Recent Developments in Device Reliability Modeling: The Bias Temperature Instability. Tibor Grasser

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Institute for Microelectronics, TU Vienna

1 Recent Developments in Device Reliability Modeling: The Bias Temperature Instability Tibor Grasser Institute for Microelectronics, TU Vienna Gußhausstraße 27 29, A-14 Wien, Austria TU Wien, Vienna, Austria

2 The Negative Bias Temperature Instability Negative bias temperature stress of pmosfets [1][2][3] Large negative gate voltage ( 5 8 MV/cm), all other terminals grounded Elevated temperatures (typically 1 C 2 C, but also at room temperature) Degradation of critical device parameters Threshold voltage Subthreshold slope Transconductance Mobility Drain current... Occurs in all four configurations Strongest in pmos with negative bias Serious reliability concern in pmosfets Huard et al., MR 6 [1] Schroder and Babcock, JAP 3 [2] Alam and Mahapatra, MR 5 [3] Huard et al., MR 6 1/37

3 The Negative Bias Temperature Instability When does the NBTI scenario occur? NBTI: V G V, V S = V D = V Example: inverter with V in = V Similar scenarios in ring-oscillators, SRAM cells, etc. What happens to the pmos transistor? V in V DD V out Kimizuka et al., VLSI Symp. 2/37

trapping sites inside the Si bandgap [1] [2] Universally acknowledged Different defect in SiON and high-k?

4 Origin of the Negative Bias Temperature Instability What happens during negative bias temperature stress? Creation of SiO 2 /Si interface defects (dangling Si bonds, P b centers) Pre-existing, but passivated by hydrogen anneal Si H bonds can be broken Results in trapping sites inside the Si bandgap [1] [2] Universally acknowledged Different defect in SiON and high-k? [3] Creation of oxide charge Most likely E centers Charge exchange mechanism? Controversial! [4] [Courtesy: PennState Univ.] [Courtesy: PennState Univ.] [1] Mahapatra et al., IRPS 7 [2] Huard et al., MR 6 [3] Campbell et al., TDMR 7 [4] Mahapatra et al., IRPS 7 3/37

5 NBTI Measurement Techniques Main problem: it is impossible to perfectly measure NBTI [1] [2] As soon as stress is removed, extremely fast recovery is observed [3] [4] [5] Strong bias dependence, in particular to positive bias A number of techniques have been suggest and used Conventional Measure/Stress/Measure [6] On-the-fly (during stress, no interruption) [7] Charge-pumping and DCIV techniques [8] Various problems Delays lead to recovery How to quantify the degradation ( V th, I D,???) Biggest problem: results do not match!!! No exact theory available that unanimously links and explains all the data [1] Ershov et al., IRPS 3 [2] Reisinger et al., IRPS 6 [3] Ang, EDL 6 [4] Huard et al., MR 6 [5] Grasser et al., IEDM 7 [6] Kaczer et al., IRPS 5 [7] Denais et al., IEDM 4 [8] Neugroschel et al., IEDM 6 4/37

6 Influence of Delay Measurement delay has a significant impact on measurement [1][2][3] Curvature in data becomes more obvious, larger (time-dependent) slope Impact of delay does not disappear at longer stress times Impact of delay is temperature dependent V th [mv] ms 1 s 1 ms 1 s 1 ms 1 s 2 o C 125 o C 5 o C Net Stress Time [s] Effective Power Law Slope o C 15 o C 1 o C 5 o C Delay Time [s] [1] Ershov et al., IRPS 3 [2] Denais et al., IEDM 4 [3] Kaczer et al., IRPS 5 5/37

Standard Model: Reaction-Diffusion Model Successful in describing constant bias stress [1][2] Cannot describe relaxation [3][4][5] Relaxation sets in too late and is then too fast, bias independent

7 Standard Model: Reaction-Diffusion Model Successful in describing constant bias stress [1][2] Cannot describe relaxation [3][4][5] Relaxation sets in too late and is then too fast, bias independent Wrong duty-factor dependence in AC stress: 8% (theory) vs. 5% (measured) Model is wrong!!! [6][7][8][9][1] Universal Relaxation Function r(ξ) Numerical H Numerical H 2 1/(1+ξ 1/2 ) Reisinger Normalized Relaxation Time ξ [1] Alam et al., MR 6 [2] Kufluoglu et al., T-ED 7 [3] Kaczer et al., IRPS 5 [4] Grasser et al., IRPS 7 [5] Huard et al., IEDM 7 [6] Grasser et al., IEDM 1 [7] Grasser et al., IRPS 1 [8] Reisinger et al., IRPS 1 [9] Kaczer et al., IRPS 1 [1] Huard et al., IRPS 1 6/37

8 Overview Introduction Stochastic NBTI on small-area devices: link NBTI and RTN New measurement technique The time dependent defect spectroscopy Anomalous defect behavior Present in all defects Stochastic model Additional metastable states, multiphonon theory Compact modeling attempt RC ladders Implications on lifetimes Conclusions 7/37

9 What is Really Going On? Study of NBTI recovery on small-area devices [1][2][3][4][5][6] Stochastic and discrete charge emission events, no diffusion [1] Huard et al., IIRW 5 [2] Reisinger et al., IIRW 9 [3] Grasser et al., IEDM 9 [4] Kaczer et al., IRPS 1 [5] Grasser et al., IRPS 1 [6] Reisinger et al., IRPS 1 8/37

10 Recoverable NBTI due to the same Defects as RTN Quasi-equilibrium: Some defects neutral, others positive, a few produce random telegraph noise (RTN) Stress: Defects switch to new equilibrium (mostly positive), a few may produce RTN Recovery: Slow transition (broad distribution of timescales) to initial quasi-equilibrium Equilibrium: RTN Non-Equilibrium: Charging Non-Equilibrium: Discharging V G = -.5V V G = -1.8V V G = -.5V Equilibrium RTN Sum #11 #1 + #8 #4 # Time [s] Charging Time [s] Discharging Time [s] 9/37

11 The Time Dependent Defect Spectroscopy (TDDS) Analyzes contributions from multiple traps via spectral maps [1][2] V th [mv] 1 5 Time Domain t s = 1ms T = 1 o C V G = -1.7V Step Height [mv] Emission Time [s] [1] Grasser et al., IRPS 1 [2] For a discussion on the step heights see Kaczer et al., IRPS 1 1/37

12 The Time Dependent Defect Spectroscopy (TDDS) Analyzes contributions from multiple traps via spectral maps V th [mv] 1 5 Time Domain t s = 1ms T = 1 o C V G = -1.7V Step Height [mv] Spectrum Emission Time [s] 1/37

13 The Time Dependent Defect Spectroscopy (TDDS) Analyzes contributions from multiple traps via spectral maps V th [mv] 1 5 Time Domain t s = 1ms T = 1 o C V G = -1.7V Step Height [mv] Spectrum Emission Time [s] 1/37

14 The Time Dependent Defect Spectroscopy (TDDS) Analyzes contributions from multiple traps via spectral maps V th [mv] 1 5 Time Domain #12 #12 t s = 1ms T = 1 o C V G = -1.7V #2 #2 #1 #1 #3 #4 #4 Step Height [mv] 6 4 #2 Spectrum 2 #12 #1 # Emission Time [s] #4 #3 1/37

15 The Time Dependent Defect Spectroscopy Function of stress time t s 11/37

16 The Time Dependent Defect Spectroscopy Function of stress time t s 11/37

17 The Time Dependent Defect Spectroscopy Function of stress time t s 11/37

18 The Time Dependent Defect Spectroscopy Function of stress time t s 11/37

19 The Time Dependent Defect Spectroscopy Function of temperature 12/37

20 The Time Dependent Defect Spectroscopy Function of temperature 12/37

21 The Time Dependent Defect Spectroscopy Function of temperature 12/37

22 The Time Dependent Defect Spectroscopy Function of temperature 12/37

23 The Time Dependent Defect Spectroscopy Different non-linear field dependence of the capture time constants Different bias dependence of emission time constant: two defect types? Capture Time Constant [s] V th ~1/I D V DD #1 125 o C #3 125 o C #4 125 o C #6 125 o C #8 125 o C trtn: τ c s 125 o C #1 175 o C #3 175 o C #4 175 o C #8 175 o C #1 175 o C # o C trtn: τ c s 175 o C Emission Time Constant [s] 1 #2 (lin/125 o C) #4 (lin/125 o C) Disappearing Switching Traps #4 (lin/175 o C) #1 (sat/125 o C) #2 (sat/125 o C) #4 (sat/125 o C) #1 (lin/125 o C) #3 (lin/125 o C) #1 (lin/175 o C) #3 (lin/175 o C) #3 (sat/125 o C) #6 (sat/125 o C) I D V G [V] Negative Readout Voltage (-V G ) [V] Compare SRH-like model: τ c = τ e β E B N v p τ e = τ e β E B e β E T e xf/v T 13/37

24 Anomalous Defect Behavior Defects disappear temporarily from the map (#7) Long term stability: defect #6 missing for a few months now 14/37

25 Anomalous Defect Behavior Temporary random telegraph noise (trtn) T = 15 o C / t s = 1s / V s = -1.7V #4 Trace 23 # V r = -.668V T = 125 o C / t s = 1ms / V s = -1.5V - V th [mv] #1 #14 #4 Trace 16 - V th [mv] V r = -.556V #1 #4 Trace 14 No Modulation Modulation Relaxation Time [ms] V r = -.459V Relaxation Time [ms] 15/37

26 Tewksbury Model Tewksbury model [1] : charging and discharging of traps via elastic tunneling Equilibrium Stress Recovery [1] Tewksbury and Lee, SSC 94 16/37

27 How Can We Model All That Properly? 17/37

28 Standard Model for RTN Model suggested by Kirton & Uren [1] Noticed that elastic tunneling cannot be it Also used lattice-relaxation multiphonon emission (LRME) Time constants depend on activation energy E B and depth x τ c = τ e β E B N v p τ e = τ e β E B e β E T e xf/v T τ 1 = N v v th σ e x/x Standard Charge Capture/Emission Model Kirton/Uren Model Precursor Neutral Defect Hole Capture LRME Charged Trap Positive Defect A + B Hole Emission LRME [1] Kirton & Uren, Adv.Phys 89 18/37

29 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

30 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

31 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

32 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

33 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

34 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

35 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

36 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

37 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

38 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

39 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

40 Lattice Relaxation and Metastability Density functional calculations (DFT) of E center charging & puckering.4 Positive Total Energy [ev] Neutral Silicon Reaction Coordinates [a.u.] Oxygen 19/37

41 Detailed Defect Model Required Neutral Stable Charge Exchange with Substrate Positive Metastable 2 + Structural Relaxation 1 2 Positive Stable + Structural Relaxation 1 Neutral Metastable Charge Exchange with Substrate 2/37

42 Model Different adiabatic potentials for the neutral and positive defect Metastable states 2 and 1 are secondary minima Thermal transitions to ground states 1 and 2 Stochastic Markov-model for defect kinetics based on multiphonon theory Lattice + Electronic Energy - E V [ev] Stress EC EV Reaction Coordinates [a.u.] 21/37

43 Qualitative Model Evaluation Normal random telegraph noise (RTN) Very similar energetical position of the minimas 1 and f 2 (+) f 1 (Neutral) f 1 (Neutral) Time [s] Lattice + Electronic Energy - E V [ev] Reaction Coordinates [a.u.] Kirton and Uren, Adv. Phys /37

Qualitative Model Evaluation Anomalous RTN Very similar energetical position of the three minima 1, 2, and 1 1 2 f 2 (+) f 1 (Neutral) f 1 (Neutral) 1

44 Qualitative Model Evaluation Anomalous RTN Very similar energetical position of the three minima 1, 2, and f 2 (+) f 1 (Neutral) f 1 (Neutral) Time [s] Lattice + Electronic Energy - E V [ev] Reaction Coordinates [a.u.] Uren et al., PRB 88 23/37

45 Qualitative Model Evaluation Temporary random telegraph noise (trtn) Very similar energetical position of the minima 2 and f 2 (+) f 1 (Neutral) f 1 (Neutral) Relaxation Time [s] Lattice + Electronic Energy - E V [ev] Stress trtn Relax Reaction Coordinates [a.u.] 24/37

46 Quantitative Model Evaluation Excellent agreement for both capture and emission time constants Capture time: particularly important for back-extrapolation of stress data Emission time: determines recovery behavior Does the defect act like a switching trap? Depends on the defect configuration 1 2 τ o C Defect #1 1 1 τ o C τ o C 1 τ o C f o C f o C 1 2 τ o C Defect #4 τ 1 1 o C τ o C 1 τ o C f o C f o C V G [V] V G [V] 25/37

47 How to Model This with SPICE? L d R 2 L C k1 V T V a C 2 R 1 C 1 R e C k2 26/37

48 Compact Modeling First attempt: approximate multi-state model by two-state model [1][2] Try to capture the notoriously difficult dynamics first Effective capture and emission time constants Differential equation for a two-state model Corresponds to an RC equivalent circuit Two branches: charging vs. discharging [1] Kaczer et al., IRPS 1 [2] Reisinger et al., IRPS 1 27/37

49 Compact Modeling Example: modeling of recovery [1] Crude approximation: 1 RC element every 3 decades [1] Reisinger et al., IRPS 1 28/37

50 Compact Modeling Example: modeling of recovery [1] Finer approximation: 2 RC elements every 3 decades [1] Reisinger et al., IRPS 1 29/37

51 Extraction of the time constants [1] Compact Modeling [1] Reisinger et al., IRPS 1 3/37

52 Application examples [1] Compact Modeling [1] Reisinger et al., IRPS 1 31/37

53 Compact Modeling Notorious: duty factor dependence [1][2][3] [1] Grasser et al., IEDM 7 [2] Grasser et al., IRPS Tutorial 8 [3] Reisinger et al., IRPS 1 32/37

54 Why Would We Care? 33/37

55 Why Would We Care? Defects determine the lifetime of the device Statistics of individual defects become important in nanoscale MOSFETs Random number of traps Random distribution of traps in space Random defect properties Interaction with random discrete dopants Discrete stochastic charge capture and emission events Fundamental implications on device reliability Lifetime is a stochastic quantity Lifetime will have a huge variance 34/37

56 How to Determine the Lifetime? Small area devices: lifetime is a stochastic quantity [1][2] Charge capture/emission stochastic events Capture and emission times distributed Number of defects follow Poisson distribution For details see Grasser et al. IEDM 1 [1] Kaczer et al. IRPS 9 [2] Grasser et al. IEDM 1 35/37

57 Conclusions NBTI/PBTI is a challenging problem to understand and model Dynamics are of utmost importance For example: DC vs. AC stress, duty factor dependence, bias dependence, etc. What happens in a circuit? Cannot be captured by existing models Measurement method: time dependent defect spectroscopy (TDDS) Operates on nanoscale MOSFETs with a handful of defects Allows extraction of τ e, τ c, and step-height over very wide range Allows simultaneous analysis of multiple defects New defect model Metastable defect states, nonradiative multiphonon theory, stochastic behavior First attempts towards compact modeling Equivalent RC circuits which deliver V th Can capture the main features, e.g. DC vs. AC Lifetime becomes a stochastic quantity 36/37

58 This work would have been impossible without the support of... The Institute for Microelectronics E. Langer, S. Selberherr,... My Ph.D. students W. Gös, Ph. Hehenberger, F. Schanovsky, and P.-J. Wagner B. Kaczer and G. Groeseneken (IMEC) Longstanding collaboration, tons of measurement data, discussion/theory M. Nelhiebel, Th. Aichinger, J. Fugger, and O. Häberlen (Infineon Villach) Financial support, measurement data, and discussion R. Minixhofer and H. Enichlmair (austriamicrosystems) Financial support, measurement data, and discussion H. Reisinger, C. Schlünder, and W. Gustin (Infineon Munich) Ultra fast measurement data, discussion/theory Reliability community P. Lenahan, J. Campbell, G. Bersuker, V. Huard, N. Mielke, A.T. Krishnan,... Funding by EU FP7 contract n (ATHENIS), ENIAC project n (MODERN), CDG 37/37

A Single-Trap Study of PBTI in SiON nmos Transistors: Similarities and Differences to the NBTI/pMOS Case

A Single-Trap Study of PBTI in SiON nmos Transistors: Similarities and Differences to the NBTI/pMOS Case Michael Waltl, Wolfgang Goes, Karina Rott, Hans Reisinger, and Tibor Grasser Institute for Microelectronics,