A Comprehensive Model for PMOS NBTI Degradation: Recent Progress

Authors1 and Authors2

1PurdueUniversity, West Lafayette, IN47906, USA

2Department of Electrical Engineering, IIT Bombay, Mumbai 400076, India

1

Abstract

Negative Bias Temperature Instability (NBTI) is a well-known reliability concern for PMOS transistors. We review the literature to find seven key experimental features of NBTI degradation. These features appear mutually inconsistent and have often defied easy interpretation. By reformulating the Reaction-Diffusion model in a particularly simple form, we show that these seven apparently contradictory features of NBTI actually reflect different facets of the same underlying physical mechanism.

Keywords: CMOS degradation, reliability physics, bias temperature instability, mathematical model, universal scaling

  1. Background

Design of any digital circuit is based on the presumption that transistor parameters will remain bounded by a certain margin (typically ±15%) during the projected lifetime of the IC. This margin consists of initial manufacturing tolerance encapsulated in CPK numbers as well as other time-dependent parameter shifts due to various transistor degradation mechanisms like Hot Carrier Degradation (HCI), Gate Dielectric Breakdown (TDDB), Negative Bias Temperature Instability (NBTI), etc. Among them, NBTI has been a persistent (and perhaps most significant) reliability concern for CMOS technology generations below 130 nm node [1-8]. Two factors – increasing oxide field (to enhance transistor performance without scaling gate oxide) and the use of oxynitrides (to prevent Boron penetration and to reduce gate leakage)[9, 10] – appear to have exacerbated this PMOS-specific reliability issue. Specifically, NBTI causes systematic reduction in transistor parameters (e.g., drain current, transconductance, threshold voltage, capacitance, etc.) when a PMOSFET is biased in inversion (VS=VD=VB=VDD and VG=0). Since this NBTI-specific biasing condition arises universally in inverting logic, SRAM cells, I/O system, dynamic logic, etc.[11-13], it is not surprising that the concern about NBTI is pervasive in the semiconductor industry.

Since NBTI has been a reliability concern from the very early days of integrated circuits in mid 1960s[14, 15], there are many reports on various aspects of NBTI degradation over the last 40 years[3]. An extensive review of the state-of-art of the pre-2003 experimental results and the possible theoretical foundations has been made in our previous article in Microelectronics Reliability[1]. After correcting for artifacts arising from incorrect stress condition leading to spuriously high degradation exponent at later stages of degradation, resolving controversies involving oxide field vs. gate voltage dependence, and addressing process specific NBTI degradation issues, the essence and consensus regarding NBTI phenomena until 2002-2003 can be summarized as follows:

(1) The degradation is field-driven and is related to interface traps at the Si/SiO2 interface[4].

(2) Threshold voltage degradation due to NBTI is given by VT ~ Aexp(-nED/kT)tn with n~0.25 (see Fig. 1) and ED~0.5 eV[1, 4, 6].

(3) Once NBTI stress is removed, a fraction of interface traps can self-anneal [6, 16-18].

None of the pre-2003 reports, however, seemed to have realized that the values of n and ED of NBTI are self-contradictory and mutually inconsistent. Since 2003, there have been reports aboutfour additional features of NBTI degradation that have further complicated the classical understanding of this degradation phenomenon:

(4) As NBTI became a long term reliability concern, many research groups looked for and found long-term reduction (quasi-saturation?) of NBTI time-exponent n from 0.25 to 0.13-0.16 [5, 8, 17].

(5) A number of groups reported that NBTI is smaller for AC stress compared to DC stress, and the ratio of AC to DC NBTI degradation is frequency independent [6, 9, 18] at least for low frequencies (< 10-100 KHz).

(6) Careful analysis of temperature-dependent NBTI data (see Fig.1) shows characteristics of dispersive transport [1, 2, 19]. If this is indeed the case, lifetime projections at various temperatures would be more difficult than previously presumed.

(7) Classical NBTI models are based on dynamics of broken Si-H bonds and these models are often validated against Charge-pumping data, yet charge pumping technique probes both broken Si-O and Si-H bonds and can not distinguish between them[7]. This raises important concerns regarding the validation of NBTI models. Moreover, the significance of hole trapping in determining the NBTI degradation continues to be an important issue.

Since the original R-D analysis of NBTI [1] did not address these post-2003 issues, there is an incorrect presumption that these new features are incompatible with the R-D model and must be interpreted with new models of NBTI [5, 20, 21]. The goal of this paper is to show that the seven features of NBTI degradation discussed above (to be referred to as Issues 1-7 for the rest of the paper) can be interpreted within the same intuitively simple framework of NBTI degradation discussed in Ref. [1], with a straightforward generalization of the R-D model. And theseven features represent various aspects of the same degradation mechanism. Although the four post-2003 NBTI features of saturation, frequency independence,dispersive temperature dependence, and indistinguishibility between SiO and SiH bonds appear to have complicated the physical picture of NBTI, in reality they hold the key to the puzzle of the pre-2003 NBTI results. In Sec. 2, we analyze the nature of the puzzle of the three observations in pre-2003 literature. In Sec. 3, we show how the post-2003 observations regarding saturation and frequency independence actually help resolve the conceptual inconsistencies. This model then allows us to connect NBTI and HCI degradation and anticipate the degradation in reduced geometry devices, as well as seek resolution of NBTI challenges through circuit techniques. Our Conclusions regarding these issues are summarized in Sec. 4.

  1. The R-D Model of NBTI Degradation: Definition of the Puzzle

In the Reaction-Diffusion (R-D) formulation of NBTI degradation [1, 8, 22], one assumes that NBTI arises due to hole-assisted breaking of Si-H bonds at the Si/SiO2 interface (see Fig. 2, top illustration). The rate of trap generation is given by,

(1*)

where N0 is the initial number of Si-H bond at the Si/SiO2 interface. NIT is the fraction of these Si-H bonds broken at time t due to NBTI stress. The dissociation rate constant kF is proportional to the number of inversion layer holes that are captured by Si-H bonds. The two-electron Si-H covalent bond is weakened once a hole is captured and this weakened bond (assisted by the electric field) is easily broken at relatively moderate temperature. The broken Si bonds acts as a donor trap [23, 24] and contributes to the shift in threshold voltage and reduction in transconductance. The H atoms released in the process can anneal the broken bonds, as described by the second term of the right hand side of (1*) (NH(0) is the H concentration at the interface, x=0), or the H atoms may diffuse (or drift) away from the interface, i.e.,

. (2*)

The last term in (2*) is negligible. The H atoms may diffuse with diffusion constant (DH) if the atomsare neutral, or drift with mobility H if they are charged.

Since the rate of trap generation in (1*) is usually small compared to the dissociation and annealing rates and since NITN0 ~ 5x1012 cm-2, therefore

. (1)

Also, (2*) may be restated as a conservation equation which requires that the number of broken Si-H bonds equal that of total H concentration in the gate stack, i.e.,

. (2)

Here x=0 is defined at the Si/SiO2 interface and x(t) defines the tip of the diffusion or drift-front (Fig. 2, middle and bottom figures). Eqs. (1) and (2) are sufficient to highlight the conceptual inconsistency of the pre-2003 NBTI literature [15]:

Consider diffusion of neutral atomic H as shown in Fig. 2 (middle figure). The diffusion distance at a given time t is x(t) ~ (DHt)1/2, therefore the right hand side of (2) can be interpreted as the area under the triangle (sometimes referred to as ‘Triangle Method’) so that

.

Inserting this expression for NIT into (1), we find

. (3)

This reproduces the classic exponent of n=1/4 which has been the signature of NBTI degradation based on wide variety of experimental results. The success of the R-D model in interpreting the NBTI exponent (see Fig. 1) led to prevailing view that NBTI degradation is characterized by diffusion of atomic H in gate dielectrics.

Based on this analysis, it is easy to see why pre-2003 NBTI literature generally did not support interpretation based on diffusion of molecular H2 or drift of H+ (proton). For example, if H-specie is released as atomic H from Si-H bonds and then convert to and diffuse as molecular H2, then the ‘Triangle Method’ would predict

.

In addition, the conversion between H and H2 would be given by the Law of Mass Action, i.e., Together with Eq. (1), diffusion of neutral H2 requires

.(4)

The exponent n=1/6 reflects the bottleneck of H-H2 conversion which results in higher H concentration at the Si/SiO2 interface [3]. This allows faster annealing of broken Si-H bonds and reduced trap generation rate. Since there had been no experimental evidence in pre-2003 literature of NBTI degradation characterized by n=1/6 exponent, a general consensus was that NBTI degradation by diffusion of molecular H2 is unlikely.

Similarly, if H drifted away from the interface as proton, we must retain the drift term in Eq. (2*), then rewrite the conservation equation 2 (in analogy to the Triangle Method) as

.

Here Eox is the velocity with which the H+ drift-front moves away from the interface as shown in Fig. 2 (bottom figure). Together with Eq. (1), we find [11]

. (5)

The n=1/2 regime has also never been seen in NBTI measurements, leading one to conclude that NBTI degradation through proton transport is unlikely.

The above analysis shows that the time exponent n is dictated by and is a sensitive measure of the diffusing specie, as also shown by numerical solution of R-D model [8, 25-27]. Among the various exponents (n=1/2 for proton, n=1/6 for molecular H2, n=1/4 for atomic H), only diffusion of atomic H appeared to be consistent with experimental results, therefore the pre-2003 literature assigned atomic H diffusion at the root cause for NBTI degradation.

In addition to time exponents, the activation energy of NBTI is also extensively studied in pre-2003 literature and various report suggest that EA~0.12-0.15 eV. If we assume that kF=kF0exp(-EF/kBT), kR=kR0exp(-ER/kBT) and DH=D0exp(-ED/kBT), then by Eq. 3,

so that the net temperature activation is EA=0.5(EF-ER) + 0.25ED. Since the specific values of activation energies of forward dissociation, EF, reverse annealing, ER, and diffusion coefficient, ED, were unknown, the inconsistency between time exponent n and temperature activation EA was initially not highlighted. However, generalized scaling arguments consistently showed that EA ~ ED/n[1, 4], with EF~ER[1, 2, 4, 28]. The measured EA therefore provided a direct measure of ED~0.5-0.6 eV, which in turn implicated H2 diffusion [29]! This is the core dilemma of pre-2003 NBTI literature: the time-exponent in Eq. (3) suggests atomic H diffusion, while temperature activation suggests H2 diffusion. Since both these parameters have significant implications for projected IC lifetime, one must reexamine the assumptions of classical NBTI analysis.

  1. The R-D Model for NBTI Degradation: Resolution of the puzzle

As mentioned in Sec.1, post-2003 NBTI experiments are characterized by four additional features: saturation of degradation at long stress times, independence of NBTI degradation with frequency, dispersive vs. Arrhenius activation, and difficulty in distinguishing between dissociation kinetics of SiO and SiH bonds. Since all these features have significant implications for lifetime projection, they mandate a reconsideration of the R-D model[5, 20, 21, 30, 31].

The saturation characteristics of NBTI was the first indication that the pre-2003 R-D analysis of NBTI may not be sufficient and one must somehow generalize the classical view by introducing new features like reflection at poly-oxide interface, depletion of Si-H bonds at the Si/SiO2 interface[5], the prevalence of hole trapping[32], etc. However, it is shown below that such modifications have significant limitations.

3.1 Analysis of Quasi-Saturation

3.1.1 Hypothesis of ‘Reflection at Poly/Oxide Boundary’

If the saturation were caused by reflection at the poly-oxide interface, one can use Fig. 3 to compute integrated H concentration for Eq. (2) by the ‘Triangle Method’

where NH(Tox) is the concentration of H at the SiO2/poly interface. In addition, the flux continuity at the interface requires

.

Taken together with Eq. 1, the solution [16]

does show onset of saturation as H diffusion front crosses the oxide-poly interface (Fig. 3, middle-left), however at long times as the H atoms stored in oxide becomes a negligible part of the total H stored in oxide and poly (Fig. 3, lower-left), the trap generation at reverts to

which restores the original pre-saturation exponent. In other words, the poly-reflection does not result in saturation in trap generation (unless one makes the unrealistic assumption that H does not diffuse in poly, i.e.,DH(poly)= 0.)

3.1.2: Hypothesis of ‘Depletion of Si-H Bonds’

Consider the second possibility of NIT-saturation caused by depletion of all Si-H bonds [5]. Since NIT may approach N0, therefore (1*) may be simplified as

.

Using this relation in (2*), we find

.

A simple integration results in

which, by Taylor expansion, can be simplified to

. (6)

where =0.25. This Stretched-exponential model do predict NBTI saturation[5, 8], but it makes the unrealistic assumption that NBTI stress breaks all Si-H bonds and predicts that voltage-dependent NBTI saturation occurs at same NIT concentration, which is not supported by experiments.

3.1.3 Hypothesis of ‘Saturation due to Measurement Delay’

It is well known that NIT generated during the stress phase of the degradation begins to recover as soon as the stress is removed[6, 8, 17, 18]. Since each measurement of NIT using conventional stress-measure-stress sequence requires a certain measurement window, one must necessarily consider the effect of such interruption of stress on the measured values themselves. In order to understand the effect of measurement delay, it is easier to begin the discussion with analysis of AC response (50% duty cycle) on NBTI degradation (Issue 5).

It was reported in Ref. [14] that the AC response in SiO2 films is frequency independent (see Fig. 4 (top)). Ref. [7] interprets this phenomenon as a delicate interplay between forward dissociation and reverse annealing rates during the stress and relaxation phases of AC degradation. Although the NIT generation/per cycle is very different at low frequency vs. high frequency, however the total NIT generated for the same duration of stress is actually the same (Fig. 4, bottom). Therefore, the integrated degradation is frequency independent, consistent with experiment. The corollary to this statement is that the ratio of the relaxation period to stress period, S, dictates the net NBTI degradation. For DC stress, S=0 and for AC stress (with 50% duty-cycle), S=1. In contrast, during NBTI measurement, the stress periods increases geometrically with time while the measurement window remains the same (Fig. 5), thus S transitions from 1 to 0: in other words, the effect of NBTI relaxation during unstressed period is more significant at early stages of stress compared to later times. The black line in Fig. 6 (top) shows that the delay-induced measurement associated with “molecular-hydrogen” diffusion anticipates a saturation behavior that is consistent with measurement. Once the delay is accounted for, however, the quasi-saturation disappears and the underlying zero-delay exponent is given by n~0.16.

This is highlighted in Fig. 7,which shows delay free measurement results obtained for various stress VG, temperature and on films having different EOT and N2 dose. The n~0.16 time exponent is found to be robust. Indeed, recent zero-delay on-the-fly measurements from a number of research groups have also supported this conclusion [8,36].

This simple reinterpretation of the NBTI saturation being an artifact of measurement delay immediately resolves the pre-2003 controversy regarding the nature of diffusing species: the exponent n~0.25 implicated H diffusion, while activation ED~0.5 eV suggested H2 diffusion. In fact, n~0.25 is not robust exponent, as indicated by the saturation of NBTI degradation observed by experiments (see Fig. 6(top)). Therefore identification of NBTI with H-diffusion is actually accidental and reflects measurement-delay induced relaxation of underlying degradation generated by H2 diffusion. The diffusing specie is H2 with consistent values of n ~ 0.16 and ED ~ 0.5 eV.

3.2 Dispersive vs. Activated Transport(Issue 6)

Our discussion above, based on careful analysis ofthe absolute value of time-exponent n, resolved that diffusion of H2 molecule would consistently interpret experimental data regarding quasi-saturation, frequency-insensitive degradation and n=1/6 exponent with “no-delay” measurements. Yet, instead of absolute values of n, the groups who focused on variation of n as a function of temperature (determined by standarddelay-basedmeasurement, Fig.8) reached an entirely different

conclusion: that the transport of H-specie is dispersive and most likely specie is H+(proton), not H2!

Consider the arguments for dispersive transport: Historically, NBTI has always been associated with Arrhenius-like activated transport. This is because if one assumes that kF=kF0exp(-EF/kBT), kR=kR0exp(-ER/kBT) and DH=D0exp(-ED/kBT), then

(the diffusing specie determine m and n, see Eq. 2-4). For Arrhenius transport, therefore, the degradation curves ( ln(NIT) vs. ln(t) ) measured at various temperatures as a function of time should be parallel to each other.

Over the years, some authorshave questioned this presumption of Arrhenius-like activation, because H transport in amorphous SiO2 is known to be dispersive[2]. This dispersive diffusion coefficient is given by DH ~ DH0 (t)-a[33-35] where a is the dispersion parameter. Therefore, Eq. (2-4) should be rewritten as

Assuming that EF-ER ~ 0 and with1-a=kBT/E0 (E0 measures of the energy-distribution of the trap-states), one finds

withand n=nKBT/E0.

For dispersive transport, therefore, both the time-exponent n as well as the prefactor, ln(A)[2],should scale linearly with T. Indeed, classical (with delay) measurement of NBTI degradation do show that n(Fig. 8)scales linearly with temperature, with dispersion parameter a=0.7 (25C)-0.57 (200C) for H+ transport (i.e., n=0.5), and a=0.4 (25C)-0.1(200C) for diffusionof atomic H (n=0.25)[1, 2]. Moreover, dispersive-drift of H+ (proton) anticipates that log(t) recovery of NIT once the stress is removed and such “log(t)” recovery has been observed in experiments [20]. Therefore, one concludes that both NBTI time-exponent as well as temperature activation are dictated by dispersive transport of H+. This conclusion of H+ transport contradicts the analysis in Sec. 3.1 which resolved that only H2 diffusion can consistently interpret NBTI experiments.

The view of H+ dispersive transport dictates NBTI, however, raises a conceptual problem. Oxides used in modern CMOS technology are so thin that the diffusion specie reaches the SiO2-poly interface within seconds [36] and the long term NBTI degradation is controlled by diffusion (or drift) in poly-silicon. The distribution of trap levels ET in poly-silicon is more localized (in energy) than oxides [E0 ~ kBT] so that a  1, therefore poly-silicon is known to be less dispersive than oxides. Yet, the dispersion parameter needed to fit the NBTI data (i.e., a ~ 0.7-0.57) is actually greater than those needed for oxides a=0.1-0.2. How can poly-silicon be more dispersive than amorphous-oxides?