A comprehensive model of PMOS NBTI degradation

TL;DR: A comprehensive model for NBTI phenomena within the framework of the standard reaction–diffusion model is constructed and it is demonstrated how to solve the reaction-diffusion equations in a way that emphasizes the physical aspects of the degradation process and allows easy generalization of the existing work.

About: This article is published in Microelectronics Reliability.The article was published on 2005-01-01 and is currently open access. It has received 710 citations till now. The article focuses on the topics: Negative-bias temperature instability.

Summary

1.1. Background

• The instability of PMOS transistor parameters (e.g., threshold voltage, transconductance, saturation current, etc.) under negative bias and relatively high temperature has been known to be a reliability concern since the 1970s [1–4], and modeling effort to understand this is also just as old [5].
• (a) Introduction of CMOS in early 1980s that has made PMOS and NMOS devices equally important for IC designs, also known as These changes include.
• Since hydrogen diffusion through poly-silicon is faster than that in oxide, scaling of gate oxides has increased NBTI susceptibilities [16].
• These technological factors, along with other circuit specific usages, have made NBTI as one of the foremost reliability concerns for modern integrated circuits (almost as important as of gate oxide TDDB reliability).

1.2. Experimental signatures of NBTI

• Any theory of NBTI must be able to explain the following observations regarding the NBTI phenomena [7–27].
• There are intriguing deviations from the perfect, single-exponent power-law degradation that needs careful analysis.
• The authors will use the above experimental observations to systematically test the R–D model whenever possible and augment the model whenever necessary.

2.1. Description of the R–D model

• Till date, the R–D model is the only model that can interpret the power-law dependence of interface trap generation during NBTI, as discussed in Section 1.2(a), without making any a priori assumption regarding the distribution of interface bond-strengths.
• Note that no field dependent term in Eq. (1c) means that the diffusing species is assumed neutral.
• S) and H. Initial interface-trap generation rate depends on Si–H val .
• This would lead to a sharper gradient interface, and would trigger enhanced interface trap generation.
• First, one can theoretically estimate the bulk-trap contribution for a given oxide thickness for every stress voltage and temperature [15,28] and subtract this contribution to extract the NIT contribution from measured DVT data.

2.2.1. Stress phase

• Also, x ¼ ðDHtÞ1=2 from Eq. (1c) implies that the hydrogen diffusion front is yet to reach the poly-silicon interface.
• This regime (n ¼ 1=2) is likely to be observed in thinner oxides where the diffusion front would reach the poly-interface within measurement window.

2.2.2. Annealing phase

• Apart from the five-phase degradation discussed above, another key prediction of the R–D model is similar multi-phase annealing of the interface traps (created during the stress phase) once the stress is removed (see Section 1.2(b)).
• Once the stress is removed, the dissociation of the Si–H bond that forced forward diffusion of hydrogen away from the interface no longer exists, therefore the hydrogen can now diffuse back and recombine with silicon dangling bonds restoring them to their passive Si–H state.
• This diffusion controlled annealing phase (analogous to the diffusion-controlled generation phase described by Eq. (2a)) can be treated analytically in the following manner [20].
• Fig. 4 shows that Eqs. (2a) and (2c) can interpret the stress and the relaxation phases of the NBTI degradation well.
• This is yet another indication that the diffusing species is charge neutral, because a positively charged species would diffuse asymmetrically with stress bias and anneal (zero) bias conditions, which would have made Eq. (2c) inconsistent with experimental data.

2.3. Discussion of the R–D model

• The R–D model successfully explains both the powerlaw dependence of interface trap generation and the mechanics of interface trap annealing––the two key features of NBTI as discussed in Section 1.2(a) and (b).
• It does so without requiring that holes be present for NBTI degradation (although it does not forbid it either) and apart from requiring that the diffusing species be neutral, the theory places no restriction on the nature or type of diffusing species involved.
• Furthermore, it offers no quantitative predictions regarding the field or temperature dependence of the NBTI phenomena.
• Therefore, one cannot optimize operating or processing conditions to reduce NBTI effects using the basic R–D model.
• Moreover, the predictions of precise power-exponents (e.g., n ¼ 1=4) also make the R–D model difficult to reconcile with wide variety of exponents observed in various experiments.

3.1. Model for NBTI field (or voltage) dependence

• According to the R–D model, the field dependence of the NBTI phenomena must be confined to the processes at the interface (kF and kR) because the diffusing species is charge neutral.
• The authors anticipate that the forward dissociation constant, kF, should depend on the number of holes (p), their ability to tunnel to the Si–H bonds , the capture cross-section of the Si–H bonds (r0), and any field dependence of Si–H bond dissociation (B), so that kFð. . .
• The authors discuss these individual processes below.

3.1.1. Role of holes and field-dependence through hole density

• The presence of holes have been linked to NBTI degradation from the beginning of the study of this process––in part because the effect was first observed in PMOS devices in inversion.
• The lack of degradation in NMOS devices stressed in accumulation with voltages similar to those used for PMOS NBTI tests have sometimes been used to argue against the role of holes in NBTI degradation [12].
• Since the authors must compare the NBTI degradation at comparable hole densities, the surface field must be same––which means that the NMOS must be stressed approximately one volt higher compared to PMOS devices for comparable NBTI effects (to take care of flatband voltage difference).
• Fig. 5 shows that this is indeed the case––this explains the experimental observation discussed in Section 1.2(c) and leads us to conclude that the presence of holes play a key role in NBTI degradation consistent with the observation in Section 1.2(c).

3.1.2. Role of hole capture and its field-dependence

• Once the holes are available, they must tunnel through the interface layer of 1–2 A to be captured by the Si–H bonds.
• The field dependent tunneling coefficient depends exponentially on the local electric field at the interface (e.g., TCOEFF expðEOX=E0), although other forms are also suitable [1,2,15,23]).
• Fig. 6 shows that this is indeed the case for oxides of various thicknesses, confirming the general validity of the approach [24–26,28].

3.1.3. Role of field-dependent bond-dissociation

• A key unknown is the influence of the electric field on the dissociation of the Si–H bond itself.
• Assuming that such modification will be associated with a reduction in the barrier height of the bond dissociation, the authors anticipate that there may be field dependent activation energy associated with this process.

3.1.4. Role of bulk traps

• Finally, as discussed earlier in the paper, it is important to realize that at high negative electric fields (especially for thicker gate oxides that involve large stress voltages) NBTI data are often contaminated by generation of bulk traps [15].
• Such contribution from bulk traps must be isolated before a universal representation of kF (Eq. (3a)) can be found.
• According to the Anode Hole Injection model, at large negative voltages in both PMOS and NMOS transistors, electrons are injected from the poly-gate into the silicon substrate.
• These energetic electrons in turn produce hot holes that are injected back into the oxide-creating bulk defects within the oxides [28].
• Once such corrections are accounted for, the authors find that field dependence of Eq. (3a) defines the forward reaction rate well and is consistent with the observation in Section 1.2.

3.2.1. Concept of universal scaling

• Eq. (2a) provides a universal scaling relationship that can used to decouple the field- and temperature-depen- dence of NBTI.
• This equation predicts that if the stress time is measured in units of (1=DH) and if the trap density is normalized by ðkFN0=kRÞ1=2, then the resulting curve should be universal.
• Moreover, since DH is a function of temperature alone and is independent of electric field, and since ðkFN0=kRÞ1=2 is field dependent, but temperature independent (approximately, see below), the NBTI curves at different temperatures (but at a constant electric field) can be scaled along the time axis to identify the activation energy of the diffusion process [14–16].
• Fig. 8 highlights the scaling methodology and shows that universal scaling holds for NBTI data measured under a wide range of stress bias and temperature.

3.2.2. Activation energy of the diffusion process

• The dissociation and annealing of Si–H bonds (kF and kR) and the diffusion of hydrogen (DH) through the oxide are not.
• The authors use two methods to determine the activation energies.
• The first method uses the time–scaling idea discussed above that allows us to determine Ea directly (Fig. 8).
• Therefore, the temperature activation of NBTI process is essentially determined by that of the diffusion process, i.e., EaðNBTIÞ EaðDHÞ=4¼ 0:12–0:15 eV-consistent with Section 1.2(e).

3.2.3. Debate regarding the nature of the diffusing species

• H, and H2O have been suggested), the activation energy of the diffusing species (EaðDHÞ ¼ 4EaðNBTIÞ 0:5 eV) appears to indicate that the diffusing species is hydrogen, most probably a molecular species [32].
• Moreover, the experiment in Ref. [10], when viewed in light of Eq. (2a), also supports the hydrogen hypothesis:.
• When hydrogen annealing of Si-dangling bonds to create Si–H bonds is replaced with deuterium annealing to create Si–D bonds, Eq. (2a) anticipates that NITðDÞ=NITðHÞ ¼ ðDD=DHÞ1=4 ¼ ðmD=mHÞ1=8 (mH and mD being the effective mass of hydrogen and deuterium respectively), making the dependence finite but weak [10].
• Note that if –OH were the diffusing species, the difference in masses of –OH and –OD would have been small, resulting in essentially indistinguishable impact of deuterium annealing.
• The lack of strong deuterium effect also highlights the chemical nature of the Si–H (or Si–D) bond breaking as opposed to the kinetic nature of Si–H bond breaking during HCI experiments.

3.2.4. Hypothesis regarding the non-standard NBTI exponents

• The R–D model predicts very precise power-law exponent that is independent of temperature, time, or oxide thickness (e.g., n ¼ 1=4 analytically, or n ¼ 0:25–0:28 numerically).
• Since the assumption of constant diffusion coefficient is only appropriate for isotropic media with spatially and temporally uniform hopping rates, this may not be appropriate for diffusion in amorphous media where the hopping distances and hopping times are exponentially distributed [33–35].
• Therefore, at lower-temperature, the observed power-exponents are typically lower, as shown in Fig. 10.
• In time however a fraction of hydrogen will eventually find themselves trapped in deeper levels with long release time, making the asymptotic n0 value similar to that of the low-temperature value [15].
• The hypothesis discussed above, if supported by other experiments, would imply that more amorphous the oxide, the better is its NBTI performance, because deep level trapping with long release time would reduce NBTI power-exponent.

4. Conclusions

• The authors have discussed a theory of NBTI that uses the theoretical framework of R–D model to encapsulate the field, temperature, and processing dependencies of the NBTI phenomena.
• This overall framework allows one to discuss and optimize the operating and processing conditions in a manner that is globally consistent and technologically relevant.
• The model presented here still lacks systematic description of the role of boron and nitrogen at the interface.
• Such processing details will surely affect the magnitudes of both kF and kR (but most probably will not modify the functional dependence on field and temperature as discussed in this paper).

Figures

Fig. 5. Time evolution of (normalized) drain current shift for PMOS inversion and NMOS accumulation NBTI stress. Degradation at low VG for all time and high VG at shorter time is due to interface-trap generation, while long-time enhanced degradation at high VG is due to bulk-trap generation [15,16]. Under identical oxide field ðVGjinv ¼ VGjacc 1 V to account for difference in flatband voltage) PMOS inversion and NMOS accumulation (short time) stress show similar degradation, which characterizes the role of holes for NBTI.

Fig. 6. Voltage- and field-acceleration factors (cV and cE, respectively) plotted as a function of oxide thickness. The thickness independence of the field acceleration factor suggests lifetime of the form s expðcEEOXÞ. Since NIT sn, therefore NIT expðEOX=E0Þ with E0 ¼ 1=ncE is the form that describes the NBTI data well.

Fig. 7. Experimental and theoretical time evolution of threshold voltage shift data for a wide range of stress VG. The calculated bulk trap contributions are shown by dashed lines [15]. Theory matches well with experiment. Bulk trap generation at large oxide fields (high VG) affects overall threshold voltage shift and must be taken into account for properly estimating the forward reaction rate of the R–D model.

Fig. 1. (a) Schematic description of the reaction–diffusion model u Broken Si–H bonds at the Si–SiO2 interface create Si þ (interface trap bond dissociation (reaction), while the later rate depends on H remo diffuser, H removal is triggered by H2 diffusion (see Section 3). (b) Hy the hydrogen profile equals generated interface traps (see Section 2). limited (1,2) and diffusion-limited (3,4) regimes. Once the diffusion fro poly ensures that the concentration of H2 at the poly-oxide interface w in the hydrogen profile resulting in faster H removal from the Si/oxide

Fig. 8. (a) Universal scaling scheme for generated interface traps versus time data. Density axis reflects higher Si–H bond dissociation (reaction) while time axis denotes faster hydrogen diffusion. Assuming neutral diffusion species, the reaction and diffusion components can be independently scaled by voltage dependent (time independent) and time dependent (voltage independent) functions respectively. (b) Universality of scaled generated interface traps versus time data. Data taken under a wide bias and temperature range validates the scaling hypothesis.

Fig. 9. Temperature activation of 1=tBREAK and DH. The DH is calculated from the universal scaling of temperature dependent (fixed oxide field) generated interface trap data. Obtained activation energy supports neutral H2 diffusion [32].

Fig. 2. Five regimes of time dependent interface-trap generation as obtained from the general solution of the reaction– diffusion equations during NBTI stress.

Fig. 10. Time evolution of threshold voltage shift under various stress temperature (fixed oxide field). Degradation exponents increases with increase in temperature.

Fig. 4. The R–D model is solved numerically for two cycles of interrupted stress (stress 1000 s, relaxation 1000 s). The simulation results (continuous line) agree well with measured data (symbols) [21]. The parameters used are kF ¼ 10 2/s, kR ¼ 10 18 cm3/s, N0 ¼ 1:24 1014/cm2 and TPHY ¼ 1:3 nm. Each 1000 s segment is characterized by a fast phase (first few seconds) followed by a slower phase of interface-trap generation, which relate to reaction-limited and diffusion-limited regimes, respectively.

Fig. 3. Time evolution of threshold voltage shift of a 26 A PMOS during NBTI stress at 125 C [16]. The degradation rate is small initially but breaks off and increases at longer time. The break time and post-break slope are insensitive to oxide field (gate voltage), suggesting the long-time enhancement is not a bulk-trap activated process [15]. Such enhancement is anticipated by the R–D model (Section 2.2, Figs. 1 and 2). Absence of field acceleration of the breakpoint suggests neutral diffusion species.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "A comprehensive model of pmos nbti degradation" ?

In this paper, the authors construct a comprehensive model for NBTI phenomena within the framework of the standard reaction–diffusion model. The authors demonstrate how to solve the reaction–diffusion equations in a way that emphasizes the physical aspects of the degradation process and allows easy generalization of the existing work. The authors also augment this basic reaction–diffusion model by including the temperature and field-dependence of the NBTI phenomena so that reliability projections can be made under arbitrary circuit operating conditions. 

Q2. What are the future works mentioned in the paper "A comprehensive model of pmos nbti degradation" ?

One of the key goal of their future work would be to clarify the role of such processing changes on NBTI performance.