- Email: [email protected]
HfO2 interfaces
Physica B 407 (2012) 2907–2910
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Physica B journal homepage: www.elsevier.com/locate/physb
Effect of O-vacancy defects on the Schottky barrier heights in Ni/SiO2 and Ni/HfO2 interfaces Hyeon-Kyun Noh, Young Jun Oh, K.J. Chang n Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305–701, Republic of Korea
a r t i c l e i n f o
abstract
Available online 26 August 2011
We perform first-principles density functional calculations to study the electronic structure of Ni/HfO2 and Ni/SiO2 interfaces and the effect of O-vacancy (VO) defects on the Schottky barrier height and the effective work function. We generate two interface models in which Ni is placed on O-terminated HfO2 (1 0 0) and a-quartz (1 0 0) surfaces. As the concentration of VO defects at the interface increases, the p-type Schottky barrier height tends to increase in the Ni/HfO2 interface, due to the reduction of interface dipoles, whereas it is less affected in the Ni/SiO2 interface. & 2011 Elsevier B.V. All rights reserved.
Keywords: Ni work function Metal gate HfO2 Schottky barrier
(FM) is described by the formula [8]
1. Introduction
jn ¼ SðFM FS Þ þ ðFS ws Þ,
ð2Þ
The continuous downscaling of complementary metal–oxidesemiconductor (CMOS) devices is hindered by significant gate leakage currents for oxide thicknesses below 1.5 nm [1]. During the last decade, high-k gate dielectrics, such as HfO2, have been considered as replacements for the conventional SiO2 material because gate leakage currents are substantially reduced for the same effective oxide thickness [2]. However, poly-Si/high-k gate stacks have shown many problems, such as Fermi-level pinning, threshold voltage instability, and gate depletion [3,4], which have led to the introduction of metal gates instead of poly-Si gates. In conventional n- and p-type CMOS devices, poly-Si gates are highly doped to retain work functions of approximately 4.05 and 5.15 eV, respectively. Therefore, the work functions of metals should be controlled to have the corresponding values in both types of conventional devices. However, when metal/high-k junctions are formed, the effective work functions change from the vacuum work function values [5]. The origin of this variation is still debated. The effective work function ðF0M Þ is defined as the sum of the dielectric electron affinity (ws) and the n-type Schottky barrier height (jn) in a metal–oxide interface:
where FS is the oxide charge neutrality level and S is the Schottky pinning factor, which varies between two extreme values: 0 (strong pinning in the Bardeen limit) and 1 (weak pinning in the Schottky limit). However, the MIGS model does not include the pinning effects of defects and local interface structures. To describe more precisely the Schottky barrier height, extrinsic effects, such as interface bonding, defects, and interface polarization should be considered. In this work, we investigate the electronic properties of Ni/oxide interfaces and the effect of O-vacancy (VO) defects on the Schottky barrier height through first-principles density functional calculations. We generate two interface structures, Ni/SiO2 and Ni/HfO2, in which Ni is placed on O-terminated a-quartz and HfO2 surfaces, respectively. As the density of VO defects at the interface increases, we find that the p-type Schottky barrier height also tends to increase in the Ni/HfO2 interface, while its variation is small in the Ni/SiO2 interface. We discuss in detail the change of interface dipoles by VO defects and its role in the variation of the Schottky barrier height.
F0M ¼ ws þ jn :
2. Calculation method
ð1Þ
In the metal-induced gap state (MIGS) model, the Schottky barrier height is solely determined by the metal-induced gap states, which are responsible for the Fermi level pinning [6,7]. Empirically, the dependence of jn on the metal work function n
Corresponding author. Tel.: þ82 42 350 2531; fax: þ82 42 350 2510. E-mail address: [email protected] (K.J. Chang).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.08.079
We perform first-principles calculations with the density functional theory [9,10]. We use the generalized gradient approximation (GGA) for the exchange-correlation potential [11] and the projectoraugmented wave potentials for the ionic potentials [12] as implemented in the VASP code [13,14]. The wave functions are expanded in plane waves with an energy cutoff of 400 eV. We generate two interface structures, specifically, Ni/HfO2 and Ni/SiO2, in which the
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H.-K. Noh et al. / Physica B 407 (2012) 2907–2910
narrow regions at the center of the oxide slabs. In the Ni/c-HfO2 interface, each interface O atom is bonded to two Hf and two Ni ˚ respectively, while the atoms with bond lengths of 2.19 and 1.91 A, O atoms are surrounded by four Hf atoms in the bulk region with a ˚ Thus, the bond lengths of the Hf–O bonds are bond length of 2.19 A. not affected at the interface. In the Ni/a-quartz structure, we also find the periodic variation of the planar-averaged local potential in the bulk region, and shifted local potential near the interface [Fig. 1(b)]. At the interface, the O atoms are bonded to one Si and ˚ two Ni atoms with bond lengths of approximately 1.63 and 1.91 A, respectively. Although the coordination number of the interfacial O atoms is reduced, the bond length of the Ni–O bonds is the same as that in the Ni/c-HfO2 interface. In the middle of the SiO2, the twofold ˚ which is coordinated O atoms have a Si–O bond length of 1.62 A, similar to that observed at the interface.
Fig. 1. Slab geometries and the planar-averaged local potential profiles in the (a) Ni/c-HfO2 and (b) Ni/a-quartz interfaces. The interface O layer is defined as the origin.
Ni (1 0 0) surface is in contact with the cubic HfO2 (1 0 0) and a-quartz (1 0 0) surfaces, respectively (Fig. 1). In both oxides, the (1 0 0) surfaces are terminated with O atoms, which are directly bonded to the Ni atoms. The O-polar surfaces are convenient for studying the effect of VO defects on the Schottky barrier height because the number of defects at the interface can be easily controlled. To reduce the lattice mismatch between the Ni and oxide, we choose the O2 O2 planar supercell for Ni, which is connected to the 1 1 planar supercell in cubic HfO2 (c-HfO2) and a-quartz. Therefore, the lattice constant of the Ni increases by about 1.8% in the Ni/HfO2 interface, whereas 7.9% tensile strain and 1.3% compressive strain are exerted on the Ni along the [0 0 1] and [0 1 0] directions, respectively, in the Ni/SiO2 interface. We employ the repeated slab geometry without a vacuum. This geometry consists of 7 Ni layers and 5 HfO2 layers in the Ni/HfO2 interface, and 5 Ni layers and 3 SiO2 layers in the Ni/SiO2 interface. Both the geometries have two interfaces and maintain the mirror symmetry by inserting one additional O layer. For the Brillouin zone integration of charge densities, we use 13 and 10 irreducible k-points for the Ni/HfO2 and Ni/SiO2 interfaces, respectively. The interface structures are fully optimized until ˚ the residual forces are less than 0.05 eV/A.
3. Results and discussion Fig. 1(a) shows the atomic structure and the planar-averaged local potential profile for the Ni/c-HfO2 interface. The planaraveraged local potential varies periodically inside the bulk region, while it is slightly shifted near the interface due to interface dipoles. We determine the average of the planar-averaged local potential along the z direction and find its value to be nearly constant in the
Fig. 2. Projected densities of states (PDOS in units of states/eV/layer) onto (a) the Hf, O, and Ni layers in the Ni/c-HfO2 interface and onto (b) the Si, O, and Ni layers in the Ni/a-quartz interface. Red (dark grey) and blue (light grey) lines represent the PDOS in the interface and bulk regions, respectively. Vertical dashed lines denote the valence band maximum (VBM), the Fermi level (EF), and the conduction band minimum (CBM). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
H.-K. Noh et al. / Physica B 407 (2012) 2907–2910
The projected densities of states (PDOS) onto the Hf, O, and Ni layers of the Ni/c-HfO2 slabs are compared in Fig. 2(a). Going from the bulk region to the interface, the PDOS onto the O layers changes significantly in the energy range between 3 and þ3 eV relative to the oxide valence band maximum (VBM). In the PDOS onto the interface Ni layer, the energy states within the oxide gap are slightly lowered relative to the oxide VBM compared with those in the bulk region. The lowering of the Ni energy states near the interface results from the tunneling of the metallic wave functions into the oxide band gap (the so-called metal-induced gap states). The decay length of the MIGS is estimated to be ˚ which is comparable to that obtained for Ni on ZrO2 [15]. 1.12 A, For energies between the Fermi level and the oxide VBM, we find some localized interface states that are formed in the interface O layer [Fig. 2(a)]. In the Ni/a-quartz structure, the PDOS exhibits several peaks at approximately 18.5, 9.0, and 5.5 eV for the Si layers in the bulk oxide region, while these peaks are reduced in the interface region [Fig. 2(b)]. In contrast to the Ni/c-HfO2 interface, the localized interface states associated with the interface O layer do not appear in the oxide band gap, indicating that the dominant states in the band gap are the MIGS. In this case, the ˚ decay length of the MIGS is slightly reduced to 0.92 A. To examine the charge transfer at the interface, we generate the Ni, c-HfO2, and a-quartz surfaces, including vacuum layers of ˚ respectively. We calculate the approximately 10, 10, and 8 A, number of electrons around the surface Ni and O atoms using the Bader charge analysis in which the cutoff radius is determined by the minimum charge density between two atoms [16], and compare the results with those for the interfacial atoms. When the Ni–O bonds are formed at the Ni/c-HfO2 interface, we find that the charge around the Ni atom decreases by about 0.47 electrons, whereas it increases by about 0.41 electrons for the O atom. Similarly, in the Ni/a-quartz interface, the Ni atom loses about 0.31 electrons, while the O atom gains about 0.67 electrons. The charge transfer from the Ni to O atoms enhances the interface dipoles. We introduce VO defects in the Ni/c-HfO2 interface and investigate their effect on the interface dipoles. The energy of a VO defect is found to be lowest at the interface, and converges to the bulk value beyond the second O layer from the interface. In this study, we consider VO defects generated at the interface. As the number of VO defects increases, we find that the number of electrons around each interfacial Ni atom increases, reducing the density of the localized interface states. To understand this trend more quantitatively, we calculate the density of interface states in the oxide band gap, which is defined as Z Z Z0 1 Ds ðEÞ ¼ NðE,rÞ dz dA, ð3Þ A A 0 where A is the interface area, N(E,r) is the local density of states, and z0 denotes the middle position of the oxide. The density of interface states is plotted as a function of energy within the oxide gap in Fig. 3. Near the Fermi level, the densities of interface states are estimated to be approximately 1015 states/eV/cm2. These high densities are mostly attributed to the localized interface states formed at the interface O layer, which are shown in Fig. 2(a). For higher energies above the Fermi level, the densities of interface states are much lower but remain non-zero with a magnitude of about 1014 states/eV/cm2. These states originate from the MIGS, and the order of magnitude is similar to that of other ionic crystals [17]. When more VO defects are introduced, the localized interface states disappear. Meanwhile, new defect levels associated with the Ni and Hf dangling bonds around the VO defect are generated. For a slab geometry of c-HfO2 with a vacuum, we note that the Hf dangling bond states are located near the CBM. Because these
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Fig. 3. Densities of interface states in the oxide band gap in Ni/c-HfO2 interfaces with different numbers of VO defects (n ¼0, 1, 2 per unit cell).
defect levels are higher than the Fermi level, electrons are transferred from the vacancy-neighboring Hf atoms to the interfacial Ni atoms, reducing the electronegativity of the interface O layer. As the interface dipoles are reduced by the charge transfer to the interfacial Ni atoms, the Fermi level is raised to higher energy (Fig. 3). However, in the Ni/a-quartz interface, the charge transfer to the Ni atoms is minimal. In this case, the defect level of the VO is characterized by the neighboring Si dangling bonds. Because the Si dangling bond level is positioned in the lower half of the oxide band gap, the number of electrons around the interfacial Ni atoms is not significantly affected. As a result, the change in the interface dipoles induced by the VO defects is much smaller in the Ni/a-quartz interface. From the local density of states, we estimate the Schottky barrier height and the effective work function in the interface. Similar to Eq. (1), the effective work function is written as
F0M ¼ ws þ ½Eg jp þ DEVBM ,
ð4Þ
where Eg is the dielectric band gap, jp is the p-type Schottky barrier height, and DEVBM is a correction to the VBM state. In the Ni/c-HfO2 interface, the GGA calculations show that the p-type Schottky barrier height is jp ¼1.37 eV in the absence of VO defects, which finding is consistent with the previous result for Ni on the O-terminated c-HfO2 surface [18]. For high-k dielectrics, quasi-particle GW calculations showed that the GGA overestimates the VBM state by about 0.5 eV [19]. Including the GW correction to the VBM of DEVBM ¼ 0.5 eV, the p-type Schottky barrier height becomes jp ¼1.87 eV, which is in better agreement with the experimental values of 2.6 3.3 eV [18]. Thus, we obtain the effective work function of F0 M ¼5.83 eV using the measured values of ws ¼ 2.0 eV and Eg ¼5.7 eV for HfO2. However, this work function is higher than the measured value of 5 eV [20]. When VO defects are generated at the interface, jp increases to 1.47 eV for one defect per unit cell, and further increases to 1.80 eV for two defects. The values further increase to 1.97 and 2.30 eV, respectively, with the inclusion of the GW correction, and the effective work function decreases to F0 M ¼5.73 and 5.4 eV, respectively. The increasing (decreasing) behavior of jp (F0 M) is attributed to the reduction of interface dipoles by the VO defects, as discussed earlier. The presence of the interface O layer actually hinders the charge transfer from the Hf to Ni atoms. A similar tendency was observed in the Pt/HfO2 interface [21], where Pt acts as a p-type metal like Ni. When the O atoms were introduced at the Pt/HfO2 interface, the effective work function of Pt was shown to increase. In the Ni/a-quartz interface without VO defects, the GGA calculations give a p-type Schottky barrier height of 2.02 eV. As the number of VO defects increases, the change of jp is less than
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0.15 eV. This small change is mainly due to the insensitivity of the interface dipoles to the defects. With the GW correction of DEVBM ¼ 2.0 eV [22], the p-type Schottky barrier height changes from 4.02 to 4.17 eV as the number of VO defects increases from one to two. When the experimentally measured values of ws ¼1.0 eV and Eg ¼9 eV are used for SiO2, the effective work functions are in the range of 5.83 5.98 eV, even in the presence of VO defects. This range is higher than the fitted value of 5.3 eV from experiments [23]. From the MIGS formula in Eq. (2), we estimate the effective work functions to be 5.2 and 5.35 eV for the Ni/HfO2 and Ni/SiO2 interfaces, respectively, which are close to the measured values. Although the MIGS theory is successful in calculating the effective work function, it cannot explain the effect of defects on it. On the other hand, our GGA calculations successfully explain the trend of the effective work function when VO defects are introduced at the interface. However, we point out that it is still difficult to make an accurate estimate for the effective work function from the GGA calculations, due to the underestimation of the band gaps.
4. Conclusion In conclusion, we have studied the effect of VO defects on the Schottky barrier height in Ni/HfO2 and Ni/SiO2 interfaces using first-principles density functional calculations. We find that the p-type Schottky barrier height is more sensitive to the concentration of VO defects in the Ni/HfO2 interface. When VO defects are introduced at the Ni/HfO2 interface, the charge transfer from the Hf to the interfacial Ni atoms reduces the interface dipoles. Thus, the p-type Schottky barrier height tends to increase with increasing defect density. On the other hand, in the Ni/SiO2 interface, the interface dipoles are not notably affected by the VO defects because the vacancy-neighboring Si dangling bonds prevent the charge transfer.
Acknowledgments This work was supported by the National Research Foundation of Korea (Grant No. NRF-2010-0093845) and by Samsung Electronics Co., Ltd.
References [1] S.-H. Lo, D.A. Buchanan, Y. Taur, W. Wang, IEEE Electron Device Lett. 18 (1997) 209. [2] J. Robertson, Eur. Phys. J. Appl. Phys. 28 (2004) 265. [3] C. Hobbs, L. Fonseca, V. Dhandapani, S. Samavedam, B. Taylor, J. Grant, L. Dip, D. Triyoso, R. Hegde, D. Gilmer, R. Garcia, D. Roan, L. Lovejoy, R. Rai, L. Hebert, H. Tseng, B. White, P. Tobin, in: Proceedings of the IEEE Symposium on VLSI Technology, 2003, p. 9. [4] Y. Kim, G. Gebara, M. Freiler, J. Barnett, D. Rieley, J. Chen, K. Torres, J. Lim, B. Foran, F. Shaapur, A. Agarwal, P. Lysagt, G.A. Brown, C. Young, S. Borthakur, H.J. Li, B. Nguyen, P. Zeitzoff, G. Bersuker, D. Derro, R. Bergmann, R.W. Murto, A. Hou, H.R. Huff, E. Shero, C. Pomarede, M. Givens, M. Mazanec, C. Werkhoven, IEEE IEDM Tech. Dig. 2001 (2001) 455. [5] V. Narayanan, V.K. Paruchuri, E. Cartier, B.P. Linder, N. Bojarczuk, S. Guha, S.L. Brown, Y. Wang, M. Copel, T.C. Chen, Microelectron. Eng. 84 (2007) 1853. [6] V. Heine, Phys. Rev. 138 (1965) A1689. [7] S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 35 (1975) 866. [8] A.M. Cowley, S.M. Sze, J. Appl. Phys. 36 (1965) 3212. [9] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [10] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. [11] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [12] P.E. Bl chl, Phys. Rev. B 50 (1994) 17953. [13] G. Kresse, J. Furthmu€ller, Phys. Rev. B 54 (1996) 11169. [14] G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758. [15] Y.F. Dong, S.J. Wang., Y.P. Feng, A.C.H. Huan, Phys. Rev. B 73 (1977) 045302. [16] W. Tang, E. Sanville, G. Henkelman, J. Phys: Condens. Matter 21 (2009) 084204. [17] S.G. Louie, J.R. Chelikowsky, M.L. Cohen, Phys. Rev. B 15 (1977) 2154. [18] K.Y. Tse, D. Liu, J. Robertson, Phys. Rev. B 81 (2010) 035325. [19] M. Gru€ning, R. Shaltaf, G.-M. Rignanese, Phys. Rev. B 81 (2010) 035330. [20] J. Robertson, J. Vac. Sci. Technol. B 27 (2009) 277. [21] J.K. Schaeffer, L.R.C. Fonseca, S.B. Samavedam, Y. Liang, P.J. Tobin, B.E. White, Appl. Phys. Lett. 85 (2004) 1826. [22] R. Shaltaf, G.-M. Rignanese, X. Gonze, F. Giustino, A. Pasquarello, Phys. Rev. Lett. 100 (2008) 186401. [23] Y.-C. Yeo, T.-J. King, C. Hu, J. Appl. Phys. 92 (2002) 7266.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Effect of O-vacancy defects on the Schottky barrier heights in Ni/SiO2 and Ni/HfO2 interfaces Hyeon-Kyun Noh, Young Jun Oh, K.J. Chang n Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305–701, Republic of Korea
a r t i c l e i n f o
abstract
Available online 26 August 2011
We perform first-principles density functional calculations to study the electronic structure of Ni/HfO2 and Ni/SiO2 interfaces and the effect of O-vacancy (VO) defects on the Schottky barrier height and the effective work function. We generate two interface models in which Ni is placed on O-terminated HfO2 (1 0 0) and a-quartz (1 0 0) surfaces. As the concentration of VO defects at the interface increases, the p-type Schottky barrier height tends to increase in the Ni/HfO2 interface, due to the reduction of interface dipoles, whereas it is less affected in the Ni/SiO2 interface. & 2011 Elsevier B.V. All rights reserved.
Keywords: Ni work function Metal gate HfO2 Schottky barrier
(FM) is described by the formula [8]
1. Introduction
jn ¼ SðFM FS Þ þ ðFS ws Þ,
ð2Þ
The continuous downscaling of complementary metal–oxidesemiconductor (CMOS) devices is hindered by significant gate leakage currents for oxide thicknesses below 1.5 nm [1]. During the last decade, high-k gate dielectrics, such as HfO2, have been considered as replacements for the conventional SiO2 material because gate leakage currents are substantially reduced for the same effective oxide thickness [2]. However, poly-Si/high-k gate stacks have shown many problems, such as Fermi-level pinning, threshold voltage instability, and gate depletion [3,4], which have led to the introduction of metal gates instead of poly-Si gates. In conventional n- and p-type CMOS devices, poly-Si gates are highly doped to retain work functions of approximately 4.05 and 5.15 eV, respectively. Therefore, the work functions of metals should be controlled to have the corresponding values in both types of conventional devices. However, when metal/high-k junctions are formed, the effective work functions change from the vacuum work function values [5]. The origin of this variation is still debated. The effective work function ðF0M Þ is defined as the sum of the dielectric electron affinity (ws) and the n-type Schottky barrier height (jn) in a metal–oxide interface:
where FS is the oxide charge neutrality level and S is the Schottky pinning factor, which varies between two extreme values: 0 (strong pinning in the Bardeen limit) and 1 (weak pinning in the Schottky limit). However, the MIGS model does not include the pinning effects of defects and local interface structures. To describe more precisely the Schottky barrier height, extrinsic effects, such as interface bonding, defects, and interface polarization should be considered. In this work, we investigate the electronic properties of Ni/oxide interfaces and the effect of O-vacancy (VO) defects on the Schottky barrier height through first-principles density functional calculations. We generate two interface structures, Ni/SiO2 and Ni/HfO2, in which Ni is placed on O-terminated a-quartz and HfO2 surfaces, respectively. As the density of VO defects at the interface increases, we find that the p-type Schottky barrier height also tends to increase in the Ni/HfO2 interface, while its variation is small in the Ni/SiO2 interface. We discuss in detail the change of interface dipoles by VO defects and its role in the variation of the Schottky barrier height.
F0M ¼ ws þ jn :
2. Calculation method
ð1Þ
In the metal-induced gap state (MIGS) model, the Schottky barrier height is solely determined by the metal-induced gap states, which are responsible for the Fermi level pinning [6,7]. Empirically, the dependence of jn on the metal work function n
Corresponding author. Tel.: þ82 42 350 2531; fax: þ82 42 350 2510. E-mail address: [email protected] (K.J. Chang).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.08.079
We perform first-principles calculations with the density functional theory [9,10]. We use the generalized gradient approximation (GGA) for the exchange-correlation potential [11] and the projectoraugmented wave potentials for the ionic potentials [12] as implemented in the VASP code [13,14]. The wave functions are expanded in plane waves with an energy cutoff of 400 eV. We generate two interface structures, specifically, Ni/HfO2 and Ni/SiO2, in which the
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H.-K. Noh et al. / Physica B 407 (2012) 2907–2910
narrow regions at the center of the oxide slabs. In the Ni/c-HfO2 interface, each interface O atom is bonded to two Hf and two Ni ˚ respectively, while the atoms with bond lengths of 2.19 and 1.91 A, O atoms are surrounded by four Hf atoms in the bulk region with a ˚ Thus, the bond lengths of the Hf–O bonds are bond length of 2.19 A. not affected at the interface. In the Ni/a-quartz structure, we also find the periodic variation of the planar-averaged local potential in the bulk region, and shifted local potential near the interface [Fig. 1(b)]. At the interface, the O atoms are bonded to one Si and ˚ two Ni atoms with bond lengths of approximately 1.63 and 1.91 A, respectively. Although the coordination number of the interfacial O atoms is reduced, the bond length of the Ni–O bonds is the same as that in the Ni/c-HfO2 interface. In the middle of the SiO2, the twofold ˚ which is coordinated O atoms have a Si–O bond length of 1.62 A, similar to that observed at the interface.
Fig. 1. Slab geometries and the planar-averaged local potential profiles in the (a) Ni/c-HfO2 and (b) Ni/a-quartz interfaces. The interface O layer is defined as the origin.
Ni (1 0 0) surface is in contact with the cubic HfO2 (1 0 0) and a-quartz (1 0 0) surfaces, respectively (Fig. 1). In both oxides, the (1 0 0) surfaces are terminated with O atoms, which are directly bonded to the Ni atoms. The O-polar surfaces are convenient for studying the effect of VO defects on the Schottky barrier height because the number of defects at the interface can be easily controlled. To reduce the lattice mismatch between the Ni and oxide, we choose the O2 O2 planar supercell for Ni, which is connected to the 1 1 planar supercell in cubic HfO2 (c-HfO2) and a-quartz. Therefore, the lattice constant of the Ni increases by about 1.8% in the Ni/HfO2 interface, whereas 7.9% tensile strain and 1.3% compressive strain are exerted on the Ni along the [0 0 1] and [0 1 0] directions, respectively, in the Ni/SiO2 interface. We employ the repeated slab geometry without a vacuum. This geometry consists of 7 Ni layers and 5 HfO2 layers in the Ni/HfO2 interface, and 5 Ni layers and 3 SiO2 layers in the Ni/SiO2 interface. Both the geometries have two interfaces and maintain the mirror symmetry by inserting one additional O layer. For the Brillouin zone integration of charge densities, we use 13 and 10 irreducible k-points for the Ni/HfO2 and Ni/SiO2 interfaces, respectively. The interface structures are fully optimized until ˚ the residual forces are less than 0.05 eV/A.
3. Results and discussion Fig. 1(a) shows the atomic structure and the planar-averaged local potential profile for the Ni/c-HfO2 interface. The planaraveraged local potential varies periodically inside the bulk region, while it is slightly shifted near the interface due to interface dipoles. We determine the average of the planar-averaged local potential along the z direction and find its value to be nearly constant in the
Fig. 2. Projected densities of states (PDOS in units of states/eV/layer) onto (a) the Hf, O, and Ni layers in the Ni/c-HfO2 interface and onto (b) the Si, O, and Ni layers in the Ni/a-quartz interface. Red (dark grey) and blue (light grey) lines represent the PDOS in the interface and bulk regions, respectively. Vertical dashed lines denote the valence band maximum (VBM), the Fermi level (EF), and the conduction band minimum (CBM). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
H.-K. Noh et al. / Physica B 407 (2012) 2907–2910
The projected densities of states (PDOS) onto the Hf, O, and Ni layers of the Ni/c-HfO2 slabs are compared in Fig. 2(a). Going from the bulk region to the interface, the PDOS onto the O layers changes significantly in the energy range between 3 and þ3 eV relative to the oxide valence band maximum (VBM). In the PDOS onto the interface Ni layer, the energy states within the oxide gap are slightly lowered relative to the oxide VBM compared with those in the bulk region. The lowering of the Ni energy states near the interface results from the tunneling of the metallic wave functions into the oxide band gap (the so-called metal-induced gap states). The decay length of the MIGS is estimated to be ˚ which is comparable to that obtained for Ni on ZrO2 [15]. 1.12 A, For energies between the Fermi level and the oxide VBM, we find some localized interface states that are formed in the interface O layer [Fig. 2(a)]. In the Ni/a-quartz structure, the PDOS exhibits several peaks at approximately 18.5, 9.0, and 5.5 eV for the Si layers in the bulk oxide region, while these peaks are reduced in the interface region [Fig. 2(b)]. In contrast to the Ni/c-HfO2 interface, the localized interface states associated with the interface O layer do not appear in the oxide band gap, indicating that the dominant states in the band gap are the MIGS. In this case, the ˚ decay length of the MIGS is slightly reduced to 0.92 A. To examine the charge transfer at the interface, we generate the Ni, c-HfO2, and a-quartz surfaces, including vacuum layers of ˚ respectively. We calculate the approximately 10, 10, and 8 A, number of electrons around the surface Ni and O atoms using the Bader charge analysis in which the cutoff radius is determined by the minimum charge density between two atoms [16], and compare the results with those for the interfacial atoms. When the Ni–O bonds are formed at the Ni/c-HfO2 interface, we find that the charge around the Ni atom decreases by about 0.47 electrons, whereas it increases by about 0.41 electrons for the O atom. Similarly, in the Ni/a-quartz interface, the Ni atom loses about 0.31 electrons, while the O atom gains about 0.67 electrons. The charge transfer from the Ni to O atoms enhances the interface dipoles. We introduce VO defects in the Ni/c-HfO2 interface and investigate their effect on the interface dipoles. The energy of a VO defect is found to be lowest at the interface, and converges to the bulk value beyond the second O layer from the interface. In this study, we consider VO defects generated at the interface. As the number of VO defects increases, we find that the number of electrons around each interfacial Ni atom increases, reducing the density of the localized interface states. To understand this trend more quantitatively, we calculate the density of interface states in the oxide band gap, which is defined as Z Z Z0 1 Ds ðEÞ ¼ NðE,rÞ dz dA, ð3Þ A A 0 where A is the interface area, N(E,r) is the local density of states, and z0 denotes the middle position of the oxide. The density of interface states is plotted as a function of energy within the oxide gap in Fig. 3. Near the Fermi level, the densities of interface states are estimated to be approximately 1015 states/eV/cm2. These high densities are mostly attributed to the localized interface states formed at the interface O layer, which are shown in Fig. 2(a). For higher energies above the Fermi level, the densities of interface states are much lower but remain non-zero with a magnitude of about 1014 states/eV/cm2. These states originate from the MIGS, and the order of magnitude is similar to that of other ionic crystals [17]. When more VO defects are introduced, the localized interface states disappear. Meanwhile, new defect levels associated with the Ni and Hf dangling bonds around the VO defect are generated. For a slab geometry of c-HfO2 with a vacuum, we note that the Hf dangling bond states are located near the CBM. Because these
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Fig. 3. Densities of interface states in the oxide band gap in Ni/c-HfO2 interfaces with different numbers of VO defects (n ¼0, 1, 2 per unit cell).
defect levels are higher than the Fermi level, electrons are transferred from the vacancy-neighboring Hf atoms to the interfacial Ni atoms, reducing the electronegativity of the interface O layer. As the interface dipoles are reduced by the charge transfer to the interfacial Ni atoms, the Fermi level is raised to higher energy (Fig. 3). However, in the Ni/a-quartz interface, the charge transfer to the Ni atoms is minimal. In this case, the defect level of the VO is characterized by the neighboring Si dangling bonds. Because the Si dangling bond level is positioned in the lower half of the oxide band gap, the number of electrons around the interfacial Ni atoms is not significantly affected. As a result, the change in the interface dipoles induced by the VO defects is much smaller in the Ni/a-quartz interface. From the local density of states, we estimate the Schottky barrier height and the effective work function in the interface. Similar to Eq. (1), the effective work function is written as
F0M ¼ ws þ ½Eg jp þ DEVBM ,
ð4Þ
where Eg is the dielectric band gap, jp is the p-type Schottky barrier height, and DEVBM is a correction to the VBM state. In the Ni/c-HfO2 interface, the GGA calculations show that the p-type Schottky barrier height is jp ¼1.37 eV in the absence of VO defects, which finding is consistent with the previous result for Ni on the O-terminated c-HfO2 surface [18]. For high-k dielectrics, quasi-particle GW calculations showed that the GGA overestimates the VBM state by about 0.5 eV [19]. Including the GW correction to the VBM of DEVBM ¼ 0.5 eV, the p-type Schottky barrier height becomes jp ¼1.87 eV, which is in better agreement with the experimental values of 2.6 3.3 eV [18]. Thus, we obtain the effective work function of F0 M ¼5.83 eV using the measured values of ws ¼ 2.0 eV and Eg ¼5.7 eV for HfO2. However, this work function is higher than the measured value of 5 eV [20]. When VO defects are generated at the interface, jp increases to 1.47 eV for one defect per unit cell, and further increases to 1.80 eV for two defects. The values further increase to 1.97 and 2.30 eV, respectively, with the inclusion of the GW correction, and the effective work function decreases to F0 M ¼5.73 and 5.4 eV, respectively. The increasing (decreasing) behavior of jp (F0 M) is attributed to the reduction of interface dipoles by the VO defects, as discussed earlier. The presence of the interface O layer actually hinders the charge transfer from the Hf to Ni atoms. A similar tendency was observed in the Pt/HfO2 interface [21], where Pt acts as a p-type metal like Ni. When the O atoms were introduced at the Pt/HfO2 interface, the effective work function of Pt was shown to increase. In the Ni/a-quartz interface without VO defects, the GGA calculations give a p-type Schottky barrier height of 2.02 eV. As the number of VO defects increases, the change of jp is less than
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0.15 eV. This small change is mainly due to the insensitivity of the interface dipoles to the defects. With the GW correction of DEVBM ¼ 2.0 eV [22], the p-type Schottky barrier height changes from 4.02 to 4.17 eV as the number of VO defects increases from one to two. When the experimentally measured values of ws ¼1.0 eV and Eg ¼9 eV are used for SiO2, the effective work functions are in the range of 5.83 5.98 eV, even in the presence of VO defects. This range is higher than the fitted value of 5.3 eV from experiments [23]. From the MIGS formula in Eq. (2), we estimate the effective work functions to be 5.2 and 5.35 eV for the Ni/HfO2 and Ni/SiO2 interfaces, respectively, which are close to the measured values. Although the MIGS theory is successful in calculating the effective work function, it cannot explain the effect of defects on it. On the other hand, our GGA calculations successfully explain the trend of the effective work function when VO defects are introduced at the interface. However, we point out that it is still difficult to make an accurate estimate for the effective work function from the GGA calculations, due to the underestimation of the band gaps.
4. Conclusion In conclusion, we have studied the effect of VO defects on the Schottky barrier height in Ni/HfO2 and Ni/SiO2 interfaces using first-principles density functional calculations. We find that the p-type Schottky barrier height is more sensitive to the concentration of VO defects in the Ni/HfO2 interface. When VO defects are introduced at the Ni/HfO2 interface, the charge transfer from the Hf to the interfacial Ni atoms reduces the interface dipoles. Thus, the p-type Schottky barrier height tends to increase with increasing defect density. On the other hand, in the Ni/SiO2 interface, the interface dipoles are not notably affected by the VO defects because the vacancy-neighboring Si dangling bonds prevent the charge transfer.
Acknowledgments This work was supported by the National Research Foundation of Korea (Grant No. NRF-2010-0093845) and by Samsung Electronics Co., Ltd.
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