1. Introduction

Silicon dioxide has served for more than three decades as the gate insulator responsible for blocking current in insulated gate field-effect transistor (IGFET) channels from the gate electrode in CMOS devices. The reason for the nearly exclusive use of silicon dioxide in this application is that silicon dioxide uniquely possesses the required combination of several properties: good mobility of holes and electrons flowing in silicon at the silicon dioxide interface, ability to keep electronic states (surface states) at this interface low, relatively low trapping rates of holes and electrons, and excellent compatibility with CMOS processing. Since the gate insulator also serves to couple the electric potential from the gate electrode to the channel of the IGFET, the best control of the channel by the gate is obtained when the gate insulator is made as thin as possible.

A lower bound for the useful gate insulator thickness is presented by the empirical observation that when a voltage is maintained on a large number of gates (which are initially excellent electrical insulators), after some time, some fraction of these gates begin to conduct current from the channel (or source or drain) of the FET as a result of gate-oxide breakdown. This onset of gate conduction can result in a failure of the circuit employing the failing FET. This behavior of oxide breakdown is usually treated statistically by using a Weibull distribution, given by

F(TBD) = 1 – exp   –  TBD ß  ,

(1)

where F is the cumulative failure probability and T_BD is the time-to-breakdown. The characteristic time, , is the time-to-breakdown at approximately the 63rd percentile, and ß is the Weibull shape factor, often called Weibull slope. Typical T_BD (or t_BD) distributions are given in Figure 1 for several oxide thicknesses. Because of the weakest-link character of oxide breakdown, the area scaling of T_BD is given by

TBD(A1) = TBD(A2)  A2 1/ß  , A1

(2)

where A₁ and A₂ correspond to two different areas of oxide films. Equations (1) and (2) apply equally well when charge-to-breakdown (Q_BD) is chosen as the breakdown variable (in place of T_BD).

Figure 1

CMOS processes in current production feature oxides as thin as 1.7 nm, and it is generally believed that this thickness must be further reduced to enable continued scaling improvements in density, performance, and power in very-large-scale integrated (VLSI) circuits; thus, understanding of the reliability of such thin oxides is critical.

Numerous researchers have projected over the last decade [1–5] that the properties of silicon dioxide gate dielectrics would present a limit to the scaling of CMOS technology at thicknesses ranging from at least 10 nm to, more recently, 2 nm. While these barriers have been circumvented, tunnel current limitations and newer dielectric reliability projections of the gate insulator continue to threaten an end to CMOS scaling unless a suitable replacement for silicon dioxide is soon developed. Physics-based models [3–5] have been extrapolated to project that the International Technology Roadmap for Semiconductors (ITRS) [6] will require either new materials by the 130-nm node or significant modification (of the roadmap) to the thicknesses of silicon-dioxide-based gate dielectrics or to the operating voltages of these technologies. Naturally, these predictions have stimulated vigorous research in this field, with attention directed, in particular, toward new, high-k gate dielectrics.

A different point of view on the question of extendibility of silicon-dioxide-based gate insulators for CMOS scaling beyond the 100-nm-technology node is presented in this paper. In particular, a very simple empirical model for the intrinsic reliability of dielectric is described and used to project maximum reliable operating voltages for SiO₂-based dielectrics with thicknesses of less than 1 nm. We find that the ITRS roadmap can be realized to at least the 50-nm node using silicon-dioxide-based gate dielectrics, provided that the issues surrounding gate-tunneling current can be satisfactorily resolved by some combination of process and design innovation.

While significant progress has been made because of the large research effort in the area of ultrathin oxide reliability [3–5, 7–35], crucial questions on this subject remain unresolved. For example, despite intensive research spanning more than three decades, no consensus has been reached about the exact oxide-breakdown mechanisms. Several physical breakdown models have been advanced [7–9], but all of these models present significant limitations in providing an adequate explanation of the breakdown data. Two approaches have commonly been employed: 1) theoretical models based on the assumption that some specific species, typically protons or holes, are directly involved in the breakdown process, and 2) models constructed using indirect methods, such as those based on physical interpretations of stress-induced leakage current (SILC) measurements. Quantitative agreement of these approaches with experimental data has not yet been demonstrated.

To construct an empirical picture of oxide breakdown, an experimental approach spanning a period of five years and many thousands of observations was adopted in order to collect breakdown data with great statistical accuracy. To cover the entire range of stress parameters, two methods were employed; one makes use of structures with differing areas, and the other, long-term stresses. Additionally, focus was placed on the self-consistency of this empirical model, ensuring that the experimental data stands on its own, without reliance on any underlying assumptions about the mechanisms involved. This approach enables the use of this extremely large database to test hypotheses regarding the underlying assumptions and predictions of various physical models and to provide an accurate extrapolation of gate-oxide reliability for sub-1-nm oxides for use in future CMOS technologies.

2. Experiment

A variety of capacitors and standard n-FETs and p-FETs were fabricated using standard IBM CMOS technologies with T_OX ranging from 1.2 to 5.0 nm. Constant-voltage stress (CVS) was used, with the initial breakdown event defining the time of oxide breakdown (irrespective of whether the event is a soft or hard breakdown). For thinner oxides, small-area structures were used in order to carefully avoid series resistance effects. Every reported T_BD (Q_BD) data point was obtained from a distribution with sample sizes between approximately forty samples and as many as hundreds of samples, depending on oxide thickness. This ensures the accuracy of the measurements [10, 11], so that the error bars associated with each reported data point are comparable to the size of symbols plotted in the figures. Throughout this work, whenever necessary, correction to the T_BD results for the effects of oxide thickness variation [11] was made using Q_BD and the average of initial tunneling currents, <J₀>, that is, T_BD = Q_BD/<J₀>. The strong area dependence of time-to-breakdown, due to shallow Weibull slopes for ultrathin oxides, was employed to expand the experimental time window by using capacitors with a wide range of areas [19, 20, 26]. This methodology avoids the potential pitfalls associated with interpreting experimental results collected using different stress parameters such as T_OX, voltages, and temperature.

3. Thickness dependence of Weibull slopes and time (charge)-to-breakdown

It was recently found that the Weibull slopes of T_BD distributions decrease with decreasing oxide thickness [12], as shown in Figure 1. This reduction in Weibull slopes can contribute to significant errors in area scaling and to extrapolation of the stress data to low failure percentiles [4, 13]. Percolation models [12, 13] and a simple analytical model [14] hypothesize that oxide breakdown is triggered by the formation of a conducting path between the cathode and anode. Such a conducting path forms when a critical defect density, N_BD, as originally proposed in [15], is reached as a result of defect generation during oxide stress. The reduction of Weibull slopes is attributed to a decrease of N_BD [12–14].

Highly accurate determination of Weibull slope directly from T_BD distributions requires thousands of samples [10]. To circumvent the enormous effort required to obtain such extreme sample sizes, the area-scaling relation of Equation (2) was employed [11]. The main advantage of this method is that it is much less sensitive to statistical uncertainty and thickness variations, with an achievable accuracy of 5% provided that a sufficiently large area ratio is used [11]. Figure 2 shows the measured Weibull slopes obtained via this method vs. T_OX ranging from 1.25 nm to 4.96 nm at a temperature of 140°C. The dashed curve represents the prediction of a percolation model [13], whereas the solid curve is a linear fit of a recently published analytical cell-based model [14]. General agreement among the experimental data and the two models, as seen in Figure 2, demonstrates the success of this simple geometrical model [12–14].

Figure 2

The decrease of N_BD with decreasing T_OX also predicts a reduction of Q_BD with decreasing T_OX, as previously reported [16]. Some typical results are compared with a cell-based model [14] in Figure 3. In order to compare our data with the analytical model [14], the independent variable was changed to 1/(T_OX + T_int). The parameter T_int is introduced in the model and interpreted as an interfacial layer thickness [14]. Good agreement of this model with the experimental data supports the general approach of the model [14]. The thickness scaling of T_BD is similar to that found for Q_BD, but in this case the thickness dependence of the tunnel current J(T_OX) must also be considered.

Figure 3

Recently it has been suggested that N_BD is dependent on voltage and temperature [17, 18]. We have conducted direct T_BD (Q_BD) measurements and found that Weibull slopes are independent of stress voltage, temperature, and polarity over a wide range of these variables [19, 20]. These results show that the simple geometric picture proposed in the percolation [12, 13] and analytical models [14] is consistent with the experimental statistics, using Q_BD (T_BD) as the breakdown variable. Moreover, it was recently shown that SILC-based measurements cannot be reliably used as a measure of the critical defect density, N_BD, because they fail to capture the correct thickness dependence of Q_BD Weibull slopes [20]. In addition, there is currently no detailed understanding of the microscopic mechanisms that cause breakdown defects. Thus, introduction of voltage or temperature dependencies into the geometrical picture of breakdown statistics must be made on an ad hoc basis.

4. Voltage dependence of oxide breakdown

Another key to accurate assessment of oxide reliability is the voltage-acceleration factor. Several important studies have been carried out [4, 5, 7–30] on this subject. Advances in the anode hole-injection model, the hydrogen model, and the thermochemical model have been made
[7–10, 21–24]. Very large voltage-acceleration factors have been reported [17, 26–28] for ultrathin oxides, and voltage dependence of the voltage-acceleration factor has recently been demonstrated [17, 26]. Historically, for thick oxides (>6 nm) stressed at high voltages in the nonballistic Fowler–Nordheim (FN) regime, oxide breakdown has been considered to be field-driven, because the electric field can affect the energy of electrons exiting from oxides [7]. For ultrathin oxides stressed or operated in ballistic FN-tunneling and direct-tunneling regimes, electron energy at the anode can directly affect the release of (secondary) species at the anode [7, 25]. Thus, electron energy, or gate voltage, was first proposed to be the controlling variable in the oxide-breakdown process [25]. However, more detailed work is required to further illuminate the role of carrier energy and oxide field in defect-generation rate and oxide breakdown. In the following discussion, gate voltage is considered to be an independent variable.

Figure 4(a) shows T_BD vs. gate voltage for several values of T_OX. Defining the (local) voltage-acceleration factor as (V) = –lnT_BD/V, to be consistent with the widely used exponential law, T_BD ~ exp(–V), the data in Figure 4(a) reveal that the voltage acceleration appears to increase for thinner oxides; however, a complication is presented by the fact that thinner oxides are stressed at lower voltages for practical reasons. In Figure 4(b), experimentally obtained T_BD values for
1.7-, 2.3-, and 2.9-nm oxides stressed at low voltages are compared to predictions of T_BD based on the exponential law, with each oxide thickness independently fitted with a constant acceleration factor. This comparison suggests that if the exponential law of voltage dependence were to remain true over the entire voltage range, including voltages as low as use conditions, the lifetime of thinner oxides would ultimately exceed that of thick oxides, as depicted in Figure 4(b). This is incompatible with the concept of the critical defect density decreasing with reduced T_OX and suggests that the apparent thickness dependence of voltage acceleration may be an artifact resulting from the necessity of collecting T_BD at lower voltages for thinner oxides.

Figure 4

To demonstrate the voltage dependence of the voltage acceleration factor, two independent experimental methods were employed: area scaling and long-term stress. Figure 5(a) shows T_BD data measured on four oxide areas for 2.67-nm oxide, on a semi-log plot. It is clear that a simple exponential fit to the data in Figure 5(a) gives nonparallel slopes (i.e., voltage-acceleration factors are different) when a wide range of voltages are used. Similarly, if the exponential law for each fit were to remain true over this range of voltage, the extrapolated lines would eventually cross over at low voltages. This in turn suggests that the lifetime of the smaller-area structures would be shorter than that of the larger-area structures, and provides yet another unphysical result, contradicting the weakest-link nature of oxide breakdown. On the basis of these results, it is readily concluded that the exponential law for T_BD (Q_BD) voltage dependence cannot hold over a wide range of voltage. In particular, one should expect that the voltage-acceleration factor must increase with decreasing voltage.

Figure 5

As an independent test of this T_BD voltage dependence, T_BD measurements at lower voltages were conducted for much longer stress times, over one-half year for 1.7-nm oxides, as shown in Figure 5(b), and down to stress voltages of ~2 V. The T_BD data (filled circles) for large-area capacitors in Figure 5(b) were normalized using Equation (2) with the ß value taken from Figure 2. A fit was made to only the higher-voltage data, typically acquired from wafer-level stress, and then the fitted curve was extrapolated to low voltages. It is clear that the low-voltage T_BD data deviate from the extrapolation made from the high-voltage data. Moreover, in Figure 5(b), a high-voltage-only fit gives a voltage acceleration, _H = 15.2, while the low-voltage-only fit yields _L = 18.6. The error bars for voltage-acceleration factors are ±0.6. The values measured at high and low voltages are statistically different. These results provide direct experimental evidence of a change of voltage-acceleration factors with voltage. Not only do the experimental results of these two independent methods support the claim that voltage-acceleration factors are voltage-dependent, but such a dependence is also consistent with the concept of electron energy or gate voltage [25] as the primary breakdown variable, as was previously demonstrated using independent (polysilicon) gate-electrode-depletion experiments [29, 30]. Figure 6 displays the voltage-acceleration factor as a function of voltage across several CMOS technologies for a wide range of oxide thickness from 1.2 nm to 5.0 nm. These voltage-acceleration factors are derived from semi-log plots such as those of Figure 5(a). Because the corresponding voltages along the horizontal axis are the average values of the voltages, these voltage-acceleration factors are only approximations of the true differential voltage-acceleration factors. The extensive volume of experimental data shown in Figure 6 demonstrates the universality and predictive capability of the power-law relation for voltage acceleration [26].

Figure 6

5. Defect-generation rate

It is widely accepted that the oxide-breakdown process related to the generation of defects as a result of stress proceeds in two steps:

1. A statistical breakdown process associated with the critical defect density, i.e., the triggering of breakdown by the density of generated defects at breakdown.
2.
2. A deterministic breakdown process associated with a defect-generation rate, i.e., the evolution of the average density of defects with time or injected charge as a function of stress conditions such as voltage and temperature
[12–14].

QBD(TOX, AOX, V, T) =  NBD(TOX, AOX)  , (V, T)

(3)

where N_BD is the critical defect density at breakdown, reflecting the statistical nature of oxide breakdown, as discussed above. This first process appears to be well understood, based on the success of percolation and analytical models in explaining the thickness and area dependences of breakdown statistics such as Weibull slopes, as discussed in the previous section. The term (V, T) describes the defect-generation rate at a given stress condition. Unfortunately, the physical nature of the second process associated with (V, T) is still under investigation and is being debated.

Considering the preceding experimental evidence of voltage-independent and temperature-independent Weibull slopes [19, 20], and in the absence of microscopic information on possible voltage and temperature dependence of N_BD, the defect-generation rate is presumed to be dependent exclusively on voltage and temperature. With this approach, and using Equation (1), the Q_BD voltage dependence can be used to measure the defect-generation rate, (V). Figure 7 shows the measured Q_BD and T_BD data vs. gate voltage using different-area capacitors. The defect-generation rate, as measured by Q_BD(V), follows an exp(B/V) dependence, indicating a much-reduced defect-generation rate with reduced voltage. It can be shown analytically, by considering Q_BD T_BDJ₀, where J₀ is the tunneling current, that the power-law T_BD voltage dependence is self-consistent with the exp(B/V) voltage dependence for Q_BD. This connection gives rise to the large value of the exponent (~40) found in the power-law relation [26]. Note that the parameter B can be voltage-dependent [10, 26].

Figure 7

6. Temperature dependence of oxide breakdown

Several experimental observations regarding both temperature and voltage dependence of ultrathin-oxide breakdown have been made. First, a very strong T_BD/Q_BD temperature dependence has been found for thin oxides as compared to thick oxides [18, 31–34]. This stronger temperature dependence for thinner oxides was first interpreted as a thickness effect in [18] and supported by other reports [31–34]. Second, a non-Arrhenius temperature dependence of oxide breakdown has also been reported for ultrathin oxides [18, 31–34]. Third, it has also been reported that the voltage-acceleration factor remains unchanged over a range of temperatures
(30°C to 200°C) but within a fixed T_BD or Q_BD window [33–35]. These results may seem confusing or even contradictory. Recently, these observations were experimentally resolved in the context of voltage-dependent voltage acceleration together with a unified, coherent global picture which is discussed below [19].

Normalized T_BD is plotted as a function of voltage for different temperatures in Figure 8. T_BD data from different-area capacitors were normalized to equivalent areas using the Weibull slopes from Figure 2. The data from different oxide thicknesses were then further normalized to isolate the uniquely voltage-dependent behavior, using a thickness-scaling law [14]. This analysis reveals some very important findings:

1. At a fixed temperature, the voltage-acceleration factor increases with decreasing voltage, as discussed in the previous section.
2. At lower temperatures, T_BD increases at a faster rate with decreasing voltage than it does at higher temperatures.
3. About a fixed voltage, the voltage-acceleration factor is larger at lower temperature than at higher temperature, while about a fixed T_BD, the voltage-acceleration factor remains unchanged with temperature.
4. At lower voltages, a more pronounced temperature dependence is observed than at higher voltages.

The results in Figure 8 also suggest that the strong Q_BD (T_BD) temperature dependence found in ultrathin oxides is not due to the small value of T_OX, as previously hypothesized [18, 31–34], but rather due to the low stress voltage. This has recently been verified by performing stresses at different voltages with T_OX fixed, using capacitors of various areas to provide the needed range of data [19]. These results demonstrate that additional reliability margin can be realized by accurately taking into account the effects of temperature when making reliability projections. In particular, the increase in T_BD and in the voltage-acceleration factor at low voltage provides significant relief in reliability projections, enabling the use of thinner oxides than conventionally projected.

Figure 8

7. Oxide breakdown vs. device circuit failure

Oxide failure is marked by a sudden jump in leakage current across the oxide film as a result of stress. For ultrathin oxides (<6.0 nm), the post-breakdown current can vary by many orders of magnitude depending on stress conditions, oxide thickness, and the external circuit environment. Breakdown is typically classified as being either “hard” or “soft” depending on whether the post-breakdown conduction is respectively at the high end or the low end of the observed distribution. Currently, there is considerable activity and debate concerning the proper interpretation of so-called soft- and hard-breakdown phenomena observed in ultrathin oxides.

Substantial progress has been made toward understanding of soft- and hard-breakdown modes and their implications for device operation and circuit function [36–49], although a universally accepted methodology has not yet emerged. Naturally, several researchers have raised the question of exactly what the best criteria are for categorizing a change in oxide electrical conduction as a breakdown event [42–49]. Several detailed studies of the effects of oxide breakdown on device failure show that oxide breakdown in the drain or source region is more detrimental to device operation than oxide breakdown in the channel region [43, 44]. On the other hand, it is found that the severity of oxide breakdown, defined as the ratio of the prevalence of soft breakdown to hard breakdown, is voltage-dependent, with soft-breakdown events becoming relatively more probable as the voltage is reduced [42, 45–49].

The voltage dependence of the fail mode (e.g., soft vs. hard) is now relatively well understood [39, 42, 46–48]. When the power dissipation through the percolation path exceeds a threshold, a hard-breakdown event is reached [45–48]. Subsequent study reveals that hard breakdown can occur only when the total amount of energy exceeds some energy threshold [47]. The experimental data on soft and hard breakdown compare satisfactorily with predictions based on such an energy model [46, 47], and a new methodology which takes this effect into account has been proposed [47]. In a circuit environment, transistors typically operate in a current-limited mode [48], that is, there are electrical elements in series with a gate-discharge path which will limit the maximum current in the event of a gate-oxide failure. The value of the current to which a breakdown is limited (by the circuit) significantly affects the post-breakdown leakage currents [48], and this in turn leads to a reduction of the oxide-failure hazard. This was experimentally demonstrated in the case of the ring oscillator circuit [49], where functionality was maintained even after a hard-breakdown event. Thus, these studies suggest that in a realistic circuit environment, the circuit functionality may be much more resilient with respect to oxide breakdown than was previously assumed in assessing the oxide reliability of integrated circuits.

Even if the occurrence of oxide breakdown does not destroy device operation, however, it is premature to claim that devices will remain completely functional. Erratic behavior of devices and a progressive degradation after (initial) oxide breakdown have been reported [11]. Significantly more research effort is required in order to understand the voltage and temperature dependence of the post-breakdown events, the eventual device breakdown, and the statistical distribution of device breakdown events. A complete methodology is needed to provide a predictive model for the ultimate impact on circuit operation, including the appropriate criteria for circuit failure as a result of oxide breakdown. Once a complete methodology is developed, it is anticipated that additional reliability margin will be realized for ultrathin oxides.

8. Reliability outlook

On the basis of our experimental investigation, a global view of time-to-breakdown for ultrathin oxides is now detailed. While the fundamental physical mechanisms behind the observed reduction in defect generation with decreasing voltages remain unknown, all of the experimental data presented in this paper are accurately captured by two simple empirical principles:

V TBD  = const = n(T) TBD V

(4)

and

d    1 TBD TBD  = 0, dT TBD V

(5)

where V and T respectively represent the stress voltage and temperature. Equation (4) describes a power-law dependence of T_BD on voltage and accurately captures the entirety of the experimental data presented in this work, without qualification. Equation (5) describes the (local) voltage acceleration at a fixed value of T_BD, irrespective of temperature or T_OX; i.e., regardless of the combination of the variables used to arrive at a given T_BD, (V) will have the same value! A complete picture for time-to-breakdown, in both the voltage and temperature domains, can be developed on the basis of these two simple principles, with the addition of a third relationship that describes T_BD temperature dependence for a given voltage:

TBD = TBD0(V) exp  a(V)  +  b(V)  , T T2

(6)

where the pre-factor, T_BD0, and the coefficients, a and b, are voltage-dependent. The second-order term, b/T², empirically inserts non-Arrhenius temperature effects. These empirical principles can now be readily used to make reliability projections for ultrathin gate oxides. Figure 9 shows a three-dimensional plot for T_BD vs. voltage and temperature constructed from these principles, using the experimental data presented in this work to determine the required constants.

Figure 9

Figure 10 displays the maximum allowable supply (gate) voltage as a function of oxide thickness. This reliability projection is based on a reliability requirement of 100-ppm failure rate and 0.1 cm² of gate area [4]. The dashed curves for sub-1.0-nm oxides are extended from the projected maximum voltages for oxide thickness 1.0 nm assuming the same thickness scaling law and the same T_BD voltage dependence as discussed below. It is evident from Figure 10 that gate-oxide reliability will not inhibit realization of the ITRS roadmap. Thus, the tunneling current, as a circuit and product design issue only, remains the limiting factor for scaling gate-oxide thickness until an alternative gate dielectric becomes available.

Figure 10

To assess the limitations of our reliability projections, in Figure 11 we plot normalized lifetime as a function of voltage for experimental results down to 1.8 V as well as reliability projections from ~2 V to ~1 V. Above ~2 V, the universal curve spanning ~20 orders of magnitude in T_BD is obtained by applying the area-scaling and thickness-scaling relationships [14] to the experimental data, as discussed in Section 3. Below ~2 V, several possible scenarios may occur, as indicated by the dashed curve and the shaded area. The dashed curve illustrates the consequences of the (ad hoc) assumption that the voltage-acceleration factor remains constant below 2 V. The shaded area represents many possible reliability projections for new (currently unknown) mechanisms. On the basis of SILC measurements, an increase in defect-generation rate described by a sigmoidal behavior has been reported [17]. However, the SILC-based measurements appear to deviate from experimental T_BD (Q_BD) when a quantitative comparison is made [4, 17]. Therefore, this possibility appears to be at odds with experimental observations. Arrows are used to indicate the potential for improvement in reliability projections should a complete methodology for soft breakdown of devices and for circuit failure criteria be realized.

Figure 11

9. Conclusions

We have conducted a systematic and extensive investigation of ultrathin-oxide breakdown based on a highly accurate experimental methodology. The thickness dependence of Q_BD/T_BD and Weibull slopes has been studied in the context of a decrease in the critical defect density with decreasing oxide thickness. Weibull slopes are found to be independent of voltage and temperature, supporting the geometrical picture proposed by percolation- and cell-based models. Direct evidence of voltage-dependent voltage acceleration has been established using two experimental, independent methods. This voltage-dependent voltage acceleration, ascribed to a power-law behavior of T_BD with voltage, was found to be universal across a wide range of oxide thickness, temperature, and voltage. Q_BD/T_BD temperature dependence and constant Weibull slope are found to be consistent with voltage-dependent voltage acceleration; thus, a global and coherent picture emerges. This large-volume experimental database, together with an accurate experimental methodology, enables timely reliability projections for advanced CMOS technologies. Provided that no new mechanisms arise for oxides thinner than 1.2 nm, it is concluded that silicon-dioxide-based gate dielectric can be reliably extended beyond the 100-nm node for CMOS technologies.

Acknowledgments

We are grateful to J. Aitken and our management for their constant support throughout this work over many years. It is our great pleasure and honor to acknowledge the stimulating and insightful discussion with Prof. J. Suñé on many aspects of oxide-breakdown phenomena. We are honored to acknowledge the technical advice and stimulating discussions of R. Vollertsen over many years of working in this field. We sincerely thank J. McKenna, R. Dufresne, C. Montrose, D. Brochu, and B. Morse for their constant technical support during this work.

References

Received October 15, 2001; accepted for publication January 18, 2002