MOS-AK //03 Characterization and modeling of RF-MOSFETs in the millimeter-wave frequency domain Sadayuki Yoshitomi, Fumie Fujii Semiconductor & Storage Products Company Toshiba Corporation Copyright 03, Toshiba Corporation.
Overview Above 00Hz fmax by advanced CMOS technology is a driving force to realize millimeter-wave CMOS chips. Accurate/Automated 60Hz Measurement is needed to find a devices nature. Environmental-sensitive measurement and large local variation made modeling work very difficult. PVT model linking process and SPICE : a OAL of this work. Accurate Probing Control 3As Automatic Measurements Accurate PVT Model 35.0 L M H 34.5 ) B d ( 34.0 p 33.5 33.0 0.6 0.7 0.8 0.9 0.0 0. 0. Itotal(A)
Contents : :Demonstration of stable S-parameter automated measurement at 60 Hz. : Demonstration of simple PVT model for 60Hz region. -MOSFET - MOM Capacitor 3
Accurate Probing Control Skating Control: Reflects stability of Measurement data. Adjacent S-PAD: used to check stability check. Hz~67Hz/Hz De-embedding check: But How often? Pitch 50um 65nm RF-CMOS inch wafer 30 Dies 4
Automatic Measurement Auto Measurement: Cascade Elite300TM Precise wafer alignment into 3 dimensions And X/Y/Z directional control of prove skating. Auto Data processing:ic-cap Wafer Pro /Data Pro Keep man-power away from time consuming S-parameter measurements. Easy data visualization (ex. Histogram, correlation Matrices) 5
Result of Stability Check (Hz~67Hz) S S 60Hz 60Hz S S 60Hz 60Hz /4/03 43 min 6
Statistical summary of used sample at 60Hz Small sigma indicates the stability of the system. Stable probing contact S S Mean=-9.86dB Sigma=0.5dB Mean=-0.98dB Sigma=0.08dB 7
NMOSFET Lg=50nm, Wg=40um (=um x 40Fingers x 3 Blocks) Measurement condition :Id=50uA/um Vd=0.6V Vg=Vth0.3V Hz~67Hz/Hz FOM at 60Hz Accurate PVT model ft, fmax, gm, gds, Rg, Cgd(s), Cds MOMCAP (M~M5 Stacked) L=0um, NF=0 Hz~69Hz/Hz W L Spacing NF 8
Auto measurement results of Mom CAP S S 30 60Hz 60Hz S 60Hz S 60Hz Stable measurement 9
Frequency dispersion of equivalent circuit parameters CS RS 30 60Hz 60Hz Q CSUB 0
Auto measurement results of NMOS Vd=0.6V Vg~Vth0.4V DC 30
Auto measurement results of NMOS RF S S 30 60Hz 60Hz S 60Hz S 60Hz 90min
Frequency dependence of MOSFETs parameters fmax ft Cgd 30 Cds Rg gm gds Distribution are frequency dependent 3
Measure of components from y-parameters Y Y Y Y C = ω m C ω DS CS R R ω C ω D R CD C C C R gd ds gs jωc C C ( C D C m ) jω( C D C m ) ( C C C C C C ) jω( C C ) R = CB Im jωc Re Im BD D ( Y ) ( Y ) Y Y = Im = Im ( Y Y ) ( Y Y ) D D m g g m ds BD D Y Y = Re = Re ( Y Y ) Starting point the formula (.7a~.7d) : Christian C.Enz, Eric A. Vittoz, Charge-based MOS Transistor Modeling Wiley 006. 4
Inter-wafer distributions of 60Hz fmax and Rg. fmax Rg High Low 5
Accurate PVT Model Challenges oal: give designers a direct insight of the process fluctuation risk on their circuit. Approach: Formulate the SPICE model parameters distribution via physical parameters Conventional Proposed model Circuit Performance VTH0 Circuit Performance Dot=Measurement ateoxide Thickness Channel Implantation Solid=Model 6
PDK Implementation toxe =Tox_par*(T_oxN/T_oxN0) toxp =Tox_par*(T_oxN/T_oxN0) toxm =Tox_par*(T_oxN/T_oxN0) ndep =Ndep0_p*(N_depN/N_depN0) vth0 =VTH0_p * KN_VTH0 k =K_p * KN_AMMA u0 =mu0_p * KN_vsat vsat =vsat_p * KN_vsat nfactor =nfact_p Model *KN_Nfactor Card pclm =pclm_p*kn_cml pdiblc =pdiblc_p * KN_CML pdiblc =pdiblc_p*kn_cml rdsw =rdsw_p * KN_RDSW lint =lint_p* KN_LINT wint =wint_p * KN_WINT cgso =cgso_p *KN_LOV cgdo =cgdo_p *KN_LOV cgbo =cgb0_p *KN_CB cjs =cjs_p *KN_cjsi0 cjsws =cjsws_p*kn_cjsi0 pbs =pbs_p*kn_vdsi0 N_depN =.7e7 T_oxN =.39e-7 LCORR_PERCENT_N=e-3 WCORR_PERCENT_N=e-3 rho_rate=0 statistics { process { vary N_depN dist=gauss std=aa percent=yes vary T_oxN dist=gauss std=bb percent=yes vary LCORR_PERCENT_N dist=gauss std=cc percent=yes vary WCORR_PERCENT_N dist=gauss std=dd percent=yes vary rho_rate dist=gauss std=ee percent=yes } } Monte Carlo Declaration Ndep /- 6% T_ox /- 6% LCORR /- 0% WCORR /- 5% R /- % Thick_Metal /- 0% 7
Overview of Model structure (Front-END) LINT WINT DLC Length of ate-s/d overlap region R ate resistance U0,VSAT Low field mobility, Saturated velocity CJ Junction Capacitancce N _ dep CJ = CJ BSIM N _ dep0 Deviation ( PB ) PB0 PB PB0 = N _ j N _ dep ln N _ i N _ j N _ dep0 ln N _ i 8
µ U0,VSAT i U0 Drift Mobility [cm/v-s] = 0000 000 00 0 U0 BSIM Carrier mobility vs. channel impurity concentration µ u u i µ max min l ( Ndep ) = µ min α α Ndep ( Ndep ) ( Ndep 0) i ref Hole Modulation N N.0E4.0E5.0E6.0E7.0E8.0E9 Impurity Concentration [cm-3] µ ref Ndep Electron Parameter A-As P B µ max (cm V - s - ) 47.0 44.0 470.5 µ min (cm V - s - ) 5. 68.5 44.9 µ l (cm V - s - ) 43.4 56. 9.0 N ref (cm -3 ) 9.68E6 9.0E6.3E7 N ref (cm -3 ) 3.43E0 3.4E0 6.0E0 α 0.68 0.7 0.79 α.0.98.0 Formula for minority carriers. D.B.M. Klaassen,, A Unified Mobility Model for Device Simulation-I. Model Equations and Concentration Dependence, Solid-State Electronics Vol.35, No.7, pp.953-959, 99.. D.B.M. Klaassen,, A Unified Mobility Model for Device Simulation-II. Temperature Dependence of Carrier Mobility and Lifetime, Solid-State Electronics Vol.35, No.7, pp.96-967, 99. 9
0 ( ) ( ) ( ) = = = = = ]. [ 0.5 4 0 0 0 0 0 0 0 0 n n n n L L n n L V I n n L V I n n L V I W I L Cgb Cgsi V I I Cox L W Cgdi Cgsi gm Cgd Cgs gm F T C T C T C T C C Ti µ µ µ µ π µ π µ π π Formulation of ft fluctuation via DLC N (Slope) factor DLC Offset arelength Mobilty LCORR = BSIM DLC DLC ( ) ( ) Ndep 0 u Ndep u i i L L L corr 0 0 n n n n. David M.Binkeley,, Tradeoffs and optimization in Analog CMOS Circuit Design, Wiley
Overview of Model structure (Back-END) ThickMetal_INT ThickMetal_INT Dist_INT ThickMetal_INT Dist_INT Dist_INT ThickMetal_INT Dist_LOC_INT ThickMetal_LOC CS0 CD0 Dist_SUB_LOC Csub Rsub SUB
The formulae of capacitance CS Vertical CDO CSO C vertical = 8.854e = 8.854e ( L W NF ) eps _ l Dist_SUB_L OC Dist_SUB_L OC 3 ( L W NF ) eps _ l Dist_INT Dist_INT Dist_INT Dist_INT Lateral C vertical = 8.854e = 8.854e ( L W ) eps _ w ( NF ) ThickMetal _ LOC ThickMetal _ INT ( L W NF ) eps _ w 3 ThickMetal _ LOC Spacing Spacing ThickMetal _ INT ThickMetal _ INT Spacing Spacing Spacing ThickMetal _ INT Spacing
Model Validation MOSFET 3
Measurement vs. Simulation correlation - fmax Rg 0.4 0.60 fmax Rg Sigma ft Sigma ft Cgd -0.74 Cds -0.56 Cgd Cds Sigma ft Sigma ft gm 0.3 gds 0.43 gm gds Sigma ft Sigma ft ft : principle component 4
Model Validation MOM CAP 5
Measurement vs. Simulation Correlation from measurement Cs Ls -0.88-0.7 Cs Ls Rs Rsub -0.4-0.86 Rs Rsub Csub -0.3 Csub Q: principle component 6
Conclusion Automated 60Hz auto measurement. Thanks to the up-to-date hardware and data processing, we could capture the fluctuation of CMOS technology. Stability in the measurement system used in this work is kept good condition. It sensed that the deviation of MOSFET performance becomes larger as the operating frequency increases. Statistical modeling Our simplified PVT model can provide with reasonable estimation of intra-wafer variation at 60Hz. 7
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