Spectroscopic studies of metal high-k dielectrics: transition ...metal d- and s-states for transition metal oxides and silicate alloys. The figure also identifies the inter The figure

phys. stat. sol. (b) 241, No. 10, 2221–2235 (2004) / DOI 10.1002/pssb.200404938

© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Spectroscopic studies of metal high-k dielectrics: transition metal oxides and silicates, and complex rare earth/transition metal oxides

G. Lucovsky*, 1, 2, 3, J. G. Hong2, C. C. Fulton2, Y. Zou1, R. J. Nemanich1, H. Ade1, D. G. Scholm4, and J. L. Freeouf 5 1 Department of Physics, North Carolina State University, USA 2 Department of Materials Science & Engineering, North Carolina State University, USA 3 Department of Electrical & Computer Engineering, North Carolina State University, USA 4 Department of Materials Science & Engineering, Pennsylvania State University, USA 5 Department of Electrical & Computer Engineering, Oregon Graduate Institute, USA

Received 1 March 2004, revised 1 May 2004, accepted 31 May 2004 Published online 28 July 2004

PACS 78.70.Dm

This paper uses X-ray absorption spectroscopy to the study of electronic structure of the transition metal oxides TiO2, ZrO2 and HfO2, Zr and Hf silicate alloys, and the complex oxides, GdScO3, DyScO3 and HfTiO4. Qualitative and quantitative differences are identified between dipole allowed intra-atomic transi-tions from core p-states to empty d*- and s*-states, and inter-atomic transitions from transition metal and oxide 1s states to O 2p* that are mixed with transition metal d*- and s*-states for transition metal oxides and silicate alloys. The complex oxide studies have focused on the O K1 edge spectra. Differences be-tween the spectral peak energies of the lowest d*-features in the respective O K1 spectra are demonstrated to scale with optical band gap differences for TiO2, ZrO2 and HfO2, as well as the complex oxides provid-ing important information relevant to applications of TM oxides as high-k gate dielectrics in advanced Si devices. This is demonstrated through scaling relationships between (i) conduction band offset energies between Si and the respective dielectrics, and the optical band gaps, and (ii) the optical band gaps, the conduction band offset energies, and the electron tunneling masses as functions of the atomic d-state en-ergies of the transition metal atoms.


1 Introduction

There has been considerable interest in transition metal (TM) and trivalent lanthanide series rare earth (RE) atom oxides, and their respective silicate and aluminate alloys as replacement high-k dielectrics for SiO2 in advanced silicon field effect transistors (FETs) requiring a gate oxide dielectric capacitance per unit area, Cox, >4 × 10–6 F cm–2 [1–3]. This capacitance can be obtained in thermally-grown SiO2 de-vices, however, the physical SiO2 thickness required is less than 1.0 nm, and this leads to excessively high tunneling leakage currents that degrade FET performance and reduce reliability. These high levels of capacitance per unit area can also be obtained in devices with high-k dielectrics. In these applications, the film thickness is increased by the ratio of their respective dielectric constants, k, to that of SiO2, ~3.9. Since typical high-k values range from at least 10 to more than 60, the thickness increases of approximately 3 to more than 10 are sufficient to suggest many orders of magnitude reduc-tions in the tunneling current. However, tunneling leakage also depends on the square root of the product of the height of the barrier between the conduction band of Si and the lowest conduction band states of

* Corresponding author: e-mail: [email protected]

2222 G. Lucovsky et al.: Spectroscopic studies of metal high-k dielectrics


the dielectric, EB, and the effective mass of the tunneling electrons, meff [4]. The spectroscopic results of this study demonstrate that band gaps of the TM and RE oxides, as well as their respective silicate and aluminate alloys, are significantly reduced with respect to the band gap of SiO2, leading to reductions in EB, and meff. These reductions scale with atomic d-state energies of TM and RE atoms, and provide important insights for identifying TM and RE oxides, silicates and aluminates that have the potential to meet interna-tional industry roadmap targets for device performance with respect to leakage current [1–6]. This paper uses X-ray absorption spectroscopy to study the electronic structure of representative high-k gate dielectrics, and complements these measurements with optical band edge spectroscopic studies. Qualitative and quantitative differences are identified between dipole allowed intra-atomic transitions from core p-states to empty d*- and s*-states, and inter-atomic transitions from transition metal and oxide 1s states to O 2p* that are mixed with transition metal d*- and s*-states. The complex oxide spec-tra have focused on the O K1 edge spectra. Differences between the spectral peak energies of the lowest d*-features in the respective O K1 spectra are demonstrated to scale with optical band gap differences for TiO2, ZrO2 and HfO2, and the complex oxides as well providing important information relevant to appli-cations of TM and RE oxides as high-k gate dielectrics in advanced Si devices. This is demonstrated through scaling relationships between (i) conduction band offset energies between Si and the respective dielectrics, and the optical band gaps, and (ii) the optical band gaps, conduction band offset energies, and the electron tunneling masses and the d-state energies of the transition metal atoms.

2 Experimental studies of electronic structure

The X-ray absorption spectroscopy (XAS) studies were performed at the National Synchrotron Light Source (NSLS) at the Brookhaven National Laboratory (BNL) using total photo-electron yield to deter-mine relative absorption strength of the spectral features [7]. Thin film samples of ZrO2 and HfO2 and their respective silicate alloys were prepared by remote plasma enhanced chemical vapor deposition (RPECVD) at 300 °C [8]. Post deposition annealing of deposited thin films was performed for 30 s to 1 min at 900 °C in Ar. TiO2 thin films were prepared by physical deposition of the Ti atoms, followed by in-situ plasma-assisted oxidation, and annealing at 600 °C [9]. Characterization by high resolution transmission electron microscopy (HRTEM) indicated that the TM oxides thin films of this study are crystalline in character, with the crystallite sizes in the nano-regime from ~3 to 10 nm. The GdScO3 and DyScO3 samples were single crystals and the growth mechanisms have been discussed in Ref. [11]. Figure 1 presents a schematic representation of the XAS transitions that are being addressed in this paper using ZrO2 as an example. These transitions include the Zr K1 and M2,3 edges, O K1 edge, and

Fig. 1 (online colour at: www.pss-b.com)Schematic representation of the intra-atomic Zr M2,3, and inter-atomic atomic Zr K1, O K1 and band edge transitions for ZrO2. The ordering of the energy states is derived from ab initio molecular orbital calculations on small neutral clusters [5, 11].

phys. stat. sol. (b) 241, No. 10 (2004) / www.pss-b.com 2223


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the optical band gap absorption edge. The schematic energy level diagrams of Fig. 1 identify the ∆(d1*,2) splittings, and the ∆(d1*,s*) energy differences. Qualitative and quantitative differences are identified between dipole allowed intra-atomic transitions from core p-states to empty d*- and s*-states [12], and inter-atomic transitions from transition metal and oxide 1s states to O 2p* that are mixed with transition metal d*- and s*-states for transition metal oxides and silicate alloys. The figure also identifies the inter-atomic band edge transitions that are studied by the spectroscopic ellipsometry.

2.1 Intra-atomic and inter-atomic transitions in TiO2, ZrO2 and HfO2

Figures 2(a), 2(b) and 2(c) display the Ti L2,3, Zr M2,3 and Hf N2,3 spectra for TiO2, ZrO2 and HfO2, re-spectively. For each of the spin–orbit split initial p-states, there are transitions to a d*-state doublet, 3d* for Ti, 4d* for Zr and 5d* for Hf, and to a 4s*-, 5s*- or 6s*-state that is at a higher energy [7]. Table 1 includes the positions of the spectral features for the Ti L2,3 and Zr M2,3 doublet components that are spectroscopically resolved, and for single broad Hf N2,3 spectral feature in which the doublet components are not resolved. The L2, M2, and N2 features are shifted in energy with respect to the corresponding L3,

Fig. 2 (a) Ti L2,3, (b) Zr M2,3 and (c) Hf N2,3 X-ray absorption spectra.



Table 1 Summary of experimental results for d* and s* features in XAS spectra of Figs. 2(a), (b) and (c), 3, 5a, b and c, and 6.

energy (±0.2 eV) energy (±0.3 eV)

spectrum d1* d2* s* ∆(d1,2*) ∆(d1*,s*)

Ti K1a 4,960 4,962.5 4,968.6 2.5 8.6

Ti M2 462.7 464.7 475.3 2.0 12.8 Ti M3 457.2 459.1 469.7 1.9 12.5 O K1(Ti) 530.1 532.8 539.5 2.7 8.4 Zr K1 18,008b 18,008b 17,998 ~3.0c ~13–14d Zr M2 345.9 347.7 357.5 2.2 11.7 Zr M3 332.6 334.8 344.5 2.2 11.9 O K1(Zr) 532.2 535.4 542.3 3.2 10.1 Hf N3 382.7b 382.7b 392.7 <3.5c 10d O K1(Hf) 532.5 536.8 541.5 4.3 9.0

a Refs. [16, 17]; b not resolved; c estimated from line width; d average separation M3, and N3 features by the spin–orbit splittings of the respective 2p-, 3p-states, and 4p-atomic states: 5.6 eV ± 0.3 eV for Ti, 13.3 ± 0 .3 eV for Zr and for 57.6 eV ± 0.3 eV for Hf. As shown in Table 2, there is excellent agreement between the experimentally obtained spin–orbit splittings of this study and handbook values [13]. Figure 3 is a deconvolved spectrum for the M2 feature in the ZrO2 XAS spectrum that displays the two 4d* and one 5s* spectral features. As indicated in Table 1, the values of ∆(d1*,2), and ∆(d1*, s*) obtained from the positions of the M2 spectral peaks in Fig. 2b are the same to within the estimated experimental uncertainty of ~0.2 eV as the values obtained from the corresponding spectral peaks of the deconvolved and fitted spectrum in Fig. 3. The relative absorption strengths for the pairs of d* and s* features in the spectra for TiO2, ZrO2 and HfO2 are markedly different. The s*-state spectral features are just above the detection limit in the TiO2 L3 and L2 spectra, whereas the corresponding absorptions strengths increase modestly for the ZrO2 M3

and M2 spectra, and then are much stronger for the HfO2 N3 and N2 spectra. The respective s*- to d*- intensity ratios for the L2, M2 and N2 spectra have been estimated to ±10% to be 3 × 10–2 for TiO2, 8.9 × 10–2 for ZrO2 and 8.5 × 10–1 for HfO2. Figure 4 presents a plot of the ratios of the integrated s*-state absorptions to the d*-state absorptions for the TM p-state spectral features as a function of calculated relative intensities based on hydrogenic Rydberg states [14]. The calculated relative intensity for HfO2 includes a geometric correction that is based on the lanthanide contraction which makes the final 5d* and 6s* states have radial wave functions that have the same radial extent of the corresponding Zr 4d* and 5s* states, but with an additional node. The x-axis value used in the plot for HfO2 is the geometric mean for transitions from (i) 4p to 4d and 5s atomic states, and (ii) 4p to 5d and 6s states. The experimental intensity ratios scale linearly with the corresponding calculated Rydberg state calculations demonstrating the atomic character of the Ti L2,3, Zr M2,3 and Hf N2,3 transitions.

Table 2 Spin–orbit splittings of Ti 2p, Zr 3p and Hf 4p core states.

p-state spin–orbit splitting (± 0.5 eV)

oxide TiO2 2p ZrO2 3p HfO2 4p

XAS spectra 5.6 13.3 57.0 data handbook* 6.4 13.7 57.5

* Ref. [13]



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Figures 5(a), 5(b) and 5(c) are O K1 edge spectra, respectively for TiO2, ZrO2 and HfO2. Each of the spectra are qualitatively similar displaying a well-resolved d*-doublet at the absorption threshold, and a broader s*-doublet at higher energies. The positions of the spectral features, and the ∆(d1*,2) and ∆(d1*, s*) spectroscopic splittings as determined from the peaks in Fig. 5 are included in Table 1. The ∆(d*) split-ting increase in going from TiO2 to ZrO2 to HfO2, by ~0.5 eV and 0.8 eV, respectively. The spectral overlap between the higher energy d*-state, d2, and the threshold for the s*-doublet absorption decreases from TiO2 and ZrO2, to HfO2. The spectral overlap is associated with (i) increases in the respective ∆(d*1,2, s*) splittings from 2.7 ± 0.2 eV in TiO2 to 3.2 eV ± 0.2 in ZrO2, and then to 4.3 eV ± 0.2 in HfO2, (ii) decreases in ∆(d2*, s1*) the average energy separations (not included in Table 2) of 6.75 ± 0.2 eV for TiO2 and ZrO2, and to 5.0 ± 0.2 eV HfO2, and (iii) increases in the spectral half-width of the d2* feature that scale monotonically with the atomic number of the TM atom. The Zr K1 spectrum for ZrO2 is shown in Fig. 6. This spectrum is similar to those presented in Ref. [15]. Markers in the spectra displayed in Ref. [15] indicate that the positions of features that assigned to 4d* and 5s* states are essentially the same for all of the crystalline phases of ZrO2. Since transitions from the Zr 1s state to Zr 4d and 5s are not dipole-allowed, the Zr K1 edge spectrum is qualitatively similar to the O K1 edge spectrum. Like the O K1 spectrum, the spectral features in the Zr K1 spectrum are consis-tent with mixing between Zr 4d* and 5s* states, and O 2p* states. This is also reflected in the tabulation of ∆(d1*,2) and ∆(d1*,s*) values in Table 1. The doublet 4d* features are not spectroscopically resolved in Fig. 5, or in the spectra in Ref. 15. The relative intensities of the d* and s* spectral features in the Zr K1 and O K1 spectra in Fig. 5b and 6 and markedly different. Ti K1 and Hf K1 edge spectra have not been obtained for our thin film samples. However, there have been several published spectral studies of TiO2 in the rutile and anatase crystal forms [16, 17]. Published results for the Ti K1 edge of TiO2 in the rutile phase are included in Table 1 [16, 17]. A comparison indi-cates a similar x-axis (energy) behavior between the O K1 spectra for the nano-crystalline TiO2 film of this study, and the published rutuile Ti K1 spectrum [16, 17]. In particular, the d-state splittings are the same to within experimental error, 2.5 ± 0.3 eV for the O K1 spectrum, and 2.7 ± 0.3 eV for the Zr K1 spectrum. The s-state energy peak separations are smaller in the O K1 edge spectrum, 3.5 ± 0.3 eV, com-pared with 7.0 ± 0.3 eV in the Zr K1 edge spectrum.

Fig. 3 Deconvolved Zr M3 spectrum shown 4d*-state doublet, and 5s*-state singlet features.

Fig. 4 Ratios of integrated s*-state absorptions to the d*-state absorptions for the Ti L3, Zr M3 and Hf N3

spectra of Figs. 2(a), (b) and (c), respectively, as a function of calculated relative intensities based on hydrogenic Rydberg states [14].



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Fig. 5 O K1 spectra for (a) TiO2, (b) ZrO2 and (c) HfO2.

Fig. 6 Absorption edge spectrum for ZrO2 annealed at 900 °C. The arrows indicate the band edge 4d* features.



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Figure 7 contains a plot of the optical absorption constant, α, versus photon energy, as obtained from an analysis of vacuum ultra-violet spectroscopic ellipsometry data [18]. The band edge, or threshold for optical absorption is at ~5.7 eV, essentially the same as reported from complementary measurements of the photoconductivity [19]. The relative intensities of the d*-state absorption between 5.7 eV and 6 eV, and the overlapping s* state absorption at higher photon energies is similar to the relative intensities of the same types of spectral features in the Zr K1 edge XAS spectrum, however the energy scales are markedly different, consistent with the difference in the initial states, the Zr 1s state for K1 spectrum, and O 2p π non-bonding valence band states for the band edge transitions.

2.2 Silicate alloys

Figure 8(a) displays the O K1 edge for three annealed and phase-separated Zr silicate alloys [8]. The phase separation products are ZrO2 and SiO2, so that to a first order approximation the O K1 edge spectra are linear combinations of the ZrO2 spectrum and the SiO2 spectrum. Based on comparisons with the O K1 edge spectra for ZrO2, and on a molecular orbital model for Zr silicate alloys [5], the first spectral peak and a shoulder shifted in energy by about 3 eV for the x ~ 0.6 or 60% ZrO2 alloy are assigned to doublet Zr 4d*-states mixed with O 2p*-states. The broad feature between 536 and 540 eV is assigned to Si 3*-states, mixed to O 2p*-states. The distinct doublet feature at about 542–544 eV for the x ~ 0.6 or 60% ZrO2 alloy has been assigned above to Zr 4s*-states, that is also mixed with O 2p* states. The dif-ferences between these three spectra with respect to narrowness of the lowest energy 4d*-state feature, and the distinct spectral peak on the Si 3s*-state feature reflect different aspects of the chemical phase separation morphology. These differences are addressed in detail in Ref. [20], with the most important aspect of the separation being in the characteristic size of the crystallites or grains in Zr phase. This is ~3 to 5 nm for x < 0.5, and in excess of 10 nm for x > 0.5. To a good approximation the spectrum for the x = 0.6 sample is a linear combination of the O K1 spectra for crystalline ZrO2, and non-crystalline or amorphous SiO2. Figure 8(b) contains a comparison between the spectrum for the annealed 60% ZrO2 alloy in trace (i) and an as-deposited alloy in trace (ii). The spectral assignments remain the same, but all of the features in trace (i) are broadened due to the non-crystalline bonding arrangements [20]. Figure 9 displays the spectra of three non-crystalline silicate alloys with concentrations of 70%, 50% and 25% HfO2, accurate to approximately ±7% [21]. The most important aspects of these spectra are that (i) the relative intensities of the lowest energy 5d* feature scales with alloy composition, while (ii) the separation between the Hf 5d* spectral peak and center of the Si 3s* band is approximately con-stant.

Fig. 7 Plot of the optical absorbtion constant as fuc-tion of photon energy for crystalline ZrO2. The arrows indicate the two 4d* spectral features.



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Fig. 8 (a) Zr silicate O K1 spectra for films annealed at 900°C, and chemically phase separated into crystalline ZrO2 and non-crystalline SiO2. (b) Comparison between O K1 spectra for a Zr silicate alloy with 60% ZrO2 (x = 0.6) as-deposited and annealed at 900 °C.

2.3 Complex transition metal-rare earth binary oxides

This section introduces an additional dimension to the spectroscopic studies of binary oxides that goes beyond TM and RE silicates and aluminates as well [11]. This involves coupling of d-states of different TM and/or RE through bonding to a common O atom in complex oxides with compositions given by, RETMO3, e.g., GdScO3, and TM(1)TM(2)O4; e.g., HfTiO4. This coupling is strong if the d*-states of the two atoms have the same symmetry, and the two TM and/or RE atoms are collinear. If these conditions are not meet there is still mixing of the respective d*-states, but is significantly weaker, and may involve removing the two- or three-fold degeneracy of either, or both of the TM/RE states, and thereby add addi-tional d*-state features to the O K1 and band edge spectra.

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a) b)



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Fig. 10 O K1 spectra for (a) Y2O3 and (b) ZrO2. The first complex oxides addressed are crystalline GdScO3 and DyScO3. These complex oxides have distorted perovskite structures in which the Gd and Dy atoms are nominally twelve fold coordinated, and the Sc atoms are six fold coordinated. The Gd or Dy atoms are bonded through O atoms to the Sc atoms. Before displaying the O K1 edge XAS spectra for these two crystals, the O K1 edges for thin film, crys-talline Y2O3 and ZrO2 are compared in Figs. 10(a) and 10(b). The most significant difference between these spectra is the spectral overlap between the TM 4d* doublets and the TM 5s* bands. In Y2O3, there is a significant overlap, whereas in ZrO2, the 4d* doublet and 5s* band features are spectroscopically resolved. This difference correlates with a difference in the energy separation of atomic 4d and 5s states in the 4dγ–25s2 atomic configurations, where γ = 3 for Y2O3 and γ = 4 for ZrO2 [22]. These splittings are ~1.5 eV for Y2O3 and ~2.8 eV for ZrO2, and are the determinant factor in the marked differences in the spectral overlap between the respective 4d*- and 5s*-states in Figs. 10(a) and (b).

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Fig. 11 O K1 spectra for (a) DyScO3 and (b) GdScO3. The weak features in each sprectrum at ∼539.5 eV are associ-ated with a splitting of the 3-fold degenerate Dy 5d* and Gd 5d* states at ∼541.2 eV being split by a uniaxial crystal distortion.

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a) b)

Fig. 12 Schematic representation of d-state coupling in complex oxides: (a) GD (Dy)O3 and (b) HfTiO4.

The O K1 edge spectra in Figs. 11(a) and 11(b) for DyScO3 and GdScO3 respectively display three distinct d* state features, as well a fourth weaker feature between the two designated as Sc 3d*, Dy(Gd) 5d* and Dy(Gd) 5d* features. As indicated Fig. 11(a), and based on the comparisons between Figs. 10(a) and (b), these d*-states overlap the Sc 4s*- and Dy 6s*-features. The features at higher energy are tentatively assigned to Sc 4p*- and Dy 6p*-states. Since the 3d/4s atomic splitting of Sc is greater by at least 2–3 eV than the corresponding 5d/6s splittings for both Gd and Dy, this suggests that the feature labeled Sc 3d* has been shifted to higher energy through interactions between Sc 3d, and Gd or Dy 5d states bonded to a common O atom [22]. It also suggests that the other d*-features marked Sc-3d* and Dy-5d* in Fig. 11(a), and Sc 3d* and Gd 5d* in Fig. 11(b) have a mixed Sc-RE atom character. The final d*-states identified as Dy 5d* in Fig. 11(a) and Gd 5d* in Fig. 11(b) are assumed to be shifted in energy by a d*-state mixing interaction and split into two components as show in Fig. 12(a). The energies of the lowest d*-state features in GdScO3 and DyScO3 as shown in Figs. 11(a) and (b), respectively, are essentially the same as the corresponding d*-state energies in ZrO2 and HfO2 as shown in Fig. 5(b) and 5(c). Based on the discussion to be presented in Section 3, this implies that their respective band gaps associated with these spectral features are 5.7 ± 0.2 eV. These values are in good agreement with band edge optical properties studied by vacuum uv spectroscopic ellipsometry; however, these states do not define the lowest energy band gap states. This is illustrated in Fig. 12(a) and (b), and con-firmed for GdScO3 directly by band edge spectroscopic measurements displayed in Figs. 13(a) and 13(b). Figure 12 presents a schematic representation of the coupling of Sc 3d*, and Dy or Gd 5d* states through bonding to a common O atom. This schematic model includes (i) the relative energies of the respective doubly degenerate “e” and triply degenerate “t” representations of (a) the Gd or Dy 12-fold coordinated atoms, and (b) the Sc 6-fold gegenerate atom d*-states, and (ii) the resulting coupled con-duction band states. This model replicates the spectral features in Figs. 11(a) and 11(b). The fifth d*-state feature has been identified in the band edge spectra discussed below. Figure 13(a) displays the optical absorption constant, α, of GdScO3 at the band edge as a function of photon energy as obtained from the analysis of VUV SE data [11]. The shoulder between about 4.8 and 5.8 eV is assigned to 3d*-stat e absorption associated with the Sc atoms. This d*-state associated with this absorption is the lowest d*-state absorption shown in Fig. 12(a). The 3d*-state bandgap of Sc2O3 is approximately 4.6 eV, and is associated with low values of α, in the range of 100 cm–1 [23]. This weak d-state absorption in both Sc2O3 and GdScO3 is attributed to a crystalline distortion associated with the dynamic Jahn–Teller effect which reduces the symmetry at the Sc site from octahedral to a distorted octahedron, and thereby removes the degeneracies of the respective Sc d-states [24]. The rapid rise of absorption at approximately 5.8 eV in GdScO3 in Fig. 13(a) marks the onset of transitions from the top of valence band, O 2p π non-bonding states, and is associated with the lowest coupled and split off “a” state in Fig. 12(a). The relatively sharp features on the shoulder at ~4.8 and 5 eV also appear in the optical absorption spectrum of Fig. 13(b) as a singlet at 4.85 eV, and a doublet centered at 5 eV. These sharp



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Fig. 13 (a) Absorption constant, a, as a function of photon energy for GdScO3 in the spectral range form 4 eV to 9 eV, as obtained from the analysis of VUV spectroscopic ellipsometry data. (b) Optical transmission as a function a function of photon energy for GdScO3 in the spectral range from 3.5 eV the 5.5 eV. features, along with the other two triplet bands at ~4eV and 4.5 eV are characteristic 4f intra-atomic optical transitions of trivalent Gd [25]. Figure 12(b) indicates the coupling of Hf 5d and Ti 3d states in HfTiO4. This figure assumes that Ti and Hf atoms retain the 6-fold and 8-fold coordinations of their respective oxides. Since the respective “e” states are at approximately the same energies this results in a single coupled doubly degenerate e-state. Due to the large energy difference between the respective atomic t-states, the energy shifts of these states are modest. Figure 14(a) is the O K1 edge spectrum for a crystallized (HfO2)0.5(TiO2)0.5 alloy with a stoichiometric titanate composition of HfTiO4. The coupled Ti 3d* and Hf 5d* states have been labeled as in the corre-sponding spectra for GdScO3 and DyScO3, which can also be written, respectively, in mixed oxide nota-tions as (Dy2O3)0.5(Sc2O3)0.5 and (Gd2O3)0.5(Sc2O3)0.5. The most significant difference between the HfTiO4 spectrum, and the GdScO3 and DyScO3 spectra is the overlap of the d* and s* states. The three d* local-ized states, and the s* state bands are spectroscopically distinct in HfTiO4, whilst the corresponding bands overlap significantly in the GdScO3 and DyScO3 spectra. Additionally, there are three d*-states in the complex oxide rather than four as in Gd(Dy)SO3.

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Fig. 14 (a) O K1 spectrum for a (HfO2)0.5(TiO2)0.5 alloy that has been annealed at 600 °C. (b) Comparison between the spectrum in (a), and a spectrum synthesized from the O K1 spectra of HfO2 and TiO2.

a) b)

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Finally Fig. 14(b) compares the O K1 edge spectrum for HfTiO4 with a normalized sum of the spectra for TiO2 and HfO2. The 532.5 eV peak of the HfTiO4 O K1 spectrum was set normalized to sum of the 532 eV features in the O K1 spectra of TiO2 and HfO2. Differences between the spectral peak energies of the features higher and lower energy features, and their respective amplitudes in the experimental and summed spectra are a clear and unambiguous indicator of the proposed d-state coupling.

3 Discussion

3.1 Spectroscopic results

This sub-section distinguishes between the intra-atomic Ti L2,3, Zr M2,3 and Hf N2,3 edge spectra of Figs. 2(a), (b) and (c), and the inter-atomic (i) Ti O K1, Zr O K1 and Hf O K1 spectra of Figs. 5(a), (b) and (c), (ii) Zr K1 edge spectra of Fig. 6, and (iii) band edge ZrO2 spectra of Fig 7. Figure 1 indicates the intra-atomic transitions that contribute to the six-distinct features the Zr M2,3 spectrum of Fig. 2(b) [7]. This schematic representation has been applied to the Ti L2,3 Hf N2,3 spectra and also applies to the corresponding group IIIB TM (Sc, Y, and La) and the trivalent lanthanide RE atom oxide spectra. The spectral features are associated with transitions from relatively deep spin–orbit split 2p, 3p and 4p-core states, typically 200 to 500 eV below vacuum, respectively, to empty 3, 4 or 5d*- and 4, 5 or 6s*-states. These transitions are atomic-like in character and are not significantly changed by 2nd neighbors as has been shown for the Zr M2,3 spectra through the comparisons that in-clude homogeneous, as well as chemically phase-separated Zr silicate alloys [7]. The relative intensities of final d*-states in the Ti and Zr spectra are consistent with the lower energy pair in each spectral com-ponent being the d3/2 state with a spectral weighting of 4, and the higher energy component being the d5/2 state with a spectral weighting of 6. Since the local symmetries of the Ti and Zr atoms are effectively six-fold coordinated in TiO2 and eight-fold coordinated in ZrO2, and since the ordering of the d*-states in the respective spectra are the same, this demonstrates that the d*-state spitting is not local symmetry deter-mined. A splitting associated with the local symmetry would have yielded the reverse ordering of the doubly and triply degenerate d*-states for six-fold coordinated TiO2 and approximately eight-fold coor-dinated ZrO2 [12]. On the other hand, the d*-state splittings, including differences between the L2 and L3, and M2 and M3 spectra, are consistent with a final state effect associated with localization of the core holes on the respective Ti and Zr atoms. The O K1 edge spectra for TiO2 in Fig. 5(a), ZrO2 in Fig. 5(b) and HfO2 in Fig. 5(c) are assigned to transitions from the O 1s-state to final band-like states that have a mixed (i) O 2p*-state, and (ii) TM 3, 4 or 5 d*- and TM 4, 5 or 6-s*-state character, respectively. In contrast to the order of magnitude intensity variation between the respective, (i) Ti and Zr, and (ii) Hf d*- and s*-spectral features in Figs. 2a and 2(b), and Fig. 2(c), the corresponding d*- and s*-related features in Figs. 5a, b and c, have relative inten-sities that differ by no more than about a factor of two. This demonstrates that the matrix elements for absorption to the d*- and s*-state features in the respective O K1 spectra are not determined by the same Rydberg-like transition probabilities as those in the Ti L2,3, Zr M2,3 and Hf N2,3 spectra [14]. The Zr K1 edge spectra in Fig. 5, and the Ti and Zr K1 spectra discussed respectively in Refs. [15–17], are also inter-atomic spectra. The transitions between the Zr and Ti 1s states to the respective atomic Zr 4d*- and 5s*-states, and atomic Ti 3d*- and 4s*-states are not dipole-allowed. Instead, the lowest energy transitions are to final states with a mixed O 2p*-state and Ti or Zr d*- and s*-state character. This inter-pretation of the Zr and Ti K1 spectra is supported by the fact that these transitions have features at higher energy that are used in extended X-ray absorption fine structure (EXAFS) studies to determine nearest neighbor Zr and O, and Ti and O bond lengths, and second and more distant neighbor inter-atomic sepa-rations [26]. Even though the final states have similar atomic character, the relative absorptions of the 4d* and 5s* features in the O K1 and Zr K1 spectra of ZrO2 are markedly different, and therefore reflect differences in the respective O 1s and Zr 1s ground state wave functions, and their effect on the transition matrix ele-ments for absorption. This comparison also holds for the relative absorptions of the 3d* and 5s* features in the O K1 and Ti K1 spectra of TiO2.



The relative absorption strengths for the 4d* and 5s* features in the Zr K1 spectrum in Fig. 6 bear a resemblance to features assigned to the same states in the band edge absorption spectrum in Fig. 7. For example, the threshold d*-state feature has a markedly lower absorption constant than other d*- and s*-states features at higher energies. This is the case even though the initial states are very different; the localized Zr 1s core state for the Zr K1 spectrum, and the more delocalized O 2p π non-bonding states for the band edge absorptions. Addtionally, and perhaps most important, a comparison between the energies of the first spectral peak of the respective O K1 spectra, 530.1 eV for TiO2, 532.4 eV for ZrO2, and 532.6 for HfO2, indicates that the differences between these energies are equal to within an experimental uncertainty of ±0.3 eV to the respective differences in reported nominal band gap energies of 3.1 eV for rutile TiO2 [12], 5.6 eV for ZrO2 [19], and 5.8 eV for HfO2 [19]. This comparison carries over to complex oxide high-k dielectrics such as GdScO3 and DyScO3 [11, 27]. Finally, the occurrence of three strong and one relatively weak d*-state features in O K1 edge spectra of the complex oxides of Section 2.3 confirms that the atomic d-states of the constituent pair of RE and TM atoms in GdScO3 and DyScO3 are coupled through bonding to a common O atom. A similar situa-tion prevails for the d* spectral features in HfTiO4. However, the details of the coupling of the respective d*-states are qualitatively different as indicated in Figs. 12(a) and 12(b).

3.2 Conduction band offset energies and tunneling

In order to reduce direct tunneling in FETs with EOT <1.5 nm, and extending below 1 nm, there has been a search for alternative dielectrics with significantly increased dielectric constants, k. This allows increases in physical thickness proportional to k, thereby having the potential to significantly reduce direct tunneling. However, increases in k are generally accompanied by decreases in the optical band gap, Eg, the conduction band offset energy with respect to Si, EB, and the effective electron tunneling mass, meff. These trade-offs are quantified by the introduction of a tunnelling figure of merit [4], Φm, given by,

Φm = k [EB meff]0.5. (1)

Robertson and coworkers have developed a model for obtaining band gaps and conduction band offset energies for representative gate dielectric materials including SiO2 and Ta2O5, as well as the high-k di-electrics of this paper [28, 29]. Figure 15(a) is plot of EB versus Eg in which the experimentally deter-mined band offset energy for SiO2, 3.15 eV used instead of the calculated values from Ref. [29]. The relationship is approximately linear, as indicated by the fit to the points in Fig. 15(a). Figure 15(b) con-tains plots of Eg and EB as a function of the atomic d-state energy of the TM atoms for the TM oxides of Fig. 15(a). As noted above, O K1 spectra of TM oxides provide quantitative information about relative band gaps for TM oxides, and for the extension of this relationship to more complex oxide alloys and compounds as well. For example, combined with Auger electron spectroscopy and X-ray photoelectron spectroscopy studies, XAS spectra have provided important information relative to the compositional dependence of conduction band offset energies in Zr and Hf silicate alloys [8, 21]. Based on these com-parisons, several of the group IVB and VB TM oxides with the highest dielectric constants, e.g., TiO2, and Nb2O3 and Ta2O3, have offset energies below 1 eV that correlate with either high tunneling leakage, and or electric field assisted injection into low-lying conduction band traps associated with these atoms [30, 31]. Based on scaling with atomic d-states, (i) the group IVB oxides of Zr and Hf and their respec-tive silicate, and aluminate alloys, as wells as (ii) the group IIIB, and lanthanide RE series oxides, and their respective silicate and aluminate alloys are expected to have conduction band offset energies greater than about 1.2–1.3 eV, and to meet roadmap targets with tunneling leakage current, provided the elec-tron tunneling mass does not decrease significantly with decreasing EB. Figure 15(c) is a plot of the electron tunneling mass, meff, versus the conduction band offset energy, EB. The linear portion of this plot for EB between about 2.5 and 4.1 eV is in accord with the Franz two-band model of Refs. [32] and [33], and applies when the conduction band states are free electron-like



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with predominantly s*-character. The projected values for meff when EB are attributed to a change in the character of the lowest conduction band states, from s*-extended states in SiO2 and Si3N4, to significantly more localized d*-states in the TM and RE dielectrics. Based on an analytic continuation of the quadratic fit in Fig. 15(c), a 1.2–1.3 eV offset energy is expected to correlate with a sufficiently high electron tunneling mass to be a good lower limit for dielectrics that will meet roadmap targets for aggressive scaling of EOT down to at least 1.0 nm.

Acknowledgements This research is supported in part by the Office of Naval Research, the Semiconductor Re-search Corporation, and the Semiconductor Research Corporation/International Sematech Front End Processes Center.

References

[1] G. D. Wilk, R. W. Wallace, and J. M Anthony, J. Appl. Phys. 87, 484 (2000). [2] G. D. Wilk, R. W. Wallace, and J. M. Anthony, J. Appl. Phys. 89, 5243 (2001). [3] International Technology Roadmap for Semiconductors (2001 ed.) at http://public.itrs.net.

Fig. 15 (a) Conduction band offset energy, EB, versus optical band gap, Eg, for representative TM oxides, and SiO2. The Eg values, as well as the EB values for the TM oxides are from Ref. [29]. The Eg value for SiO2 is also from Ref. [29]; however, the EB value is the accepted experimental value, 3.15 eV, and is about 0.35 eV less than the calculated value of Ref. [29]. (b) EB and Eg for the TM oxides of (a), as functions of the TM atom d-states in the n + 1 s2, ndγ – 2 configurations [22], where γ = 4 and 5, for the respective group IVB and VB oxides. (c) meff versus EB for representative gate dielectrics. The solid line is a quadratic fit to the points.

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[4] C. L. Hinkle C. Fulton, R. J. Nemanich, and G. Lucovsky, Microelectron. Eng. 74, 257(2004). [5] G. Lucovsky, G. B. Rayner, Y. Zhang, G. Appel, and J. L. Whitten, Appl. Surf. Sci. 216, 215 (2003). [6] E. W. A. Young and V. Kauschik, in: High-k gate dielectrics, edited by M. Houssa (Inst. of Physics, Bristol,

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J. L. Whitten, Appl. Phys. Lett. 79, 1775 (2001). [8] G. B. Rayner Jr., D. Kang, Y. Zhang, and G. Lucovsky, J. Vac. Sci. Technol. B 20, 1748 (2002). [9] C. C. Fulton, G. Lucovsky, and R. J. Nemanich, Appl. Phys. Lett. 84, 580 (2004). [10] G. B. Rayner, D. Kang, and G. Lucovsky, J. Vac. Sci. Technol. B 21, 1783 (2003). [12] P. A. Cox, Transition Metal Oxides (Oxford Science Publications, Oxford, 1992), Chapter 2. [13] A. Thompson et al. (Eds.), X-ray Data Handbook (Lawrence Berkeley National Laboratory, University of

California, Berkeley, CA, 2001). [14] E. U. Condon and G. H. Shortly, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, UK,

1957), Chap. V. [15] P. Lim, I.-W. Chen, J. E. Penner-Han, Phys. Rev. B 48, 10063 (1993). [16] L. A. Grunes, R. D. Leapman, C. N. Nilker, R. Hoffman, and A. B. Kunz, Phys. Rev. B 25, 7157 (1983). [17] L. A. Grunes, Phys. Rev. B 27, 2111 (1983). [18] N. A. Stoute, D. E. Aspnes, and G. Lucovsky, unpublished. [19] V. V. Afanas’ev and A. Stesmans, in: High-k gate dielectrics, edited by M. Houssa (Inst. of Physics, Bristol,

2003), p. 217. [20] G. B. Rayner, D. Kang, and G. Lucovsky, J. Vac. Sci. Technol. B 21, 1783 (2003). [21] J. G. Hong, Ph. D. Dissertation (North Carolina State University, 2003). [22] W. A. Harrision, Elementary Electronic Structure (World Scientific Publishing, Singapore, 1999), The Solid

State Table. [23] H. H. Tippins, J. Phys. Chem. Solids 27, 1069 (1966). [24] L. Orgel, Introduction to transition metal chemistry (Wiley, New York, 1960). [25] D. S. McClure, Electronic Spectra of Molecules and Ions in Crystals (Academic Press, New York, 1959). [26] D. C. Koningsberger and R. Prins (Eds.), X-Ray Absorption: Principles, Applications, Techniques of EXAFS,

SEXAFS and XANES (Wiley, New York, 1988). [27] G. Lucovsky and D. G. Schlom, unpublished. [28] J. Robertson and C. W. Chen, Appl. Phys. Lett. 74, 1164 (1999). [29] J. Robertson, J. Vac. Sci. Technol. B 18, 1785 (2000). [30] R. S. Johnson, J. G. Hong, and G. Lucovsky, J. Vac. Sci. Technol. B 19, 1606 (2001). [31] R. S. Johnson, J. G. Hong, C. L. Hinkle, and G. Lucovsky, J. Vac. Sci. Technol. B 20, 1126 (2002). [32] W. Franz, in: Handbuch der Physik, edited by S. Flugge (Springer, Berlin 1965) Vol. XVIII, p. 155. [33] J. Maserjian, J. Vac. Sci. Tech. 11, 996 (1974).

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Spectroscopic studies of metal high-k dielectrics: transition ...metal d*- and s*-states for transition metal oxides and silicate alloys. The figure also identifies the inter The figure

Spectroscopic studies of metal high-k dielectrics: transition ...metal d- and s-states for transition metal oxides and silicate alloys. The figure also identifies the inter The figure