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Work function control at metal high-dielectric-constant gate oxide interfaces
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Microelectronic Engineering 85 (2008) 9–14 www.elsevier.com/locate/mee
Work function control at metal high-dielectric-constant gate oxide interfaces K. Tse, J. Robertson
*
Engineering Department, Cambridge University, Cambridge CB2 1PZ, UK Received 6 November 2006; accepted 30 January 2007 Available online 12 February 2007
Abstract There has been difficulty in finding metals of sufficiently large or small effective work function to act as metal electrodes on high-dielectric-constant gate oxides. To understand the factors affecting the effective work function, we have calculated the Schottky barrier heights (SBH) of a range of metals at different configurations on (1 0 0) and (1 1 0) HfO2 surfaces. On (1 0 0) surfaces, different O-terminations are found to be able to shift the SBH by up to 1 eV. Metals of different work function from Y to Ni are found to be able to shift the SBH by over 1 eV. This is a key conclusion which contrasts with the ‘Fermi level pinning’ on HfO2 found by some groups. On the non-polar (1 1 0) surface, the low work function metals like Al and Hf are found to bond to O sites, whereas high work function metals like Ni can bond to both Hf and O sites. Thus, many factors such a termination and stoichiometry control the SBH and the effective work function of a metal. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Metal gates; High K oxides
1. Introduction The continued scaling of complementary metal oxide semiconductor (CMOS) transistors requires the replacement of SiO2 gate oxide by oxides of high dielectric constant (j) such as HfO2 [1,2]. However, poly crystalline Si gate electrodes are incompatible with HfO2 due to a reaction of HfO2 with the Si to form Hf silicide [3–5]. In addition, n- and p-doped poly-Si electrodes on HfO2 appear to be unable to shift the surface work function of the gate completely across the band gap of the Si channel [6,7]. This has sometimes been called ‘Fermi level pinning’. Thus there is considerable effort to find compatible metals to act as gate electrodes instead of poly-Si in high K-based devices [8–19]. This led to an intensive study of the ‘effective’ work function (EWF) from CV measurements of various thermally stable metal systems. The EWF of various metals on HfO2 and ZrO2 appears to show a restricted range of *
Corresponding author. Tel.: +44 1223 748331; fax: +44 1223 332662. E-mail address: [email protected] (J. Robertson).
0167-9317/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.01.240
values, according to the data of Schaeffer et al. [8]. The barrier heights of metals of Afanasev et al. [9] also show a restricted range, consistent with some Fermi level pinning. On the other hand, the data of Majhi et al. [11] shows a wider range of values. Recently, a number of groups have developed metal electrodes which show EWF values close enough to n- and p-band edge values. Examples are TaC [15] and various La based layers [16,17] for n-metals and AlTaN for p-metal [18]. In addition there is the strong extrinsic effect of oxygen defects [19]. This all suggests that the fundamental factors controlling effective work functions and the Schottky barrier heights of metals on oxides are not fully understood. Further study of interfaces would be of benefit. Normally, the simplest method to study Schottky barrier heights would be the model of metal induced gap states (MIGS) [20–22,10]. This describes the charge transfer at a metal–nonmetal interface in terms of the alignment of a charge neutrality level with the metal Fermi level. However, this model excludes the effect of specific interface terminations [23–25]. In general, a more complete model
10
K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
is required. A disadvantage is that this would require us to study many possible interface combinations. Some effort at this has been achieved for the case of metals on GaAs [24]. Here we calculate the barrier heights of different metals on cubic HfO2. We consider both non-polar and polar oxide interfaces. There are three types of surfaces for ionic materials according to Tasker [26], as shown schematically in Fig. 1. A type 1 interface is non-polar, it has an equal number of positive and negative ions of it. An example is GaAs (1 0 0) or HfO2 (1 1 0). A type 2 interface appears polar but does not possess an electric field across it. This is because it is formed from layer units which are overall neutral, and so it is non-polar overall. An example of this is the HfO2 (1 1 1) surface, cut in the correct place. Perpendicular to (1 1 1), the cell consists of units of O2, Hf4+ and O2 which are overall neutral. Type 3 surfaces are polar. Examples of this are GaAs (1 1 1) and HfO2 (1 0 0). Tasker [26] notes that types 1 and 2 surfaces have finite surface e energies but type 3 surfaces have infinite surface energies, because of the field. The cohesiion of oxide-metal interfaces has been studied for many years. There has been some confusion in the literature because the nature of the cohesion changes with metal coverage. When a monolayer of metal is placed on an oxide, the metal becomes fully ionised, and the cohesion is ionic [27]. When more than a monolayer of metal atoms is involved, the stability is due to polarisation effects [27], as in the image charge model of Stoneham and Tasker [28]. The ionic charges in the oxide give rise to an image in the metal. The ions are attracted to their image. This force is less than for the monolayer. Because of screening, all interface types 1–3 with metals are possible, and type 3 now has a finite energy. The image model is simple enough that it does not treat the metal as a lattice. However, more complete treatments must use models of the oxide and metal with latticematched interfaces. This is a severe limitation. The Ni:HfO2 (1 0 0) interface is lattice matched, if the Ni lattice is rotated by 45°. Both Ni and HfO2 are cubic and their lattice constants are 3.52 and 5.12 A, respectively.
type 1
type 2
- + - + + - + - + - + - + + + -
type 3
-
+ + + + +
-
+ + + + +
+ + -
+ + +
+ 2+ + 2+ -
+ + +
Fig. 1. Different surfaces of ionic oxides, 1 – non-polar, 2 – non-polar units, and 3 – polar.
The Ni (1 0 0) is parallel to HfO2 (1 0 0) and the Ni [1 1 0] direction is parallel to HfO2 [1 0 0], as seen in Fig. 2. It is also possible to create lattice matched (1 1 0) interfaces, with Ni (1 1 0)k HfO2 (1 1 0), as seen in Fig. 3. However, because of the rotation, it is not possible to create a simple (1 1 1) matched interface. Some metal atoms are so large that they lattice match without rotation. A case is La. We can make La (1 0 0)kHfO2 (1 0 0) and La [1 1 0]kHfO2 [1 1 0], see Fig. 4. We can also make an (1 1 0) interface, with La (1 1 0)k HfO2 (1 1 0) and La [1 0 0]k HfO2 [1 0 0], as seen in Fig. 4. Because the lattice constants of the metal and oxide are now equal, we can also form a lattice matched (1 1 1) interface. This has La (1 1 1)k HfO2 (1 1 1) and La [1 1 0]k HfO1 [1 1 0]. 2. Method We have studied the lattice-matched interfaces of many metals on cubic HfO2. The metals are taken in their fcc phase. Most of the relevant metals are transition or rare earth metals, which are normally face-centred cubic (fcc). Of those that are not fcc, Fe is taken in its fcc c-Fe phase. Mo which is normally bcc shows a range of vacuum work functions and is taken as fcc. The supercells consist of metal and oxide slabs and two interfaces, with no vacuum. The total energy of the supercells is calculated by the ab initio plane wave pseudopotential method, using the CASTEP code [29]. The atoms are represented by ultra-soft pseudopotentials and the electronic exchange-correlation potential is given by the generalized gradient approximation (GGA). The supercells contain typically 29 or 31 atoms, consisting of seven layers of metal, 5 Hf and 10 or 12 oxygen atoms. The plane wave cut-off energy is 380 eV. The energy is minimized by allowing atom positions to move, super-cell lengths to vary, but keeping the super-cell angle fixed at 90°. The calculated valence band offsets will be plotted against the experimental work functions. Work functions are taken from tabulations [30]. A problem that still exists in the present method is that it needs lattice-matched interfaces, and HfO2 only matches well a few metals such as Ni. Hence either large lateral unit cells are needed, or the large lattice mismatch can shift the calculated band offsets by a deformation potential. 3. Results The interfacial energy is calculated from the total energy of the slab and that of the bulk metal and oxide using Eint ¼ ETotal ½nEHfO2 þ mEM þ ll0 =2q Here, the factor 2 takes into account that there are 2 interfaces per supercell, q is the number of interface metal atoms per cell, n is the number of HfO2 units in the cell, EHfO2 is the free energy of HfO2 per unit, m is the number of metal atoms in the cell, EM is the free energy of solid
K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
11
Fig. 2. (a) Side and top view of the (1 0 0) Ni–oxide interface, O4. Oxygen – red, Hf – brown, and metal – blue, (b) side and top view of the O6 interface, and (c) side and top view of the O3 interface. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
metal per atom, l is the number of excess oxygen atoms not in a HfO2 unit, and l0 is the chemical potential of oxygen, a variable. Various configurations of the (1 0 0) and (1 1 0) interfaces were studied. For the O-terminated (1 0 0) interface with Ni metal, the most stable interface has the Ni atom lying above two oxygen ions of the top layer, as in Fig. 2a. Thus, this O4 interfacial O is 4-fold coordinated, to two Ni atoms in the metal and to two Hf atoms in the oxide. A less stable interface has Ni lying above four O atoms, so the O is 6fold coordinated, denoted O6, as in Fig. 2b. Another configuration has the Ni above a single O atom. This gives 3-fold coordinated O, denoted O3, with O bonded to one
Ni and two Hf’s. These results are similar to those found elsewhere [31–36]. For the non-polar (1 1 0) interface, the metal atom lies between two oxygen ions, so that it makes bonds to two oxygen ions and two metal ions in the top layer, as from the side and top in Fig. 3. The large, electropositive metals such as La form a (1 0 0) interface with only half the metal atom density. The most stable interface configuration is shown from the side and top in Fig. 4a. The (1 1 0) interface is shown in Fig. 4b. The interfacial energy of the polar (1 0 0) interface varies strongly with metal work function or electronegativity. The
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K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
Fig. 3. Side and top view of the (1 1 0) Ni–oxide interface.
Fig. 4. Atomic configurations at the La (1 0 0) and (1 1 0) metal–oxide interfaces. La atoms are yellow. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
interfacial energy of the non-polar (1 1 0) interface is much less dependent on metal work function. This we can express the stability difference (1 0 0)–(1 1 0) as a function of metal work function, as shown in Fig. 5. The actual value of the interfacial energy for the polar interface depends on the oxygen chemical potential, but not for the non-polar interface. We can choose any reference potential. Some choices are the chemical potential in O2, SiO2, or HfO2. We choose RuO2 as reference. This uses the free energies of formation from thermodynamic data Tables. Fig. 5 shows the variation of the difference of interfacial energy of (1 1 0) and (1 0 0) per metal site for different metals in
their FCC phase on HfO2. The low-density interfaces of the metals La and Y are shown separately. There is some scatter, showing that the interface energy is not a monotonic function of WF. We see that there is a cross-over in relative stability of the two interfaces occurs around the work function of Ru. For metals of higher work function and more noble that Ru, the (1 1 0) non-polar interface is more stable. For metals of lower work function and more reactive than Ru, the (1 0 0) interface is more stable. At (1 0 0) interfaces, the metal bonds only to O atoms, and this is favoured for electropositive metals. At (1 1 0), the metal can bond to
(110) - (100) energy difference (eV)
K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
Y
4
Cr
V
3
Ti
La Al
2 Mo Zn
1
Ru
Nb
(100) stabler
0
(110) stabler Cu
-1 2.5
3
3.5 4 4.5 Work function (eV)
Co
Ni
5
5.5
Fig. 5. Difference of interface energy of the (1 0 0) and (1 1 0) interfaces, vs. metal work function.
both Hf and oxygen ions, and this is favoured for electronegative (noble) metals. This is supports the observation of Shiraishi et al. [34]. they noted that noble metals of high work function such as Ni or Pt prefer to bond to the non-polar (1 1 0) faces, so as to form both M–O and M–M 0 bonds, while reactive, low work function metals like Ti or Al tend to bond to the polar, O-terminated (1 0 0) faces, as this allows them to maximize the number of M–O bonds. We then calculated the local density of states of atoms in the metal and oxide. From this, using the ‘bulk’ atoms well inside the metal and oxide slabs, we can calculate the band offset of the valence band energies. The p-type Schottky barrier heights (SBHs) or valence band offsets (VBOs) were calculated for both (1 0 0) and (1 1 0) interfaces, Fig. 6. They show some interesting effects. First, the VBO increases as the metal’s work function decreases. The VBO is found to vary in a linear fashion with the metal work function, with a slope of close to 1. Recall that the Schottky barrier height varies according to /n ¼ SðUM US Þ þ ðUS vs Þ
where UM is the work function of the metal, vs is the electron affinity of the oxide, US is a charge neutrality level of the oxide, and S is a Schottky barrier ‘pinning factor’. Thus the S factor is found to be S 1 for a specific interface type. Second, the VBO shows a strong dependence on the oxide termination. The VBO is much larger for the (1 1 0) interface than the (1 0 0) interface. Thus, the interface dipole depends strongly on interface type, polar or nonpolar. On the other hand the O4 and O6 interfaces have the same VBO. Note that the work function and thus VBO will vary with the lattice constant [37]. This is the finite deformation potential of the metal and the oxide. Thus, our calculated VBOs need to take account of the forced lattice match of metal to the underlying oxide. Finally, the VBO values show some scatter. This is still being studied. It is partly due to the enforced lattice-matching which does not occur at real interfaces. We may draw two conclusions. Firstly it is possible to vary the VBO or Schottky barrier height by well over 1 eV or the Si band gap by varying the metal, or by varying the interface type. This means that it should be possible to design n- and p-type metal electrodes. It is interesting that if one removes the less stable interface configurations, leaving the (1 1 0) for high WF and the (1 0 0) for low WF, as shown in Fig. 7, then the net variation of VBO with WF is lower, closer to S 0.5. This is the experimental value in one case [9]. Our results for one interface are similar to those of Dong et al. [36], but here the result is more general. Note that the work function and thus VBO will vary with the lattice constant. The ability to shift the effective work function by over 1 eV indicates that simple MIGS models are not adequate. This was known previously [38]. This arises because the density of MIGS is not sufficient to provide strong pinning. It does occur for states within the bands, which is why band oxides of Si to oxides may be given correctly, but this model is less good for metals on oxides.
3.5
3.5
(110)
Ti Zr
2.5
(110) Al
Cr
2 Y
(100) 1.5
La 3
3.5
Zr
3
Ru
(100)
Zn
Ti
(100)
Ru
Al
2.5
Ni
Cr
(110)
S~0.5
2
Ni
Cu 4 4.5 WF (eV)
VBO (eV)
VBO (eV)
3
1
13
5
5.5
Fig. 6. Calculated VB offset at the (1 0 0) and (1 1 0) interfaces vs. metal work functions.
1.5
3
3.5
4 4.5 WF (eV)
5
5.5
Fig. 7. Calculated VB offsets for the stable (1 0 0) or (1 1 0) interface for various metals.
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K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
4. Conclusions We have developed a modelling scheme to model the interfaces of metal oxides and metals for metals of a range of electronegativities. Metals of high work function from 4.7 eV and above tend to form non-polar interfaces which allow metal–metal bonds, while metals of lower work function below 4.7 eV tend to form polar, oxygen terminated interfaces. The valence band offset of the oxide with the metals was calculated and is found to vary linearly with metal work function, with a slope of close to one. In addition, the VBO has a sizeable difference for the two types of interfaces. Hence, in principle, it is possible to control the effective work function of a metal at a metal–oxide interface over more than a range of 1.1 eV, which is as required for CMOS. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
G. Wilk, R.M. Wallace, J.M. Anthony, J. Appl. Phys. 89 (2001) 5423. J. Robertson, Rep. Prog. Phys. 69 (2006) 327. E.P. Gusev et al., Microelectron. Eng. 59 (2001) 341. D. Gilmer et al., Microelectron. Eng. 59 (2003) 341. P.C. McIntyre et al., Appl. Phys. Lett. 81 (2002) 1417. C. Hobbs, et al., Tech. Digest VLSI, 2003. C. Hobbs et al., IEEE Trans. ED 51 (2004) 978. J. Schaeffer et al., Tech. Digest IEDM, 2004. p. 287. V. Afanasev, M. Houssa, A. Stesmans, M.M. Heyns, J. Appl. Phys. 91 (2002) 3079 and private communication. [10] Y.C. Yeo, T.J. King, C. Hu, J. Appl. Phys. 92 (2002) 7266. [11] P. Majhi et al., in: Int Symp Advanced Gate Stacks 2 (Sematech, October 2005); see also B.H. Lee, J. Oh, H.H. Tseng, R. Jammy, H. Huff, Mater. Today 9 (June) (2006) p. 32. [12] C. Ren, H.Y. Yu, J.F. Wang, H.H.H. Ma, Y.C. Yeo, D.S.H. Chan, M.F. Li, D.L. Kwong, IEEE ED Lett. 25 (2004) 580.
[13] H.J. Li, M.J. Gardner, IEEE ED Lett. 26 (2005) 441. [14] H. Yang, Y. Son, S. Baek, H. Hwang, H. Lim, H.S. Jung, Appl. Phys. Lett. 86 (2005) 092107. [15] H.H. Tseng et al., IEDM (2004) p. 821. [16] V. Narayanan, N.A. Bojarczuk, B.P. Linder, B. Doris, Y.H. Km, S. Zafar, J. Stathis, S. Brown, J. Arnold, M. Copel, M. Steen, E. Cartier, J.P. Locquet, S. Guha, T.C. Chen, in: Tech. Digest VLSI Symp., Paper 22.2, 2006. [17] X.P. Wang, C. Shen, M.F. Li, H.Y. Yu, Y. Sun, Y.P. Feng, A. Lim, H.W. Sik, Y.C. Yeo, P. Lo, D.L. Kwong, in: Tech. Digest VLSI Symp., Paper 2.2, 2006; H.N. Alshareef et al., App. Phys. Lett. 89 (2006) 232103. [18] H.N. AlShareef et al., Appl. Phys. Lett. 88 (2006) 072108. [19] E. Cartier, et al., in: Tech. Digest VLSI Symp., 2005. [20] J. Robertson, J. Vac. Sci. Technol. B 18 (2000) 1785. [21] P.W. Peacock, J. Robertson, J. Appl. Phys. 92 (2002) 4712. [22] W. Mo¨nch, Phys. Rev. Lett. 58 (1987) 1260. [23] R.T. Tung, Phys. Rev. Lett. 84 (2000) 6078. [24] C. Berthold, N. Binggeli, A. Baldereschi, Phys. Rev. B 68 (2003) 085323. [25] P.W. Peacock, J. Robertson, Phys. Rev. Lett. 92 (2004) 057601. [26] P.W. Tasker, J. Phys. C 12 (1979) 4977. [27] A. Bogicevic, D.R. Jennison, Phys. Rev. Lett. 82 (1999) 4050. [28] A.M. Stoneham, P.W. Tasker, J. Phys. C 18 (1985) L543. [29] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens. Mat. 14 (2002) 2717. [30] H.B. Michaelson, J. Appl. Phys. 48 (1977) 4729; D.E. Eastman, Phys. Rev. B 2 (1970) 1. [31] W. Zhang, J.R. Smith, A.G. Evans, Acta Metall. 50 (2002) 3803. [32] J.L. Beltran, S. Gallego, J. Cerda, J.S. Moya, M.C. Munoz, Phys. Rev. B 68 (2003) 075401. [33] I.G. Batirev, A. Alavi, M.W. Finnis, T. Deutsch, Phys. Rev. Lett. 82 (1999) 1510. [34] K. Shiraishi, et al., Tech. Digest IEDM, 2005. p. 43. [35] Y.F. Dong, S.J. Wang, J.W. Chai, Y.P. Feng, A.C.H. Huan, Appl. Phys. Lett. 86 (2005) 132103. [36] Y.F. Dong, S.J. Wang, Y.P. Feng, A.C.H. Huan, Phys. Rev. B 73 (2006) 045302. [37] N.D. Lang, W. Kohn, Phys. Rev. B 3 (1971) 1215. [38] S.B. Zhang, M.L. Cohen, S.G. Louie, Phys. Rev. B 32 (1985) 3955.
Microelectronic Engineering 85 (2008) 9–14 www.elsevier.com/locate/mee
Work function control at metal high-dielectric-constant gate oxide interfaces K. Tse, J. Robertson
*
Engineering Department, Cambridge University, Cambridge CB2 1PZ, UK Received 6 November 2006; accepted 30 January 2007 Available online 12 February 2007
Abstract There has been difficulty in finding metals of sufficiently large or small effective work function to act as metal electrodes on high-dielectric-constant gate oxides. To understand the factors affecting the effective work function, we have calculated the Schottky barrier heights (SBH) of a range of metals at different configurations on (1 0 0) and (1 1 0) HfO2 surfaces. On (1 0 0) surfaces, different O-terminations are found to be able to shift the SBH by up to 1 eV. Metals of different work function from Y to Ni are found to be able to shift the SBH by over 1 eV. This is a key conclusion which contrasts with the ‘Fermi level pinning’ on HfO2 found by some groups. On the non-polar (1 1 0) surface, the low work function metals like Al and Hf are found to bond to O sites, whereas high work function metals like Ni can bond to both Hf and O sites. Thus, many factors such a termination and stoichiometry control the SBH and the effective work function of a metal. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Metal gates; High K oxides
1. Introduction The continued scaling of complementary metal oxide semiconductor (CMOS) transistors requires the replacement of SiO2 gate oxide by oxides of high dielectric constant (j) such as HfO2 [1,2]. However, poly crystalline Si gate electrodes are incompatible with HfO2 due to a reaction of HfO2 with the Si to form Hf silicide [3–5]. In addition, n- and p-doped poly-Si electrodes on HfO2 appear to be unable to shift the surface work function of the gate completely across the band gap of the Si channel [6,7]. This has sometimes been called ‘Fermi level pinning’. Thus there is considerable effort to find compatible metals to act as gate electrodes instead of poly-Si in high K-based devices [8–19]. This led to an intensive study of the ‘effective’ work function (EWF) from CV measurements of various thermally stable metal systems. The EWF of various metals on HfO2 and ZrO2 appears to show a restricted range of *
Corresponding author. Tel.: +44 1223 748331; fax: +44 1223 332662. E-mail address: [email protected] (J. Robertson).
0167-9317/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.01.240
values, according to the data of Schaeffer et al. [8]. The barrier heights of metals of Afanasev et al. [9] also show a restricted range, consistent with some Fermi level pinning. On the other hand, the data of Majhi et al. [11] shows a wider range of values. Recently, a number of groups have developed metal electrodes which show EWF values close enough to n- and p-band edge values. Examples are TaC [15] and various La based layers [16,17] for n-metals and AlTaN for p-metal [18]. In addition there is the strong extrinsic effect of oxygen defects [19]. This all suggests that the fundamental factors controlling effective work functions and the Schottky barrier heights of metals on oxides are not fully understood. Further study of interfaces would be of benefit. Normally, the simplest method to study Schottky barrier heights would be the model of metal induced gap states (MIGS) [20–22,10]. This describes the charge transfer at a metal–nonmetal interface in terms of the alignment of a charge neutrality level with the metal Fermi level. However, this model excludes the effect of specific interface terminations [23–25]. In general, a more complete model
10
K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
is required. A disadvantage is that this would require us to study many possible interface combinations. Some effort at this has been achieved for the case of metals on GaAs [24]. Here we calculate the barrier heights of different metals on cubic HfO2. We consider both non-polar and polar oxide interfaces. There are three types of surfaces for ionic materials according to Tasker [26], as shown schematically in Fig. 1. A type 1 interface is non-polar, it has an equal number of positive and negative ions of it. An example is GaAs (1 0 0) or HfO2 (1 1 0). A type 2 interface appears polar but does not possess an electric field across it. This is because it is formed from layer units which are overall neutral, and so it is non-polar overall. An example of this is the HfO2 (1 1 1) surface, cut in the correct place. Perpendicular to (1 1 1), the cell consists of units of O2, Hf4+ and O2 which are overall neutral. Type 3 surfaces are polar. Examples of this are GaAs (1 1 1) and HfO2 (1 0 0). Tasker [26] notes that types 1 and 2 surfaces have finite surface e energies but type 3 surfaces have infinite surface energies, because of the field. The cohesiion of oxide-metal interfaces has been studied for many years. There has been some confusion in the literature because the nature of the cohesion changes with metal coverage. When a monolayer of metal is placed on an oxide, the metal becomes fully ionised, and the cohesion is ionic [27]. When more than a monolayer of metal atoms is involved, the stability is due to polarisation effects [27], as in the image charge model of Stoneham and Tasker [28]. The ionic charges in the oxide give rise to an image in the metal. The ions are attracted to their image. This force is less than for the monolayer. Because of screening, all interface types 1–3 with metals are possible, and type 3 now has a finite energy. The image model is simple enough that it does not treat the metal as a lattice. However, more complete treatments must use models of the oxide and metal with latticematched interfaces. This is a severe limitation. The Ni:HfO2 (1 0 0) interface is lattice matched, if the Ni lattice is rotated by 45°. Both Ni and HfO2 are cubic and their lattice constants are 3.52 and 5.12 A, respectively.
type 1
type 2
- + - + + - + - + - + - + + + -
type 3
-
+ + + + +
-
+ + + + +
+ + -
+ + +
+ 2+ + 2+ -
+ + +
Fig. 1. Different surfaces of ionic oxides, 1 – non-polar, 2 – non-polar units, and 3 – polar.
The Ni (1 0 0) is parallel to HfO2 (1 0 0) and the Ni [1 1 0] direction is parallel to HfO2 [1 0 0], as seen in Fig. 2. It is also possible to create lattice matched (1 1 0) interfaces, with Ni (1 1 0)k HfO2 (1 1 0), as seen in Fig. 3. However, because of the rotation, it is not possible to create a simple (1 1 1) matched interface. Some metal atoms are so large that they lattice match without rotation. A case is La. We can make La (1 0 0)kHfO2 (1 0 0) and La [1 1 0]kHfO2 [1 1 0], see Fig. 4. We can also make an (1 1 0) interface, with La (1 1 0)k HfO2 (1 1 0) and La [1 0 0]k HfO2 [1 0 0], as seen in Fig. 4. Because the lattice constants of the metal and oxide are now equal, we can also form a lattice matched (1 1 1) interface. This has La (1 1 1)k HfO2 (1 1 1) and La [1 1 0]k HfO1 [1 1 0]. 2. Method We have studied the lattice-matched interfaces of many metals on cubic HfO2. The metals are taken in their fcc phase. Most of the relevant metals are transition or rare earth metals, which are normally face-centred cubic (fcc). Of those that are not fcc, Fe is taken in its fcc c-Fe phase. Mo which is normally bcc shows a range of vacuum work functions and is taken as fcc. The supercells consist of metal and oxide slabs and two interfaces, with no vacuum. The total energy of the supercells is calculated by the ab initio plane wave pseudopotential method, using the CASTEP code [29]. The atoms are represented by ultra-soft pseudopotentials and the electronic exchange-correlation potential is given by the generalized gradient approximation (GGA). The supercells contain typically 29 or 31 atoms, consisting of seven layers of metal, 5 Hf and 10 or 12 oxygen atoms. The plane wave cut-off energy is 380 eV. The energy is minimized by allowing atom positions to move, super-cell lengths to vary, but keeping the super-cell angle fixed at 90°. The calculated valence band offsets will be plotted against the experimental work functions. Work functions are taken from tabulations [30]. A problem that still exists in the present method is that it needs lattice-matched interfaces, and HfO2 only matches well a few metals such as Ni. Hence either large lateral unit cells are needed, or the large lattice mismatch can shift the calculated band offsets by a deformation potential. 3. Results The interfacial energy is calculated from the total energy of the slab and that of the bulk metal and oxide using Eint ¼ ETotal ½nEHfO2 þ mEM þ ll0 =2q Here, the factor 2 takes into account that there are 2 interfaces per supercell, q is the number of interface metal atoms per cell, n is the number of HfO2 units in the cell, EHfO2 is the free energy of HfO2 per unit, m is the number of metal atoms in the cell, EM is the free energy of solid
K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
11
Fig. 2. (a) Side and top view of the (1 0 0) Ni–oxide interface, O4. Oxygen – red, Hf – brown, and metal – blue, (b) side and top view of the O6 interface, and (c) side and top view of the O3 interface. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
metal per atom, l is the number of excess oxygen atoms not in a HfO2 unit, and l0 is the chemical potential of oxygen, a variable. Various configurations of the (1 0 0) and (1 1 0) interfaces were studied. For the O-terminated (1 0 0) interface with Ni metal, the most stable interface has the Ni atom lying above two oxygen ions of the top layer, as in Fig. 2a. Thus, this O4 interfacial O is 4-fold coordinated, to two Ni atoms in the metal and to two Hf atoms in the oxide. A less stable interface has Ni lying above four O atoms, so the O is 6fold coordinated, denoted O6, as in Fig. 2b. Another configuration has the Ni above a single O atom. This gives 3-fold coordinated O, denoted O3, with O bonded to one
Ni and two Hf’s. These results are similar to those found elsewhere [31–36]. For the non-polar (1 1 0) interface, the metal atom lies between two oxygen ions, so that it makes bonds to two oxygen ions and two metal ions in the top layer, as from the side and top in Fig. 3. The large, electropositive metals such as La form a (1 0 0) interface with only half the metal atom density. The most stable interface configuration is shown from the side and top in Fig. 4a. The (1 1 0) interface is shown in Fig. 4b. The interfacial energy of the polar (1 0 0) interface varies strongly with metal work function or electronegativity. The
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K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
Fig. 3. Side and top view of the (1 1 0) Ni–oxide interface.
Fig. 4. Atomic configurations at the La (1 0 0) and (1 1 0) metal–oxide interfaces. La atoms are yellow. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
interfacial energy of the non-polar (1 1 0) interface is much less dependent on metal work function. This we can express the stability difference (1 0 0)–(1 1 0) as a function of metal work function, as shown in Fig. 5. The actual value of the interfacial energy for the polar interface depends on the oxygen chemical potential, but not for the non-polar interface. We can choose any reference potential. Some choices are the chemical potential in O2, SiO2, or HfO2. We choose RuO2 as reference. This uses the free energies of formation from thermodynamic data Tables. Fig. 5 shows the variation of the difference of interfacial energy of (1 1 0) and (1 0 0) per metal site for different metals in
their FCC phase on HfO2. The low-density interfaces of the metals La and Y are shown separately. There is some scatter, showing that the interface energy is not a monotonic function of WF. We see that there is a cross-over in relative stability of the two interfaces occurs around the work function of Ru. For metals of higher work function and more noble that Ru, the (1 1 0) non-polar interface is more stable. For metals of lower work function and more reactive than Ru, the (1 0 0) interface is more stable. At (1 0 0) interfaces, the metal bonds only to O atoms, and this is favoured for electropositive metals. At (1 1 0), the metal can bond to
(110) - (100) energy difference (eV)
K. Tse, J. Robertson / Microelectronic Engineering 85 (2008) 9–14
Y
4
Cr
V
3
Ti
La Al
2 Mo Zn
1
Ru
Nb
(100) stabler
0
(110) stabler Cu
-1 2.5
3
3.5 4 4.5 Work function (eV)
Co
Ni
5
5.5
Fig. 5. Difference of interface energy of the (1 0 0) and (1 1 0) interfaces, vs. metal work function.
both Hf and oxygen ions, and this is favoured for electronegative (noble) metals. This is supports the observation of Shiraishi et al. [34]. they noted that noble metals of high work function such as Ni or Pt prefer to bond to the non-polar (1 1 0) faces, so as to form both M–O and M–M 0 bonds, while reactive, low work function metals like Ti or Al tend to bond to the polar, O-terminated (1 0 0) faces, as this allows them to maximize the number of M–O bonds. We then calculated the local density of states of atoms in the metal and oxide. From this, using the ‘bulk’ atoms well inside the metal and oxide slabs, we can calculate the band offset of the valence band energies. The p-type Schottky barrier heights (SBHs) or valence band offsets (VBOs) were calculated for both (1 0 0) and (1 1 0) interfaces, Fig. 6. They show some interesting effects. First, the VBO increases as the metal’s work function decreases. The VBO is found to vary in a linear fashion with the metal work function, with a slope of close to 1. Recall that the Schottky barrier height varies according to /n ¼ SðUM US Þ þ ðUS vs Þ
where UM is the work function of the metal, vs is the electron affinity of the oxide, US is a charge neutrality level of the oxide, and S is a Schottky barrier ‘pinning factor’. Thus the S factor is found to be S 1 for a specific interface type. Second, the VBO shows a strong dependence on the oxide termination. The VBO is much larger for the (1 1 0) interface than the (1 0 0) interface. Thus, the interface dipole depends strongly on interface type, polar or nonpolar. On the other hand the O4 and O6 interfaces have the same VBO. Note that the work function and thus VBO will vary with the lattice constant [37]. This is the finite deformation potential of the metal and the oxide. Thus, our calculated VBOs need to take account of the forced lattice match of metal to the underlying oxide. Finally, the VBO values show some scatter. This is still being studied. It is partly due to the enforced lattice-matching which does not occur at real interfaces. We may draw two conclusions. Firstly it is possible to vary the VBO or Schottky barrier height by well over 1 eV or the Si band gap by varying the metal, or by varying the interface type. This means that it should be possible to design n- and p-type metal electrodes. It is interesting that if one removes the less stable interface configurations, leaving the (1 1 0) for high WF and the (1 0 0) for low WF, as shown in Fig. 7, then the net variation of VBO with WF is lower, closer to S 0.5. This is the experimental value in one case [9]. Our results for one interface are similar to those of Dong et al. [36], but here the result is more general. Note that the work function and thus VBO will vary with the lattice constant. The ability to shift the effective work function by over 1 eV indicates that simple MIGS models are not adequate. This was known previously [38]. This arises because the density of MIGS is not sufficient to provide strong pinning. It does occur for states within the bands, which is why band oxides of Si to oxides may be given correctly, but this model is less good for metals on oxides.
3.5
3.5
(110)
Ti Zr
2.5
(110) Al
Cr
2 Y
(100) 1.5
La 3
3.5
Zr
3
Ru
(100)
Zn
Ti
(100)
Ru
Al
2.5
Ni
Cr
(110)
S~0.5
2
Ni
Cu 4 4.5 WF (eV)
VBO (eV)
VBO (eV)
3
1
13
5
5.5
Fig. 6. Calculated VB offset at the (1 0 0) and (1 1 0) interfaces vs. metal work functions.
1.5
3
3.5
4 4.5 WF (eV)
5
5.5
Fig. 7. Calculated VB offsets for the stable (1 0 0) or (1 1 0) interface for various metals.
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4. Conclusions We have developed a modelling scheme to model the interfaces of metal oxides and metals for metals of a range of electronegativities. Metals of high work function from 4.7 eV and above tend to form non-polar interfaces which allow metal–metal bonds, while metals of lower work function below 4.7 eV tend to form polar, oxygen terminated interfaces. The valence band offset of the oxide with the metals was calculated and is found to vary linearly with metal work function, with a slope of close to one. In addition, the VBO has a sizeable difference for the two types of interfaces. Hence, in principle, it is possible to control the effective work function of a metal at a metal–oxide interface over more than a range of 1.1 eV, which is as required for CMOS. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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