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Breakdown and anti-breakdown events in high-field stressed ultrathin gate oxides
Solid-State Electronics 45 (2001) 1327±1332
Breakdown and anti-breakdown events in high-®eld stressed ultrathin gate oxides E. Miranda a, J. Su~ ne b,*, R. Rodrõguez b, M. Nafrõa b, X. Aymerich b a
Departamento de Fõsica, Facultad de Ingenierõa, Universidad de Buenos Aires, Paseo Col on 850, CP 1063 Buenos Aires, Argentina b Departament dÕEnginyeria Electr onica, Universitat Aut onoma de Barcelona, 08193 Bellaterra, Spain Received 20 March 2000
Abstract As a high-®eld voltage sweep proceeds, the post-breakdown I±V characteristic of an ultrathin gate oxide shows abrupt upward and downward steps which are a clear manifestation of the local area character of the associated conduction mechanism. Moreover, the leakage current through the breakdown spots exhibits conductance values very similar to those found in quantum point contacts, indicating that the conductive paths connecting both electrodes have atomic-scale dimensions. In this work, we propose that some of these jumps in the I±V characteristic might be caused by a local rearrangement of atoms or defects due to the high current density forced to ¯ow through the breakdown path. This is a well-known eect in point contacts where the so-called electron wind force encourages the atomic motion. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: MOS electron devices; Oxide reliability; Dielectric breakdown; Silicon dioxide
1. Introduction In spite of the important advances achieved in the last few years, the physical understanding of the breakdown phenomenon of the SiO2 dielectric layer in a MOS device is quite far from being complete. As evidenced by the huge number of publications concerning ultrathin oxides, the subject has almost been entirely focused from the reliability viewpoint, disregarding the study of the physics of such dramatic event. In addition, as a consequence of the use of ever thinner oxides, it has become necessary to consider new features in the analysis of the phenomenon such as the ballistic nature of the electron transport [1] and the eects of the stress-induced leakage current [2], which make the dierence respect to thicker oxides. The issue of what kind of structure develops across the insulator at the moment of the breakdown
* Corresponding author. Tel.: +34-93-581-3217; fax: +34-93581-1350. E-mail addresses: [email protected] (J. Su~ ne), emirand@ tron.®.uba.ar (E. Miranda).
event and how the conduction problem should be faced are still open questions. Nevertheless, there is a wide agreement in considering that the breakdown path connecting the electrodes is highly localized as well as that its origin is somehow related to the defects generated during the application of a previous wear-out condition [3±6]. Here, after a brief review of selected topics related to the ®eld, we further explore the physics of the SiO2 breakdown phenomenon, with special emphasis on the switching behavior exhibited by the I±V characteristic. The subject is not new and current ¯uctuations in the post-breakdown regime have been reported before (see Ref. [3] and references therein). In this regard, due to the few sites which are believed to participate in the conduction process through an ultrathin oxide (the average radius of the defects has been estimated to be around 0.45 nm [7]) a high sensitivity of the current due to local rearrangements (spatial or energetic) in the atomic con®guration of the breakdown path is expectable. We suggest that these eects are visible in the I±V characteristics, as it occurs in metal nanobridges [8,9] where changes in resistance can be induced under a high bias stress.
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2. The physics of post-breakdown According to the severity of the event, recognized by the associated leakage current level, the oxide breakdown is usually classi®ed as soft (SBD) or hard (HBD). Both breakdown modes can be obtained by applying a constant voltage or current stress, and even by ramped voltage or current measurements [10,11]. In addition, more than one SBD and HBD spots can be induced on the same sample by a proper choice of the stressing condition. Although several models have been proposed to account for the post-breakdown I±V characteristic, almost all of them (we only know of one exception) are aimed exclusively to explain the SBD mode. Mechanisms such as direct tunneling through a local thinned down oxide spot [12,13], trap assisted tunneling [14], variable range hopping [15,16], percolation in non-linear conduction networks [17], inelastic quantum tunneling [18] and Fowler±Nordheim (FN) conduction [19] have been invoked. On the other hand, Ting's model [20], based on the conduction properties of a matrix of threedimensional cylindrical structures embedded in a fresh oxide, in which resonant tunneling takes place, accounts for both SBD and HBD at once in a consistent way. The author considered the funneling of the electron wave functions into quantum wires connecting partially (SBD) or totally (HBD) the opposite electrodes. However, it is worth mentioning that to reach the actual experimental current levels, a damaged area of about 10% of the total structure area is ®nally required. Concerning the functional dependence of the posthard breakdown current on the applied bias, the literature on the subject is surprisingly scarce. Indeed, few works have paid attention to the issue and this is perhaps motivated by the fact that the broken down oxide merely presents a resistor-like behavior for voltages higher than about 1 V. In Ref. [3], the authors suggested that the I±V characteristic presented a diode-like dependence for very low applied voltages, proposing that the oxide becomes transparent to the electron transport at these voltages. Other features observed at higher voltages were ascribed to spreading resistance eects. This transport mechanism was also invoked by Umeda and Taniguchi [21]. In a recent paper [22], we presented an alternative explanation for the conduction mechanism in broken down oxides. It was based on the conceptual framework of the physics of mesoscopic devices and the point contact conduction theory [23]. The breakdown path across the oxide was treated as a three-dimensional constriction in which a subband structure arises as a consequence of the lateral con®nement of the electron wave functions. The model assumes abrupt potential drops at the two ends of the constriction and spot areas in the nanometer range. This initial approach has been subsequently extended to account for the SBD conduc-
tion mechanism by including the transmission properties of narrow constrictions [10,24]. It is worth recalling that ®rst point contact experiments were performed on metal±insulator±metal structures by inducing electrical breakdowns of the insulator layer in such a way that the two metal electrodes became connected by a metallic short circuit [25]. In the case of the breakdown of ultrathin MOS structures, however, we are convinced that such destructive thermal eects do not occur, at least in the cases of more basic and applied interest. However, the issue of whether HBD is essentially linked to an irrecoverable thermal damage is still a matter of debate. Even though the local melting of the oxide at the very moment of the breakdown event is a well established fact for thick oxides, these eects seem likely to be at least less important in the ultrathin oxide thickness range. First works in this area, such as those due to Klein [26], Solomon [27] and Shatzkes et al. [28], involved SiO2 ®lms with thickness in the order of several hundred of nanometers. These thick ®lms showed important thermal eects at the breakdown which in some cases were clearly visible in TEM and SEM photos. This is consistent with subsequent observations such as those due to Sugino et al. [29], who presented experimental results showing that the intrinsic breakdown spot is a melting composed of crystallized silicon. More recently, Lombardo et al. [30] have reported new interesting results about thermal and propagation eects occurring during the hard breakdown of much thinner oxides. These authors have shown, by means of TEM analysis, that the breakdown spot can laterally propagate on the MOS surface along a quasi-1D line, thus giving rise to complex structures composed of many breakdown spots. Moreover, they found that a 35 nm oxide showed spots with coarse crystal grains epitaxially aligned to the silicon substrate. In contrast, these eects could not be detected in oxides of 9.3 and 5.6 nm thick, stressing the fact that the breakdown of a thin oxide is a process of a very dierent nature. In any case, the occurrence of thermal eects strongly depends on the features of the MOS structure (area, thickness, etc.) and on the characteristics of the measurement setup (series impedance, stress current or voltage, etc.). Both determine the dynamics of power dissipation at the very moment of the breakdown [31,32] and the level of destructive damage of the breakdown path. In particular, it has been demonstrated that if thermal eects are limited by the sample itself and/or by the measurement setup, the HBD events can eventually be switched o [33,34] In these cases, irreversible thermal damage is clearly absent. Actually, we think that (although the origin of the breakdown is always the same [35]) there is experimental evidence to distinguish at least three dierent situations which correspond to three dierent states of the breakdown spot (we will refer to these as breakdown modes): SBD, HBD, and thermal HBD. In all the cases, the post-
E. Miranda et al. / Solid-State Electronics 45 (2001) 1327±1332
breakdown characteristic will not strongly depend on the oxide thickness (at least for oxides under 15 nm) nor on the oxide area, but the relative probability of occurrence of these breakdown modes certainly depends on the features of the oxide and on the stress conditions (no SBD is found in oxides thicker than 5 nm under FN stress, for example). Since the post-breakdown I±V does not strongly depend on oxide thickness or area, we can also identify the breakdown modes by the magnitude of post-breakdown current level (values are given at 5 V): a current of the order of 10 7 ±10 6 A is measured after SBD, a current of the order of 10 3 A is measured after HBD (this is also the current level measured after HBD induced by substrate hot electron injection [21,36]) and a much higher current of the order of 10 mA to 1 A are measured after the occurrence of thermal or propagation eects [30]. In this work, we deal with some eects which appear after the (non-thermal) HBD: conductance quantization and on-o switching ¯uctuations. 3. Experimental results 3.1. The samples and the experimental setup The devices used in this study are conventional n polysilicon-gate MOS capacitors fabricated on N-type (1 0 0) Si substrates N 1015 cm 3 with tox 3:0, 3.8 and 4.9 nm. The area of the capacitors is 6:5 10 5 cm2 and the gate was always positively biased (electron injection from substrate to gate). Further details concerning these devices can be found elsewhere [11]. The measurements were all performed at dark and at room temperature with a semiconductor parameter analyzer HP4145B. In order to stop the measurements after the occurrence of a switching event, we made use of the long integration time option of the HP4145B. This analysis mode is associated with a very low voltage sweep rate.
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Fig. 1. I±V characteristics associated with the SBD and HBD conduction modes. Each HBD I±V characteristic was measured after the detection of a breakdown event induced by a high-®eld voltage sweep.
down of an ultrathin oxide is a multiple event process, where the current steps are associated with the creation of new HBD spots (this is also supported by optical experiments [37]). It is also worth noting that, independently of the gate bias, all the current jumps are of the same order of magnitude. This means that the damage caused to the gate oxide is always very similar and therefore that each HBD spot contributes approximately with the same amount of current. To realize what is actually happening, Fig. 3 shows the I±V characteristic of a fresh sample, the I±V characteristic measured on the same sample after the occurrence of the ®rst HBD event, and their dierence. As noted, the latter curve exhibits a breakpoint where it deviates downwards. This is due to the shift of the background FN I±V characteristics
3.2. Breakdown events Fig. 1 compares the dierent breakdown modes of an ultrathin gate oxide. Notice that for this particular combination of oxide thickness and gate area, the occurrence of a SBD event is very dicult to detect. The reason is simple: from moderate to high bias, the SBD current component is comparable to the direct or FN tunneling component which ¯ows in parallel through the non-damaged oxide area. On the contrary, the HBD leakage current is well distinguishable and it completely masks the other current components in the whole bias range. However, at high voltages, it is still possible to detect the background FN tunneling current. Fig. 1 shows several HBD I±V characteristics, each one being obtained after the detection of a current jump like those shown in Fig. 2. This ®gure indicates that the break-
Fig. 2. Multiple breakdown events during a high-®eld voltage sweep. Each current jump is associated with the appearance of a breakdown spot.
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Fig. 4. Current and conductance vs. voltage characteristics for ®rst and second breakdown events.
Fig. 3. The solid line shows the FN I±V characteristic of a fresh sample. The squares indicate the HBD I±V characteristic measured after the detection of the ®rst breakdown event. The dashed line corresponds to the dierence between these curves.
towards higher voltages caused by the additional voltage drop in the semiconductor series resistance due to the current which ¯ows through the new breakdown spot. This happens each time a HBD event is triggered and it is in agreement with the equivalent circuit for the postbreakdown conduction proposed in Ref. [3]. To stress this fact, Fig. 4 shows that a second HBD path shifts the background FN current even farther away. The dierential conductance G dI=dV of these curves is also depicted in the same ®gure. The plot reveals three voltage regions: (i) Below 1.5±2 V there is a gradual conductance increase due to the potential drops in the silicon electrodes. (ii) Then, the G±V characteristics enters in the point contact conduction regime. The traces exhibit plateaus of the order of the quantum conductance unit 2e2 /h, e and h being the electron charge and the Planck's constant respectively. This a well-known feature of atomic-size constrictions and even of onedimensional chains of atoms [38]. (iii) Finally, as explained above, the steep increase in the G±V curves corresponds to the appearance of the background FN tunneling current.
3.3. Anti-breakdown events The fact that not all the post-breakdown characteristics exhibit the same behavior shown in Fig. 2 is clearly illustrated by Fig. 5. The ®gure shows the existence of
Fig. 5. Switching behavior of the HBD I±V characteristic during a high-®eld voltage sweep.
backwards current steps of the same order of magnitude of the HBD events, which are identi®ed as anti-breakdown (aHBD) events. These type of events were also reported during constant voltage stresses of samples that had suered one or several HBD events [3,34], and similar on/o ¯uctuations have also been observed in the post-SBD I±V characteristics [11,39]. To further analyze these switching events, let us consider Fig. 6, which shows two successive voltage sweeps applied to the same sample. The ®rst current step in the solid trace corresponds to the transition from FN to HBD. At a certain bias point, the current suddenly drops and it remains in this low state (unless the stress is continued and a second HBD event is triggered). If the measurement is stopped immediately after the detection of the aHBD event, so as to avoid the triggering of a new HBD event, a second voltage sweep (dotted line in Fig. 6) reveals that the current level corresponds to that observed after the occurrence of the aHBD event. That is, we still have a single HBD spot which has somehow changed its conducting properties. Fig. 7 shows that the non-linear
E. Miranda et al. / Solid-State Electronics 45 (2001) 1327±1332
Fig. 6. Two consecutive voltage sweeps applied to the same sample. FN refers to Fowler±Nordheim injection.
Fig. 7. Two consecutive voltage sweeps applied to the same sample.
current increment which usually appears prior to an aHBD event is totally reproducible if the voltage sweep is stopped before the occurrence of the aHBD event (solid line). Additionally, Fig. 7 shows that the current ¯owing through the structure after the detection of the second HBD event cannot be regarded as the extrapolation of the I±V characteristic prior to the occurrence of the aHBD event.
4. Discussion We suggest that the switching behavior in the HBD I±V characteristics re¯ects changes in the atomic topology of the leakage spots. This might explain why the magnitude of the current jumps is very similar both for the HBD and aHBD events. In fact, their origin is essentially the same, namely a modi®cation of the elec-
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Fig. 8. Constant current stress of a P-type substrate sample showing and anti-breakdown event. In this case the gate was negatively biased.
trical connections which link the conducting sites. The reversibility of the breakdown events indicates that irrecoverable thermal eects are not very likely to occur in ultrathin oxides. In this regard, Fig. 8 shows the appearance and disappearance of a breakdown spot during a constant current stress. Note that the recovery after the ®rst sudden jump in the gate voltage is gradual, lasting a few seconds. Moreover, recent results of molecular-dynamics simulation [40], have shown that the main eect of increased temperature is the enhanced thermal motion of the atoms that promotes the relaxation into stable con®gurations. Actually, pure thermal instabilities due to Joule heating are unlikely unless the temperature reaches values close to the melting point. We suggest that electromigration eects at the atomic scale can be responsible for the atomic changes of the breakdown path. It is worth pointing out that the rearrangement of defects encouraged by the direct force of the electric ®eld or by the so-called electron wind force has been previously proposed to explain changes induced by high bias in gold quantum point contacts [9]. While the direct force is expected to be negligible in a one-dimensional path [8], we can show that the electron wind force is a reasonable hypothesis. If we consider that the current ¯owing through a HBD spot is of the order of 1 mA, and that the spot area is of the order of 10 14 ± 10 12 cm2 [3], the current density is of the order of 109 ± 1011 A/cm2 . This is an extremely high density, but this is the order of magnitude found in point contacts. The wind force can be estimated from [9]: ~ p=e FW 2I~
1
where ~ p is the momentum of the electrons, I is the current, and e is the electron charge. For the measured current of 1 mA and the momentum corresponding to
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an energy of 0.1 eV (a reasonable value for an electron in a silicon accumulation layer), the electron wind force is estimated to be of about 2 nN. To give a more intuitive idea, we can calculate the electric ®eld required to applying a force of 2 nN to a particle with the charge of one electron. This results in an equivalent electric ®eld of approximately 125 MV/cm, which is clearly able to modify the breakdown path, moving atoms and breaking bonds. Thus, current-induced atomic motion (i.e. atomic-scale electromigration) is a reasonable picture to explain the HBD ¯uctuations. 5. Conclusion We have analyzed the switching behavior exhibited by the post-breakdown I±V characteristic of ultrathin oxides. The measured conductance values con®rm the atomic scale of these leakage paths. It was also shown that a high-®eld voltage sweep can induce changes within the breakdown paths which are detected as ¯uctuations in the I±V characteristics. Mesoscopic electromigration eects have been suggested to explain the atomic-scale modi®cation of the breakdown paths.
Acknowledgements DGES is acknowledge for supporting this work under project no. PB96-1162. The authors are grateful to F. Campabadal and L. Fonseca of the Centro Nacional de Microelectr onica-Barcelona for sample fabrication. References [1] DiMaria D. Solid-State Electron 1997;41:957. [2] Ricc o B, Gozzi G, Lanzoni M. IEEE Trans Electron Dev 1998;45:1554. [3] Nafrõa M, Su~ ne J, Aymerich X. J Appl Phys 1993;73:205. [4] Su~ ne J, Placencia I, Barniol N, Farres E, Martõn F, Aymerich X. Thin Solid Films 1990;185:347. [5] Dumin D, Maddux J, Scott R, Subramoniam R. IEEE Trans Electron Dev 1994;41:1570. [6] Stathis J. J Appl Phys 1999;86:5757. [7] Degraeve R, Groeseneken G, De Wolf I, Maes H. Microelectron Engng 1995;28:313. [8] Ralls K, Ralph D, Buhrman R. Phys Rev B 1989;40:11561. [9] Yasuda H, Sakai A. Phys Rev B 1997;56:1069.
[10] Miranda E, Su~ ne J, Rodrõguez R, Nafrõa M, Aymerich X. Microelectron Engng 1999;48:171. [11] Miranda E, Su~ ne J, Rodrõguez R, Nafrõa M, Aymerich X, Fonseca L, Campabadal F. IEEE Trans Electron Dev 2000;47:82. [12] Lee S, Cho B, Kim J, Choi S. Proc IEDM 1994;605. [13] Yoshida T, Miyazaki S, Hirose M. Proc SSDM 1996; 539. [14] Depas M, Nigam T, Heyns M. IEEE Electron Dev 1996;43:1499. [15] Okada K, Taniguchi K. Appl Phys Lett 1997;70:351. [16] Okada K. Proc SSDM 1997;92. [17] Houssa M, Nigam T, Mertens P, Heyns M. J Appl Phys 1998;84:4351. [18] Nigam T. PhD thesis, Katholieke Universiteit Leuven 1999. p. 64. [19] Tomita T, Utsunomiya H, Sakura T, Kamakura Y, Taniguchi K. IEEE Trans Electron Dev 1999;46:159. [20] Ting D. Appl Phys Lett 1999;74:585. [21] Umeda K, Taniguchi K. J Appl Phys 1997;82:297. [22] Su~ ne J, Miranda E, Nafrõa M, Aymerich X. Appl Phys Lett 1999;75:959. [23] Datta S. Electronic transport in mesoscopic systems. Cambridge: Cambridge University Press; 1997. [24] Miranda E, Su~ ne J, Rodrõguez R, Nafrõa M, Aymerich X. Proc Mat Res Soc 1999, in press. [25] Yanson A. Sov Phys JETP 1974;39:506. [26] Klein N. IEEE Trans Electron Dev 1966;13:281. [27] Solomon P. J Vac Sci Technol 1977;14:1122. [28] Shatzkes M, Av-Ron M, Anderson R. J Appl Phys 1974;45:2065. [29] Sugino R, Nakanishi T, Takasaki K, Ito T. Proc SSDM 1995;920. [30] Lombardo S, La Magna A, Spinella C, Gerardi C, Crupi F. J Appl Phys 1999;86:6382. [31] Toriumi A, Satake H. Proc Mat Res Soc 1999, in press. [32] Nigam T, Degraeve R, Groeseneken G, Heyns M, Maes H. Proc Mat Res Soc 1999, in press. [33] Jackson J, Robinson T, Oralkan O, Dumin D, Brown G. Appl Phys Lett 1997;71:3682. [34] Su~ ne J, Farres E, Placencia I, Barniol N, Martõn F, Aymerich X. Appl Phys Lett 1989;55:128. [35] Su~ ne J, Mura G, Miranda E. IEEE Electron Dev Lett 2000, in press. [36] Lombardo S, La Magna A, Gerardi C, Alessandri M, Crupi F. Appl Phys Lett 1999;75:1161. [37] Degraeve R. Tutorial ESREF. 1998;28. [38] Mozos J, Wan C, Taraschi G, Wang J, Guo G. Phys Rev B 1997;56:R4351. [39] Miranda E, Su~ ne J, Rodrõguez R, Nafrõa M, Aymerich X. Appl Phys Lett 1998;73:490. [40] Bratkovsky A, Sutton A, Todorov T. Phys Rev B 1995;52:5036.
Breakdown and anti-breakdown events in high-®eld stressed ultrathin gate oxides E. Miranda a, J. Su~ ne b,*, R. Rodrõguez b, M. Nafrõa b, X. Aymerich b a
Departamento de Fõsica, Facultad de Ingenierõa, Universidad de Buenos Aires, Paseo Col on 850, CP 1063 Buenos Aires, Argentina b Departament dÕEnginyeria Electr onica, Universitat Aut onoma de Barcelona, 08193 Bellaterra, Spain Received 20 March 2000
Abstract As a high-®eld voltage sweep proceeds, the post-breakdown I±V characteristic of an ultrathin gate oxide shows abrupt upward and downward steps which are a clear manifestation of the local area character of the associated conduction mechanism. Moreover, the leakage current through the breakdown spots exhibits conductance values very similar to those found in quantum point contacts, indicating that the conductive paths connecting both electrodes have atomic-scale dimensions. In this work, we propose that some of these jumps in the I±V characteristic might be caused by a local rearrangement of atoms or defects due to the high current density forced to ¯ow through the breakdown path. This is a well-known eect in point contacts where the so-called electron wind force encourages the atomic motion. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: MOS electron devices; Oxide reliability; Dielectric breakdown; Silicon dioxide
1. Introduction In spite of the important advances achieved in the last few years, the physical understanding of the breakdown phenomenon of the SiO2 dielectric layer in a MOS device is quite far from being complete. As evidenced by the huge number of publications concerning ultrathin oxides, the subject has almost been entirely focused from the reliability viewpoint, disregarding the study of the physics of such dramatic event. In addition, as a consequence of the use of ever thinner oxides, it has become necessary to consider new features in the analysis of the phenomenon such as the ballistic nature of the electron transport [1] and the eects of the stress-induced leakage current [2], which make the dierence respect to thicker oxides. The issue of what kind of structure develops across the insulator at the moment of the breakdown
* Corresponding author. Tel.: +34-93-581-3217; fax: +34-93581-1350. E-mail addresses: [email protected] (J. Su~ ne), emirand@ tron.®.uba.ar (E. Miranda).
event and how the conduction problem should be faced are still open questions. Nevertheless, there is a wide agreement in considering that the breakdown path connecting the electrodes is highly localized as well as that its origin is somehow related to the defects generated during the application of a previous wear-out condition [3±6]. Here, after a brief review of selected topics related to the ®eld, we further explore the physics of the SiO2 breakdown phenomenon, with special emphasis on the switching behavior exhibited by the I±V characteristic. The subject is not new and current ¯uctuations in the post-breakdown regime have been reported before (see Ref. [3] and references therein). In this regard, due to the few sites which are believed to participate in the conduction process through an ultrathin oxide (the average radius of the defects has been estimated to be around 0.45 nm [7]) a high sensitivity of the current due to local rearrangements (spatial or energetic) in the atomic con®guration of the breakdown path is expectable. We suggest that these eects are visible in the I±V characteristics, as it occurs in metal nanobridges [8,9] where changes in resistance can be induced under a high bias stress.
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2. The physics of post-breakdown According to the severity of the event, recognized by the associated leakage current level, the oxide breakdown is usually classi®ed as soft (SBD) or hard (HBD). Both breakdown modes can be obtained by applying a constant voltage or current stress, and even by ramped voltage or current measurements [10,11]. In addition, more than one SBD and HBD spots can be induced on the same sample by a proper choice of the stressing condition. Although several models have been proposed to account for the post-breakdown I±V characteristic, almost all of them (we only know of one exception) are aimed exclusively to explain the SBD mode. Mechanisms such as direct tunneling through a local thinned down oxide spot [12,13], trap assisted tunneling [14], variable range hopping [15,16], percolation in non-linear conduction networks [17], inelastic quantum tunneling [18] and Fowler±Nordheim (FN) conduction [19] have been invoked. On the other hand, Ting's model [20], based on the conduction properties of a matrix of threedimensional cylindrical structures embedded in a fresh oxide, in which resonant tunneling takes place, accounts for both SBD and HBD at once in a consistent way. The author considered the funneling of the electron wave functions into quantum wires connecting partially (SBD) or totally (HBD) the opposite electrodes. However, it is worth mentioning that to reach the actual experimental current levels, a damaged area of about 10% of the total structure area is ®nally required. Concerning the functional dependence of the posthard breakdown current on the applied bias, the literature on the subject is surprisingly scarce. Indeed, few works have paid attention to the issue and this is perhaps motivated by the fact that the broken down oxide merely presents a resistor-like behavior for voltages higher than about 1 V. In Ref. [3], the authors suggested that the I±V characteristic presented a diode-like dependence for very low applied voltages, proposing that the oxide becomes transparent to the electron transport at these voltages. Other features observed at higher voltages were ascribed to spreading resistance eects. This transport mechanism was also invoked by Umeda and Taniguchi [21]. In a recent paper [22], we presented an alternative explanation for the conduction mechanism in broken down oxides. It was based on the conceptual framework of the physics of mesoscopic devices and the point contact conduction theory [23]. The breakdown path across the oxide was treated as a three-dimensional constriction in which a subband structure arises as a consequence of the lateral con®nement of the electron wave functions. The model assumes abrupt potential drops at the two ends of the constriction and spot areas in the nanometer range. This initial approach has been subsequently extended to account for the SBD conduc-
tion mechanism by including the transmission properties of narrow constrictions [10,24]. It is worth recalling that ®rst point contact experiments were performed on metal±insulator±metal structures by inducing electrical breakdowns of the insulator layer in such a way that the two metal electrodes became connected by a metallic short circuit [25]. In the case of the breakdown of ultrathin MOS structures, however, we are convinced that such destructive thermal eects do not occur, at least in the cases of more basic and applied interest. However, the issue of whether HBD is essentially linked to an irrecoverable thermal damage is still a matter of debate. Even though the local melting of the oxide at the very moment of the breakdown event is a well established fact for thick oxides, these eects seem likely to be at least less important in the ultrathin oxide thickness range. First works in this area, such as those due to Klein [26], Solomon [27] and Shatzkes et al. [28], involved SiO2 ®lms with thickness in the order of several hundred of nanometers. These thick ®lms showed important thermal eects at the breakdown which in some cases were clearly visible in TEM and SEM photos. This is consistent with subsequent observations such as those due to Sugino et al. [29], who presented experimental results showing that the intrinsic breakdown spot is a melting composed of crystallized silicon. More recently, Lombardo et al. [30] have reported new interesting results about thermal and propagation eects occurring during the hard breakdown of much thinner oxides. These authors have shown, by means of TEM analysis, that the breakdown spot can laterally propagate on the MOS surface along a quasi-1D line, thus giving rise to complex structures composed of many breakdown spots. Moreover, they found that a 35 nm oxide showed spots with coarse crystal grains epitaxially aligned to the silicon substrate. In contrast, these eects could not be detected in oxides of 9.3 and 5.6 nm thick, stressing the fact that the breakdown of a thin oxide is a process of a very dierent nature. In any case, the occurrence of thermal eects strongly depends on the features of the MOS structure (area, thickness, etc.) and on the characteristics of the measurement setup (series impedance, stress current or voltage, etc.). Both determine the dynamics of power dissipation at the very moment of the breakdown [31,32] and the level of destructive damage of the breakdown path. In particular, it has been demonstrated that if thermal eects are limited by the sample itself and/or by the measurement setup, the HBD events can eventually be switched o [33,34] In these cases, irreversible thermal damage is clearly absent. Actually, we think that (although the origin of the breakdown is always the same [35]) there is experimental evidence to distinguish at least three dierent situations which correspond to three dierent states of the breakdown spot (we will refer to these as breakdown modes): SBD, HBD, and thermal HBD. In all the cases, the post-
E. Miranda et al. / Solid-State Electronics 45 (2001) 1327±1332
breakdown characteristic will not strongly depend on the oxide thickness (at least for oxides under 15 nm) nor on the oxide area, but the relative probability of occurrence of these breakdown modes certainly depends on the features of the oxide and on the stress conditions (no SBD is found in oxides thicker than 5 nm under FN stress, for example). Since the post-breakdown I±V does not strongly depend on oxide thickness or area, we can also identify the breakdown modes by the magnitude of post-breakdown current level (values are given at 5 V): a current of the order of 10 7 ±10 6 A is measured after SBD, a current of the order of 10 3 A is measured after HBD (this is also the current level measured after HBD induced by substrate hot electron injection [21,36]) and a much higher current of the order of 10 mA to 1 A are measured after the occurrence of thermal or propagation eects [30]. In this work, we deal with some eects which appear after the (non-thermal) HBD: conductance quantization and on-o switching ¯uctuations. 3. Experimental results 3.1. The samples and the experimental setup The devices used in this study are conventional n polysilicon-gate MOS capacitors fabricated on N-type (1 0 0) Si substrates N 1015 cm 3 with tox 3:0, 3.8 and 4.9 nm. The area of the capacitors is 6:5 10 5 cm2 and the gate was always positively biased (electron injection from substrate to gate). Further details concerning these devices can be found elsewhere [11]. The measurements were all performed at dark and at room temperature with a semiconductor parameter analyzer HP4145B. In order to stop the measurements after the occurrence of a switching event, we made use of the long integration time option of the HP4145B. This analysis mode is associated with a very low voltage sweep rate.
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Fig. 1. I±V characteristics associated with the SBD and HBD conduction modes. Each HBD I±V characteristic was measured after the detection of a breakdown event induced by a high-®eld voltage sweep.
down of an ultrathin oxide is a multiple event process, where the current steps are associated with the creation of new HBD spots (this is also supported by optical experiments [37]). It is also worth noting that, independently of the gate bias, all the current jumps are of the same order of magnitude. This means that the damage caused to the gate oxide is always very similar and therefore that each HBD spot contributes approximately with the same amount of current. To realize what is actually happening, Fig. 3 shows the I±V characteristic of a fresh sample, the I±V characteristic measured on the same sample after the occurrence of the ®rst HBD event, and their dierence. As noted, the latter curve exhibits a breakpoint where it deviates downwards. This is due to the shift of the background FN I±V characteristics
3.2. Breakdown events Fig. 1 compares the dierent breakdown modes of an ultrathin gate oxide. Notice that for this particular combination of oxide thickness and gate area, the occurrence of a SBD event is very dicult to detect. The reason is simple: from moderate to high bias, the SBD current component is comparable to the direct or FN tunneling component which ¯ows in parallel through the non-damaged oxide area. On the contrary, the HBD leakage current is well distinguishable and it completely masks the other current components in the whole bias range. However, at high voltages, it is still possible to detect the background FN tunneling current. Fig. 1 shows several HBD I±V characteristics, each one being obtained after the detection of a current jump like those shown in Fig. 2. This ®gure indicates that the break-
Fig. 2. Multiple breakdown events during a high-®eld voltage sweep. Each current jump is associated with the appearance of a breakdown spot.
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Fig. 4. Current and conductance vs. voltage characteristics for ®rst and second breakdown events.
Fig. 3. The solid line shows the FN I±V characteristic of a fresh sample. The squares indicate the HBD I±V characteristic measured after the detection of the ®rst breakdown event. The dashed line corresponds to the dierence between these curves.
towards higher voltages caused by the additional voltage drop in the semiconductor series resistance due to the current which ¯ows through the new breakdown spot. This happens each time a HBD event is triggered and it is in agreement with the equivalent circuit for the postbreakdown conduction proposed in Ref. [3]. To stress this fact, Fig. 4 shows that a second HBD path shifts the background FN current even farther away. The dierential conductance G dI=dV of these curves is also depicted in the same ®gure. The plot reveals three voltage regions: (i) Below 1.5±2 V there is a gradual conductance increase due to the potential drops in the silicon electrodes. (ii) Then, the G±V characteristics enters in the point contact conduction regime. The traces exhibit plateaus of the order of the quantum conductance unit 2e2 /h, e and h being the electron charge and the Planck's constant respectively. This a well-known feature of atomic-size constrictions and even of onedimensional chains of atoms [38]. (iii) Finally, as explained above, the steep increase in the G±V curves corresponds to the appearance of the background FN tunneling current.
3.3. Anti-breakdown events The fact that not all the post-breakdown characteristics exhibit the same behavior shown in Fig. 2 is clearly illustrated by Fig. 5. The ®gure shows the existence of
Fig. 5. Switching behavior of the HBD I±V characteristic during a high-®eld voltage sweep.
backwards current steps of the same order of magnitude of the HBD events, which are identi®ed as anti-breakdown (aHBD) events. These type of events were also reported during constant voltage stresses of samples that had suered one or several HBD events [3,34], and similar on/o ¯uctuations have also been observed in the post-SBD I±V characteristics [11,39]. To further analyze these switching events, let us consider Fig. 6, which shows two successive voltage sweeps applied to the same sample. The ®rst current step in the solid trace corresponds to the transition from FN to HBD. At a certain bias point, the current suddenly drops and it remains in this low state (unless the stress is continued and a second HBD event is triggered). If the measurement is stopped immediately after the detection of the aHBD event, so as to avoid the triggering of a new HBD event, a second voltage sweep (dotted line in Fig. 6) reveals that the current level corresponds to that observed after the occurrence of the aHBD event. That is, we still have a single HBD spot which has somehow changed its conducting properties. Fig. 7 shows that the non-linear
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Fig. 6. Two consecutive voltage sweeps applied to the same sample. FN refers to Fowler±Nordheim injection.
Fig. 7. Two consecutive voltage sweeps applied to the same sample.
current increment which usually appears prior to an aHBD event is totally reproducible if the voltage sweep is stopped before the occurrence of the aHBD event (solid line). Additionally, Fig. 7 shows that the current ¯owing through the structure after the detection of the second HBD event cannot be regarded as the extrapolation of the I±V characteristic prior to the occurrence of the aHBD event.
4. Discussion We suggest that the switching behavior in the HBD I±V characteristics re¯ects changes in the atomic topology of the leakage spots. This might explain why the magnitude of the current jumps is very similar both for the HBD and aHBD events. In fact, their origin is essentially the same, namely a modi®cation of the elec-
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Fig. 8. Constant current stress of a P-type substrate sample showing and anti-breakdown event. In this case the gate was negatively biased.
trical connections which link the conducting sites. The reversibility of the breakdown events indicates that irrecoverable thermal eects are not very likely to occur in ultrathin oxides. In this regard, Fig. 8 shows the appearance and disappearance of a breakdown spot during a constant current stress. Note that the recovery after the ®rst sudden jump in the gate voltage is gradual, lasting a few seconds. Moreover, recent results of molecular-dynamics simulation [40], have shown that the main eect of increased temperature is the enhanced thermal motion of the atoms that promotes the relaxation into stable con®gurations. Actually, pure thermal instabilities due to Joule heating are unlikely unless the temperature reaches values close to the melting point. We suggest that electromigration eects at the atomic scale can be responsible for the atomic changes of the breakdown path. It is worth pointing out that the rearrangement of defects encouraged by the direct force of the electric ®eld or by the so-called electron wind force has been previously proposed to explain changes induced by high bias in gold quantum point contacts [9]. While the direct force is expected to be negligible in a one-dimensional path [8], we can show that the electron wind force is a reasonable hypothesis. If we consider that the current ¯owing through a HBD spot is of the order of 1 mA, and that the spot area is of the order of 10 14 ± 10 12 cm2 [3], the current density is of the order of 109 ± 1011 A/cm2 . This is an extremely high density, but this is the order of magnitude found in point contacts. The wind force can be estimated from [9]: ~ p=e FW 2I~
1
where ~ p is the momentum of the electrons, I is the current, and e is the electron charge. For the measured current of 1 mA and the momentum corresponding to
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an energy of 0.1 eV (a reasonable value for an electron in a silicon accumulation layer), the electron wind force is estimated to be of about 2 nN. To give a more intuitive idea, we can calculate the electric ®eld required to applying a force of 2 nN to a particle with the charge of one electron. This results in an equivalent electric ®eld of approximately 125 MV/cm, which is clearly able to modify the breakdown path, moving atoms and breaking bonds. Thus, current-induced atomic motion (i.e. atomic-scale electromigration) is a reasonable picture to explain the HBD ¯uctuations. 5. Conclusion We have analyzed the switching behavior exhibited by the post-breakdown I±V characteristic of ultrathin oxides. The measured conductance values con®rm the atomic scale of these leakage paths. It was also shown that a high-®eld voltage sweep can induce changes within the breakdown paths which are detected as ¯uctuations in the I±V characteristics. Mesoscopic electromigration eects have been suggested to explain the atomic-scale modi®cation of the breakdown paths.
Acknowledgements DGES is acknowledge for supporting this work under project no. PB96-1162. The authors are grateful to F. Campabadal and L. Fonseca of the Centro Nacional de Microelectr onica-Barcelona for sample fabrication. References [1] DiMaria D. Solid-State Electron 1997;41:957. [2] Ricc o B, Gozzi G, Lanzoni M. IEEE Trans Electron Dev 1998;45:1554. [3] Nafrõa M, Su~ ne J, Aymerich X. J Appl Phys 1993;73:205. [4] Su~ ne J, Placencia I, Barniol N, Farres E, Martõn F, Aymerich X. Thin Solid Films 1990;185:347. [5] Dumin D, Maddux J, Scott R, Subramoniam R. IEEE Trans Electron Dev 1994;41:1570. [6] Stathis J. J Appl Phys 1999;86:5757. [7] Degraeve R, Groeseneken G, De Wolf I, Maes H. Microelectron Engng 1995;28:313. [8] Ralls K, Ralph D, Buhrman R. Phys Rev B 1989;40:11561. [9] Yasuda H, Sakai A. Phys Rev B 1997;56:1069.
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