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Amorphous morphology, thermal stability and electronic structure of non-crystalline transition-metal elemental and binary oxides, and chalcogenides
Journal of Non-Crystalline Solids 299–302 (2002) 231–237 www.elsevier.com/locate/jnoncrysol
Section 4. Disorder and structure
Amorphous morphology, thermal stability and electronic structure of non-crystalline transition-metal elemental and binary oxides, and chalcogenides Gerald Lucovsky
*
Departments of Physics, Electrical and Computer Engineering, and Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695-8202, USA
Abstract The primary motivation for this research is to identify alternative high-k gate dielectrics for advanced crystalline Si complementary metal oxide semiconductor (CMOS) devices. A novel and systematic approach to the classification of candidate elemental and binary non-crystalline oxides that is based on relative bond ionicity separates these dielectrics into three groups with different amorphous morphologies: continuous random networks, modified continuous random networks in which metal atoms disrupt and modify the covalently bonded network structure, and random close packed ionic structures. This approach identifies the importance of the oxygen atom co-ordination, providing useful insights into the bonding in chalcogenide alloys as well. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 61.43.)j; 71.15.Fv; 77.55.+f; 78.70.Dm
1. Introduction Non-crystalline alloys of group IIIB and IVB transition-metal and rare-earth oxides, e.g., Y2 O3 and ZrðHfÞO2 , and GdðDyÞ2 O3 , respectively, with SiO2 and Al2 O3 , have been proposed as alternative high-k gate dielectrics for advanced Si devices with decreased dimensions and increased levels of integration [1]. Increases in k relative to SiO2 permit the use of physically thicker films to obtain the
*
Tel.: +1-919 515 3301; fax: +1-919 515 7331. E-mail address: [email protected] (G. Lucovsky).
same effective capacitance as thinner SiO2 dielectrics, providing the potential for significantly decreased direct tunneling. However, decreases in tunneling anticipated from increased physical thickness are in part mitigated by reductions in conduction-band offset energies that define the tunneling barrier between the Si substrate and the dielectric. This paper develops a classification scheme for non-crystalline oxide dielectrics [2], and uses this as the basis for molecular orbital (MO) calculations. These calculations have identified important correlations between atomic d-state energies of transition and rare-earth metals, and oxide band gaps and conduction-band offset energies important for gate dielectric applications.
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2. Classification scheme for non-crystalline oxides Zallen [3] has discussed three distinct atomicscale amorphous morphologies for non-crystalline solids: (i) continuous random networks (crns) exemplified by SiO2 with predominantly covalent bonding between the constituent atoms, (ii) modified continuous random networks (mcrns) exemplified by silicate alloys in which metal atom ionic bonding disrupts and modifies the covalently bonded crn structure, and (iii) random close packed (rcp) solids comprised of negative and positive ions. A classification scheme based on bond ionicity separates non-crystalline oxide dielectrics into these three different bonding morphologies. An empirical definition of bond ionicity, Ib , introduced by Pauling, is the basis for the classification scheme [4]. If X ðOÞ is the Pauling electronegativity of oxygen, 3.44, and X ðSiÞ is the corresponding electronegativity of silicon, 1.90, then the electronegativity difference between these two atoms, DX ¼ X ðOÞ X ðSiÞ, is 1.54. Using Pauling’s empirical definition of Ib ; i.e., Ib ¼ 1 2 expð0:25ðDX Þ Þ, gives a value of 45% for Si–O bonds. The range of DX for the insulating oxides of this paper is from 1.5 to 2.4. Within this range, Ib varies approximately linearly with DX , so that DX and Ib are effectively equivalent scaling variables. The non-crystalline oxides, as well as As and Ge chalcogenides, with DX up to 1.5 form covalently bonded crns, in which constituent atoms have a co-ordination of 8 N that reflects their primary chemical valence; e.g., two for O, S and Se, three for N, P and As, four for C, Si and Ge. The glassforming properties of these crns, as well as their low defect densities in thin films and bulk glasses, are correlated with the number of bonding constraints per atom; details are presented in papers published elsewhere [5–8]. The second class of non-crystalline dielectrics are modified crns, namely mcrns, in which ionically bonded metal atoms modify and disrupt the network structure. This class of dielectrics is characterized by values of DX between about 1.6 and 2.0, or equivalently bond ionicities between 47% and 67%. The most extensively studied oxides in this group are melt-quenched silicates, e.g.,
SiO2 alloyed with Na2 O, CaO, TiO2 , ZrO2 , etc. This class also includes deposited thin-film metal oxides such as Al2 O3 , TiO2 and Ta2 O5 , as well as transition-metal atom silicate alloys such as ðZrðHfÞO2 Þx ðSiO2 Þ1x in the composition range up to x 0:5. The non-crystalline range of alloy formation in deposited mcrn films is increased significantly with respect to what it is in melt-quenched bulk glasses. The co-ordination of oxygen in crns is typically 2, and increases to 3 in the mcrns (see Fig. 1). As examples, the co-ordination is 2.8 in Ta2 O5 , 3.0 in Al2 O3 , and increases from 2 to 3 in the group IVB silicate alloys as the ZrO2 or HfO2 fraction, x, is increased from doping levels of less than 0.01 up to 0.5. The third group of non-crystalline oxides has a random close packed ionic morphology. This class is correlated with DX > 2, or Ib greater than 67%, and includes transition-metal oxides deposited by low-temperature techniques including plasma deposition, and sputtering with postdeposition oxidation [1]. The co-ordination of oxygen atoms in this group is typically 4. Fig. 1 contains a plot of average oxygen atom co-ordination as a function of average bond ionicity, Ib (or equivalently DX ) for the materials considered. The linear variation reveals a fundamental correlation between charge localization on the oxygen atom and bonding co-ordination. A classification scheme for chalcogenides can also be
Fig. 1. Plot of the average oxygen atom co-ordination as a function of the average bond ionicity, Ib .
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formulated in terms of DX or Ib , although this scale is severely compressed due to the decreased electronegativities of S, Se and Te with respect to O. However, a classification based on bonding coordination of chalcogen atoms is more enlightening. For example, it separates chalcogenides into groups with different amorphous morphologies, the most important of which are crns and mcrns.
3. Molecular orbital calculations and scaling Fig. 2 is a molecular orbital energy level diagram for a group IVB transition-metal, e.g., Ti, in an octahedral bonding arrangement with six oxygen neighbors [9,10]. Each oxygen atom provides one r and two p 2p-electrons for potential bonding with neutral group IVB atoms, each of which contributes four additional electrons. The symmetries and p or r character of the calculated orbitals are determined by symmetries of the atomic states. The calculations show that spatial localization of transition-metal atomic d-states
Fig. 2. Molecular orbital energy level diagram for a group IV transition-metal, e.g., Ti, in an octahedral bonding arrangement with six oxygen neighbors.
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makes the resulting anti-bonding states relatively insensitive to second-neighbor metal or alloy atoms. The top of the valence band is associated with non-bonding p orbitals of the oxygen atom 2p-states, and the first two conduction-bands are associated with transition-metal d-states. In order of increasing energy, these conduction-bands have t2g ðp Þ, and eg ðr Þ symmetries. The next conduction-band is derived from transition-metal s-states with a1g ðr Þ character. The energy separation between the top of the valence band and the bottom of a1g ðr Þ band defines an effective ionic band gap with essentially the same energy as non-transitionmetal insulating oxides, 8–9 eV [10]. Higher lying conduction-bands are derived from transitionmetal p-states. The ordering of the first three conduction-bands in crystalline TiO2 has been verified by electron energy loss and X-ray spectroscopies, which confirm the relative sharpness of the t2g ðp Þ, and eg ðr Þ bands, the increased width of the a1g ðr Þ band, and the lowest and ionic band energies, respectively, of approximately 3, and 8–9 eV [10]. A group theoretical analysis of the relative energies and symmetries of valence and conductionband orbitals for four- and sixfold co-ordinated transition-metal atoms in tetrahedral and octahedral bonding environments [9,10] reveals a reversal in ordering of the t2g and eg d-state derived bands. The lowest lying conduction-bands are evolved from triply degenerate t2g d-states for octahedral bonding, and doubly degenerate eg d-states for tetrahedral bonding. There are several aspects of the energy band scheme in Fig. 2 that are important for band gap and conduction-band offset scaling: (i) the symmetry character of the highest valence bonding states, non-bonding p-states with an orbital energy approximately equal to the energy of the atomic 2p-state, (ii) the weak p-bonding of the transition-metal atoms locks the lowest anti-bonding state to the atomic nd-state energy of the transition-metal, and (iii) the energy separation between the antibonding nd and n þ 1s derived states is correlated with the difference between the atomic nd and n þ 1s states.
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Fig. 3 contains plots of (a) the lowest optical band gap versus the absolute value of the energy difference between the transition-metal atomic ndstate and the oxygen-atom p-state, and (b) the conduction-band offset energies with respect to Si versus the absolute value of the energy difference between the transition-metal atomic nd and n þ 1sstates. The linearity of these plots supports the qualitative universality of the energy band scheme of Fig. 2. The band gap scaling displays a slope of approximately 1, indicating quantitative agreement with the energy band scheme as well. Fig. 4 contains plots of the lowest optical band gap versus the energy of the atomic p-states of oxygen, sulfur and selenium for (i) HfO2 , HfS2 and HfSe2 [11], and (ii) MnO, MnS, and MnSe [12]. Since the transition-metal is fixed and only the anion is changed, the scaling in this Fig. 4 is equivalent to that in Fig. 3. In particular, the highest valence band states in metal sulfides and selenides are also derived from non-bonding p-states, and have orbital energies equal to their respective 3p and 4p atomic states.
Fig. 4. Plots of lowest optical band gap versus the energy of the atomic p-states of oxygen, sulfur and selenium for (i) HfO2 , HfS2 and HfSe2 , and (ii) MnO, MnS, and MnSe. The MnTe point lies below the linear fit due to overlap between d-states of Mn with p-states of Te.
4. Experimental results for oxides Fig. 5 displays X-ray absorption spectroscopy, XAS, spectra for a series of Zr silicate alloys, ðZrO2 Þx ðSiO2 Þ1x , obtained at the Brookhaven National Synchrotron Light Source. Spectral fea-
Fig. 3. Plots of (a) the lowest band gap versus the absolute value of the energy difference between the transition-metal atomic nd-state and the oxygen-atom p-state, and (b) the conduction-band offset energies with respect to Si versus the absolute value of the energy difference between the transitionmetal atomic nd-state and the transition-metal n þ 1s-state.
Fig. 5. XAS, spectra for series of Zr silicate alloys, ðZrO2 Þx ðSiO2 Þ1x . The dashed-lines are as deposited at 300 °C, and the solid lines after a 30 s 900 °C anneal in Ar.
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tures in Fig. 5 are assigned to dipole allowed transitions between M2;3 p-core states of the Zr atoms, and empty conduction-band states derived from the 4d (a and b, and a0 and b0 ) and 5s (c and c0 ) atomic states of Zr. As-deposited alloys prepared by plasma deposition are non-crystalline and pseudo-binary with Si–O and Zr–O bonds, but no detectable Zr–Si bonds. After annealing at 900 °C, the x ¼ 0:5 alloy phase separates in to SiO2 and crystalline ZrO2 , and the x ¼ 1:0 also crystallizes. The energies of the highlighted features in these XAS spectra are independent, up to an experimental uncertainty of 0:1 eV, of alloy composition and state of crystallinity. The independence of these spectral features on alloy composition is consistent with the MO description and in particular d-state spatial localization; i.e., the relevant MOs are then determined by co-ordination and p-state energies of the oxygen neighbors. Alloys of Al2 O3 and Ta2 O5 with different concentrations of Ta2 O5 have been prepared by remote plasma-assisted deposition onto hydrogen terminated Si(1 0 0) substrates, and then incorporated into MOS capacitors [13]. Fig. 6 indicates leakage current from an nþ Si substrate as a function of reciprocal temperature. Flat-band
voltage shifts, and hysteresis in capacitance–voltage (C–V) traces in the low-temperature regime, are consistent with electron trapping, whereas C–V data in the high-temperature regime are consistent with emission out of these trapping states, i.e., a Poole–Frenkel bulk transport mechanism. Combining C–V and current density–voltage, J –V , data with the energy band scheme of Fig. 2, the activation energy in the low-temperature regime, 0.3 eV, for electron trapping is assigned to the difference in energy between the Si conduction-band and the lowest lying t2g ðp Þ states of sixfold coordinated Ta atoms, and the activation energy at higher temperatures, 1.5 eV, is assigned to emission out of these Ta d-state traps into the conduction-band of the Al2 O3 matrix. In particular, the two activation energies are consistent with the band offset energy of Ta2 O5 with respect to Si, 0.3 eV, and the energy difference between the Si band offset energies of 1.7 eV for Al2 O3 and Ta2 O5 ; both offset energies have been determined by X-ray photoelectron spectroscopy (XPS) [14]. There is a significant enhancement of the dielectric constant for low-concentration Zr and Hf silicate alloys (see Fig. 7) [15]. This increase has been ascribed to a change in bonding co-ordination
Fig. 6. Current versus 1=T for a capacitor with a Ta2 O5 –Al2 O3 alloy dielectric, x 0:4. The activation energy of 0:30 0:05 eV is for thermal activation in localized Ta d-states, and the activation energy of 1:44 0:07 eV is for thermal activation out of the Ta d-state traps into conduction-band states of the Al2 O3 component of the alloy.
Fig. 7. Dielectric constant versus Zr(Hf) silicate alloy composition: a comparison between experimental data and a model calculation (curved line) based on compositionally dependent bonding co-ordination. The straight line is a linear interpolation between end members that applies to mixtures of oxides but not pseudo-binary alloys, and neglects molar volume and local-field corrections.
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of Zr and Hf. In the low concentration regime, analysis of extended X-ray absorption fine structure spectra (EXAFS) gives a Zr atom co-ordination of about 4, whilst for the stoichiometric silicates, e.g., ZrSiO4 , the co-ordination is increased to 8. The bonding geometry at the fourfold site is presumed to be tetrahedral, whereas at the higher concentrations it is assumed to be in a distorted cubic geometry as in the crystalline zircon phase [24]. An empirical model indicates a decrease in eT by at least a factor of two between these two geometries, with the effective charge being larger in the more symmetric tetrahedral geometry. A linear combination of the transitionmetal eg d-states can be directed along the tetrahedral directions when there is mixing with the transition-metal s-states. These four orbitals are equivalent in character; hence the higher bonding symmetry and dynamic effective charge for this co-ordination. An increase to eightfold co-ordination in a distorted cubic geometry does not provide equivalent orbitals that point directly toward their oxygen atom ligands; hence a reduction in symmetry, and a decreased dynamic effective charge.
5. Experimental results for chalcogenide alloys Building on comparisons made between transition-metal oxide, sulfide, and selenide band gaps, there are two issues that are qualitatively different for the corresponding tellurides: (i) band overlap between the valence band states of Te and the dstates of the transition-metals, and (ii) changes in crystalline structure and atomic co-ordination associated with Te substitutions. Consider first MnO and the Mn chalcogenides. The results in Fig. 4 and in [12], indicate: (i) scaling between optical band gaps for the oxide, sulfide and selenide, and the atomic energy of the valence band p-state of the anion, and (ii) a breakdown of this scaling for MnTe as indicated by the experimental point for MnTe that is below the linear fit. This has been attributed to a qualitatively different electronic structure for MnTe in which the d-states of Mn overlap the p-states of Te. This overlap also pro-
motes a change in the crystal structure from rocksalt, NaCl, to the nickel arsenide, NiAs. In this example MnTe is still a semiconductor, whereas in the transition-metal dichalcogenides that involve a smaller number of d-electrons, a similar overlap results in metallic behavior [11]. The Te-doped alloys used in electronic and optical switching [16,17] generally have significantly reduced band gaps with respect to their S and Se analogs, and in addition can display transitions to metallic conductivity. Differences in the properties between Te containing non-crystalline chalcogenides and those containing S and Se are correlated with increased co-ordination of the Te atoms [18]; i.e., a breakdown of the 8 N rule. This requires the use of dorbitals of Te changing the electronic structure and resulting properties. The large differences in the band gap and optic mode vibrational frequencies between crystalline and amorphous Te are consistent with changes in co-ordination and the resulting valence band structure [19]. The 8 N rule also breaks down in As2 Se3 –Cu2 Se alloys in which the Se concentration increases from 2 to 4 as the Cu concentration is increased [20]. Two different effects have been reported for Nidoped chalcogenides: (i) crystallization resulting in metallic conductivity [21], and (ii) metallic conductivity in the non-crystalline state that occurs above a threshold concentration of Ni [18,22]. The second of these is attributed to local bonding arrangements comprised of (i) Ni with six Se neighbors, and (ii) an increase in the co-ordination of Se as well. Based on the atomic 3d-state energy of Ni, the occupancy of these d-states, and the valence p-state energy of Te, the Ni d-band overlaps the Te valence states, so that at a sufficiently high concentration of Ni, electrons can be transported.
6. Conclusions This paper has presented a classification scheme that separates elemental and binary dielectrics into three groups based on relative bond ionicity, revealing a significant relationship between oxygen
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atom co-ordination and bond ionicity. Based on criteria of relative dielectric constant and thermal stability against chemical phase separation and crystallization, transition-metal silicate and aluminate alloys have emerged as potential candidates for applications as alternative gate dielectrics for scaled Si complementary metal oxide semiconductor (CMOS) devices, e.g., devices for mobile applications where tunnel current is more important than device current. The application of ab initio MO theory has revealed a universal energy band scheme applicable for transition-metal and rare-earth dielectrics. The lowest lying conduction-band states are derived from transition-metal/ rare-earth d-states and their energies, relative to the top of the valence band, derived from oxygenatom p-states, determine band gaps, and band offset energies with respect to crystalline Si. XAS spectra for Zr silicate alloys (Fig. 5), and interpretation of C–V and J–V characteristics for Ta aluminate alloys (Fig. 6) are consistent with the MO band scheme. Combined with scaling relationships in Figs. 3 and 4, and high levels of fixed charge at interfaces with Si or SiO2 [1,13], these results have identified significant intrinsic obstacles for implementation of transition-metal/rare-earth oxide, silicate and aluminate alloys into high performance desk-top devices. The MO calculations are equally applicable to transition-metal sulfur and selenium chalcogenide alloys. Owing to a compression of the bond ionicity scale, a more appropriate approach to classification for chalcogenides, and the way their unique properties can be exploited, is based on the bonding co-ordination of the chalcogen atoms. For example, the materials that have shown promise for optical and electrical memory applications have modified crn structures in which the 8 N rule does not apply. These alloys include telluride and antimonide chalcogenides, as well as the transition-metal chalcogenide alloys.
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Acknowledgements Supported by ONR, AFOSR, SRC and Sematich/SRC FEP center. References [1] G. Wilk, R.W. Wallace, J.M. Anthony, J. Appl. Phys. 89 (2001) 5243. [2] G. Lucovsky, J. Vac. Sci. Technol. A 19 (2001) 1553. [3] R. Zallen, The Physics of Amorphous Solids, Wiley, New York, 1983 (Chapter 2). [4] L. Pauling, The Nature of the Chemical Bond, 3rd Ed., Cornell University, Ithaca, NY, 1948 (Chapter 2). [5] J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. [6] J.C. Phillips, J. Non-Cryst. Solids 43 (1981) 37. [7] G. Lucovsky, J.C. Phillips, J. Non-Cryst. Solids 227 (1998) 1221. [8] J.C. Phillips, X. Kerner, Solid State Commun. 117 (2001) 47. [9] J. Ballhausen, H.B. Gray, Molecular Orbital Theory, Benjamin, New York, 1964 (Chapter 8). [10] A. Cox, Transition-Metal Oxides, Oxford Science, Oxford, 1992 (Chapter 2). [11] J.A. Wilson, A.D. Yoffe, Adv. Phys. 18 (1969) 193. [12] J.A. Allen, G. Lucovsky, J.C. Mikkelsen Jr., Solid State Commun. 24 (1977) 367. [13] R.S. Johnson, G. Lucovsky, J. Hong, Appl. Surf. Sci. (2001). [14] S. Miyazaki, M. Narasaki, M. Ogasawaya, M. Hirose, Microelectron. Eng. 59 (2001) 373. [15] G. Lucovsky, G.B. Rayner, Appl. Phys. Lett. 77 (2000) 2912. [16] S.R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. [17] J. Feinleib, S. Iwasa, S.C. Moss, J.P. DeNeuville, S.R. Ovshinsky, J. Non-Cryst. Solids 8–10 (1972) 909. [18] S.R. Ovshinsky, in: W.E. Spear (Ed.), Amorphous and Liquid Semiconductors, University of Edinburgh, 1977, p. 519. [19] G. Lucovsky, Phys. Stat. Sol. B 49 (1972) 633. [20] S.H. Hunter, A. Bienenstock, T.M. Hayes, in: W.E. Spear (Ed.), Amorphous and Liquid Semiconductors, University of Edinburgh, 1977, p. 78. [21] Y. Sawan, F. Wakim, M. Abu-Zeid, M. El-Gabaly, in: Proceedings of the 15th International Conference on Physics of Semiconductors, Kyoto, 1980, J. Phys. Soc. Jpn. 49 (Suppl. A) (1980) 1163. [22] R. Flasck, M. Izu, K. Sapru, T. Anderson, S.R. Ovshinsky, H. Fritzsche, in: W.E. Spear (Ed.), Amorphous and Liquid Semiconductors, University of Edinburgh, 1977, p. 524.
Section 4. Disorder and structure
Amorphous morphology, thermal stability and electronic structure of non-crystalline transition-metal elemental and binary oxides, and chalcogenides Gerald Lucovsky
*
Departments of Physics, Electrical and Computer Engineering, and Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695-8202, USA
Abstract The primary motivation for this research is to identify alternative high-k gate dielectrics for advanced crystalline Si complementary metal oxide semiconductor (CMOS) devices. A novel and systematic approach to the classification of candidate elemental and binary non-crystalline oxides that is based on relative bond ionicity separates these dielectrics into three groups with different amorphous morphologies: continuous random networks, modified continuous random networks in which metal atoms disrupt and modify the covalently bonded network structure, and random close packed ionic structures. This approach identifies the importance of the oxygen atom co-ordination, providing useful insights into the bonding in chalcogenide alloys as well. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 61.43.)j; 71.15.Fv; 77.55.+f; 78.70.Dm
1. Introduction Non-crystalline alloys of group IIIB and IVB transition-metal and rare-earth oxides, e.g., Y2 O3 and ZrðHfÞO2 , and GdðDyÞ2 O3 , respectively, with SiO2 and Al2 O3 , have been proposed as alternative high-k gate dielectrics for advanced Si devices with decreased dimensions and increased levels of integration [1]. Increases in k relative to SiO2 permit the use of physically thicker films to obtain the
*
Tel.: +1-919 515 3301; fax: +1-919 515 7331. E-mail address: [email protected] (G. Lucovsky).
same effective capacitance as thinner SiO2 dielectrics, providing the potential for significantly decreased direct tunneling. However, decreases in tunneling anticipated from increased physical thickness are in part mitigated by reductions in conduction-band offset energies that define the tunneling barrier between the Si substrate and the dielectric. This paper develops a classification scheme for non-crystalline oxide dielectrics [2], and uses this as the basis for molecular orbital (MO) calculations. These calculations have identified important correlations between atomic d-state energies of transition and rare-earth metals, and oxide band gaps and conduction-band offset energies important for gate dielectric applications.
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2. Classification scheme for non-crystalline oxides Zallen [3] has discussed three distinct atomicscale amorphous morphologies for non-crystalline solids: (i) continuous random networks (crns) exemplified by SiO2 with predominantly covalent bonding between the constituent atoms, (ii) modified continuous random networks (mcrns) exemplified by silicate alloys in which metal atom ionic bonding disrupts and modifies the covalently bonded crn structure, and (iii) random close packed (rcp) solids comprised of negative and positive ions. A classification scheme based on bond ionicity separates non-crystalline oxide dielectrics into these three different bonding morphologies. An empirical definition of bond ionicity, Ib , introduced by Pauling, is the basis for the classification scheme [4]. If X ðOÞ is the Pauling electronegativity of oxygen, 3.44, and X ðSiÞ is the corresponding electronegativity of silicon, 1.90, then the electronegativity difference between these two atoms, DX ¼ X ðOÞ X ðSiÞ, is 1.54. Using Pauling’s empirical definition of Ib ; i.e., Ib ¼ 1 2 expð0:25ðDX Þ Þ, gives a value of 45% for Si–O bonds. The range of DX for the insulating oxides of this paper is from 1.5 to 2.4. Within this range, Ib varies approximately linearly with DX , so that DX and Ib are effectively equivalent scaling variables. The non-crystalline oxides, as well as As and Ge chalcogenides, with DX up to 1.5 form covalently bonded crns, in which constituent atoms have a co-ordination of 8 N that reflects their primary chemical valence; e.g., two for O, S and Se, three for N, P and As, four for C, Si and Ge. The glassforming properties of these crns, as well as their low defect densities in thin films and bulk glasses, are correlated with the number of bonding constraints per atom; details are presented in papers published elsewhere [5–8]. The second class of non-crystalline dielectrics are modified crns, namely mcrns, in which ionically bonded metal atoms modify and disrupt the network structure. This class of dielectrics is characterized by values of DX between about 1.6 and 2.0, or equivalently bond ionicities between 47% and 67%. The most extensively studied oxides in this group are melt-quenched silicates, e.g.,
SiO2 alloyed with Na2 O, CaO, TiO2 , ZrO2 , etc. This class also includes deposited thin-film metal oxides such as Al2 O3 , TiO2 and Ta2 O5 , as well as transition-metal atom silicate alloys such as ðZrðHfÞO2 Þx ðSiO2 Þ1x in the composition range up to x 0:5. The non-crystalline range of alloy formation in deposited mcrn films is increased significantly with respect to what it is in melt-quenched bulk glasses. The co-ordination of oxygen in crns is typically 2, and increases to 3 in the mcrns (see Fig. 1). As examples, the co-ordination is 2.8 in Ta2 O5 , 3.0 in Al2 O3 , and increases from 2 to 3 in the group IVB silicate alloys as the ZrO2 or HfO2 fraction, x, is increased from doping levels of less than 0.01 up to 0.5. The third group of non-crystalline oxides has a random close packed ionic morphology. This class is correlated with DX > 2, or Ib greater than 67%, and includes transition-metal oxides deposited by low-temperature techniques including plasma deposition, and sputtering with postdeposition oxidation [1]. The co-ordination of oxygen atoms in this group is typically 4. Fig. 1 contains a plot of average oxygen atom co-ordination as a function of average bond ionicity, Ib (or equivalently DX ) for the materials considered. The linear variation reveals a fundamental correlation between charge localization on the oxygen atom and bonding co-ordination. A classification scheme for chalcogenides can also be
Fig. 1. Plot of the average oxygen atom co-ordination as a function of the average bond ionicity, Ib .
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formulated in terms of DX or Ib , although this scale is severely compressed due to the decreased electronegativities of S, Se and Te with respect to O. However, a classification based on bonding coordination of chalcogen atoms is more enlightening. For example, it separates chalcogenides into groups with different amorphous morphologies, the most important of which are crns and mcrns.
3. Molecular orbital calculations and scaling Fig. 2 is a molecular orbital energy level diagram for a group IVB transition-metal, e.g., Ti, in an octahedral bonding arrangement with six oxygen neighbors [9,10]. Each oxygen atom provides one r and two p 2p-electrons for potential bonding with neutral group IVB atoms, each of which contributes four additional electrons. The symmetries and p or r character of the calculated orbitals are determined by symmetries of the atomic states. The calculations show that spatial localization of transition-metal atomic d-states
Fig. 2. Molecular orbital energy level diagram for a group IV transition-metal, e.g., Ti, in an octahedral bonding arrangement with six oxygen neighbors.
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makes the resulting anti-bonding states relatively insensitive to second-neighbor metal or alloy atoms. The top of the valence band is associated with non-bonding p orbitals of the oxygen atom 2p-states, and the first two conduction-bands are associated with transition-metal d-states. In order of increasing energy, these conduction-bands have t2g ðp Þ, and eg ðr Þ symmetries. The next conduction-band is derived from transition-metal s-states with a1g ðr Þ character. The energy separation between the top of the valence band and the bottom of a1g ðr Þ band defines an effective ionic band gap with essentially the same energy as non-transitionmetal insulating oxides, 8–9 eV [10]. Higher lying conduction-bands are derived from transitionmetal p-states. The ordering of the first three conduction-bands in crystalline TiO2 has been verified by electron energy loss and X-ray spectroscopies, which confirm the relative sharpness of the t2g ðp Þ, and eg ðr Þ bands, the increased width of the a1g ðr Þ band, and the lowest and ionic band energies, respectively, of approximately 3, and 8–9 eV [10]. A group theoretical analysis of the relative energies and symmetries of valence and conductionband orbitals for four- and sixfold co-ordinated transition-metal atoms in tetrahedral and octahedral bonding environments [9,10] reveals a reversal in ordering of the t2g and eg d-state derived bands. The lowest lying conduction-bands are evolved from triply degenerate t2g d-states for octahedral bonding, and doubly degenerate eg d-states for tetrahedral bonding. There are several aspects of the energy band scheme in Fig. 2 that are important for band gap and conduction-band offset scaling: (i) the symmetry character of the highest valence bonding states, non-bonding p-states with an orbital energy approximately equal to the energy of the atomic 2p-state, (ii) the weak p-bonding of the transition-metal atoms locks the lowest anti-bonding state to the atomic nd-state energy of the transition-metal, and (iii) the energy separation between the antibonding nd and n þ 1s derived states is correlated with the difference between the atomic nd and n þ 1s states.
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Fig. 3 contains plots of (a) the lowest optical band gap versus the absolute value of the energy difference between the transition-metal atomic ndstate and the oxygen-atom p-state, and (b) the conduction-band offset energies with respect to Si versus the absolute value of the energy difference between the transition-metal atomic nd and n þ 1sstates. The linearity of these plots supports the qualitative universality of the energy band scheme of Fig. 2. The band gap scaling displays a slope of approximately 1, indicating quantitative agreement with the energy band scheme as well. Fig. 4 contains plots of the lowest optical band gap versus the energy of the atomic p-states of oxygen, sulfur and selenium for (i) HfO2 , HfS2 and HfSe2 [11], and (ii) MnO, MnS, and MnSe [12]. Since the transition-metal is fixed and only the anion is changed, the scaling in this Fig. 4 is equivalent to that in Fig. 3. In particular, the highest valence band states in metal sulfides and selenides are also derived from non-bonding p-states, and have orbital energies equal to their respective 3p and 4p atomic states.
Fig. 4. Plots of lowest optical band gap versus the energy of the atomic p-states of oxygen, sulfur and selenium for (i) HfO2 , HfS2 and HfSe2 , and (ii) MnO, MnS, and MnSe. The MnTe point lies below the linear fit due to overlap between d-states of Mn with p-states of Te.
4. Experimental results for oxides Fig. 5 displays X-ray absorption spectroscopy, XAS, spectra for a series of Zr silicate alloys, ðZrO2 Þx ðSiO2 Þ1x , obtained at the Brookhaven National Synchrotron Light Source. Spectral fea-
Fig. 3. Plots of (a) the lowest band gap versus the absolute value of the energy difference between the transition-metal atomic nd-state and the oxygen-atom p-state, and (b) the conduction-band offset energies with respect to Si versus the absolute value of the energy difference between the transitionmetal atomic nd-state and the transition-metal n þ 1s-state.
Fig. 5. XAS, spectra for series of Zr silicate alloys, ðZrO2 Þx ðSiO2 Þ1x . The dashed-lines are as deposited at 300 °C, and the solid lines after a 30 s 900 °C anneal in Ar.
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tures in Fig. 5 are assigned to dipole allowed transitions between M2;3 p-core states of the Zr atoms, and empty conduction-band states derived from the 4d (a and b, and a0 and b0 ) and 5s (c and c0 ) atomic states of Zr. As-deposited alloys prepared by plasma deposition are non-crystalline and pseudo-binary with Si–O and Zr–O bonds, but no detectable Zr–Si bonds. After annealing at 900 °C, the x ¼ 0:5 alloy phase separates in to SiO2 and crystalline ZrO2 , and the x ¼ 1:0 also crystallizes. The energies of the highlighted features in these XAS spectra are independent, up to an experimental uncertainty of 0:1 eV, of alloy composition and state of crystallinity. The independence of these spectral features on alloy composition is consistent with the MO description and in particular d-state spatial localization; i.e., the relevant MOs are then determined by co-ordination and p-state energies of the oxygen neighbors. Alloys of Al2 O3 and Ta2 O5 with different concentrations of Ta2 O5 have been prepared by remote plasma-assisted deposition onto hydrogen terminated Si(1 0 0) substrates, and then incorporated into MOS capacitors [13]. Fig. 6 indicates leakage current from an nþ Si substrate as a function of reciprocal temperature. Flat-band
voltage shifts, and hysteresis in capacitance–voltage (C–V) traces in the low-temperature regime, are consistent with electron trapping, whereas C–V data in the high-temperature regime are consistent with emission out of these trapping states, i.e., a Poole–Frenkel bulk transport mechanism. Combining C–V and current density–voltage, J –V , data with the energy band scheme of Fig. 2, the activation energy in the low-temperature regime, 0.3 eV, for electron trapping is assigned to the difference in energy between the Si conduction-band and the lowest lying t2g ðp Þ states of sixfold coordinated Ta atoms, and the activation energy at higher temperatures, 1.5 eV, is assigned to emission out of these Ta d-state traps into the conduction-band of the Al2 O3 matrix. In particular, the two activation energies are consistent with the band offset energy of Ta2 O5 with respect to Si, 0.3 eV, and the energy difference between the Si band offset energies of 1.7 eV for Al2 O3 and Ta2 O5 ; both offset energies have been determined by X-ray photoelectron spectroscopy (XPS) [14]. There is a significant enhancement of the dielectric constant for low-concentration Zr and Hf silicate alloys (see Fig. 7) [15]. This increase has been ascribed to a change in bonding co-ordination
Fig. 6. Current versus 1=T for a capacitor with a Ta2 O5 –Al2 O3 alloy dielectric, x 0:4. The activation energy of 0:30 0:05 eV is for thermal activation in localized Ta d-states, and the activation energy of 1:44 0:07 eV is for thermal activation out of the Ta d-state traps into conduction-band states of the Al2 O3 component of the alloy.
Fig. 7. Dielectric constant versus Zr(Hf) silicate alloy composition: a comparison between experimental data and a model calculation (curved line) based on compositionally dependent bonding co-ordination. The straight line is a linear interpolation between end members that applies to mixtures of oxides but not pseudo-binary alloys, and neglects molar volume and local-field corrections.
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of Zr and Hf. In the low concentration regime, analysis of extended X-ray absorption fine structure spectra (EXAFS) gives a Zr atom co-ordination of about 4, whilst for the stoichiometric silicates, e.g., ZrSiO4 , the co-ordination is increased to 8. The bonding geometry at the fourfold site is presumed to be tetrahedral, whereas at the higher concentrations it is assumed to be in a distorted cubic geometry as in the crystalline zircon phase [24]. An empirical model indicates a decrease in eT by at least a factor of two between these two geometries, with the effective charge being larger in the more symmetric tetrahedral geometry. A linear combination of the transitionmetal eg d-states can be directed along the tetrahedral directions when there is mixing with the transition-metal s-states. These four orbitals are equivalent in character; hence the higher bonding symmetry and dynamic effective charge for this co-ordination. An increase to eightfold co-ordination in a distorted cubic geometry does not provide equivalent orbitals that point directly toward their oxygen atom ligands; hence a reduction in symmetry, and a decreased dynamic effective charge.
5. Experimental results for chalcogenide alloys Building on comparisons made between transition-metal oxide, sulfide, and selenide band gaps, there are two issues that are qualitatively different for the corresponding tellurides: (i) band overlap between the valence band states of Te and the dstates of the transition-metals, and (ii) changes in crystalline structure and atomic co-ordination associated with Te substitutions. Consider first MnO and the Mn chalcogenides. The results in Fig. 4 and in [12], indicate: (i) scaling between optical band gaps for the oxide, sulfide and selenide, and the atomic energy of the valence band p-state of the anion, and (ii) a breakdown of this scaling for MnTe as indicated by the experimental point for MnTe that is below the linear fit. This has been attributed to a qualitatively different electronic structure for MnTe in which the d-states of Mn overlap the p-states of Te. This overlap also pro-
motes a change in the crystal structure from rocksalt, NaCl, to the nickel arsenide, NiAs. In this example MnTe is still a semiconductor, whereas in the transition-metal dichalcogenides that involve a smaller number of d-electrons, a similar overlap results in metallic behavior [11]. The Te-doped alloys used in electronic and optical switching [16,17] generally have significantly reduced band gaps with respect to their S and Se analogs, and in addition can display transitions to metallic conductivity. Differences in the properties between Te containing non-crystalline chalcogenides and those containing S and Se are correlated with increased co-ordination of the Te atoms [18]; i.e., a breakdown of the 8 N rule. This requires the use of dorbitals of Te changing the electronic structure and resulting properties. The large differences in the band gap and optic mode vibrational frequencies between crystalline and amorphous Te are consistent with changes in co-ordination and the resulting valence band structure [19]. The 8 N rule also breaks down in As2 Se3 –Cu2 Se alloys in which the Se concentration increases from 2 to 4 as the Cu concentration is increased [20]. Two different effects have been reported for Nidoped chalcogenides: (i) crystallization resulting in metallic conductivity [21], and (ii) metallic conductivity in the non-crystalline state that occurs above a threshold concentration of Ni [18,22]. The second of these is attributed to local bonding arrangements comprised of (i) Ni with six Se neighbors, and (ii) an increase in the co-ordination of Se as well. Based on the atomic 3d-state energy of Ni, the occupancy of these d-states, and the valence p-state energy of Te, the Ni d-band overlaps the Te valence states, so that at a sufficiently high concentration of Ni, electrons can be transported.
6. Conclusions This paper has presented a classification scheme that separates elemental and binary dielectrics into three groups based on relative bond ionicity, revealing a significant relationship between oxygen
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atom co-ordination and bond ionicity. Based on criteria of relative dielectric constant and thermal stability against chemical phase separation and crystallization, transition-metal silicate and aluminate alloys have emerged as potential candidates for applications as alternative gate dielectrics for scaled Si complementary metal oxide semiconductor (CMOS) devices, e.g., devices for mobile applications where tunnel current is more important than device current. The application of ab initio MO theory has revealed a universal energy band scheme applicable for transition-metal and rare-earth dielectrics. The lowest lying conduction-band states are derived from transition-metal/ rare-earth d-states and their energies, relative to the top of the valence band, derived from oxygenatom p-states, determine band gaps, and band offset energies with respect to crystalline Si. XAS spectra for Zr silicate alloys (Fig. 5), and interpretation of C–V and J–V characteristics for Ta aluminate alloys (Fig. 6) are consistent with the MO band scheme. Combined with scaling relationships in Figs. 3 and 4, and high levels of fixed charge at interfaces with Si or SiO2 [1,13], these results have identified significant intrinsic obstacles for implementation of transition-metal/rare-earth oxide, silicate and aluminate alloys into high performance desk-top devices. The MO calculations are equally applicable to transition-metal sulfur and selenium chalcogenide alloys. Owing to a compression of the bond ionicity scale, a more appropriate approach to classification for chalcogenides, and the way their unique properties can be exploited, is based on the bonding co-ordination of the chalcogen atoms. For example, the materials that have shown promise for optical and electrical memory applications have modified crn structures in which the 8 N rule does not apply. These alloys include telluride and antimonide chalcogenides, as well as the transition-metal chalcogenide alloys.
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