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) 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  

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

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.

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.

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

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

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. Now the great thing about being in a industrial lab is that people are actually faced with problems and if you had couple of friends in the reliability group, if you by them lunch, they will tell you about problems …. And I knew the problem, the best way to solve them is to look it up in the literature ….

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

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

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

The Reaction-Diffusion Model Silicon Gate oxide Poly 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 Si H Si H Si H Si H H2 Si H Si H NH distance NH: Hydrogen density DH: Hydrogen diffusion coefficient mH: Hydrogen mobility People are not saying that that diffusion does not occur or that annealing term is non-existent, they are simply saying that relatively speaking, these are unimportant. n=1 n=0 n=1/4 n=1/2 log (time) log (NIT)

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

Field Dependent Problem ? 3.2 V p p n 4.2 V We did not worry about this in 1970s, because for thick oxides it made very little difference. n n p Indeed it is, therefore at least we are headed in the right direction ….!

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

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

Note 3: R-D Model applies to Si-H Bonds only SILC Si-H bonds Si-O 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)

Note 4: Relaxation and Time Exponents 102 101 100 10-1 103 109 105 107 Time (sec) VT Shift (mV) Apparent exponent Real Exponent 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”.

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

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

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

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

Dipersive Diffusion: explanation of non-rational n NH x Shkrob, PRB, 1996; 54:15073 NH NH x x nideal ndis H 0.25 0.20-0.25 H2 0.16 0.128-0.144 H2+ 0.33 0.264-0.297 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)

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

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

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

ln (NIT) ln (time) ln (NIT) T1 T2 ln (time) ln (NIT) T1 T2 ln (time) ln (NIT) T1 T2 ln (time)

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

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. ln (time) ln (degradation) Vstress Vop 10 yr

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 ln (time) ln (degradation)

Hard-Saturation in R-D Model: Stretched Exponential Limit NH x ln (time) ln (degradation) If trap generation rate is small, and if NIT much smaller than N0, then 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.

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

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

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

The Good and the Bad of Soft Saturation Due to Interface NH x ln (time) ln (degradation) 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

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

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)

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, DC V=high, f=low ln (degradation) V=low, DC V=low, f=high ln (time)

NIT R-D Model at Very Low Frequencies (0.001 HZ!) H2 density [a.u.] stress 1 relax 1 stress 2 relax 2 NIT 3000 4000 1000 time (sec) 1017 1002 s 3002 s 2450 s 2 sec 1016 95 sec H2 density [a.u.] 1450 s 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)

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

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

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.

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

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

The Physics of Frequency Independence High Freq Low Freq 100 104 108 1012 1016 1020 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!

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

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

Instantaneous Reaction in Standard R-D model SiH + hole = Si+ + H dNIT dt = kF(N0 – NIT) – kR NHNIT substrate f Si H Si H Si H kF = kF0 [tcap-1/(f + tcap-1) ] kR = kR0 [tanneal-1/(f + tanneal-1) ] H 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

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

Conclusions: Relaxation Characteristics Solution to R-D model can interpret experimental relaxation data. At low frequencies, NIT improvement (x2) is frequency dependent. Increase lifetime by a factor of 4 to 8. At higher frequencies, further improvement is possible and is anticipated from R-D model. ln (time) ln (degradation) V=high, f=low V=low, f=high

Broad Conclusions: ? ln (degradation) ln (degradation) The analytical reformulation R-D model is a powerful framework for NBTI studies All NBTI models can be shown to be approximation of R-D model Relaxation Trap Generation Saturation ln (time) ln (degradation) V=high, f=low V=low, f=high ln (time) ln (degradation) ln (time) ln (degradation) Vstress ? Vop 10 yr Factor 4-8 improvement at low frequency. Freq. independence at low frequencies Better lifetime at high frequencies. Robust 0.3-0.12 H2 diffusion Field dependence Exponential activation Soft-saturation interface related Vertical scaling improves lifetime, but one needs to be careful.

What have we covered so far ….. 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 I did not go in details. Details can be found in S. Tan, APL, 2003; 82:1881. Ushio, APL, 2002; 81:1818. Schroder, JAP; 2003;94:1; Reddy, IRPS 2002; 248. Voltage and temperature acceleration Statistical aspects I did not have time to cover it, but you can review Hess, IEDM 2000 and Penzin, TED, 2003. 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 and Scaling impact Conclusion