Non Volatile Memories Compact Models for Variability Evaluation

Transcription

1 Non Volatile Memories Compact Models for Variability Evaluation Andrea Marmiroli MOS-AK/GSA Workshop April 2010 Sapienza Università di Roma

2 Outline Reasons to address variability aspects Physics based compact models: Charge based Phase change based Further effects and model updates Overall concepts Examples Applications Flash cell applications Phase Change cell applications Perspectives Page 2

3 Reasons to address variability in Memories To predict window budgets To start the design of sensing circuits To define the correction algorithms 1s EV R PV 0s Voltage To optimize technology Ranking the sources of variability To optimize design algorithms in terms of time/accuracy trade-offs Writing/reading/erasing/verifying Page 3

4 Outline Reasons to address variability aspects Physics based compact models: Charge based Phase change based Further effects and model updates Overall concepts Examples Applications Flash cell applications Phase Change cell applications Perspectives Page 4

5 Non Volatile Memory Compact Models Physically based models easier implementation of variability effects correlation directly implemented (e.g. threshold/tox) more accurate extrapolations not easy model implementation model sometimes not completely understood Computationally efficient models to allow variability analysis (large number of simulations) coupled with more accurate models - typical of TCAD domain - to maintain physical soundness Page 5

6 Non Volatile Memory Models: Flash cell Model developed with Universita` di Modena e Reggio Emilia (L. Larcher, P. Pavan) Control Gate Better description of capacitive couplings: for different operations - Write, Read, Erase - and for the different cells writing status. Exploitation of models developed for MOS transistors including their extraction procedures Drain Floating Gate I W/E Body C CG V FG Source Page 6

7 PCM Working Principle 1/2 PCM material is the Ge x Sb y Te z (GST) alloy: Polycrystalline Amorphous Reversible Phase Change High conductivity SET Low conductivity RESET Page 7

8 PCM Working Principle 2/2 PCM cell sketch and symbol ELECTRICAL pulses GST T melt t QUENCH < 10 ns RESET active region HEATER T X SET t QUENCH > 100 ns Page 8

9 The electro-thermal thermal model ELECTRICAL network V I THERMAL network T V I R GST (T) R HEATER (T) V I + R th Room Temperature C th T Page 9

10 SET I-V: Measure and Simulation I_PCM [ua] Measure (pulsed I-V) Simulated I-V Simulated Temperature T melt Temperature [ o C] V_PCM [V] Page 10

11 Geometrical dependence current flow t GST α GST x dr GST = ρ GST dx W(L + 2x tan α) t HEATER HEATER W R GST t GST ρgst 2t = dr = ln(1 + 2W L 0 GST ) L R = HEATER ρ HEATER t HEATER WL Page 11

12 Non Volatile Memory Models: PCM The full model describes: read set switch reset switch designed to describe partial set Page 12

13 Outline Reasons to address variability aspects Physics based compact models: Charge based Phase change based Further effects and model updates Overall concepts Examples Applications Flash cell applications Phase Change cell applications Perspectives Page 13

14 Variability aspects The presented basic models seem a good starting point for the mentioned variability analysis, as relatively accurate and at the same physically based and sound Not all the effects are captured: TCAD or more detailed inputs are required to improve such models: Some examples. Page 14

15 1. FLASH Discrete nature of charge: sub-poissonian-injection statistics Cpp R = Cpp P =Cpp σ V T = q C pp V T Cpp P < Cpp R =Cpp σ V T = q γ C pp γ VT ( 1 e ) Page 15

16 2. FLASH RTS 0.8 GIANT RTS 0.6 Current [µa] I D /I D Time [sec.] Control Gate Bias [V] Page 16

17 2. FLASH RTS - Doping Dependence Simulation Power Law fit Experiments Simulation log(σ) [a.u.] σ-σ ref [a.u.] Doping [1/cm 3 ] V T -V T,ref [V] Doping increase larger inhomogeneous conduction due to: stronger confinement at the interface more discrete dopants near interface larger percolation effect Page 17

18 2. FLASH: RTS - Geometry Dependence 10 2 Simulations Template MOSFET σ [mv] 10 1 W=22nm L=22nm L=W 1/L 0.5 1/W 1/WL technology node [nm] Steeper dependence on W than L W and L independent Page 18

19 2. FLASH: RTS - V T Sensitivity Analysis Single trap V T st + Trap Dens. N T Switch time τ e, τ c Experimental V T Probability a) larger N T b) larger σ Increasing N T, RTS distribution rigidly shifts upward Increasing σ, RTS distribution widens σ key element to assess RTS reliability implications V T [a.u.] V T [a.u.] Page 19

20 Page PCM: Drift - Poole/Poole-Frenkel model PF A P A PF P PF P K V K V K K q U + = / + = PF A P A PF P kt E T PF P K V K V K K kt q e dz qan I A sinh 2 0 / τ 1 / = PF P PF P U U U F READ Ref: Ielmini, Zhang JAP102, 2007

21 3. PCM: Drift - Pre-drift and Post-drift Tech. & Physical parameters A, dz, E A, u a, N T, ε GST, ν Post-bake Pre-bake R ( ) Drift = ( law ) t t R t 0 t 0 υ Page 21 21

22 Outline Reasons to address variability aspects Physics based compact models: Charge based Phase change based Further effects and model updates Overall concepts Examples Applications Flash cell applications Phase Change cell applications Perspectives Page 22

23 Outline Reasons to address variability aspects Physics based compact models: Charge based Phase change based Further effects and model updates Overall concepts Examples Applications Flash cell applications Phase Change cell applications Perspectives Page 23

24 NAND Array statistical modeling DSL WL31 41 nm NAND technology WL16 WL15 WL14 WL0 SSL IRPS 2010 Page 24 BACK

25 RESET current distribution Tech. & Physical parameters A, dz, E A, u a, τ 0, N T, ε GST, P/PF - model Statistical sim. Page 25 25

26 Technological spreads Δt GST GST Δρ GST Resistivity spreads Δt HEATER Dimensional spreads HEATER Δρ HEATER ΔW ΔL Page 26

27 Distributions: Measure and Simulation SET-MIN Measure (64Kbit) SET-MIN simulation "cell only" Vread Counts Current [a.u] Monte Carlo simulation with only technological spreads is not able to reproduce the experimental SET distribution! Page 27

28 Simulation with BJT selector Vread SET-MIN Measure (64Kbit) SET-MIN Simulation "with BJT" ΔV BE Process monitor Counts Current [a.u] A tighter distribution is obtained by including the BJT selector Better matching of the Gaussian right-side But the exponential tail is still unmatched Page 28

29 Spice model Exponential tail can be taken into account in Spice model by weighting the full crystallized GST resistance R GST with a logarithmic function: R Partial-SET ~ R GST (- log(α)) with α = uniform[0:1] In this way the Gaussian technological spreads are combined with the exponential distribution of percolation mechanism Page 29

30 Finite-Element model probability 80% 20% active region SET RESET ρ uniform spread 2-D FE model composed of rectangular GST sub-domains is implemented in order to mimic a partial SET Page 30

31 Complete Spice simulation Counts SET-MIN Measure (64Kbit) Complete Spice model simulation 2 3 Current [a.u.] A very satisfactory agreement is obtained between measure and MC simulation Page 31

32 Conclusions and perspectives Variability models have been used for: Window budget evaluations identification of main process steps contributions to distribution width Physical models show the advantage of an easier implementation of variability effects Various contributions have to be exploited for variability effects evaluation (TCAD, ad hoc characterization) Continuously define the trade-offs between accuracy / physic based models and speed / model understanding and implementation Variability models could be used for algorithms optimization (read / write / verify / read): need to evaluate possible showstoppers. Page 32

33 Acknowledgments I do acknowledge the contribution of my colleagues A. Benvenuti A. Calderoni G. Carnevale E. Carniti P. Fantini A. Ghetti A. Mauri A. Spessot L. Vendrame D. Ventrice Part of the activity here described was carried out in the frame of the project: ENIAC MODERN Page 33

34 References (not complete) C. Monzio Compagnoni, A. S. Spinelli, R. Gusmeroli, S. Beltrami, A. Ghetti, and A. Visconti, Ultimate accuracy for the NAND Flash program algorithm due to the electron injection statistics, IEEE Trans. Electron Devices, vol. 55, no. 10, pp , Oct C. Monzio Compagnoni, R. Gusmeroli, A. S. Spinelli, A. L. Lacaita, M. Bonanomi, and A. Visconti, Statistical model for random telegraph noise in flash memories, IIEEE Trans. Electron Devices, vol. 55, no. 1, pp , Jan A.Ghetti, M. Bonanomi, C. Monzio Compagnoni, A. S. Spinelli, A. L. Lacaita, and A. Visconti, Physical modeling of single-trap RTS statistical distribution in flash memories, in Proc. IRPS, 2008, pp C. Monzio Compagnoni, A. S. Spinelli, R. Gusmeroli, A. L. Lacaita, S. Beltrami, A. Ghetti, and A. Visconti, First evidence for injection statistics accuracy limitations in NAND Flash constant current Fowler Nordheim programming, in IEDM Tech. Dig., 2007, pp L. Larcher, A. Padovani, P. Pavan, P. Fantini, A. Calderoni, A. Mauri, and A. Benvenuti, Modeling NAND Flash memories for IC design, IEEE Electron Dev. Lett., vol. 29, pp , Oct D. Ventrice, A. Calderoni, A. Spessot, P. Fantini, A. Sanasi, S. Braga, A. Cabrini and G. Torelli, Statistical Modeling of Bit Distributions in Phase Change Memories, Proc. of 38th European Solid-State Device Research Conference, ESSDERC. Athens Sept pp L. Larcher, P. Pavan, F. Gattel, L. Albani, A. Marmiroli, A new compact model of Floating Gate non-volatile memory cells in Proc. MSM Modeling and Simulation of Microsystems 2001, March 19-21, Hilton Head Island, (SC) USA, pp Calderoni et al. Reset current distributions in Phase Change Memories, IRPS 2010 Spessot et al., Variability Effects on the VT Distribution of Nanoscale NAND Flash Memories, IRPS 2010 Page 34

35 Page 35