Structural and electronic properties of cubic HfO2 surfaces

pe H hy ne 6 t ap at t c. T ons itho PACS: 68.35.Md; 68.47.Gh; 73.20.At; 81.10.Aj Keywords: High j; HfO ; Surfaces; First-principles formance of HfO2 dielectric integrated into silicon technol- ogy is essentially determined by the upper interface on the consideration of lattice matching. Although these modeling studies have successfully predicted some physical for interfaces related to HfO2, a complete understanding of surface properties of HfO film is required. Research [16], suggesting that the termination of outmost surface layer significantly affects the surface electronic structures of HfO2 films. It has been shown that the crystal field effects in HfO2 polymorphs mainly result in the different width of lower conduction bands [17], therefore, we alternatively choose cubic phase of HfO2 to detailedly * Corresponding author. E-mail address: xggong@fudan.edu.cn (X.G. Gong). Available online at www.sciencedirect.com Computational Materials Scien between gate electrode and HfO2 as well as the bottom interface between HfO2 and Si channel. The study on sur- face properties of HfO2 is preliminary and necessary for understanding the behavior of these two interfaces. In pre- vious theoretical studies on interfaces of metal gate/HfO2 [3,4], HfO2=Si [5–8], and HfO2=SiO2 [9], the orientation of HfO2 layers is mostly chosen as (001) surfaces based 2 work on this topic is still limited, and only monoclinic HfO2 surfaces have been reported [10]. Furthermore, the effect of termination layer of surfaces on electronic struc- ture of HfO2 films was neglected in the work of Mukho- padhyay et al. [10]. However, an effective metallization of HfO2 surface by heating to T > 600 �C was detected by low energy ion spectroscopy in recent experimental study 2 1. Introduction Hafnium dioxide (HfO2) recently attracts much atten- tion in the gate stack of metal oxide semiconductor field- effect transistors (MOSFETs) due to its relatively high dielectric constant, wide bandgap and good stability upon Si, and so on [1]. In 2006 it was reported hafnium based oxides was successfully employed as gate dielectric in 45 nm transistor technology by Intel [2]. However the per- properties of interfaces, first-principles calculations on sur- face energies of monoclinic HfO2 have shown that [10] ð�111Þ and (111) surfaces are thermodynamically favored surfaces while the (001) face is kinetically favored, which are also supported by the X-ray diffraction (XRD) spectra of HfO2 thin films grown or annealed at different tempera- tures [11–15]. For gate stack of MOSFETs, HfO2 gate dielectric must be thermodynamically stable on Si sub- strate. Therefore, in order to build more realistic model Structural and electronic pro G.H. Chen, Z.F. Surface Physics Laboratory and Department of P Available onli Abstract Using the first-principles method within the generalized gradien tural and electronic properties of cubic HfO2 surfaces. We find th minated with single oxygen layer, both of which are stoichiometri exhibits very similar behavior, i.e. cations relax inward while ani the Hf–O bond. Both of the two surfaces studied are insulating w � 2008 Elsevier B.V. All rights reserved. 0927-0256/$ - see front matter � 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.01.051 rties of cubic HfO2 surfaces ou, X.G. Gong * sics, Fudan University, Shanghai 200433, China March 2008 proximation, we have performed a systematic study on the struc- he most energetically favorable surfaces are (110) and (111) ter- he atomic relaxation in top layers of surface (111)-O and (110) outward. This could be well understood by the ionic feature of ut any surface state in the energy gap. www.elsevier.com/locate/commatsci ce 44 (2008) 46–52 Administrator 线条 Administrator 线条 Administrator 线条 Administrator 铅笔 3. Results and discussions 3.1. Bulk properties The lattice constant a of 5.06 A˚ and the bulk modulus B0 of 261 GPa for cubic HfO2 bulk are obtained in present work. Both of them are in good agreement with other cal- culation results [17,25] and available experimental value (aexpt ¼ 5:08 A˚) [26]. The density of states (DOS) of bulk cubic HfO2 is shown in Fig. 2. The valence bands are split into two discontinuous groups. The lower part between �20 eV and �15 eV is mostly composed of O s states and the upper one mainly comes from O p states along with a fraction of Hf d states. While Hf d states mainly contribute to the conduction bands. It can also be seen that the valence band maximum (VBM) and the conduction band minimum (CBM) of bulk cubic HfO2 mostly come from the O p states and Hf d states, respectively. Thus, our results indicate that Hf–O bonding in HfO2 exhibits strong ionic characteristics with weak covalency. These are in Fig. 1. The ball and stick model for the surface structures of cubic HfO2. ‘–Hf’, ‘–O’, and ‘–OO’ mean the surfaces are terminated by one Hf atom layer, one O atom layer, and two O atom layers, respectively. Big balls represent Hf atoms, and small ones for O atoms. Ma understand the surface properties of HfO2. In this work, first-principles calculations are performed to systematically study the atomic structures, stabilities, and electronic struc- tures of low Miller index surfaces (i.e. (100), (110) and (111)) with various termination layers of cubic HfO2. This paper is organized as follows. The next section describes the computational details of this study. In the third section we discuss the bulk properties, surface ener- gies, atomic relaxations of surfaces, and surface electronic structures of cubic HfO2 as well. In the last section we draw some general conclusions. 2. Computational details All simulations here are carried out using plane wave pseudopotential method as implemented in the Vienna ab initio simulation package (VASP) [18,19]. The exchange- correlation functional is treated within the generalized gra- dient approximation and parameterized by Perdew–Wang formula [20]. The interaction between ions and electrons is described by ultra-soft Vanderbilt pseudopotentials [21,22]. The wave functions are expanded in plane wave up to a cutoff energy of 495 eV. Brillouin-zone integrations are approximated by using the special k-point sampling of Monhkorst–Pack scheme [23]. Atomic relaxations are per- formed within the conjugated gradient scheme and the force on each atom is converged to be less than 0.01 eV/ A˚. For the electronic minimization the special Davison block iteration algorithm [24] is adopted and a tolerance of 0.02 meV for absolute difference of total energy is used during the electronic self-consistent loop. In the calcula- tions of cubic HfO2 bulk, a mesh size of 5� 5� 5 is used for k-point sampling. To model the surfaces of cubic HfO2, we used the well- known ‘‘slab” approach, in which periodic boundary con- ditions are applied to the surface supercell including a slab of atomic layers and a vacuum region as shown in Fig. 1. In present work, we focus on the surface energies and cor- responding local relaxations rather than the complex reconstructions, therefore, 1� 1 unit cells are used for the low Miller index (i.e. (100), (110), and (111)) surfaces of cubic HfO2 in our calculations. To guarantee surfaces on both sides of the slab being equivalent and eliminate the net dipole moment, we employ a slab with a mirror symmetry. For cubic HfO2, its (100) surface may be termi- nated either by one atomic Hf or O layer (labeled as –Hf and –O, respectively), and its (111) surface could be termi- nated by one atomic Hf layer, one atomic O layer, or two atomic O layers (labeled as –Hf, –O, and –OO, respec- tively). The vacuum layer of 10 A˚ is enough to avoid the interactions between periodic slabs of atomic layers. 11 or 12 atomic layers are used in the slab for each case. The structures of supercells for the surfaces of cubic HfO2 studied here are shown in Fig. 1. The k-meshes 11� 11� 1, 8� 12� 1, and 12� 12� 1 are used in the G.H. Chen et al. / Computational calculations of (100), (110) and (111) surfaces of cubic HfO2, respectively. terials Science 44 (2008) 46–52 47 good agreement with previously calculated results of cubic HfO2 based on a variety of computational methods [27,28]. Administrator 高亮 Administrator 高亮 Administrator 高亮 lHfO2Hf þ 2lHfO2O ¼ EHfO2tot : ð2Þ Because the formation energy ðDEHfO2f Þ of bulk HfO2 is defined as: DEHfO2f ¼ EHfO2tot � l0Hf � 2l0O; ð3Þ where l0Hf is the chemical potential of Hf and taken as the total energy of bulk Hf per f.u., we can obtain the variation range of lO: l0O þ 1 2 DEHfO2f 6 lO 6 l0O: ð4Þ The calculated surface energies for low Miller index sur- Materials Science 44 (2008) 46–52 The bonding characteristics in cubic structure of HfO2 is essentially similar to that in monoclinic HfO2 [29], although the atomic coordinations are slightly different. In monoclinic structure, the oxygen atom is either threefold or fourfold coordinated, while all the Hf atoms are in a sev- enfold-coordinated configuration [25,29]. In cubic phase, the coordination number of Hf is eight, while the O atom is fourfold coordinated [25]. Previous study on electronic structures of HfO2 polymorphs suggests that the crystal 0 2 4 6 8 0 1 2 3 D en sit y of S ta te s ( sta tes /H fO 2) 0 1 2 3 s p d -20 -15 -10 -5 0 5 Energy (eV) 0 0.5 1 1.5 -20 -10 0 0 0.5 1 1.5 EVBMa b c Fig. 2. (a) Total density of states (DOS) of cubic HfO2, (b) partial DOS of Hf atom, and (c) partial DOS of O atom. EVBM denotes the valence band maximum. 48 G.H. Chen et al. / Computational field effects due to atomic coordinations mainly result in different width of lower conduction bands [17], thus we expect surface electronic structures of cubic HfO2 discussed below could be extended to those of other phases. 3.2. Surface energies To compare the stability of various surfaces, the surface energies (Esurf ) should be taken into account. For HfO2, Esurf is calculated as: Esurf ¼ 1 2A fEslabtot � NHfEHfO2tot � ðNO � 2NHfÞlOg; ð1Þ where Eslabtot refers to the total energy of the slab supercell, EHfO2tot is the energy for bulk HfO2 per formula unit (f.u.), and A is the surface area. NHf and NO are numbers of Hf atoms and oxygen atoms in the slab, so the ðNO � 2NHfÞ equals to excessive oxygen beyond stoichiometric HfO2 units in the slab. lO is the chemical potential of oxygen. In order to study the dependence of surface stability on the environment, lO is assumed to vary between thermody- namically allowed chemical potential l0O and l HfO2 O , where l0O is the chemical potential of oxygen and taken as half of total energy of one O2 molecule, and l HfO2 O is related with lHfO2Hf through faces of cubic HfO2 are listed in Table 1. Both the values of surface energies before and after structural relaxation are listed for comparison, and the change of surface energies due to relaxation is given by %DEsurf . %DEsurf is defined as [30], %DEsurf ¼ ½Esurfrelaxed � Esurfunrelaxed�=Esurfunrelaxed; ð5Þ where Esurfunrelaxed and E surf relaxed are the surface energies before and after structural relaxation, respectively. It can be seen that the surface energies of all low Miller index surfaces of cubic HfO2 are decreased by structural relaxation. The var- iation order of the absolute value of surface energies of cu- bic HfO2 due to structural relaxation is: ð110Þ > ð111Þ-OO > ð100Þ-O > ð100Þ-Hf > ð111Þ-Hf > ð111Þ-O. Obviously the surface energy of (110) surface changes most drastically. In order to compare the stability of sur- faces of cubic HfO2, the surface energies of relaxed (100)-Hf, (100)-O, (110), (111)-Hf, (111)-OO, and (111)-O surfaces versus the chemical potential of oxygen are plotted in Fig. 3. Under oxygen-rich conditions the sta- bility of low Miller index surfaces of cubic HfO2 follows in the sequence as: ð111Þ-O > ð110Þ > ð100Þ-O > ð111Þ- OO > ð100Þ-Hf > ð111Þ-Hf, while under oxygen-deficient conditions it changes to: ð111Þ-O > ð110Þ > ð100Þ-Hf > ð111Þ-Hf > ð100Þ-O > ð111Þ-OO. It indicates that (111)- O and (110) are the most stable surfaces. This is basically similar to surfaces of cubic ZrO2 with same structure of HfO2. The unrelaxed surface energies of (100), (110) and (111) surfaces of cubic ZrO2 have been calculated by Christensen and Carter [31], they found that (111) surface Table 1 Calculated surface energies Esurf ðmJ=m2Þ for low-index surfaces of cubic HfO2 Face Esurf ðlO ¼ l0OÞ Esurf ðlO ¼ l0O þ 12DEHfO2f Þ Relaxed Unrelaxed %DEsurf Relaxed Unrelaxed %DEsurf (100) -Hf 2650 2808 5.63 9353 9511 1.66 (100)-O 10175 10410 2.26 3472 3707 6.34 (110) 1526 2230 31.6 1526 2230 31.6 (111) -Hf 2673 2811 4.91 10416 10554 1.31 (111) 12537 12916 2.93 4794 5172 7.31 -OO (111)-O 934 996 6.22 934 996 6.22 Dz is negative, it indicates that atom moves toward the inner layer by relaxation, otherwise, atom moves toward outer layer. We should point out that two or three atomic layers in center part of the slab are fixed during the struc- tural relaxations in our calculations. Dd is defined as the difference between drelaxed and dunrelaxed (i.e. Dd ¼ drelaxed� 9 12 E ne rg y (J/ m2 ) {100} -Hf {100} -O {110} {111} -Hf {111} -OO {111} -O Table 3 Atomic relaxations in (111)-O surface of cubic HfO2 n Atom Dzn Ddn;nþ1 1 O 0.032 0.068 2 Hf �0.035 �0.005 3 O �0.03 �0.048 4 O 0.018 0.007 5 Hf 0.011 – n is layer number, Dzn (A˚) is the displacement of atom along z-direction (the positive indicates atoms move outward and the negative means inward) and Ddn;nþ1 (A˚) denotes change of distance between layer n and n+1 due to relaxation. G.H. Chen et al. / Computational Materials Science 44 (2008) 46–52 49 of cubic ZrO2 is the most stable one. These could be under- stood by that (111) surfaces of cubic HfO2 and ZrO2 sat- isfy the compactness and electrostatic conditions [31]. In addition, because the (111)-O and (110) surfaces of cubic HfO2 are stoichiometric, their surface energies are indepen- dent of the variation of chemical potential of oxygen. 3.3. Surface relaxation -10 -5 Chemical Potential of O (eV) 0 3 6 Su rfa ce Fig. 3. Surface energies for various surfaces of cubic HfO2 versus chemical potential of oxygen. In present work, we focus on the atomic relaxation along the surface normal and neglect the reconstruction. Since the (111)-O and (110) surfaces of cubic HfO2 are energetically the most stable ones as discussed in above sec- tion, here we particularly present and discuss the atomic relaxations in these two surfaces. To obtain the detailed information of atomic relaxation in each atomic layer, we calculate the absolute displace- ment Dz of each atomic layer and the change of layer dis- tance Dd. During our calculations, the surface normal was chosen as the z-axis. Here, the Dz is given by Dz ¼ zrelaxed � zunrelaxed, where zunrelaxed and zrelaxed are z coor- dinates of atom before and after relaxation, respectively. If Table 2 Atomic relaxation in (110) surface of cubic HfO2 n Dzn Ddn;nþ1 zOn � zHfn Hf O Hf O 1 �0.225 0.049 �0.408 0.053 0.274 2 0.183 �0.004 0.243 �0.012 �0.187 3 �0.06 0.008 – – 0.068 n is layer number, Dzn (A˚) is the absolute displacement of atom along z- direction and Ddn;nþ1 (A˚) denotes change of distance between layer n and n + 1 due to relaxation. zOn � zHfn (A˚) denotes the rumpling of Hf and O atoms layers. Fig. 4. Projected bulk band structures of various surfaces: (a) Hf- terminated (100), (b) Hf-terminated (111), (c) O-terminated (100), (d) double O atom layer terminated (111) surface, (e) (110) and (f) one O atom layer terminated (111). The position of the Fermi level EF of surface is marked by the dotted line. dunrelaxed), where drelaxed and dunrelaxed are the distances between two neighboring layers in relaxed and unrelaxed surfaces, respectively. If Dd is positive, it indicates that atomic layer distance in surfaces is increased by relaxation. The absolute displacement of each atomic layer and the change of layer distance in (110) and (111)-O surfaces of cubic HfO2 are listed in Tables 2 and 3, respectively. For (110) surface of cubic HfO2, each atomic layer is stoichi- ometric and nonpolar because the ratio of Hf:O in each lay is 1:2. As listed in Table 2, Hf atoms in the first top layer move inward and those in the second top layer out- ward due to the relaxation. Consequently the relaxation results in the atomic layer distance between the first and second top Hf atom layers (DdHf1;2) decreased (see Table 2). The O atoms in the first and second top layers move outward and inward by relaxation, respectively, which are different from that of Hf atoms. This means that the atomic layer distance between the first and second top O atom layers is increased (DdO1;2) (see Table 2) by relaxation. While the atomic layer distance between the second and third Hf atom layers (DdHf2;3) is increased, Dd O 2;3 decreased. All of above results clearly demonstrate a trend of rum- pling, which is common in some ionic crystals, appears in (110) surface of cubic HfO2. In order to make this clear, we also list the rumpling between Hf atom layer and O atom layer (defined as zOn � zHfn ) due to relaxation in Table 2. The first top layer exhibits the strongest rumpling. For the (111)-O surface, the first top layer only con- tains O atoms and which move outward by relaxation. The second top layer only contains Hf atoms which move inward. Consequently the layer distance between the first and second top layers (Dd12) is increased by relaxation (see Table 3). There are only O atoms in the third top layer, in which the O atoms move inward and the layer distance between the second and third layers (Dd23) is slightly decreased by relaxation. In addition, our results indicate both of the O atoms in the fourth top layer and the Hf atoms in the fifth top layer move outward. But the absolute value of displacement of the former is slightly larger, corresponding to a layer distance increase by relaxation. Actually, no matter atoms move inward or outward due to relaxation, atomic relaxation in these surfaces of cubic HfO2 could be well understood by the ionic characteristics of Hf–O bonding. When the surface is formed by cleaving a crystal, the balance of forces exerting on anions or cations in outmost layers of HfO2 surface is broken, resulting in the redistribution of the electrons. In this way the ions are polarized. As the anions have larger polarizability and volumes than the cations, they undergo larger forces from the dipole induced by the electrons and relax out- ward. In contrast, the top layer cations is apt to move inward. As a result, rumpling occurs, i.e. the electrical dou- ble layer can be formed to make the surface energy lower. ner 50 G.H. Chen et al. / Computational Materials Science 44 (2008) 46–52 0 2 4 6 0 2 4 6 bulk (100) -Hf 0 2 4 D en sit y of S ta te s (st ate s/H fO x ) 0 2 4 bulk (100) -O -20 -15 -10 -5 0 5-20 -10 0 0 2 4 bulk (110) EF E EF EF Fig. 5. Density of states of surfaces. For comparison, valence band maximum ( surface is marked by the dashed line. bulk (111) - Hf bulk (111) - OO -20 -15 -10 -5 0 5 bulk (111) -O gy (eV) EF EF EF VBM) of cubic HfO2 bulk has been aligned at zero. The Fermi level of each Administrator 高亮 Administrator 高亮 Administrator 高亮 [14] J. Aarik, H. Ma¨ndar, M. Kirm, L. Pung, Thin Solid Films 466 (2004) Ma 3.4. Electronic properties In this section, we turn to discuss the electronic struc- tures of cubic HfO2 surfaces. The projected band structures of (100)-Hf, (111)-Hf, (100)-O, (111)-OO, (110) and (111)-O surfaces are shown in Fig. 4. For Hf-terminated surfaces, i.e. (100)-Hf and (111)-Hf, there are occupied sur- face states within the band gap of bulk cubic HfO2. The (100)-Hf and (111)-Hf surfaces can hence exhibit metallic properties. For (100)-O and (111)-OO surfaces, empty sur- face states occur in the vicinity of valence band maximum (VBM) of bulk cubic HfO