A characteriza+on/reliability oriented simula+on framework modeling charge transport and degrada+on in dielectric stacks

Transcription

1 A characteriza+on/reliability oriented simula+on framework modeling charge transport and degrada+on in dielectric stacks Luca Larcher University of Modena and Reggio Emilia MDLab Italy

2 Outline Simula=on framework Charge transport I G - V G simula=ons PBTI simula=ons: V TH increase Voltage stress simula=ons: I G - =me, TDDB distribu=on Conclusions

3 Simula+on framework Simula=on of charge transport and degrada=on phenomena in dielectric stacks using a microscopic descrip=on Defect parameters depends on atomic configura=ons Mul=- scale simula=on of electrical measurements and reliability tests to allow extrac=ng defect parameters and cross- correla=on I G - V G Bias Temperature Instability: V T shim Voltage stress: TDDB, V BD, I G - =me C- V / G- V Charge- Pumping: I CP Drain/gate current noise: RTN, Power spectral density

4 Simula+on framework Device/stacks geometry, bias Defect and ion/atom distribu=on t = t + Δt V(t ) update 3D field map 3D charge transport 3D power dissipa=on map DC AC Transient, Periodic Steady State (PSS), kine=c Monte- Carlo 3D temperature map 3D rates of bond- breakage, i.e. defect genera=on 3D rates of vacancy/ion diffusion and recombina=on

5 Charge transport mechanisms Transport mechanisms for electrons and holes direct & FN tunneling drim/diffusion in CB/VB and defect sub- bands (e.g. at BD) Poole- Frenkel and thermoionic emission (typically negligible) mul=- phonon TAT through isolated defects - dominant electron- phonon coupling and la]ce structural relaxa=on paths comprised by mul=ple random defects and ohmic region sta=s=cs due to the random defect proper=es

6 τ 1 c,j = m j 1 The mul+phonon TAT model TAT dominates charge transport in dielectric stacks Charge capture (Ca) and emission (Em) probabili=es includes carrier- phonon coupling and la]ce relaxa=on 1 N (E j,m ) f j 1 τ e,j = Nj+ 1(E j,n) 1 j+ n (E j,m ) P T ( E ) j 1,m [ f (E )] P ( E ) 1 j,m T j,n Ca Em j,m j,n N: density of the states f: occupa=on probability P T : tunnelling probability Ca = capture probability Em = emission probability E TH (D q- 1 ) capture (a) initial (c) final emission nħω mħω (b) defect E f L. Larcher, IEEE TED, 23 L. Vandelli et al., IEEE TED 211

7 The mul+phonon TAT model La]ce relaxa=on (D q D q- 1 ) described by the mul=phonon transi=on probability Non- adiaba=c interac=on and field- assisted transi=on Sets the temperature dependence of the current (E capt ) E (a) initial D capture D (b) E TH (D q- 1 ) capture (a) initial E capt (b) defect emission mħω E f E R =Sħω (c) final nħω (b) defect mħω D q D q- 1 Q L. Larcher, IEEE TED, 23 L. Vandelli et al., IEEE TED 211

8 Outline Simula=on framework Charge transport I G - V G simula=ons PBTI simula=ons: V TH increase Voltage stress simula=ons: I G - =me, TDDB distribu=on Conclusions

9 I G - V G simula+ons /1 / 3nm HfO 2 / 1.1nm SiO x TAT / nm HfO 2 / 1.1nm SiO x TAT DT L. Vandelli et al., IEEE TED 211

10 I G - V G simula+ons /2 Electron TAT dominates also in thinner sampler Small SILC because dominant defects are in HfO 2 Hole TAT dominated by HfO 2 traps Lower relaxa=on energy compared to electron / 2 nm HfO 2 /. nm SiO x / nm HfO 2 / 1.1nm SiO x L. Vandelli et al., IEEE TED 211

11 I G - V G simula+ons /3 SrTiO (STO) MIM: TAT dominates RuOx / 8. nm SrTiO / RuOx STO defects: N T =2 1 2 cm - 3 E T =. 1eV E REL =1.7eV Electron TAT through O vacancy defects in both Al 2 O 3 and ZrO 2 InGaAs (p- type, Nd=1e17) band and valley descrip=on included / nm ZrO 2 /1nm Al 2 O 3 /InGaAs

12 Outline Simula=on framework Charge transport I G - V G simula=ons PBTI simula=ons: V TH increase Voltage stress simula=ons: I G - =me, TDDB distribu=on Conclusions

13 (P)BTI model Fast V TH shim aiributed to charge trapping into every defect Trap occupancy F j calculated from TAT capture and emission rates solving charge balance and Poisson Transient I G consistently calculated Slow (long- term) V TH shim: different op=on F j / t = R in,j (t) (1 F j (t)) R out,j (t) F j (t) V TH (t)= j=1 N T V TH,j ( F j (t) F j ()) F T 1x1 1x1-1 1x1-2 1x1-3 R 24 R 34 R 23 R 32 R 1 R 1 2 D ef#1 D ef#2 D ef#3 D ef#4 D ef# D ef#6 3 R 12 R 21 R 3 R 3 R 13 R 31 1 R 14 R 41 R 1 R 1 1x1-4 L. Vandelli et al., submitted to IEEE TED 213 1x1-1x1-1 1x1-13 1x1-11 1x1-9 1x1-7 1x1-1x1-3 1x1-1 tim e(s )

14 Fast PBTI simula+ons /1 Fast V TH increase and recovery accurately simulated (t<1sec) Same defect parameters used for I G - V G simula=ons / nm HfO 2 / 1.1 nm SiO x /Si L. Vandelli et al., submitted to IEEE TED 213

15 Fast PBTI simula+ons /2 Simula=on of temperature dependence of fast ΔV T at satura=on Good simula=on HfO 2 / 3 nm HfO 2 / 1.1 nm SiO x /nsi ΔV TH (mv) Rates (s - 1 ) R IN T R IN 1 2,2 1, , / nm HfO 2 / 1.1 nm SiO x /nsi 2V 3K 2V 4K 2.V 3K 2.V 4K T z(nm) F T,SS solid 3K dashed 4K T R OUT 1,,9,8,7,6,,4,3 Occupancy L. Vandelli et al., submitted to IEEE TED t(s )

16 1 8 Long- term PBTI simula+ons Long- term V TH shim due to metastable states switching precursors ac=va=on (e.g. E centers) reversible defect crea=on (e.g. reac=on and diffusion of H, O - can also be consistently simulated!) defects with much higher relaxa=on energy (e.g. in SiO 2 ) 2V 2.V / nm HfO 2 / 1.1 nm SiO x /nsi 1 8 2V 2.V ΔV TH (mv) T=4K solid: "fast" + "slow" traps dashed: only "fast" traps t(s ) ΔV TH (mv) 6 4 L. Vandelli et al., submitted to IEEE TED T=3K solid: "fast" + "slow" traps dashed: only "fast" traps t(s )

17 Outline Simula=on framework Charge transport I G - V G simula=ons PBTI simula=ons: V TH increase Voltage stress simula=ons: I G - =me, TDDB distribu=on Conclusions

18 Degrada+on simula+on framework Device/stacks geometry, bias Defect, ion (I), vacancy (V) distribu=on 3D field map t = t + Δt V(t ) update 3D current calcula=on 3D power dissipa=on map 3D rates of defect (bong breakage, V/ I) genera=on 3D temperature map 3D rates of V/I diffusion MC event selec=on 3D rates of V/I recombina=on (defect annealing)

19 Power and temperature 3D power dissipa=on map calculated from the power released to every defect by TAT electrons 3D temperature map calculated by solving the heat Fourier equa=on TAT Power dissipation Temperature (c) final emission nħω E TH (D q- 1 ) capture mħω (b) defect (a) initial E f V> [pw] [ K] L. Vandelli et al., IEDM 211 L. Vandelli et el., IEEE TED 213 L. Larcher et al., IEDM 212

20 I G [A] Defect genera+on & BD simula+ons Monte- Carlo genera=on of stress- induced defects, i.e. O vacancies Local genera=on rate (bond breaking) - thermochemical model BD simula=on during a CVS V G = 3.3 V; T=3K 1-8 other simulated GBs 1-9.E+ 4.E E E E+2 16 time[s] /7nm HfO 2 /TIN I G [A] ν = the bond vibra=on frequency b = the bond polariza=on factor E A = the ac=va=on energy (b) Experimental V G = 3.3 V; T=3K 1-7.E+ 4.E E E+3 time[s] L. Vandelli et al., IEEE TED 213 J. Mc Pherson, IEEE TED 24

21 BD simula+on during CVS BD transient simulated on a 7nm HfO 2 (a) (d) (g) (l) cluster (b) (e) (h) (m) [pw] (c) 7 (f) 7 (i) 7 (n) 7 [ C] TIME A TIME B TIME C TIME D

22 TDDB simula+ons Simula=on of voltage and temperature effects on TDDB distribu=ons in MIM stacks Weibull slope correctly predicted ln(- ln(1- F)) / 7 nm HfO 2 / Area: 1 - cm 2 V G = 3.3V C 7 C 1 C 12 C simulations E E E E+ 1 time to BD[s] ln(- ln(1- F)) L. Vandelli et al., IEEE- TED 213 / nm HfO 2 / Area: 1-8 cm 2 T = 12 C 3.1V 3.2V simulations E E E E+ 1 time to BD[s]

23 Conclusions Characteriza=on/reliability oriented simula=on somware Novel microscopic simula=on framework of charge/ion/ vacancy transport and degrada=on in dielectric stacks physical parameters depend on atomic configura=on Simulates electrical measurement tests, allowing cross- correla=ng results between different techniques Iden=fies nature of electrically ac=ve defects Allows performance op=miza=on, life=me predic=on, mul=- layer stack engineering Can be used to extract compact models (also analy=cally) for reliability of electronic devices