Aging model for a 40 V Nch MOS, based on an innovative approach F. Alagi, R. Stella, E. Viganò

Transcription

1 Agng model for a 4 V Nch MOS, based on an nnovatve approach F. Alag, R. Stella, E. Vganò ST Mcroelectroncs Cornaredo (Mlan) - Italy

2 Agng modelng WHAT IS AGING MODELING: Agng modelng s a tool to smulate devces performance after a long perod of operaton (years) Smulated degradaton depends on both tme and operatng condtons PURPOSE: To estmate the possble degradaton of a devce durng ts lfe To allow the desgners to take nto account the relablty ssues at desgn level MAIN FEATURES: The effect of a DC or perodc stress can be smulated. Dfferent degradaton mechansms may be consdered: Hot carrer njecton NBTI PBTI 2

3 Introducton (1) Commercal agng smulaton tools (Eldo UDRM, RelXpert) work usng the followng scheme: Stress calculaton: A functon stress rate s(v) s defned for each degraded nstance Durng a transent smulaton, s s ntegrated to gve Total Stress S: ( T ) = s( V ( t) ) Assumng a perodc stress waveform, Cumulated Stress at the end of the devce lfetme (even years) s extrapolated: S Post-stress smulaton S s Parameters value after degradaton s computed as a functon of S: P = f (3) Degraded crcut s smulated Ts Tme ( S ) dt ( Tme ) = s( V ( t) ) dt Ts Ts (1) (2) 3

4 Introducton (2) Wth ths flow, degradaton durng AC Stress s accurately modelled only f DC parameter degradaton knetc s of the form: t ( ) P DC = f τ V where only the characterstc tme τ depends on bas (4) Then, degradaton after a generc (perodc) stress s gven by: dt P = f τ ) ( V (t ).e., comparng t wth (2) : Stress rate: s ( V ) = 1/ τ ( V ) (5) (6.a) Parameters update: P = f ( S) (6.b) Ths s a lmtaton: not all the expermental cases satsfy ths condton We propose a way to extend agng model to a wder class of knetcs 4

5 Introducton (3) Improvement: f DC drft s wrtten as the sum of components, each of whch has the requred form... P DC = f t t 1 ( ) + f ( ) + f τ V τ V τ 3( V ) t... (7) Then a perodc stress can be accurately smulated, treatng each component as ndependent: S 1 Ts ( T ) = s ( V ( t) ) s 1 dt = Ts τ 1 dt V ( ( t) ) S 2 Ts ( T ) = s ( V ( t) ) s 2 dt = Ts τ 2 dt V ( ( t) ) (8) P = f ( S ) + f ( S ) (9) We developed a physcal model for HCI-nduced Ron drft (adoptng a dspersve frst-order knetcs) n whch degradaton knetcs satsfy ths condton (f some physcal assumpton are satsfed) 5

6 New method (1) Target: To model HCI-nduced Ron drft S Poly G D Ron drft s due to the actvaton of defects at S/SO 2 nterface or n SO 2 Defects are actvated by hot carrers njecton (electron or holes) n hotspots One or more hotspots may be present; they re assumed to be ndependent n+ n+ Oxde pwell HV nwell 6

7 New method (2) Physcal assumptons: Ron Drft s proportonal to the number of actvated defects No new defects generated durng stress Rate depends on defect actvaton energy, whch has a dstrbuton D(φ) (dspersve knetcs) φ= ( t) = α D( φ ) p( φ t) dφ Ron, dp dt Actvaton rate s gven by a 1 st order knetcs ( φ, t) = k ( φ, V ( t) )( 1 p( φ, t) ) (1) (11) D(φ) = p(φ,t) = defect energy dstrbuton probablty that a defect of energy has been actvated at the tme t. k(φ,v(t)) = rate constant of actvaton reacton Depends on nstantaneous devce bas Calculaton s shown for one hotspot; f more hotspots are present the extenson s straghtforward drfts are planly summed 7

8 New method (3) From the above equatons we have: Ron p ( φ, t) = 1 exp k( φ, V ( t') ) dt' Durng DC stress, tme ntegral s trval and degradaton reduces to: Ron Probablty Drft DC, φ= Thus, DC drft knetcs would not satsfy condton (4) P DC =f( t/τ(v) ) t t φ= ( t) = α D( φ) [ 1 exp( k( φ V ) t) ] dφ ( t) = α D( φ) 1 exp k( φ, V ( t') ) dt' dφ DC (12) (13) (14) Indeed, the energy ntegral may be dscretzed n a sum: Ron DC N ( t) = α D( φ )[ exp( k( φ, V ) t) ] = 1 φ DC = α N = Ron DC φ (15) 8

9 New method (4) Then, total Ron s the sum of ndependent contrbutons, each of whch s due to defects of a gven energy A sngle energy level contrbutes wth a term: ( φ )[ 1 exp( k( φ, V t) ] DC Ron = D DC ) (16) Each sngle contrbuton can be mplemented n a smulator snce t s n the form: P DC = f τ t V ( ) DC havng 1 τ ( VDC ) = k( φ, V DC ) (17) Total Ron drft s then the sum of elements of the form f( t/τ(v) ): t satsfes condton (7) It can thus be ntegrated n the smulator lke n eqs. (8), (9) (even f condton (4) s not satsfed) 9

10 Agng model mplementaton (1) Ths method was used to mplement an agng model n Eldo UDRM, the relablty smulaton tool suppled wth Eldo smulator (by Mentor Graphcs) The same flow could be appled to other commercal agng smulators, as long as they follow the same smulaton scheme The mplementaton n RelXpert, by Cadence, could be less straghtforward because ts agng API s qute rgd Range of defects energes s dvded n a gven number of ntervals (e.g. 5) For each energy nterval, a stress rate s s defned; t represents the contrbuton to the degradaton of the defects wth energy n the nterval 1

11 Agng model mplementaton (2) As usual, agng smulaton s performed n two steps. Stress calculaton Let s consder a transent smulaton, wth a perodc sgnal (havng perod T). For each energy value, stress rate s s computed, dependng on devce bas and energy; stress rates s then ntegrated (see eq. (8) ), gvng stress parameters S 1 S N. S S ts ts T dt ts 1 ( ts ) = s1( V ( t) ) dt = = ( ( )) ( ( )) k φ1, V t' dt' τ V t T 1 T ts ( ts ) = k( φ, V ( t' )) dt' T In usual agng model, there would be a sngle stress parameter S; now, one per each energy value (18) Perodc sgnal ntegral over 1 perod 11

12 Agng model mplementaton (3) Model parameters update: The contrbuton to Ron drft of every component s then calculated Ron ( t) = D( φ )[ 1 exp( S )] (18) and summed gvng total degradaton Ron ncrement s added to the dran seres resstance We obtaned an accurate descrpton of Ron drft durng AC stress Drawback: smulaton requres more computatonal resources than usual agng models (5 stress ntegratons vs. 1) Ron N ( t) = α Ron φ = α D( φ )[ 1 exp( S )] φ = N = may be an ssue for CMOS (Mllons devces n a chp), less for HV devces Possble upgrade: the same method could be extended to models beyond 1 st order knetcs, as long as s vald that: dp dt ( φ, t) = k ( φ, V ( t) ) g( p( φ, t) ) (19) (2) 12

13 HCI on 4V Nch drft model detals Our method was appled to descrbe the Ron degradaton of a 4V Nch drft Electrcal model: complex subcrcut ncludng BSIM3 MOS model Modelng equatons used: Two hotspots: one of electrons, one of holes Modelng functons used: Defect energy dstrbutons: Gaussan ( ) D φ 1 exp 2π ( φ φ ) = 2 2σ Rate of defect actvaton k(φ,v): (modfed) Lucky electron n=carrers densty at hotspot φ k φ, V = Kn( V, )exp DS VGS qλf( V, ) F=Effectve electrcal feld at hotspot DS VGS λ=carrers mean free path ( ) 2 (21) (22) F,n from TCAD smulaton λ conventonal <φ>, σ, K ftted to expermental data 13

14 HCI on 4V Nch drft model results (1) Drft of On-state resstance measured at: Vgs=3.3V, Vds=.1V DC measure vs. model Smulator: Eldo Stress condtons: Vgs-Vth=.25 V Vds=44 5 V step 2 V 14

15 HCI on 4V Nch drft model results (2) Drft of On-state resstance measured at: Vgs=3.3V, Vds=.1V DC measure vs. model Smulator: Eldo Stress condtons: Vgs-Vth=1 V Vds=4 5 V step 2 V 15

16 HCI on 4V Nch drft model results (3) DC measure vs. model Vgs-Vth=1 V Vds=4 5 V step 2 Measure Model (total) Electron Holes Electrons and holes contrbutons (2 dfferent hotspots) are shown 16

17 HCI on 4V Nch drft model results (4) Measure/model comparson durng a perodc stress Vd=44V Vg pulsed (trapezoal wave) Duty cycle: 1% hgh Vg low: Vth+.8V Vg hgh: Vth+2V Perod: 1 µs Rse t, fall t: 1.4 µs Vgs waveform Ron vs stress tme 17

18 HCI on 4V Nch drft Dscretzaton of the energy ntegral Ron drft vs tme (Vds=36V, OVD=1V ) Dfferent number N of dscretzaton levels n energy ntegral Only a slght mprovement changng from 2 to 3 levels N>3 ensures a good approxmaton of the ntegral

19 Conclusons A model for hot-carrers-nduced Ron drft has been developed, based on the assumptons that Drft s due to the actvaton of pre-exstng defects, wth a gven actvaton energy dstrbuton Knetcs s descrbed by a 1 st order equaton (dspersve 1 st order knetcs approach) The model s sutable for the mplementaton n a smulator (Eldo) even f DC knetcs doesn t satsfy the condton Ron=f(t/τ(V)) Implementaton n RelXpert not straghtforward The methodology has been appled to a 4V NMOS Drft Model has been extracted by DC measurements and shows a suffcent accuracy even durng a AC test 19

20 References 1. R.H Tu, E. Rosenbaum, W. Y. Chan, C. C. L, E. Mnam, K. Quader, P. K. Ko, C.Hu Berkeley Relablty Tools-BERT - IEEE Transactons On Computer-Aded Desgn Of Integrated Crcuts And Systems, Vol. 12, No. 1, October F. Alag, DMOS FET parameter drft knetcs from mcroscopc modelng, Mcroelectroncs Relablty, Volume 5, Issue 1, January F. Alag, A frst-order knetcs ageng model for the hot-carrer stress of hgh-voltage MOSFETs, Mcroelectroncs Relablty, Volume 51, Issue 2, February Eldo 21.1 user manual, Mentor Graphcs 2