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IRPS 2005 Tutorial on Negative Bias Temperature Instability

IRPS 2005 Tutorial on Negative Bias Temperature Instability. Muhammad A. Alam Basic modeling (1:30 - 3:00 pm) Anand T. Krishnan Process/Circuits (3:30 - 5:00 pm). Broad Outline of the Tutorial. Part I: Basics and Models (Muhammad A. Alam)

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IRPS 2005 Tutorial on Negative Bias Temperature Instability

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  1. IRPS 2005 Tutorial on Negative Bias Temperature Instability Muhammad A. Alam Basic modeling (1:30 - 3:00 pm) Anand T. Krishnan Process/Circuits (3:30 - 5:00 pm)

  2. Broad Outline of the Tutorial • Part I: Basics and Models (Muhammad A. Alam) • Introduction: NBTI defined and a brief history of NBTI • NBTI degradation kinetics • Nature of NBTI precursor and created traps • Voltage and temperature acceleration • Statistical aspects • Recovery and frequency dependence • Part II (Anand T. Krishnan) • Process dependency (a) Nitrogen (b) Fluorine (c) Other  • Device impact (GM,VT, ION, IOFF, CGD,mobility etc.) • Circuit impact • Scaling impact • Conclusion

  3. Negative Bias Temperature Instability Basics/Modeling Muhammad A. Alam Purdue University West Lafayette, IN alam@purdue.edu

  4. Collaboration and References Experiments: S. Mahapatra, S. Kumar, D. Saha, IIT Bombay [1] Mahapatra and Alam, IEDM 2002, p. 505. [2] Mahapatra, Kumar, & Alam, IEDM 2003, p. 337. [3] Mahapatra et al. IEDM 2004, p. 105. Theory: M. Alam, H. Kufluoglu, Purdue University [1] Alam, Weir, & Silverman, IWGI 2001, p. 10. [2] Alam, IEDM 2003, p. 346. [3] Kufluoglu & Alam, IEDM 2004, p. 113. • For convenience, most of the figures of this talk are taken from these references. I will use other figures to • illustrate difference in opinions or to generalize results.

  5. Introduction: What is NBTI all about ? VDD VDD GND NBTI: Negative Bias Temperature Instability Gate: GND, Drain: VDD, Source: VDD Gate negative with respect to S/D Other degradation modes: TDDB, HCI, etc.

  6. D S 4 15 3 Spec. 10 % degradation 2 5 Warranty 1 0 101 103 105 107 109 Stress Time (sec) NBTI Degradation and Parametric Failure before stress ID (mA) after stress 0 1 2 3 4 VD (volts)

  7. -10% t=10 yr IC Failure Rationale of 10% Criterion: Process, Reliability, Design Design Process -5% -15% +15% t=0 ID ID,nom So we do not have too much margin, especially during the ramp-up period of manufacturing ….

  8. A Brief History of NBTI: And it does have a history! • Experiments in late 1960s by Deal and Grove at Fairchild • Role of Si-H bonds and BTI vs. NBTI story (J. Electrochem Soc. 1973;114:266) • Came out naturally as PMOS was dominant • Important in FAMOS and p-MNOS EEPROMS (Solid State Ckts 1971;6:301) • Theory in late 1970s by Jeppson (JAP, 1977;48:2004) • Generalized Reaction-Diffusion Model • Discusses the role of relaxation, bulk traps, ….. • Comprehensive study of available experiments • Early 1980s • Issue disappears with NMOS technology and buried channel PMOS • Late 1980s and Early 1990s • Begins to become an issue with dual poly gate, but HCI dominates device reliability • Late 1990s/Early 2000(Kimizuka, IRPS97;282. Yamamoto, TED99;46:921. Mitani, IEDM02;509) • Voltage scaling reduces HCI and TDDB, but increasing field & temperature reintroduce NBTI concerns for both analog and digital circuits • Numerical solution is extensively used for theoretical modeling of NBTI.

  9. Vstress Relaxation Saturation Vop V=high, f=low ln (degradation) ? 10 yr ln (degradation) ln (degradation) ln (time) V=low, f=high ln (time) ln (time) • Physics of relaxation • Freq. Dependence • Hard/soft saturation • Extrapolation The Need for NBTI Theory and Measurements Trap Generation • Time Exponent • Voltage Acceleration Before 1980 After 2000

  10. Three Issues of NBTI • Time Dependence • Geometry-dependent NBTI exponents • H vs. H2 diffusion • Charged or neutral species • Temperature-dependent exponents and anomalous diffusion • Saturation Characteristics • Soft saturation due to interfaces/lock-in • Hard Saturation and stretched exponentials • Frequency Dependence • Low frequency • High frequency

  11. Three Issues of NBTI • Time Dependence • Geometry-dependent NBTI exponents • H vs. H2 diffusion • Charged or neutral species • Temperature-dependent exponents and anomalous diffusion • Saturation Characteristics • Soft saturation due to interfaces/Lock-in • Hard Saturation and stretched exponentials • Frequency Dependence • Low frequency • High frequency

  12. H2 kF: Si-H dissociation rate const. Creates broken-bond NIT kR : Rate of reverse annealing of Si-H N0: Total number of Si-H bonds NH H H distance n=1/2 NH: Hydrogen density DH: Hydrogen diffusion coefficient mH: Hydrogen mobility log (NIT) n=1/4 n=0 n=1 log (time) Si Si Si Si Si Si H H H H The Reaction-Diffusion Model Poly Silicon Gate oxide

  13. Time-dependence Temp-dependence Field-dependence The meaning of the Parameters poly oxide N0

  14. Field Dependent Problem ? 3.2 V p p n 4.2 V n n p Indeed it is, therefore at least we are headed in the right direction ….!

  15. Note 1: Many Phenomenological Models: All Approximations to R-D Theory! • Diffusion Limited Reaction-Diffusion Model (R-D) • Jeppson, JAP 1977; 48: 2004 Single region, simple analytical solution • Ogawa, PRB, 1995; 51: 4218 Detailed analytical solution] • Alam, IWGI 2001; 10 Multi-region analytical/numerical • Alam, IEDM 2003; 346 Freq. Dependence: analytical/numerical • Kufluoglu & Alam, IEDM 2004. Geometrical aspects: numerical/analytical • Chakravarthi, IRPS 2003. H2 exponents • Drift Limited Stretched Exponential Model (S-E) • Blat, JAP, 1991; 69:1712. Simple exponential • Kakalios, PRL,1987; 1037 Dispersive diffusion • Sufi Zafar (VLSI 2004) Derivation for Stretched Exponential • Bond-dissociation limited Reaction Model (B-D) • Hess (IEDM00), Penzin (TED03)Power-law, multiple exponents

  16. ... just as we do not need to know the microscopic physics of Dn, Dp, mn, mp, ks, etc. to understand the operation of bipolar transistor and MOSFETs. (1) We need not know the micro- scopic physics of kF and kR, DH, mH to understand the features of NBTI, …. ….. just as all we need for DD equations is detailed-balance relationship like Einstein relationship. (2) All we need, is just a few detailed-balance relationships like how kFand kRare related, … …. just as detailed analysis of scattering based on Fermi Golden rule or dielectric response help illuminate the physics of mobility and diffusion. (3) First principle calculations involving nature of traps, physics of diffusion, etc. help illuminate the physics of the coefficients and is very useful, …. Note2: R-D Model is a phenomenological Model R-D model for NBTI is analogous to Drift-diffusion model for devices

  17. Si-O bonds SILC Note 3: R-D Model applies to Si-H Bonds only Si-H bonds CP NIT by charge pumping = Broken Si-H bond + broken Si-O bond Signature of bulk Si-O bonds …… Stress Induced Leakage Current Only part of NIT(identified by CP) that is not correlated to SILC should be compared to the predictions of Reaction-Diffusion Model Total VT shift = contribution from Si-H bonds (R-D Model) + contributions from Si-O bonds at bulk & interface (AHI model)

  18. Apparent exponent 102 101 VT Shift (mV) Real Exponent 100 10-1 101 103 105 107 109 Time (sec) Note 4: Relaxation and Time Exponents Nit = Atn ln (Nit) = ln (A) + n ln(t) R-D model predictions to be compared with “real exponent” which is smaller than “apparent exponent”.

  19. If trap generation rate is small, and if NIT much smaller than N0, then NH x NH (Neutral) x (Charged) A Reformulation of R-D Theory for Analytical Modeling Si H H H Poly Si H Si sub. H H Si H

  20. Combining these two, we get H Si H H Poly Si H H Si sub. H Si H n=1/4 even with two sided diffusion n ~ 1/4 is a possible signature of neutral H diffusion Reproduces results of Jeppson, JAP, 1977. Trap Generation with Neutral H Diffusion NH x

  21. NH2 NH H2 x Combining these two, we get Trap Generation with Neutral H2 Diffusion H2 Si H H2 Poly Si H H2 Si sub. H2 H2 Si H • n ~ 1/6 is a possible signature of neutral H2 diffusion • Small exponent because • generation is more difficult. Reproduces results of Chakravarthi, IRPS, 2003.

  22. H+ Si H+ H+ Poly Si H+ H+ Si sub. H+ Si H • n ~ 1/2 is a possible signature of charged H diffusion • Rapid removal of H+ by Eox field increase NIT gen. rate. NH x Reproduces results of Ogawa, PRB, 1995. Trap Generation with charge H (Proton) Diffusion Combining these two, we get Did not find any such NIT vs. time result

  23. H2+ Si H+ H2+ Poly Si H H2+ Si sub. H2+ Si H Combining these two, we get NH2 x Trap Generation with charge H2+ Diffusion • n ~ 1/3 is a possible signature of charged H2+ diffusion • Exponents above 1/3 seldom seen in charge-pumping expt. (uncorrelated to SILC).

  24. NH NH x x Dipersive Diffusion: explanation of non-rational n Shkrob, PRB, 1996; 54:15073 NH NH x x • R-D model predicts n=0.30-0.12 • More amorphous oxides for better NBTI • For finite oxides, at very long time all n • must be rational (no problem > 10 yrs)

  25. Theory of Standard Diffusion: Real Distribution Real-Space Energy-Space Standard Distribution NH NHf NH x No Temperature Activation

  26. NHf NH NHb Theory of Activated Diffusion: Real Distribution Real-Space Energy-Space Standard Distribution NH x with

  27. Theory of Dispersive Diffusion: Real-Space Energy-Space Moment-Space M ……

  28. ln (NIT) T1 T2 ln (NIT) ln (time) ln (time) T1 T1 T2 T2 ln (NIT) ln (NIT) ln (time) ln (time)

  29. H, H2, (H2+) ? Ea suggest diffusion of neutral H2 assumption*, if we can assume EF-ER is small, can we ? M. L. Reed, JAP, p.5776, 1998

  30. Vstress Vop ln (degradation) 10 yr ln (time) Conclusions: Trap Generation Rate • Trap generation is well-described by a power-law, consistent with reaction-diffusion model. These are robust power-laws correct for many decades in time. • The analytical methodology presented is universally consistent with numerical solution of R-D model. In fact, this even work for 2D and 3D solutions (Kuflouglu, IEDM 2004). • Reaction-diffusion model predicts generation exponent in the range of 0.3-0.12 • However, only rational exponent n=0.33,0.25,0.16 corresponding to H2+, H2, and H are robust. Other n improve IC lifetime, but should be used carefully. • NBTI activation energy of 0.12 eV suggests that the diffusing species may be neutral H2. • The most probable form of field dependence is sqrt(Eox)exp(-Eox/kT). NBTI is field dependent, but does not depend on voltage explicitly.

  31. ln (degradation) ln (time) Three Issues of NBTI • Time Dependence • Geometry-dependent NBTI exponents • H vs. H2 diffusion • Charged or neutral species • Saturation Characteristics • Soft saturation due to interfaces/Lock-in • Hard Saturation and stretched exponentials • Frequency Dependence • Low frequency • High frequency

  32. NH If trap generation rate is small, and if NIT much smaller than N0, then x ln (degradation) ln (time) Hard-Saturation in R-D Model: Stretched Exponential Limit • R-D solution for hard saturation (all Si-H bonds broken) can be approximated by stretched-exponential function. • Since only lateral shift is allowed, such • saturation increase lifetime modestly.

  33. exponents need not be rational if diffusion is dispersive. • is rational, i.e. 1/4,1/6,1/2,1/3 Reproduces results from Blat, PRB, 1991. Zafar, VLSI, 2004 Stretched Exponential Limit: Additional Points ln (degradation) ln (time)

  34. (2) Combining, at short time, we get Soft Saturation: Reflection at Poly Interface Oxide Poly Si H H H H (1) Si H H Si H NH (3) x And at long time ….

  35. oxide Si Poly NH x S. Rangan et al. 2003 IEDM Proc. Proof that it is Poly Interface: Enhancement and Lock-in oxide Si Poly NH x

  36. The Good and the Bad of Soft Saturation Due to Interface NH x ln (degradation) ln (time) • Good: Vertical scaling is possible, with orders of magnitude in increased lifetime. • Bad: Saturation is not permanent. Initial Exponent would return. Kufluoglu & Alam, unpublished results NH x ln (degradation) ln (time)

  37. Aside: The diffusing species is H2 Within reasonable approximation, diffusing species is H2.

  38. Conclusions: Saturation Characteristics • We identified two types of saturation: Hard Saturation: When all Si-H bonds are broken Soft Saturation: When diffusion front reaches poly interface. (Also see Chakravarthi, IRPS 2004). • The stretched exponential form, sometimes taken as an alternative to R-D model, is simply the hard saturation limit of R-D model. • Hard saturation requires lateral scaling; lifetime improvement is small. • Soft-saturation, which is in better accord with experiment, is related to interface reflection. • The horizontal shift associated with soft-saturation increases lifetime greatly; but beware that this saturation is not robust and the rate will increase at a later time! ln (degradation) ln (time)

  39. Three Issues of NBTI • Time Dependence • Geometry-dependent NBTI exponents • H vs. H2 diffusion • Charged or neutral species • Saturation Characteristics • Soft saturation due to interfaces/Lock-in • Hard Saturation and stretched exponentials • Frequency Dependence • Low frequency • High frequency V=high, f=low V=high, DC ln (degradation) V=low, DC V=low, f=high ln (time)

  40. R-D Model at Very Low Frequencies (0.001 HZ!) relax 1 relax 2 stress 1 stress 2 NIT 3000 4000 1000 time (sec) 1017 1002 s 3002 s 2450 s 2 sec 1016 95 sec 1450 s H2 density [a.u.] 450 sec 2002 s 3450 s 1015 1014 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 distance into the Oxide (A)

  41. Analytical Model: Relaxation Phase oxide Si NH0(0) 1017 1016 H2 concentration [a.u.] NH0 1015 (Dt0)1/2 1014 0 10 20 30 40 Distance [A]

  42. New model New model Numerical Numerical VT = a – bt1/4 VT = a – bt1/4 Other Approximate Analytical Models linear plot log plot 50 40 abs (VT) Shift (mV) 30 20 10 0.5x104 1x104 1.5x104 100 101 102 103 104 105 Time (sec)

  43. NBTI Recovery: Frequency Independence 35 DC DC(meas.) 0.5 Hz (meas.) 25 VT Shift [mV] 0.1 Hz 15 1 Hz 5 0 250 500 750 1000 Time (sec) G. Chen et al., EDL, 23(12), p. 734, 2002.

  44. 50 40 30 20 10 0 Frequency Dependence: Simulation vs. Measurement meas. simulation VT Shift [mV] 10-1 101 103 105 107 Frequency [Hz] Symmetry in R-D model requires frequency-independent degradation

  45. 1020 1016 1012 108 104 100 The Physics of Frequency Independence High Freq Low Freq Low Frequency (1 cycle) High Frequency (1 cycle) H2 concentration [a.u.] 0 20 40 60 80 100 Distance into the Oxide [A]

  46. 1020 1016 1012 108 104 100 The Physics of Frequency Independence High Freq Low Freq 100/200 cycle 200/400 cycle H2 concentration [a.u.] 0 20 40 60 80 100 Distance into the Oxide [A] R-D model anticipates Frequency Independence!

  47. NBTI Lifetime Improvement: DC vs. AC 102 TDC TAC TAC ~ 4-8 VT Shift [mV] TDC 101 100 100 101 102 103 Time (sec) At least a factor of 4-8 improvement in lifetime is expected

  48. At low frequencies, electro-chemical or reaction diffusion model indicates frequency independent improvement …. M. Alam, IEDM Proc. 2003.

  49. Si dNIT = kF(N0 – NIT) – kR NHNIT dt H H Si Si H H Instantaneous Reaction in Standard R-D model SiH + hole = Si+ + H substrate f kF = kF0 [tcap-1/(f + tcap-1) ] kR = kR0 [tanneal-1/(f + tanneal-1) ] f = tcap-1 Oxide ln (kF, kR) f = tanneal-1 Poly ln(f) Time delays in kF and kR may introduce freq. dependence in R-D model

  50. 50 40 30 20 10 0 Frequency Dependence at High Frequencies Meas.(Chen, IRPS03) DC Meas.(Abadeer, IRPS03) VT Shift [mV] 10-1 101 103 105 107 Frequency [Hz] Standard R-D model is inconsistent with high frequency data

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