Electron transport through electrically induced nanoconstrictions in HfSiON gate stacks

A microscopic picture for the progressive leakage current growth in electrically stressed HfxSi1−xON∕SiON gate stacks in metal-oxide-semiconductor transistors based on the physics of mesoscopic conductors is proposed. The breakdown spot is modeled as a nanoconstriction connecting two electron reservoirs. We show that after eliminating the tunneling current component that flows through the nondamaged device area, the postbreakdown conductance exhibits levels of the order of the quantum unit 2e2∕h, where e is the electron charge and h the Planck’s constant, as is expected for atomic-sized contacts. Similarities and differences with previous studied systems are discussed.

Electron transport through electrically induced nanoconstrictions in HfSiON gate stacks E. Miranda, 1,a͒ P. Falbo, 2,b͒ M. Nafría, 1,c͒ and F. Crupi A microscopic picture for the progressive leakage current growth in electrically stressed Hf x Si 1−x ON / SiON gate stacks in metal-oxide-semiconductor transistors based on the physics of mesoscopic conductors is proposed.The breakdown spot is modeled as a nanoconstriction connecting two electron reservoirs.We show that after eliminating the tunneling current component that flows through the nondamaged device area, the postbreakdown conductance exhibits levels of the order of the quantum unit 2e 2 / h, where e is the electron charge and h the Planck's constant, as is expected for atomic-sized contacts.Similarities and differences with previous studied systems are discussed.© 2008 American Institute of Physics.͓DOI: 10.1063/1.2949748͔ In the relentless race toward the miniaturization of metal-oxide-semiconductor devices, the gate oxide material properties and the quality of its interface with the channel region play an ever increasing technological role.In this connection, the use of high permittivity ͑high-͒ dielectrics addresses the problem of the large tunneling current by increasing the oxide thickness while at the same time allows preserving the oxide capacitance to the values required for standard operating conditions. 1 However, not all high-'s are useful to this purpose and the search for the most appropriate materials is still in progress.In particular, we have investigated the degradation dynamics of hafnium silicate nitride ͑Hf x Si 1−x ON͒ films, one of the best positioned candidates to replace SiO 2 as gate insulator.A number of experimental works have pointed out that HfSiON exhibits not only good electrical properties in terms of leakage current 2,3 and reliability 4 but also presents a high protection barrier against boron penetration. 5In addition, the inclusion of a thin interfacial layer of SiON between the high-and the Si substrate further improves the system's properties by providing better thermal stability and a lower density of interface states. 6hile the conduction characteristic in the fresh stack has been ascribed to tunneling, 7 there is no clear picture about the electron transport mechanism after the occurrence of a breakdown ͑BD͒ event.It has been reported that, for low applied biases, these structures exhibit the so called progressive BD ͑PBD͒ mode, 8 i.e., a gradual increase in localized leakage current over time.In this letter, we explore this behavior in detail and show that the evolution of the current can be interpreted within the framework of the physics of mesoscopic conductors.Because of the particular conductance levels reached at the earliest stages of degradation, we propose that the current mainly flows across the oxide layer through nanoconstrictions only a few atoms wide.In order to find key features governing the PBD phenomenon in thin gate dielectrics, we compare the BD trajectory in HfSiON with previously reported results for SiO 2 .
The devices used in this study are transistors ͑channel length= 0.8 m ϫ channel width= 10 m͒ with HfSiON / SiON gate dielectric and poly-Si gate.The substrate is p-type Si with acceptor doping N A =5ϫ 10 17 cm −3 .The Hf content was 23% and the dielectric was deposited by metal-organic chemical vapor deposition.The high-deposition was followed by a 1 min postdeposition annealing in NH at 800 °C and the poly-Si was activated at a 10 s 1000 °C spike.From capacitance-voltage measurements, an interfacial SiON thickness of 0.9 nm and a Hf silicate of 2 nm were extracted, with a nominal total equivalent oxide thickness of 1.6 nm.In all cases, the stress voltage was V G = 3.5 V. Figure 1͑a͒ illustrates the evolution of the post-BD current for three cases of particular interest.These curves were selected from a set of 50 I-t characteristics whose stationary levels are shown in the histogram of Fig. 1͑b͒.The values were taken at the end of the BD transients and before the detection of any sign of additional degradation caused by a͒ Author to whom correspondence should be addressed.Electronic mail: enrique.miranda@uab.es.b͒ Electronic mail: subguitar2002@yahoo.it.c͒ Electronic mail: montse.nafria@uab.es.d͒ Electronic mail: crupi@unical.it. the application of a long-term stress.In all cases, the timeto-BD is less than 35 s and the transient time not longer than 5 s.The distribution of the tunneling currents in the fresh samples ͓see Fig. 1͑b͔͒ arises as a consequence of oxide thickness variations.While the leftmost and rightmost curves in Fig. 1͑a͒exhibit a current jump followed by a gradual evolution toward steady-state current levels, the central curve reaches similar levels by means of a progressive trajectory.The fact that regardless of the type of evolution the plateaus coincide may be indicative of preferred atomic configurations within the BD path.Moreover, since the two transients in the central curve are almost identical, they may arise from similar microscopic arrangements.The peak corresponding to the uppermost final current level in Fig. 1͑b͒is a remarkably feature that supports this conjecture.We have defined three regions, A, B, and C, which will help us discuss the different stages that, in our view, take place during the formation of the BD path.In order to assess whether the aforementioned current saturation levels can be linked to the atomic scale of the constriction, we need first to isolate the current component that flows through the BD path, I BD .To this aim, we assume that our system can be represented by the equivalent electrical circuit depicted in Fig. 2, so that the post-BD conductance G BD reads where V OX is the potential drop across the insulator.The parameters A = 3.75ϫ 10 −8 A and B = 3.34 V −1 for the tunneling current flowing through the nondamaged device area I T and the series resistance R S = 1.66 K⍀ were extracted from the fresh I-V characteristic following the procedure described in Ref. 9. From Eq. ͑1͒we can separately evaluate I BD and I T , as shown in Fig. 2, for the two-level curve in Fig. 1͑a͒.It is worth pointing out that at the outset of the BD event, I BD does not coincide with I G but that the difference becomes less significant as the degradation proceeds.This means that the final current level in stage B is practically independent of the tunneling model considered.To get further insight into the degradation dynamics, we have plotted in Fig. 3 the evo-lution of G BD in units of 2e 2 / h = ͑12.9k⍀͒ −1 , i.e., the quantum conductance unit.Remarkably, the two transients level off at integer values of this quantity.This behavior closely resembles the formation of a quantum point contact ͑QPC͒ and can be explained as follows ͑see Fig. 4͒.First, phase A corresponds to the formation of a single atom constriction.In this case, the atoms located at the apices of the defects clusters determine the bottleneck of the leakage path.Notice that a symmetric arrangement is represented for the sake of simplicity.As the defect density increases or reaccommodates as a consequence of the electron wind force, the lateral confining potential widens and the first energy subband level in the propagation direction ͑solid line͒ drops below the energy window of the passing electrons.This is the transition from soft-BD to hard-BD ͑Ref.10͒ or, in terms of electron transport in QPCs, from tunneling to contact regime. 11,12Under this condition, there is no electron backscattering and the conductance reaches one quantum unit. 13In phase B, the creation of new defects leads to the progressive opening of a second bridge ͑dashed line͒ until it reaches phase C. To get an idea about the size of the defects in HfSiON, recall that the radius of conduction considered in percolation models is 0.45 nm. 4 FIG. 2. Evaluation of the current components that flow through the gate oxide stack using the equivalent circuit shown in the inset.I G is the measured gate current, I BD the current through the BD spot, and I T the tunneling current through the nondamaged area.V OX is the potential drop across the oxide layer and R S is a series resistance.Even though the systems investigated are different, Ohnioshi et al. reported clear evidences that there is a link between structure and conductance level. 14They found that a double strand of atoms attached to two electrodes has twice the quantum conductance unit if the interaction between the two individual rows is not strong.A similar correlation between atomic structure and conductance behavior has been established for nanowires 15 and the appearance of conductance steps has been ascribed to the overlap of molecular 16 or atomic 17 orbitals even in a one-atom contact geometry.It is not unlikely that analogous phenomena can occur in a system like the one investigated here if we regard that the conduction properties of the BD path are dominantly determined by the nature of a few atoms only.Intermediate conductance levels such as those observed in Fig. 1͑b͒ can be attributed to the formation of interacting BD paths or to stationary dissipative structures. 18It is worth emphasizing that conductance data spread is a common feature to a wide variety of mesoscopic systems with nonadiabatic constrictions 13 and that the proposed picture still holds even in the case of having uncorrelated BD spots.Finally, in Fig. 3, we have included for comparison a PBD curve measured for a 2-nm-thick SiO 2 film.The fact that the curve levels off at 2e 2 / h too, seems to indicate that the conduction properties of the BD paths are more related to their atomic scales rather than to the specific features of the surrounding material.Notice that in spite of the SiO 2 layer has been stressed at a higher bias, V G ͑SiO 2 ͒ = 3.75 V, the PBD curve exhibits a lower degradation rate dG BD / dt than that of the HfSiON sample.Perhaps the difference has to be looked for in the strength of the atomic bondings rather than on the series resistance effect, which are very similar R S ͑SiO 2 ͒ = 1.75 K⍀ and R S ͑HfSiON͒ = 1.66 K⍀, but this point needs to be further investigated.
The search for a reliable gate oxide material requires a deep understanding of the physics associated with the degradation mechanisms that leads to the loosening of its insulating capabilities.In this work, we have proposed a simple picture for the formation and evolution of nanoconstrictions in HfSiON layers subject to electrical stress following an analogy with the conduction problem in mesoscopic struc-tures.This connection suggests that the progressive degradation of gate oxides could be analyzed invoking the theoretical tools developed for low-dimensionality systems.
This work was partially supported by the Erasmus Exchange Programme and by Ministerio de Educación y Ciencia ͑Spain͒ under Project Nos.TEC2006-13731-C02-01 and TEC2004-00798.The authors wish to thank IMEC for sample provision.
FIG. 1. ͑a͒ Evolution of the leakage current under a constant voltage stress of 3.5 V in three different samples.A, B, and C identify the regions of interest discussed in the text.͑b͒ Histogram for the stationary current levels of 50 samples.

FIG. 3 .
FIG.3.Post-BD conductance as a function of time for the gate stack under investigation and for a 2-nm-thick SiO 2 film in units of 2e 2 / h.