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Grain boundary mediated leakage current in polycrystalline HfO2 films
Microelectronic Engineering 88 (2011) 1272–1275
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Grain boundary mediated leakage current in polycrystalline HfO2 films K. McKenna a,b,⇑, A. Shluger a,b, V. Iglesias c, M. Porti c, M. Nafría c, M. Lanza c, G. Bersuker d a
World Premier International Research Center, Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom c Dept. Enginyeria Electrònica, Universitat Autònoma de Barcelona, Edifici Q, 08193 Bellaterra, Spain d SEMATECH, Austin, 78741 TX, USA b
a r t i c l e
i n f o
Article history: Available online 3 April 2011 Keywords: HfO2 Grain boundaries Leakage current Atomic force microscopy Density functional theory
a b s t r a c t In this work, we combine conductive atomic force microscopy (CAFM) and first principles calculations to investigate leakage current in thin polycrystalline HfO2 films. A clear correlation between the presence of grain boundaries and increased leakage current through the film is demonstrated. The effect is a result of a number of related factors, including local reduction in the oxide film thickness near grain boundaries, the intrinsic electronic properties of grain boundaries which enhance direct tunnelling relative to the bulk, and segregation of oxygen vacancy defects which increase trap assisted tunnelling currents. These results highlight the important role of grain boundaries in determining the electrical properties of polycrystalline HfO2 films with relevance to applications in advanced logic and memory devices. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Polycrystalline metal oxide materials are finding ever widening applications in microelectronics. For example, advanced semiconductor field effect transistor devices employ polycrystalline highk materials in place of the conventional amorphous SiO2 gate oxides. Polycrystalline oxide films exhibiting the resistive switching effect are also emerging as highly energy efficient non-volatile memory devices [1,2]. In both cases, extended defects in the polycrystalline oxide film, such as grain boundaries (GBs) and dislocations, are thought to play an important role in determining its electrical characteristics. For example, it has been suggested that charge trapping defects, such as oxygen vacancies, preferentially aggregate at GBs providing preferential percolation paths for leakage current [3–7]. Models of the resistive switching effect also often invoke extended defects as preferential defect diffusion pathways [8]. However, standard device characterisation techniques provide only averaged information about the electrical properties of polycrystalline films. Therefore, in spite of many speculations, there is little quantitative data on the electrical properties of GBs in polycrystalline materials. In this paper, we combine conductive atomic force microscopy (CAFM) and first principles calculations to investigate the electrical properties of GBs in thin polycrystalline HfO2 films. HfO2 is a convenient material for this study because of extensive experience in processing and treatment, and detailed understanding of its struc⇑ Corresponding author at: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom. E-mail address: [email protected] (K. McKenna). 0167-9317/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2011.03.024
tural and electrical properties [9]. By performing CAFM in ultra high vacuum (UHV) we achieve the high lateral resolution required to correlate the morphological and electrical properties of the nanocrystalline dielectric. The measurements demonstrate a clear spatial correlation between the presence of GBs and increased leakage current through the film. However, experimentally, it is difficult to separate the different factors which may be responsible for this effect. For example, GBs may possess intrinsic electronic properties (different from those of the bulk-like grains) which may promote electron tunnelling. There may also be a contribution to the observed current from defect assisted tunnelling, e.g. due to oxygen vacancy defects segregated at the GB. Therefore, to better understand these issues we have performed first principles calculations of the properties of a GB in HfO2 which support and help explain the experimental observations. 2. Methods The HfO2 film was grown on a p-type Si epitaxial substrate with a 1 nm thick native SiO2 layer. A HfO2 film of 5 nm thickness was deposited onto the substrate by atomic layer deposition and annealed at 1000 °C. The annealing induced crystallisation of the HfO2 layer, forming grains of average lateral size 15 nm. The thickness of the film was chosen to ensure that the grains spanned the full thickness of the film (as a multi-layered granular structure would complicate the interpretation of the CAFM images). Current and topography maps for the crystallised film were then obtained by CAFM in UHV (10 10 mbar) using diamond-coated silicon tips [7,10]. The measurements were made in contact mode with a constant voltage (6.5 V) applied to the tip (substrate grounded).
K. McKenna et al. / Microelectronic Engineering 88 (2011) 1272–1275
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A theoretical model for a GB in m-HfO2 was constructed using methods similar to those described previously for MgO [11–13]. First, empirical pair potentials and the METADISE code are used to generate a number of prospective low energy boundary configurations for a given grain misorientation [14]. These structures are then optimised using periodic density functional theory (DFT) to determine the most stable GB structure. The DFT calculations were performed using the projector-augmented wave (PAW) method and the Perdew–Burke–Ernzerhof (PBE) functional as implemented in the VASP code [15,16]. For the results that will be described in this paper, plane waves with energies up to 400 eV were included and the Brillouin zone of the periodic supercell was sampled using a 3 3 1 Monkhorst–Pack grid. The ion coordinates and supercell length perpendicular to the GB plane were optimised to within a force tolerance of 0.01 eV Å 1. 3. Results We first present the results of the CAFM characterisation of the HfO2 film. The topographical image, Fig. 1a, shows that the film consists of grains of average lateral size 15 nm, between which GBs appear as depressions. These depressions are a manifestation of the well known thermal grooving effect [17] (also see Fig. 2b). From a statistical analysis, we estimate the grooves are on average about 4 nm wide and 1 nm deep. Fig. 1b shows the corresponding current image for the same surface region depicted in Fig. 1a. There is a clear correlation between the topographical and current images with higher leakage current detected at the GBs. There are also spots (leakage sites) located along the GBs where the current is significantly higher than the background level (by tens of pA). Fig. 1c shows profiles, for both the height and current, along a line which passes through a leakage site (shown in Fig. 1a and b). From analysis of many different leakage sites in the film, we estimate a mean width of about 3 nm. In addition to leakage sites, spots with much larger currents in the nA range are observed (which we refer to as breakdown spots). The breakdown spots are generally much larger than the leakage sites, 20 nm, and are also located along the GBs. It is likely that the breakdown spots are created by the voltage applied during the scan [7]. To elucidate the different factors which contribute to the observed increase in leakage current at GBs we have performed first
Fig. 1. (a) Topographical image of the HfO2 film showing a granular structure with GBs appearing as depressions (image dimensions: 168 168 nm). (b) Current image obtained at 6.5 V for the same region depicted in (a). (c) Height (dashed line) and current (continuous line) profiles along the path indicated in (a) and (b).
Fig. 2. (a) The supercell model of the (1 0 1) tilt grain boundary in m-HfO2 (supercell dimensions: 10.35 7.87 34.67 Å). Large green spheres represent Hf ions and small red ions represent O ions. The GB plane is indicated by the dashed line. (b) An illustration of the development a thermal groove at the surface of a polycrystal. The equilibrium groove angle b is determined by a balance between the GB and surface free energies (cGB and cs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
principles calculations of the structural and electronic properties of a symmetric HfO2 (1 0 1) tilt GB. This particular boundary was chosen based on the principle that the most stable boundaries should have a high degree of site coincidence between grains. The GB was modelled within a periodic supercell (Fig. 2a) containing 80 Hf and 160 O ions with dimensions 10.35 7.87 34.67 Å. In the optimised structure all O ions are at least three-coordinated and all Hf ions are seven-coordinated as is the case in the bulk. The main differences with respect to the bulk are confined within a region about 5 Å on either side of the GB plane. In this region, the electrostatic potential varies by about 0.3 V and bond lengths deviate from the bulk by about 2%. The calculated formation energy per unit area of the GB is 0.60 Jm 2 (defined with respect to the perfect bulk crystal). As this boundary has very low energy and no undercoordinated ions we consider this to be a best case scenario and more general boundaries may have stronger perturbations near the interface. As noted above, the depressions that are observed in the CAFM topographical images are a result of thermal grooving which occurs when GBs emerge to intersect the surface of a hot polycrystal [17]. The structure of the groove results from the balance between the GB free energy (cGB) and the two surface free energies (cs) along the line of intersection (Fig. 2b). The familiar condition for the equilibrium groove angle b is 2cs sin b = cGB [18]. Using the calculated GB formation energy (0.60 Jm 2) and an average value for the energy of low index surfaces of HfO2 (1.5 Jm 2) [19], one arrives at an estimated groove angle of 11.5°. This prediction compares favourably with the angle that can be estimated from the line profile in Fig. 1c – about 8°. We now turn to the intrinsic electronic properties of the stoichiometric HfO2 (1 0 1) GB to investigate whether it can promote electron tunnelling. To do this, we have calculated the electronic density of states (DOS) of the GB supercell and compared it to that of bulk HfO2. We find that the GB introduces additional electronic states near the bulk valence band maximum and conduction band minimum (Fig. 3a). The occupied valence band GB states are split by less than 0.1 eV from the bulk valence band, and the unoccupied conduction band GB states span a wider 0.3 eV window a below the bulk conduction band minimum. Importantly, the presence of the unoccupied GB states lowers the barrier for electron tunnelling in the vicinity of the GBs, thereby increasing the leakage current. In Fig. 3b, we show how the lowest unoccupied electronic state is
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Fig. 3. (a) Calculated density of states (DOS) of the stoichiometric HfO2 (1 0 1) tilt GB. The shaded regions indicate interface states which are introduced by the GB within the bulk HfO2 band gap. (b) Spatial localisation of the lowest unoccupied electronic state perpendicular to the GB plane (Z = 0).
confined within about 1 nm of the GB plane. This range is comparable to the width of the experimental current profile determined from CAFM (Fig. 1c). However, quantitative comparison is difficult as the experimental current profile is also convoluted with the oxide thickness variation in the vicinity of the GB. HfO2, like most metal oxide materials, are not usually stoichiometric and often contain significant concentrations of oxygen vacancies which can contribute to leakage current. Therefore, it is important to consider how oxygen vacancies interact with the GB. In a previous paper we showed that, in the dilute limit, oxygen vacancies are more stable at the GB than in the bulk of a grain by up to 0.8 eV [20]. Therefore, as a result of segregation, vacancies will be on average closer together at GBs, presenting favourable percolation paths for electron tunnelling through the film. This idea is supported by recent simulations of leakage current in TiN/ HfO2/TiN capacitors under constant voltage stress [6], and is the most probable origin of the leaky sites experimentally observed. We now consider how the properties of the GB are affected as the concentration of vacancies segregated at the GB is increased beyond the dilute limit. First, to assess the stability of the oxygen deficient GB, the formation energy per oxygen defect has been calculated as a function of the concentration of neutral oxygen vacancies segregated to the GB (Fig. 4a). At low concentrations there is an initial rise in the formation energy indicative of repulsive interactions between vacancies. However, for concentrations higher than about 5.1018 m 2, the formation energy per defect begins to fall and level off until the GB is fully depleted of oxygen ions. Importantly, for all the concentrations considered, neutral oxygen vacancies are more stable at the GB than in bulk HfO2. Fig. 4b shows how the electronic DOS is modified as the vacancy concentration is increased (i–v). At low concentrations (i and ii) the defects induce localised states in the band gap which involve bonding and anti-bonding combinations of neighbouring vacancy states. For concentrations greater than 5.1018 m 2 (iii–v), the GB core becomes essentially metallic and a sub-band is formed in the HfO2 gap. We suggest that such highly oxygen deficient GBs may be responsible for the breakdown spots in the CAFM images, as they are able to sustain the much higher leakage currents that are measured.
4. Discussion and conclusions The depressions observed in the AFM images of the polycrystalline HfO2 film can be explained in terms of the well known thermal
Fig. 4. (a) The formation energy of neutral oxygen vacancies as a function of their concentration at the GB. The horizontal line indicates the formation energy for neutral oxygen vacancies in the bulk. (b) The modification of the electronic density of states (DOS) as the concentration of vacancies segregated to the GB is increased (see labels i–v).
grooving effect. While the theoretical prediction of the GB grooving angle is similar to that observed by AFM, quantitative analysis to determine the GB energy is difficult as the line profile near the groove minimum is affected by the finite tip radius and there is a lack of experimental data for HfO2 surface energies. Nevertheless, an important consequence of thermal grooving is that the oxide film thickness is reduced near the GBs, which leads to increased direct tunnelling current. This in part explains the observed correlation between the height and current images in Fig. 1. The theoretical calculations also predict that GBs present a reduced barrier to electron tunnelling which should further enhance the
K. McKenna et al. / Microelectronic Engineering 88 (2011) 1272–1275
direct tunnelling current. Importantly, both of these effects serve to increase the leakage current at GBs. The CAFM images also show a number of spots (leakage and breakdown sites), predominantly located at GBs, where the current is enhanced with respect to the rest of the film. Leakage sites, with currents of the order pA, can be explained as a result of trap assisted tunnelling through oxygen vacancies which are segregated at GBs. The breakdown sites which are also observed by CAFM carry much larger currents, in the nA range. The theoretical calculations suggest that these sites could be associated with highly oxygen deficient regions at GBs. Although a detailed model of breakdown is beyond the scope of the current paper, we note that electric field driven vacancy diffusion could lead to oxygen depletion under electrical stress. In this respect, the fact that breakdown sites are observed to occur at positions where the film is thinner, corresponding to higher local electric fields under bias, may be significant [10]. In summary, the CAFM characterisation and theoretical calculations described in this paper demonstrate that GBs in polycrystalline HfO2 films are associated with higher leakage currents. This can be explained by (1) the local reduction in oxide film thickness due to thermal grooving, (2) the intrinsic electronic properties of GBs which present a reduced barrier to tunnelling electrons, and (3) the segregation of oxygen vacancies to GBs which from preferential percolation paths for electron tunnelling and can also cause metallisation at high vacancy concentrations. These results serve to highlight the fact that improving the performance and reliability of HfO2 based electronic devices, such as resistive switching memories and transistors, depends on controlling both the defect content and grain structure of the polycrystalline dielectric film.
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Acknowledgements KPM also acknowledges support from MEXT KAKENHI Project No. 2274019. This work was also supported by the Spanish MICINN (TEC2007-61294/MIC, TEC2010-16126 and BES-2008-007947). Computer resources on the HECToR service were provided via our membership of the UK’s HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/F067496). Additional computer resources on the Chinook supercomputer were provided by the Environmental Molecular Sciences Laboratory (US Department of Energy). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
R. Waser et al., Nat. Mater. 6 (2007) 833. J. Borghetti et al., Nature 464 (2010) 873. J. Narayan et al., J. Appl. Phys. 49 (1978) 5977. K. Kukli et al., J. Appl. Phys. 92 (2002) 5698. V. Yanev et al., Appl. Phys. Lett. 92 (2008) 252910. G. Bersuker et al., in: Proceedings of the European Solid-State Device Research Conference, 2010, p. 333, doi:10.1109/ESSDERC.2010.5618225. V. Iglesias et al., J. Vac. Sci. Technol. B 29 (2011) 01AB02. R. Waser et al., Adv. Mater. 21 (2009) 2632. J. Robertson, Rep. Prog. Phys. 69 (2006) 327. V. Iglesias et al., Appl. Phys. Lett. 97 (2010) 262906. K.P. McKenna et al., Model Simul. Mater. Sci. Eng. 17 (2009) 084004. K.P. McKenna et al., Microelectron. Eng. 86 (2009) 1751. K.P. McKenna et al., Phys. Rev. B 79 (2009) 224116. G.W. Watson et al., J. Chem. Soc., Faraday Trans. 92 (1996) 433. G. Kresse et al., Phys. Rev. B 54 (1996) 11169. G. Kresse et al., J. Comput. Mater. 6 (1996) 15. W.W. Mullins, J. Appl. Phys. 28 (1957) 333. G.L.J. Bailey et al., Proc. Phys. Soc. B 63 (1950) 350. A.B. Mukhopadhyay et al., Phys. Rev. B 73 (2006) 115330. K. McKenna et al., Appl. Phys. Lett. 95 (2009) 222111.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Grain boundary mediated leakage current in polycrystalline HfO2 films K. McKenna a,b,⇑, A. Shluger a,b, V. Iglesias c, M. Porti c, M. Nafría c, M. Lanza c, G. Bersuker d a
World Premier International Research Center, Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom c Dept. Enginyeria Electrònica, Universitat Autònoma de Barcelona, Edifici Q, 08193 Bellaterra, Spain d SEMATECH, Austin, 78741 TX, USA b
a r t i c l e
i n f o
Article history: Available online 3 April 2011 Keywords: HfO2 Grain boundaries Leakage current Atomic force microscopy Density functional theory
a b s t r a c t In this work, we combine conductive atomic force microscopy (CAFM) and first principles calculations to investigate leakage current in thin polycrystalline HfO2 films. A clear correlation between the presence of grain boundaries and increased leakage current through the film is demonstrated. The effect is a result of a number of related factors, including local reduction in the oxide film thickness near grain boundaries, the intrinsic electronic properties of grain boundaries which enhance direct tunnelling relative to the bulk, and segregation of oxygen vacancy defects which increase trap assisted tunnelling currents. These results highlight the important role of grain boundaries in determining the electrical properties of polycrystalline HfO2 films with relevance to applications in advanced logic and memory devices. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Polycrystalline metal oxide materials are finding ever widening applications in microelectronics. For example, advanced semiconductor field effect transistor devices employ polycrystalline highk materials in place of the conventional amorphous SiO2 gate oxides. Polycrystalline oxide films exhibiting the resistive switching effect are also emerging as highly energy efficient non-volatile memory devices [1,2]. In both cases, extended defects in the polycrystalline oxide film, such as grain boundaries (GBs) and dislocations, are thought to play an important role in determining its electrical characteristics. For example, it has been suggested that charge trapping defects, such as oxygen vacancies, preferentially aggregate at GBs providing preferential percolation paths for leakage current [3–7]. Models of the resistive switching effect also often invoke extended defects as preferential defect diffusion pathways [8]. However, standard device characterisation techniques provide only averaged information about the electrical properties of polycrystalline films. Therefore, in spite of many speculations, there is little quantitative data on the electrical properties of GBs in polycrystalline materials. In this paper, we combine conductive atomic force microscopy (CAFM) and first principles calculations to investigate the electrical properties of GBs in thin polycrystalline HfO2 films. HfO2 is a convenient material for this study because of extensive experience in processing and treatment, and detailed understanding of its struc⇑ Corresponding author at: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom. E-mail address: [email protected] (K. McKenna). 0167-9317/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2011.03.024
tural and electrical properties [9]. By performing CAFM in ultra high vacuum (UHV) we achieve the high lateral resolution required to correlate the morphological and electrical properties of the nanocrystalline dielectric. The measurements demonstrate a clear spatial correlation between the presence of GBs and increased leakage current through the film. However, experimentally, it is difficult to separate the different factors which may be responsible for this effect. For example, GBs may possess intrinsic electronic properties (different from those of the bulk-like grains) which may promote electron tunnelling. There may also be a contribution to the observed current from defect assisted tunnelling, e.g. due to oxygen vacancy defects segregated at the GB. Therefore, to better understand these issues we have performed first principles calculations of the properties of a GB in HfO2 which support and help explain the experimental observations. 2. Methods The HfO2 film was grown on a p-type Si epitaxial substrate with a 1 nm thick native SiO2 layer. A HfO2 film of 5 nm thickness was deposited onto the substrate by atomic layer deposition and annealed at 1000 °C. The annealing induced crystallisation of the HfO2 layer, forming grains of average lateral size 15 nm. The thickness of the film was chosen to ensure that the grains spanned the full thickness of the film (as a multi-layered granular structure would complicate the interpretation of the CAFM images). Current and topography maps for the crystallised film were then obtained by CAFM in UHV (10 10 mbar) using diamond-coated silicon tips [7,10]. The measurements were made in contact mode with a constant voltage (6.5 V) applied to the tip (substrate grounded).
K. McKenna et al. / Microelectronic Engineering 88 (2011) 1272–1275
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A theoretical model for a GB in m-HfO2 was constructed using methods similar to those described previously for MgO [11–13]. First, empirical pair potentials and the METADISE code are used to generate a number of prospective low energy boundary configurations for a given grain misorientation [14]. These structures are then optimised using periodic density functional theory (DFT) to determine the most stable GB structure. The DFT calculations were performed using the projector-augmented wave (PAW) method and the Perdew–Burke–Ernzerhof (PBE) functional as implemented in the VASP code [15,16]. For the results that will be described in this paper, plane waves with energies up to 400 eV were included and the Brillouin zone of the periodic supercell was sampled using a 3 3 1 Monkhorst–Pack grid. The ion coordinates and supercell length perpendicular to the GB plane were optimised to within a force tolerance of 0.01 eV Å 1. 3. Results We first present the results of the CAFM characterisation of the HfO2 film. The topographical image, Fig. 1a, shows that the film consists of grains of average lateral size 15 nm, between which GBs appear as depressions. These depressions are a manifestation of the well known thermal grooving effect [17] (also see Fig. 2b). From a statistical analysis, we estimate the grooves are on average about 4 nm wide and 1 nm deep. Fig. 1b shows the corresponding current image for the same surface region depicted in Fig. 1a. There is a clear correlation between the topographical and current images with higher leakage current detected at the GBs. There are also spots (leakage sites) located along the GBs where the current is significantly higher than the background level (by tens of pA). Fig. 1c shows profiles, for both the height and current, along a line which passes through a leakage site (shown in Fig. 1a and b). From analysis of many different leakage sites in the film, we estimate a mean width of about 3 nm. In addition to leakage sites, spots with much larger currents in the nA range are observed (which we refer to as breakdown spots). The breakdown spots are generally much larger than the leakage sites, 20 nm, and are also located along the GBs. It is likely that the breakdown spots are created by the voltage applied during the scan [7]. To elucidate the different factors which contribute to the observed increase in leakage current at GBs we have performed first
Fig. 1. (a) Topographical image of the HfO2 film showing a granular structure with GBs appearing as depressions (image dimensions: 168 168 nm). (b) Current image obtained at 6.5 V for the same region depicted in (a). (c) Height (dashed line) and current (continuous line) profiles along the path indicated in (a) and (b).
Fig. 2. (a) The supercell model of the (1 0 1) tilt grain boundary in m-HfO2 (supercell dimensions: 10.35 7.87 34.67 Å). Large green spheres represent Hf ions and small red ions represent O ions. The GB plane is indicated by the dashed line. (b) An illustration of the development a thermal groove at the surface of a polycrystal. The equilibrium groove angle b is determined by a balance between the GB and surface free energies (cGB and cs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
principles calculations of the structural and electronic properties of a symmetric HfO2 (1 0 1) tilt GB. This particular boundary was chosen based on the principle that the most stable boundaries should have a high degree of site coincidence between grains. The GB was modelled within a periodic supercell (Fig. 2a) containing 80 Hf and 160 O ions with dimensions 10.35 7.87 34.67 Å. In the optimised structure all O ions are at least three-coordinated and all Hf ions are seven-coordinated as is the case in the bulk. The main differences with respect to the bulk are confined within a region about 5 Å on either side of the GB plane. In this region, the electrostatic potential varies by about 0.3 V and bond lengths deviate from the bulk by about 2%. The calculated formation energy per unit area of the GB is 0.60 Jm 2 (defined with respect to the perfect bulk crystal). As this boundary has very low energy and no undercoordinated ions we consider this to be a best case scenario and more general boundaries may have stronger perturbations near the interface. As noted above, the depressions that are observed in the CAFM topographical images are a result of thermal grooving which occurs when GBs emerge to intersect the surface of a hot polycrystal [17]. The structure of the groove results from the balance between the GB free energy (cGB) and the two surface free energies (cs) along the line of intersection (Fig. 2b). The familiar condition for the equilibrium groove angle b is 2cs sin b = cGB [18]. Using the calculated GB formation energy (0.60 Jm 2) and an average value for the energy of low index surfaces of HfO2 (1.5 Jm 2) [19], one arrives at an estimated groove angle of 11.5°. This prediction compares favourably with the angle that can be estimated from the line profile in Fig. 1c – about 8°. We now turn to the intrinsic electronic properties of the stoichiometric HfO2 (1 0 1) GB to investigate whether it can promote electron tunnelling. To do this, we have calculated the electronic density of states (DOS) of the GB supercell and compared it to that of bulk HfO2. We find that the GB introduces additional electronic states near the bulk valence band maximum and conduction band minimum (Fig. 3a). The occupied valence band GB states are split by less than 0.1 eV from the bulk valence band, and the unoccupied conduction band GB states span a wider 0.3 eV window a below the bulk conduction band minimum. Importantly, the presence of the unoccupied GB states lowers the barrier for electron tunnelling in the vicinity of the GBs, thereby increasing the leakage current. In Fig. 3b, we show how the lowest unoccupied electronic state is
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Fig. 3. (a) Calculated density of states (DOS) of the stoichiometric HfO2 (1 0 1) tilt GB. The shaded regions indicate interface states which are introduced by the GB within the bulk HfO2 band gap. (b) Spatial localisation of the lowest unoccupied electronic state perpendicular to the GB plane (Z = 0).
confined within about 1 nm of the GB plane. This range is comparable to the width of the experimental current profile determined from CAFM (Fig. 1c). However, quantitative comparison is difficult as the experimental current profile is also convoluted with the oxide thickness variation in the vicinity of the GB. HfO2, like most metal oxide materials, are not usually stoichiometric and often contain significant concentrations of oxygen vacancies which can contribute to leakage current. Therefore, it is important to consider how oxygen vacancies interact with the GB. In a previous paper we showed that, in the dilute limit, oxygen vacancies are more stable at the GB than in the bulk of a grain by up to 0.8 eV [20]. Therefore, as a result of segregation, vacancies will be on average closer together at GBs, presenting favourable percolation paths for electron tunnelling through the film. This idea is supported by recent simulations of leakage current in TiN/ HfO2/TiN capacitors under constant voltage stress [6], and is the most probable origin of the leaky sites experimentally observed. We now consider how the properties of the GB are affected as the concentration of vacancies segregated at the GB is increased beyond the dilute limit. First, to assess the stability of the oxygen deficient GB, the formation energy per oxygen defect has been calculated as a function of the concentration of neutral oxygen vacancies segregated to the GB (Fig. 4a). At low concentrations there is an initial rise in the formation energy indicative of repulsive interactions between vacancies. However, for concentrations higher than about 5.1018 m 2, the formation energy per defect begins to fall and level off until the GB is fully depleted of oxygen ions. Importantly, for all the concentrations considered, neutral oxygen vacancies are more stable at the GB than in bulk HfO2. Fig. 4b shows how the electronic DOS is modified as the vacancy concentration is increased (i–v). At low concentrations (i and ii) the defects induce localised states in the band gap which involve bonding and anti-bonding combinations of neighbouring vacancy states. For concentrations greater than 5.1018 m 2 (iii–v), the GB core becomes essentially metallic and a sub-band is formed in the HfO2 gap. We suggest that such highly oxygen deficient GBs may be responsible for the breakdown spots in the CAFM images, as they are able to sustain the much higher leakage currents that are measured.
4. Discussion and conclusions The depressions observed in the AFM images of the polycrystalline HfO2 film can be explained in terms of the well known thermal
Fig. 4. (a) The formation energy of neutral oxygen vacancies as a function of their concentration at the GB. The horizontal line indicates the formation energy for neutral oxygen vacancies in the bulk. (b) The modification of the electronic density of states (DOS) as the concentration of vacancies segregated to the GB is increased (see labels i–v).
grooving effect. While the theoretical prediction of the GB grooving angle is similar to that observed by AFM, quantitative analysis to determine the GB energy is difficult as the line profile near the groove minimum is affected by the finite tip radius and there is a lack of experimental data for HfO2 surface energies. Nevertheless, an important consequence of thermal grooving is that the oxide film thickness is reduced near the GBs, which leads to increased direct tunnelling current. This in part explains the observed correlation between the height and current images in Fig. 1. The theoretical calculations also predict that GBs present a reduced barrier to electron tunnelling which should further enhance the
K. McKenna et al. / Microelectronic Engineering 88 (2011) 1272–1275
direct tunnelling current. Importantly, both of these effects serve to increase the leakage current at GBs. The CAFM images also show a number of spots (leakage and breakdown sites), predominantly located at GBs, where the current is enhanced with respect to the rest of the film. Leakage sites, with currents of the order pA, can be explained as a result of trap assisted tunnelling through oxygen vacancies which are segregated at GBs. The breakdown sites which are also observed by CAFM carry much larger currents, in the nA range. The theoretical calculations suggest that these sites could be associated with highly oxygen deficient regions at GBs. Although a detailed model of breakdown is beyond the scope of the current paper, we note that electric field driven vacancy diffusion could lead to oxygen depletion under electrical stress. In this respect, the fact that breakdown sites are observed to occur at positions where the film is thinner, corresponding to higher local electric fields under bias, may be significant [10]. In summary, the CAFM characterisation and theoretical calculations described in this paper demonstrate that GBs in polycrystalline HfO2 films are associated with higher leakage currents. This can be explained by (1) the local reduction in oxide film thickness due to thermal grooving, (2) the intrinsic electronic properties of GBs which present a reduced barrier to tunnelling electrons, and (3) the segregation of oxygen vacancies to GBs which from preferential percolation paths for electron tunnelling and can also cause metallisation at high vacancy concentrations. These results serve to highlight the fact that improving the performance and reliability of HfO2 based electronic devices, such as resistive switching memories and transistors, depends on controlling both the defect content and grain structure of the polycrystalline dielectric film.
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Acknowledgements KPM also acknowledges support from MEXT KAKENHI Project No. 2274019. This work was also supported by the Spanish MICINN (TEC2007-61294/MIC, TEC2010-16126 and BES-2008-007947). Computer resources on the HECToR service were provided via our membership of the UK’s HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/F067496). Additional computer resources on the Chinook supercomputer were provided by the Environmental Molecular Sciences Laboratory (US Department of Energy). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
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