APPLIED PHYSICS LETTERS 93, 262902 共2008兲

The radial distribution of defects in a percolation path X. Li,1,2,a兲 C. H. Tung,2 and K. L. Pey1,b兲 1

Microelectronics Center, School of EEE, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore 2 Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), 11 Science Park Road, Singapore Science Park II, Singapore 117685, Singapore

共Received 24 October 2008; accepted 4 December 2008; published online 29 December 2008兲 Our results show that the defect distribution within a nanometer size percolation path is nonuniform. The defects, which are shown as oxygen vacancies, spread out radially from the center of the percolation path. The conduction band edges of the defective oxide are lowered for 0.14– 0.78 eV when the Si–O composition changes from SiO1.76 to SiO0.7. © 2008 American Institute of Physics. 关DOI: 10.1063/1.3056659兴 Over the past years, efforts have been made to understand the trap/defect generation,1–3 percolation path formation,4–6 and degradation7–9 in amorphous SiO2 in attempts to predict the occurrence of the time dependent dielectric breakdown accurately under device operating conditions. There are a few well accepted physical models2,10,11 which describe the importance of different trap/defect generation processes as well as their impacts to the dielectric breakdown 共BD兲. It is commonly agreed that the defects generated during pre- and post-BD stress are responsible for the various leakage current profiles observed in the accelerated tests. Among the proposed defects, oxygen vacancy and its related species serve as strong candidates responsible for the oxide wearing-out process, from stress induced leakage current1,2 to progressive breakdown 共or soft-BD兲.8,12,13 It is therefore important to know the distribution of oxygen deficiency in a BD path and understand its role in the oxide degradation process. In this letter, we study the defective oxide using scanning transmission electron microscope 共STEM兲 with electron energy loss spectroscopy 共EELS兲, and the distribution of oxygen deficiency in a percolation path is mapped and discussed. Figure 1共a兲 shows the high angle annular dark field 共HAADF兲 image of a typical metal oxide semiconductor 共MOS兲 gate stack 共L ⫻ W = 0.5⫻ 0.15 ␮m2兲 after dielectric breakdown, which is isolated using focused ion beam 共FIB兲 milling. The initial BD was created using a constant voltage stress of Vgstress = 4.1 V and compliance current limit Igl = 1.0 ␮A. It was further stressed to the post-BD phase using a lower voltage Vgstress = 3.1 V with Igl = 2.0 ␮A. The dielectric layer is a 22 Å nitrided amorphous SiO2 共N % ⬃ 3 % 兲. A dielectric breakdown induced epitaxy14 共DBIE兲 nanomarker is identified at the BD location. Electron energy loss spectra, both Si L2,3 edge and O K edge, were acquired at positions 1–6 in the oxide layer to get the information of the breakdown. To access the local properties from a 22 Å layer, a fine probe size as well as a good energy resolution is needed. In this experiment, the STEM probe size was set to be around 3 Å in diameter and the EELS energy resolution was 0.7 eV. The plots of Si L2,3 edge spectra are shown in Fig. 1共b兲; only spectra at positions 1–3 共half of the symmetrical DBIE兲 are displayed for discussion. The different Si oxidation states are a兲

Electronic mail: [email protected]. Electronic mail: [email protected].

b兲

0003-6951/2008/93共26兲/262902/3/$23.00

labeled in the figure. The Si4+ signals 共onsets at 105 eV兲 are originated from the bulk SiO2 bonding in the central region of the oxide layer. It reveals the electronic structures at the bottom of the oxide conduction band.15 The changes in the peak shape and intensity for defective oxide at positions 2 and 3 共outer and inner shell of percolation path兲 are similar as reported previously.12 Since the weaker signals below 105 eV are delocalized counts from adjacent suboxide region,12,15 we could then separate the contributions and use the flat portion of the peak below 105 eV as the reference for

FIG. 1. 共Color online兲 共a兲 HAADF image showing the gate stack of a typical n-type MOS transistor after BD. A DBIE nanomarker is identified. EEL spectra at positions 1–6 共indicated in the oxide layer兲 were acquired at the breakdown spot, respectively. The TEM sample was prepared using FIB with low energy 共2 kV兲 clean and in situ lift-out. The STEM/EELS experiments were performed on a FEI TITAN microscope operated at 80 kV. 共b兲 The Si L2,3 edge spectra collected at positions 1–3. The different Si oxidation states are labeled. The inserted graph shows the zoomed-in plot from 103 to 106.5 eV, which is the onset portion of Si4+ signals. The intersections of the fitted onset slopes shift towards lower energy which indicate that the local oxide conduction band minimum are lowered for 0.14– 0.78 eV as moving from position 1 to 3.

93, 262902-1

© 2008 American Institute of Physics

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262902-2

Appl. Phys. Lett. 93, 262902 共2008兲

Li, Tung, and Pey

FIG. 2. 共Color online兲 共a兲 The as-measured O K edge intensities 共532– 552 eV兲 at all the 6 positions near the breakdown spot. The diameter of the percolation path 共defective oxide area laterally兲 is estimated to be around 30 nm. 共b兲 Top view schematic diagram of the oxide area with a breakdown in the TEM sample. A three-shell percolation model is proposed for the thickness correction. The O K edge intensities at position 3, 5, and 6 are used for the calculation. The different dimensions in the percolation path are labeled as d and the TEM sample thickness is T. 共c兲 The corrected oxygen deficiency in the percolation path. The O deficiency in the center of the percolation path is as high as 65% 共SiO0.7兲.

tion path 共defective oxide area laterally兲 is estimated to be 30 nm for the post-BD leakage current of 2 ␮A, corresponding to a very soft breakdown case in our study. Since the O-K edge intensities are originated from the entire oxide volume in the thickness direction of the TEM sample, it is therefore essential to back calculate the contribution from the defective oxide and extract only the signals from the percolation path. Generally, the inner shell signal depends proportionally on 共1兲 the core edge ionization cross section ␴, 共2兲 the number of atoms per area, and 共3兲 the number of incident electrons 共can be measured using low loss spectrum including the unscattered and inelastically scattered electrons兲.16 In this experiment, we focus only on the O-K edge signals at different locations near the breakdown spot with exactly same experimental conditions such as the collection semiangle ␤ and acquisition time. The variables in 共1兲 and 共3兲 could be neglected here since we compare the relative change in oxygen intensities with respect to the same reference spectrum 共assumed as SiO2兲. Based on the low loss spectra acquired at the area of interest, the local sample thicknesses are relatively uniform 共⫾1 nm兲,17 which is also a characteristic of a FIB sample.18 It is therefore believed that the oxygen intensity difference in Fig. 2共a兲 are originated from the defective oxide in the percolation path which give rise to the different number of oxygen atoms per area in 共2兲. Like the usual EELS composition quantification, we could then be able to decouple the signal contributions from the defective oxide in the percolation path. Figure 2共b兲 illustrates the top view schematic diagram of the oxide area with a breakdown path embedded in the TEM sample. Based on the separation of probing positions in Fig. 1共a兲, a three-shell percolation path model is proposed for the thickness correction. The defective oxide in each shell is denoted as SiOx1, SiOx2, and SiOx3, respectively. The asmeasured O-K edge intensities at positions 3, 5, and 6 are used for the calculation. The TEM sample thickness T from the low loss measurement was found to be around 80 nm and the percolation path diameter D is 30 nm. The electron probe at position 6 transmits through the sample with d1 in shell-1 of percolation path and 共T − d1兲 in the nondefective oxide. The as-measured intensity at position 6 is therefore

冕

T

Oposition 6dt =

0

Si4+ peak onsets. The inserted graph in Fig. 1共b兲 shows the zoomed-in plot of the spectra from 103 to 106.5 eV, which highlights the onset part of Si4+ signal. As illustrated in the plot, the intersections of the fitted onset slopes shift from 104.76 共position 1兲 to 104.62 共position 2兲, 104.55 共position 3 upper slope between 109.5 and 111 eV兲, and 103.98 eV 共position 3 lower slope between 107 and 109 eV兲. This suggests that the local oxide conduction band minimum is lowered for 0.14– 0.78 eV, as moving from positions 1 to 3. The as-measured O-K edge intensities in between 532 and 552 eV at 6 positions are shown in Fig. 2共a兲. The parabolic profile of the oxygen defect distribution clearly shows that the defects composed of the percolation path are radially distributed. The deficiency of oxygen is higher at/near to the center of the percolation path. The diameter of the percola-

冕

d1

Ox1dt +

0

冕

T−d1

O2dt,

共1兲

0

where Ox1 and O2 are the number of oxygen atoms at the defective oxide 共shell-1兲 and nondefective oxide, respectively. We can also formulate the intensities at positions 3 and 5 as follows:

冕

T

0

冕 冕

d21

Oposition 5dt =

Ox2dt +

0

冕

d2−d21

Ox1dt

0

T−d2

+

O2dt,

共2兲

0

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262902-3

冕

Appl. Phys. Lett. 93, 262902 共2008兲

Li, Tung, and Pey

T

冕 冕

d31

Oposition 3dt =

0

Ox3dt +

0

冕

d11−d31

0

d3−d11

+

Ox1dt +

0

Ox2dt

冕

T−d3

O2dt.

共3兲

0

If we use the oxygen signal measured outside the percolation path, i.e., position 1, as the reference signal for SiO2, we get

冕

T

0

Oposition 1dt =

冕

T

O2dt ⬅ 2.0.

共4兲

0

By knowing the separation of the probing position to the origin of the percolation path, we can calculate every distance d labeled in each shell according to the geometries. From Eqs. 共1兲 and 共4兲, we can get the x1 value in shell-1. And using Eqs. 共2兲 and 共4兲 and x1 value, we can get the value for x2 in shell-2. The x3 value in shell-3 is therefore obtained from Eqs. 共3兲 and 共4兲 and x1 and x2. The corrected oxygen deficiency in the percolation path is shown in Fig. 2共c兲. As probing from the outer shell to the inner shell of the percolation path, the deficiency of oxygen changes from 10% to 30% and reaches the maximum 65% in the center of the percolation path. The radial distribution of the oxygen vacancies suggests that the defect generation as a result of electrical stress is nonuniform. The inner shell of the percolation path 共somewhere near position 3兲 is likely to be the location where the percolation path initially forms. Since the local current density is enormous, it is believed that the trap/defect generation rate in the vicinity of the percolation path is much faster than the surrounding oxide area. The percolation path therefore dilates radially as more defects are generated at the BD site. Meanwhile, it is worth to note that this radial distribution profile is not symmetrical. One of the possible reasons for the asymmetrical pattern could be the location of the percolation path along the channel length L. For this transistor, the location of the BD spot is located at 0.36L from the source terminal 共i.e., at 180 nm from the source terminal兲. The current leaked through the percolation path goes to the source and drain terminals via the inversion channel with different magnitudes 共determined by the respective channel resistances兲.19 In this case, it is expected to have a faster growth rate towards the source terminal since there is more current flowing to the source side. Eventually, the asymmetrical growth of the percolation path creates a positive feedback to the leakage current and Si–O bond breakage. It further degrades the oxide and leads to a hard breakdown when a direct short between the gate and source/drain is reached. The location of the percolation path is therefore significant in the postbreakdown reliability assessments.20 Comparing the results in Figs. 1共b兲 and 2共c兲, we could also correlate the oxygen deficiency with the local conduction band lowering. The onset of Si4+ signal shifts by 0.14 eV at position 2, which corresponds to a defective oxide SiO1.76. At position 3, the edge onset drop is 0.78 eV for a defective oxide SiO0.7. The actual lowering SiO2 conduction band edge could be different from the value obtained from fitting the slopes of the Si4+ edge onset, especially with signal delocalization.21,22 However, this semiquantitative correla-

tion still provides us a clear evidence of the material property change in the percolation path. The energy gap of the oxide shrinks as the oxygen atoms are washed out. This observation forms the basis of the insulator to conductor transition observed in various oxide materials23,24 for resistive switching applications.25 In summary, the lateral distribution of defects in a dielectric breakdown induced percolation path is demonstrated experimentally. Our results show that the deficiency of oxygen spreads out radially from the center of the percolation path to its surrounding area. The Si–O composition changes from SiO1.76 to SiO0.7 as moving to the center of the percolation path, which corresponds to the lowering of conduction band edge from 0.14 to 0.78 eV. Such understanding shall be useful for the modeling of the dielectric breakdown as well as the device lifetime assessments. The new understanding is also useful to provide detailed insight of insulator to conductor transition observed in oxide materials for resistive switching applications. We thank Dr. Michel Bosman for technical discussions and Chartered Semiconductor Manufacturing for providing the samples. This work was supported by Ministry of Education 共MOE兲 Grant Nos. T206B1205 and NTU RGM 12/07. P. E. Blöchl and J. H. Stathis, Phys. Rev. Lett. 83, 372 共1999兲. J. Sune and E. Y. Wu, Phys. Rev. Lett. 92, 087601 共2004兲. 3 J. W. McPherson, J. Appl. Phys. 99, 083501 共2006兲. 4 R. Degraeve, G. Groeseneken, R. Bellens, M. Depas, and H. E. Maes, Tech. Dig. - Int. Electron Devices Meet. 1995, 863. 5 J. H. Stathis, J. Appl. Phys. 86, 5757 共1999兲. 6 J. Sune, E. Y. Wu, and S. Tous, Microelectron. Eng. 84, 1917 共2007兲. 7 S. Lombardo, A. La Magna, C. Spinella, C. Gerardi, and F. Crupi, J. Appl. Phys. 86, 6382 共1999兲. 8 S. Lombardo, J. H. Stathis, and B. P. Linder, Phys. Rev. Lett. 90, 167601 共2003兲. 9 V. L. Lo, K. L. Pey, C. H. Tung, and X. Li, Tech. Dig. - Int. Electron Devices Meet. 2007, 497. 10 K. F. Schuegraf and C. M. Hu, IEEE Trans. Electron Devices 41, 761 共1994兲. 11 J. W. McPherson and H. C. Mogul, J. Appl. Phys. 84, 1513 共1998兲. 12 X. Li, C. H. Tung, and K. L. Pey, Appl. Phys. Lett. 93, 072903 共2008兲. 13 X. Li, C. H. Tung, K. L. Pey, and V. L. Lo, Tech. Dig. - Int. Electron Devices Meet. 共to be published兲. 14 C. H. Tung, K. L. Pey, L. J. Tang, M. K. Radhakrishnan, W. H. Lin, F. Palumbo, and S. Lombardo, Appl. Phys. Lett. 83, 2223 共2003兲. 15 P. E. Batson, Nature 共London兲 366, 727 共1993兲. 16 R. F. Egerton, Ultramicroscopy 3, 243 共1978兲. 17 X. Li, G. Zhang, C. H. Tung, and K. L. Pey, “Probing the electronic structure of defective oxide: An EELS approach,” Proceedings of the 47th International Reliability Physics Symposium, April 2009 共to be presented兲. 18 P. L. Potapov, H. J. Engelmann, E. Zschech, and M. Stöger-Pollach, Micron 40, 262 共2009兲. 19 K. L. Pey, R. Ranjan, C. H. Tung, L. J. Tang, W. H. Lim, and M. K. Radhakrishnan, in Proceedings of the 42nd International Reliability Physics Symposium, 2004, p. 117. 20 K. L. Pey, T. A/L Selvarajoo, C. H. Tung, D. S. Ang, and V. L. Lo, in Proceedings of the 45th International Reliability Physics Symposium, 2007, p. 221. 21 D. A. Muller and J. Silcox, Ultramicroscopy 59, 195 共1995兲. 22 R. F. Egerton, Ultramicroscopy 107, 575 共2007兲. 23 K. Szot, W. Speier, G. Bihlmayer, and R. Waser, Nature Mater. 5, 312 共2006兲. 24 R. Waser and M. Aono, Nature Mater. 6, 833 共2007兲. 25 D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, Nature 共London兲 453, 80 共2008兲. 1 2

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