BSIM4.3.0 Model. Enhancements and Improvements Relative to BSIM4.2.1

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1 BSIM4.3.0 Model Enhancements and Improvements Relative to BSIM4.. Xuemei (Jane) Xi, Jin He, Mohan Dunga, Ali Niknejad, Chenming Hu University of California, Berkeley

2 OUTLINE New Features of BSIM4.3.0 beta release Stress ect model New temperature model Holistic ise model enhancement Unified current saturation model Velocity saturation Velocity overshoot Source injection thermal velocity limit New document for multi-layer gate tunneling Forward body bias

3 Model for Isolation-induced Stress Effects Trench isolation edge L SA SB W LOD SD Instance parameters added: SA, SB, SD SD is neighbour finger distance which is constant throughout all the fingers. Stress ect calculation only if: ) both SA and SB are given and are larger than 0 for finger number NF=; ) SA, SB and SD are all given and are larger than 0 for NF > Intermediate geometry definitions : LOD = SA + SB + NF L + ( NF ) SD 3

4 Mobility Model With STI Stress Define : r m = m / mo = ( m mo ) / m = m m o o (relative mobility change due to stress) So, m m o =+ r m (Vth insensitive to Lod, SA and/or SB) 4

5 Stress Effects Model-/LOD Model Simple stress distribution function: /(SA+L/), /(SB+L/) ρ µ Inv _ sa = SA expression with LOD, L, W, and T dependence ku0 Kstress _u0 L drawn ( Inv _ sa Inv _sb) r = + m Inv _sb = SB L drawn LKU0 WKU0 Kstress _u0 = + + LLODKU0 WLODKU0 ( Ldrawn + XL ) (Wdrawn + XW + WLOD ) + PKU0 Temperatur e + TKU TNOM LLODKU0 WLODKU0 ( Ldrawn XL ) (Wdrawn XW WLOD ) Inv _sa = All data can be fitted well with only one set of parameters (ie. Global model for LOD ect) and do t need extra binning parameters if binning is desired. For multi-finger device: NF NF Inv _ sa = i= 0 SA L + i ( SD + L ) NF i= 0 SB L + i ( SD + L ) drawn drawn drawn drawn NF S = For irregular LOD device: n n sw i swi = = W sa L SB L i= W sb L A Ldrawn i drawn i drawn drawn drawn i 5 drawn

6 Stress Effect m, u sat Model m + r = + r m m ( ( SA,SB ) SA ref,sb ref ) m o u sat + = + K K r r m m ( ( SA, SB ) SA ref, SB ref u ) sato u µ sato Where o, are low field mobility, saturation velocity at SA ref, SB ref 6

7 Stress Effect Model to VTH0, K, ETA0 Kstress _vth0 = + ( L + LKVTH0 LLODKVTH drawn + XL ) (Wdrawn + XW + LLODKVTH ( Ldrawn + XL ) (Wdrawn + XW + + PKVTH0 WKVTH0 WLOD ) WLOD) WLODKVTH WLODKVTH VTH 0 = VTH 0 K = K original ETA0 = ETA0 original original KVTH0 + Kstress_vth0 STK + Kstress_vth0 LODK STETA0 + Kstress_vth0 ( Inv _ sa + Inv _ sb Inv _ sa Inv _ sb ) ( Inv _ sa + Inv _ sb Inv _ sa Inv _ sb ) LODETA0 ref ( Inv _ sa + Inv _ sb Inv _ sa Inv _ sb ) ref ref ref ref ref 7

8 Stress Effect Model Verification Drain current relative change (%) with SAref=5mm SA=SB 8

9 Stress Effect Model Verification 9

10 Stress Effect Model Verification Drain current relative change (%) with SAref=5mm 0

11 Temperature Model Enhancement Temperature mode TEMPMOD created: TEMPMOD = 0: current model with VFB enhancement TEMPMOD = : New format for vsat, prt, ua, ub, uc: PARAM (T ) = PARAM (TNOM ) [ + TEMP _COEFF ( T TNOM) ]

12 Holistic Thermal Noise Model Enhancement q ti b ti Refer to Chapter 9 of BSIM4 manual = RNOIB + TNOIB L = RNOIA + TNOIA L V E gst sat V E sat L gst L (9..5) (9..6) Default RNOIA=0.577; RNOIB=0.37

13 Unified Current Saturation -Velocity Overshoot Model Price s approximation to HD model: l E y J = qnme y( + ) + qd me x y n x Approximate solution of Price s equation yields unified current expression that includes velocity saturation and velocity overshoot: I DS 0 I DS,HD = V where E + L ds Vds Vds + LAMBDA Esat litl + L Vds Vds + Esat litl E OV sat + OV V = E sat sat m = + ds I DS 0 I DS ( BSIM 4.. ) L Esat 3

14 Unified Current Saturation: -Source end Velocity Limit HD transport source carrier velocity: and Quasi-Ballistic Transport v = shd I DS,HD Wq s Ballistic transport source carrier velocity: where VTL: thermal velocity, r = r v sbt = VTL + r L XN L + LC XN 3.0 Unified current expression with velocity saturation, velocity overshoot and source velocity limit: DS,HD I DS = / MM [ ( ) ] MM + v / v shd I sbt 4

15 Direct Tunneling through Multiple- Layer Gate Stacks Gate Current modeled as For a single layer For two layer case a double = a f + a T J G = Q exp( at T exp( ( f ) + f ( oxe a new INV t ) Vox f ) 3h oxe f K IMP T ) where qm f B K qm f B α is the tunneling attenuation coicient already modeled in BSIM4, f = Toxe / Toxe Stands for multiple layers(n ) as well. Using new tunneling attenuation coicient and interpreted with tunneling equations in BSIM4, BSIM4 is w capable of modeling multi-layer gate tunneling. 5

16 Verification Verified with data of existing gate stack of HfO and silicon oxynitride. Very good fit observed using BSIM model. BSIM4 direct tunneling equation thus models the multi-layer case. Gate st layer nd layer 6

17 Forward Body Bias To ensure a good model behavior of body ect, body bias is usually bounded between (Vbsc, and f s0 where f s0 = 0.95 f s ). BSIM4.. already has the smooth function for Vbs low bound. Following is the upper bound smooth function: Where: ' ( 0. 95Φ V d ) Φ ' Vbs 0. 95Φ s Φ s Vbs d + s bs d. 95 = s ( V V δ ) + ( V V δ ) V bs bc bs bc 4δ Vbs = Vbc bc Is the low bound smooth function. d = 0.00V, and V bc is the maximum allowable V bs and found from dv th /dv bs = 0 to be V bc K = 0.9 Φ s 4K 7

18 Gate Current Partition Bugfix From Original: PIGCD Vds + exp Igcs = Igc PIGCD ( PIGCD V ) V ds ds +. 0e e 4 and Igcd = Igc ( PIGCD V + ) exp( PIGCD V ) ds PIGCD V ds +. 0e 4 ds +. 0e 4 To: PIGCD V Igcs = Igc Igcd = Igc ds + exp PIGCD ( PIGCD V + ) exp( PIGCD V ) ds PIGCD ( PIGCD V ) V ds V ds ds +. 0e e e 4 ds +. 0e 4 8

19 Gate Current Partition Bugfix.0x0 -.8x0 -.6x0 - Igc with bugfix Original Igc I GC (A).4x0 -.x0 -.0x0 - VDS increase 8.0x0-6.0x V GS (V) Effect of gate current bug fix Comparison with experimental data 9

20 New Parameters in BSIM Stress Effect Parameter Name Description Default Value Binnab le? Note SA INSTANCE parameter: Distance between OD edge to Poly from one side 0.0 If t given or ( 0.0), stress ect will be turned off SB INSTANCE parameter: Distance between OD edge to Poly from the other side 0.0 If t given or ( 0.0), stress ect will be turned off SD INSTANCE parameter: Distance between neighbour fingers 0.0 for NF >: if t given or ( 0.0), stress ect will be turned off saref Reference distance between OD edge to poly of one side.e-06[m] >0.0 sbref Reference distance between OD edge to poly of the other side.e-06[m] >0.0 wlod Width parameter for stress ect 0.0 [m] ku0 Mobility degradation/enhancement coicient for stress ect 0.0 [m] kvsat Saturation velocity degradation/enhancement parameter for stress ect 0.0[m] - kvsat tku0 Temperature coicient of ku0 0.0 lku0 Length dependence of ku0 0.0 [m llodku0 ] 0

21 New Parameters in BSIM Stress Effect Parameter Name Description Default Value Binnable? Note wku0 Width dependence of ku0 0.0 [m wlodku0 ] pku0 Cross-term dependence of ku0 0.0[m llodku0+wlodku0 ] llodku0 Length parameter for u0 stress ect 0.0 >0 wlodkuo Width parameter for u0 stress ect 0.0 >0 kvth0 Threshold shift parameter for stress ect 0.0[V*m] lkvth0 Length dependence of kvth0 0.0[V*m llodku0 ] wkvth0 Width dependence of kvth0 0.0[V*m wlodku0 ] pkvth0 Cross-term dependence of kvth0 0.0[V*m llodku0+wlodku0 ] llodvth Length parameter for Vth stress ect 0.0 >0 wlodvth Width parameter for Vth stress ect 0.0 >0 stk K shift factor related to Vth0 change 0.0[m] lodk K shift modification factor for stress ect.0 >0 steta0 eta0 shift factor related to Vth0 change 0.0[m] lodeta0 eta0 shift modification factor for stress ect.0 >0

22 New Model Parameters in BSIM4.3.0 Parameter Name Description -Unified Current Saturation Default Value Binnable? Note LAMBDA Velocity overshoot coicient 0.0 yes If t given or ( 0.0), velocity overshoot will be turned off VTL LC Thermal velocity Velocity back scattering coicient.0e5 [m/s] 0.0[m] yes If t given or ( 0.0), source end thermal velocity limit will be turned off ~5e-9(m) at room temperature XN Velocity back scattering coicient 3.0 yes Temperature Model TEMPMOD Temperature mode selector 0 If=0, original model will be used If=, new format will be used Holistic Thermal Noise RNOIA Thermal ise coicient RNOIB Thermal ise coicient 0.37