, Cornell University) TWO KINDS OF EXPLICIT ANALYTICAL MODEL Charge-based model th model! J. G. Fossum et al., UFDG and Nanoscale FinFET CMOS Design and Performance Projections, IEEE ICICT, 005.! A.. Kammula et al., A long Channel Model for the Asymmetric DG MOSFET alid in All Regions of Operation, IEEE Southwest Symposium Mixed-Signal Design, pp.56-6, 003.! G. Pei, A Physical Compact Model of DG MOSFET for Mixed-Signal Circuit Applications Part: Model Description, IEEE Transac. On Electron Devices, vol.50, n 0, Oct

16 005 EXPLICIT ANALYTICAL MODELING ADANTAGES OF AN EXPLICIT ANALYTICAL MODEL Better physical understanding Easier to use for circuit design because of speed and convergence whatever the number of transistors DISADANTAGES OF AN EXPLICIT ANALYTICAL MODEL Less accurate in moderate inversion Difficulties to get well derivatives 6

17 005 EXPLICIT ANALYTICAL MODELING CHARGE-BASED MODEL Weak inversion for both interfaces g DG = capacitor divider C ox ψ s C si ψ s C ox ψ ψ s s = = ( ( C C si si C C si + si + C C ox ox ) ) g g Csi + C + C si si ox Csi + C + C ox g g T si olume inversion Silicon film olume current g Strong inversion for both interfaces I ds SI Both channels are independent SI SI SI I = ds I + ds I ds T si Silicon film Surface current I ds SI 7

18 005 EXPLICIT ANALYTICAL MODELING CHARGE-BASED MODEL One interface is in strong inversion and the other one in weak inversion. Second integration of Poisson s equation Asymptotic case : ψ s thus exp(-ψ s ) 0 Boundary conditions SI WI Ids = Ids + Ids T si I ds SI Surface current olume current I ds WI 8

19 005 EXPLICIT ANALYTICAL MODELING CHARGE-BASED MODEL LIMITS: unification between different operating modes I ds (A) g unification Atlas simulations Model g from 0. to 0.3 ds = 5m g (olt) I ds (A) CURRENT T si =5nm L=0.5µm W=µm I ds (A ) ds unification Atlas simulations Model ds () g =. g =. g =. g =0.! Unification problem when g is high.! Problems to have a continuous transconductance th -based model is developping: charge and current model take into account interface coupling I ds (A) Atlas simulations Model g =. ds =5m g () 9

20 005 EXPLICIT ANALYTICAL MODELING th -BASED MODEL ASSUMPTION: no current flows from a channel to the other one (checked by TCAD simulations) PRINCIPLE: DGMOS = SGMOS in parallel Q inv = Q inv + Q inv I ds = I ds + I ds + INTERFACE COUPLING DESCRIPTION + CORRECTION FACTOR DEFINITION to well describe strong inversion UNIFICATION OF THE DIFFERENT OPERATING MODES 0

21 005 EXPLICIT ANALYTICAL MODELING th -BASED MODEL ( ) = t g g Si eq t g g Si eq t g th th U C C U C C U n n. ' '. ' ' tanh ln.. '. ' 0 ( ) = t g g Si eq t g g Si eq t g th th U C C U C C U n n. ' '. ' ' tanh ln.. '. ' 0 FRONT & BACK th

22 005 EXPLICIT ANALYTICAL MODELING n represents interface coupling th -BASED MODEL Q Q invwi INTERFACE COUPLING DESCRIPTION Example: front interface in weak inversion invsi n = + C ox Csi. Cox ( C + C g th imref ( x) = q. n i. ut.exp n. ut si ox ) n. φ CORRECTION FACTOR TO WELL DESCRIBE STRONG INERSION W = µ oxi gi thi i imref L ( ). ε ( x) ( x) C. ' ' n. φ ( x) ε i represents the dependance of the interface strong inverted versus its gate voltage ( ) i

23 005 EXPLICIT ANALYTICAL MODELING th -BASED MODEL off =ε ( g - th ) UNIFICATION OF THE DIFFERENT OPERATING MODES g unification gt = u n t g th exp utn ln + g + exp utn off th gt Weak inversion = u n t exp g off th u n t Strong inversion = gt g th off ds unification dsieff ( ) dsati ds δ δ = + + dsati dsati ds δ 4 dsati 3

24 005 EXPLICIT ANALYTICAL MODELING th -BASED MODEL I ds (A) I ds (A) Logarithmic scale ds = 5m g = 0. to. Model Atlas simulations g () Linear scale g = 0.8 to. Atlas simulations Model g = ds () T si =0nm L=0.5µm W=µm I ds (A) CURRENT I ds (A) ds =5m Linear scale Atlas simulation Model g () Atlas simulation Model g =0. to. Linear scale g =. g =0.8 to ds () 4

25 005 EXPLICIT ANALYTICAL MODELING th -BASED MODEL CHARGE MODELING CAPACITANCE CAPACITANCE T si =0nm L=0.5µm W=3.5µm Capacitance (ff) ds =0.0 g =0.0 C gs C gd C ds g () Capacitance (ff) g =. g =0.0 C ds C gs C gd ds () 5

26 005 EXPLICIT ANALYTICAL MODELING th -BASED MODEL LIMITS T si < 0nm: problem in derivative ADG but SYMMETRICAL BEHAIOR Transconductance (µs) Pink : numerical model Bleue : th model KINK ds =5m L=µm, W=0µm T si = 5nm g () 6

27 005 EXPLICIT ANALYTICAL MODELING EXAMPLE OF SIMULATION CIRCUITS USING th MODEL IN ERILOG-A INERTORS CHAIN COMPOSED OF 8 TRANSISTORS ARE SIMULATED IN TRANSIENT REGIME The model took into account:!classical SCE ( th ( ds ))!access resistance 7

28 005 CONCLUSION SUMMARY MAIN WAYS TO MODEL ADG MOSFET: IMPLICIT ANALYTICAL MODEL: ITERATIE RESOLUTION EXPLICIT ANALYTICAL MODEL: FULLY ANALYTICAL EXPRESSIONS CHARGE-BASED OR t MODEL EFFECTS WHICH SHALL BE ADDED Accurate Short Channel Effects Quantum effects Ballistic transport 8

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