Many-body effects in X-ray photoemission spectroscopy and electronic properties of solids

Spectrochimica Acta Part B 54 (1999) 123–131

Review

Many-body effects in X-ray photoemission spectroscopy and electronic properties of solids ✩ Shigemi Kohiki* Kyusyu Institute of Technology, Faculty of Engineering, Department of Materials Science, Kita-kyusyu, 804-8550, Japan Accepted 29 May 1998

Abstract Photoemission from a solid is evidently a many-body process since the motion of each electron cannot be independent of the motions of other electrons. In this article we review the reported many-body effects in X-ray photoemission such as extraatomic relaxation energy, charge transfer satellite and energy loss structure which are informative in relation to the characteristics of solids. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: X-ray photoemission spectroscopy; electronic properties; solids; extra-atomic relaxation energy; charge transfer satellite; energy loss structure

1. Introduction X-ray photoemission spectroscopy (XPS) is suitable for examination of the electronic structure and dielectric response of a solid. It is assumed that the photoexcitation of the electron, the transport to the surface and emission of the electron into the vacuum take place subsequently and independently in the three step model of photoemission [1]. Usually, the observed spectral features are labeled in terms of oneelectron quantum numbers, however, photoemission from a solid is evidently a many-body process since the motion of each electron cannot be independent of the motions of other electrons. It is generally stated that the actual photon absorption process occurs nearly instantaneously (ⱗ 10 −17 s) ✩

This paper is published in the Special Issue of Spectrochimica Acta Part B ‘‘Instrumentation Chemistry’’, dedicated to Y. Gohshi. * Corresponding author. Fax: +81-938-84-3300; e-mail: [email protected]

and the hole switching occurs in a time less than 10 −16 s. The localized screening response (10 −16 –10 −15 s) is very fast in contrast to the delocalized screening response (10 −13 –10 −12 s). Delocalized screening is accompanied with core–valence–valence (CVV) Auger transitions [2]. Negative charge flows towards the photo-hole in order to screen suddenly created positive charge. Relaxation energy, lowering observed binding energy (E b) of the photoelectrons than that expected from Koopmans’ theorem, is the result of this flow of negative charge. It is impossible to measure directly the extra-atomic relaxation energy (R ex) in photoemission from solids, though it is possible to evaluate the variation in R ex with the change in the electronic structure using Auger parameter [3–6]. Charge transfer (CT) satellite typically observed in XPS of cuprate superconductor is also a resultant from relaxation process of core-hole state in a many-electron system and is due to strong Coulomb interaction between a core-hole and the half-filled antibonding orbital [7].

0584-8547/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S 05 84 - 85 4 7( 9 8) 0 01 8 2- 7

124

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131

The Coulomb field accompanied by a moving electron in approach to the solid surface interacts with the electrons of the solid via long-range dipole fields. A longitudinal plasma wave traversing a crystal produces density fluctuations of its charges in the direction of propagation due to the long-range Coulomb interactions between positive and negative charges accompanied by the excitation of collective oscillations. High-resolution XPS can reveal the characteristic energy loss structure due to both single particle excitations (interband transitions) and collective oscillations of the valence electrons (plasma oscillations) excited by energetic photoelectrons on the lower kinetic energy side of core lines [8]. In XPS of solids we can observe three kinds of many-body effects; extra-atomic relaxation energy, charge transfer satellite and energy loss structure. Many-body effects in XPS provide useful parameters for design, synthesis and characterization of solids. Here, we review the reported many-body effects such as extra-atomic relaxation energy, charge transfer satellite and energy loss structure informative in relation to the characteristics of solids.

2. Extra-atomic relaxation energy and Auger parameter Photoelectrons and Auger electrons are emitted from the surface of materials irradiated by X-rays. Relaxation of the core-hole state which is produced by photoelectron emission results in an Auger transition. Wagner [9] proposed a quantity named the ‘Auger parameter’. The Auger parameter is defined as the difference between the kinetic energies (E ks) of the Auger electron and of the photoelectron of the same element in the same sample. The Auger parameter is attractive because static charge correction and work function correction are not necessary. Wagner et al. [10] introduced the idea of a ‘modified Auger parameter’. The modified Auger parameter is defined by the combination of the photoelectron E b and the Auger electron E k. From a practical point of view it is better to use a modified Auger parameter. The Auger parameter and modified Auger parameters may be used as a ‘fingerprint’ for the chemical state. This straightforward approach often makes use of a ‘mixed Auger parameter’ [11]. According to

Kowalczyk et al. [12] and to Wagner [9], half of the difference in the Auger parameters between two compounds corresponds to the difference in the extra-atomic relaxation energy (polarization energy) for the one-hole state of the atom under study in the two compounds. It is well known that the photon absorption process causes photoemission and Auger electron emission processes. The E b of a level j, E b(j), is the difference in the total energy of the system in its ground state and in the state with one electron missing in the orbital j. The E b(j) relative to the Fermi level is defined by the following equation: E b(j) = Ebv (j) − f sp. Here, Ebv denotes the E b relative to the vacuum level and f sp is the work function of the spectrometer. The E b(j) in the solid phase relative to the Fermi level can be expressed [13] as Eb (j) = − ␧(j) − R D (j)

(1)

Here, − ␧(j) is the term for the orbital energy calculated by solving the Hartree–Fock (HF) equations by Koopmans’ theorem, and R D(j) is the one-hole dynamic relaxation energy related to the photoemission process after Shirley [14]. The relaxation energy is the result of a flow of negative charge towards the hole created in the photoemission process in order to screen the suddenly appearing positive charge. The screening lowers the measured E b as well. The relaxation energy (R) can be partitioned into two terms: intra-atomic relaxation energy (R in) and extra-atomic relaxation energy (R ex). The former is constant for the core-electrons of a given atom. The latter varies with changes in chemical and physical states. According to Eq. (1), the photoelectron E b shift can be written as DEb (j) = − D␧(j) − DR D ex (j)

(2)

For most situations encountered in photoemission, the Eq. (2) is close enough to discuss the chemical shift [15]. The E k relative to the Fermi level of an Auger electron emitted from a transition jkk is given by the following equation [16]: Ek (jkk) = Eb (j) − 2Eb (k) − F(kk) + R s (kk)

(3)

where E b(j) and E b(k) are the binding energies of the electrons j and k, respectively. The processes of electron emission (j and k) include the dynamic relaxation,

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131

relatively and electron correlation effects. The correction energy due to the presence of the k hole should also be considered in the process of Auger electron emission. F(kk) is the two-electron interaction energy, introduced by Asaad and Burhop [17], describing the unscreened coupling of the two holes in the k level. In this discussion the spectroscopic term in the multiplet final-state is neglected. The bare two-hole interaction energy can be estimated by standard atomic multiplet coupling theory [18] and by tabulated F- and G- Slater integrals [19]. R s(kk) is the static relaxation energy. Here, R s(kk) = R T(kk) − 2R D(k). The difference between the total two-hole relaxation energy R T(kk) and twice the one-hole dynamic relaxation energy is equal to the static relaxation energy. It gives the additional relaxation shift of the total energy associated with two localized holes relative to that of two isolated holes. Differences in relaxation energies are dominated by Coulomb interactions. So, we have R T(kk) = 4R D(k). The static relaxation energy is twice the dynamic relaxation energy. According to Eq. (3), the Auger electron E k shift can be written as DEk (jkk) = DEb (j) − 2DEb (k) + 2DR D ex (k)

(4)

F(kk) is the atomic term; therefore, DF(kk) is zero. The Auger parameter is defined by the combination of the photoelectron E b and the Auger electron E k as follows [10]: a = Eb (j) + Ek (jkk)

(5)

The difference in the Auger parameters for the element in two different environments can be written Da=DEb (j)+DEk (jkk) = 2DEb (j) −2DEb (k) + 2DR D ex (k) (6) If the assumption DE b(j) = DE b(k) is valid, we obtain the following result: Da = 2DR D ex (k)

(7)

The chemical shift in the Auger parameter is equivalent to twice the difference in dynamic extra-atomic relaxation energies of an atom considered in different environments [9,12]. If the assumption DR D ex (k) = DR D ex (j) is valid, we can derive the following equation from Eq. (2): Eb (j) = − D␧(j) − (1=2)Da

(8)

125

Fig. 1. The Si 2p E b vs the Si or N Auger parameter (N Auger parameter is used for non-stoichiometric SiN x). 1, Si; 2, SiN 0.3; 3, SiN 0.9; 4, SiN 1.3; 5, SiN 1.3; 6, SiN 1.3; and 7, SiO 2 [6]. Measured Si Auger parameters of 1, 5 and 7 are in good agreement with those by Wagner [11].

This assumption makes use of the mixed Auger parameter to evaluate the change in dynamic extra-atomic relaxation energy. Changes in the Auger parameter, the modified Auger parameter, and the mixed Auger parameter from one compound to another are identical. E bs relative to the Fermi level of the Si 2p electrons are plotted as a function of the Auger parameter of the Si in Fig. 1 [6]. For non-stoichiometric amorphous(a)SiN x, the Si 2p E bs were plotted as a function of the Auger parameter of the N. The values of the Auger parameter of Si and N were aligned at a-SiN 1.3. The changes in the Auger parameter of Si going from Si to SiN 1.3 and to SiO 2 are −2.2 and −3.9 eV, respectively. Hence, we can estimate the changes in the extraatomic relaxation energy from Si to SiN 1.3 and to SiO 2 as −1.1 and −2.0 eV, respectively. The Si–Si bond is covalent whereas the Si–N and Si–O bonds have some ionic character1 [20]. In ionic crystals the polarization energy of an ion is given by the following equation in atomic units [21]: Epol = ( − 1=2r)[1 − (1=␧)]

(9)

1 The difference in electronegativity for the Si–O bond is larger than that of the Si–N bond. The bond ionicity of SiO 2 is 0.61.

126

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131

Where r is the effective hole radius and ␧ is the dielectric constant at optical frequencies. DR D ex = DE pol can be assumed in this situation. From Eq. (9) one obtains the following expressions. DR D ex (Si → SiN1:3 ) = ( − 1=2r)[(1=␧SiN1:3 ) − (1=␧Si )] (10) DR D ex (Si → SiO2 ) = ( − 1=2r)[(1=␧SiO2 ) − (1=␧Si )] (11) ␧ SiO 2, ␧ SiN 1.3, and ␧ Si are 2.2, 3.9 and 12, respectively. r ˚ which is the Si 3p orbital radius. So, we have is 1.4 A the following results: DR D ex (Si → SiN1:3 ) = − 0:9 eV DR D ex (Si → SiO2 ) = − 1:9 eV D The values of DR D ex (Si → SiN 1.3) and DR ex (Si → SiO 2) derived from the changes in the Auger parameter are in good agreement with those derived from the changes in the polarization energy.

3. Charge transfer satellite in cuprate superconductors In this section we review the many-body features in XPS of the typical cuprate superconductors such as and Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2), La 2-xSr xCuO 4 (x = 0,0.13) and RBa 2Cu 3O 7-x (R:Er,Y). The Cu 2p photoelectron spectra of the cuprate superconductors show prominent main and satellite lines due to |cd 10Li and |cd 9i final states. Here, c and L represent, respectively, the states of a hole on the Cu 2p and O 2p orbitals. The main and satellite structures have been predicted as the result of charge fluctuation due to strong Coulomb interaction between a Cu 2p hole and the half-filled antibonding orbital of the Cu d-O p bond in the D 4h local symmetry [22–24]. A simple model can explain the physical origin of the satellite [22–25], that includes fundamental parameters (U cd, D and T) for a two-band Hamiltonian in the study of correlated systems. In this model the ground state is described by the configuration interactions of two symmetrized states: |d 9i and |d 10Li. |d 10Li represents the state with one electron removed from the 2p orbitals of surrounding oxygen atoms (ligand) to fill the Cu |d 9i state, which leaves a hole L in the ligand p

orbitals. The final state of Cu 2p photoemission involves the linear combinations of symmetrized |cd 10Li and |cd 9i states. The transfer integral T and the charge transfer energy D are defined as follows: T = hd 9|H|d 10Li, where H is the Hamiltonian, and D = hd 10L|H|d 10Li − hd 9|H|d 9i. D is the energy required to move one electron from the ligand p to Cu d orbitals. In the states with the core-hole present, the |d 10Li configuration is pulled down relative to the |d 9i configuration by the Coulomb interaction energy between a core-hole and a valence-hole U cd. The energy separation between the main and satellite peaks W is the difference of the eigenvalues: W = {(D − U cd) 2 + 4T 2} 1/2. The intensity ratio of the main peak to satellite peak, I m/I s, is given by I m/I s = tan 2(v⬘ − v), where v⬘ and v are defined as tan(2v) = 2T/D and tan(2v⬘) = 2T/(D − U cd), respectively. The I m/I s is value is proportional to the square of the increment of covalency which is represented by the increment of the molecular orbital coefficient from the ground state to the core-hole state. At present, it is still of great interest to clarify the relationship between many-body effects and characteristics of cuprate superconductors. In Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2) and La 2−xSr xCuO 4 (x = 0,0.13) systems, high-T c superconductivity can be realized only by the stacking of the Cu–O and Ca layers and by the Sr substitution for La, respectively. For Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2) and La2 − x Srx CuO 4 (x = 0,0.13), fairly intense charge transfer satellite was observed [7]. The main and satellite peaks correspond to the |cd 10Li and |cd 9i final states. On the basis of the multiplet coupling between a Cu 2p hole and a Cu 3d hole, and the anisotropic hybridization between the Cu 3d hole and O 2p (VB) holes, the spectral change with x in the system can be understood as due to the changes of T [23]. In La 2−xSr xCuO 4 (x = 0,0.13) the multiplet structure of the satellite lines is different compared with that of the Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2) system. This structure can be reproduced well by McMahan’s energy-dependent hybridization parameter [26] as pointed out by Okada and Kotani [23]. The spectral change with x in the system can be understood as due to the changes of T. In Bi-Sr-Ca-Cu-O and La-Sr-Cu-O systems, highT c superconductivity is realized without chemical oxidation of copper. ErBa 2Cu 3O 7−x has the same crystal structure as YBa 2Cu 3O 7−x since Er can substitute for Y. Reported T cs are similar for both systems, and

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131

T c of the systems varies with x. In ErBa 2Cu 3O 7−x oxidation and reduction of copper directly affect superconductivity. By using the X-ray irradiation technique [27], the superconducting properties and Cu valence of the system can be changed homogeneously without orthorhombic-to-tetragonal crystal structure transformation. The ErBa 2Cu 3O 7−x film showed a typical 90 K superconductivity. The ErBa 2Cu 3O 7−y (x ⬍ y) film treated by X-ray irradiation process showed semiconductor like behavior below 80 K superconducting transition. The ErBa 2Cu 3O 7−x showed an intense peak corresponding to the |cd 9i state, though the intensity of the peak due to the |cd 9i state was very small for the ErBa 2Cu 3O 7−y (x ⬍ y). Increases of the I m/I s and W values corresponded with the change of characteristics from superconducting to semiconducting with the deterioration of T c. This seems to be interpreted as the result of Cu 1+ formation due to the X-ray irradiation process, however, Cu 2+-to-Cu 1+ conversion cannot widen the separation between the main and satellite peaks. This result represents a peculiar feature of the electronic states of the Er–Ba–Cu–O system. In the YBa 2Cu 3O 7−x system Ramaker et al. [28,29] suggested that electron–electron interaction effects correlate with T c of cuprate superconductors. Increases of the values of I m/I s and W in the 2p spectra with increasing x were reported [28–30] and interpreted as due to a decrease of D [30,31]. Yeh [31] concluded that Sr substitution for La enlarges D in the La-Sr-Cu-O system, however, we could not find any evidences for the enlargement of D. An enlargement of T, not D, of covalent Cu–O bonds in Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2) and La 2−xSr xCuO 4 (x = 0,0.13)systems brings about high-T c superconductivity. The I m/I s and W values in the Cu 2p photoelectron spectra are listed in Table 1 for the Bi-Sr-Ca-Cu-O, La-Sr-Cu-O, Er-Ba-Cu-O systems, and related materials. It is readily understood that there is a tendency toward increase of the I m/I s value, corresponding to an increase of the W value in the cuprate superconductors. However, the relationship between these many-body effect parameters (I m/I s and W) and the superconducting properties is so complicated. Enlargements of the I m/I s and W values correspond with the change of characters from superconducting to semiconducting with the deterioration of T c in the Er-Ba-Cu-O and Y-Ba-Cu-O systems, while for the

127

Bi-Sr-Ca-Cu-O and La-Sr-Cu-O systems, increases of the I m/I s and W values correspond to the change from a semiconductor to a superconductor. Furthermore, both the I m/I s and W values increase with T c in the Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2) system. In Fig. 2 (upper plot) the (T/D) 2 was transformed from I m/I s by assuming a relationship I m/I s = tan 2(T/D). The main to satellite peak separation, W 2 corresponds to (D − U cd) 2 + 4T 2. The lower plot of Fig. 2 shows the calculated characteristics of W and I m/I s as a function of T (broken lines) and of D (solid lines). High-T c superconductivity for the Bi-SrCa-Cu-O and La-SrCu-O systems was realized by increasing T in the region of the parameters of U cd = 7–8 eV and D = 3.5–4 eV. On the contrary, in the Bi-Sr-CaCu-O and La-Sr-Cu-O systems, 90 K superconductivity in the Er-Ba-Cu-O and YBa-Cu-O systems was realized by increasing D in the region of the parameters of U cd = 8 eV and T = 4 eV. An attempt to apply the assumption of an enhancement of the covalency of the Cu–O bond to the Er-Ba-Cu-O and Y-Ba-Cu-O systems faces some difficulties since D becomes larger in the superconducting samples as pointed out by Yeh et al. [30,31]. The oxygen coordination number around Ba atoms in higher-T c sample is larger than that in lowerT c sample, while the number of cations remains the same. D must be redefined as the energy required to create a hole in the extended ligand states composed of the valence states of oxygen and cations (Ba and Cu) to take into account the strong hybridization of the valence states.

4. Energy loss structure in the background of core-level spectra Electron energy loss spectroscopy (EELS) and optical reflectance spectroscopy are widely used to examine the dielectric loss function of materials. In EELS of insulators electron beam irradiation in ultrahigh vacuum causes substantial deformation of the electronic structure through reduction of oxides (radiation damage). In optical reflectance spectroscopy it is necessary to collect the spectral response in a wide range of photon energies to perform a Kramers–Kronig analysis, however, synchrotron radiation is still not generally used as a light source. At present, XPS is widely used for examination of the

128

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131

Table 1 Main to satellite intensity ratios and separations of cuprate superconductors and related materials Substance Bi 2Sr 2Ca xCu 1+xO 6+2x x = 2 supr. T c 120 K x = 1 supr. T c 90 K x = 0 semi. La 2−xSr xCuO 4 x = 0.13 supr. T c 35 K x = 0 semi. Nd 2−xCe xCuO 4 x = 0.15 supr. T c 24 K x = 0 semi. CuO (powder) ErBa 2Cu 3O 7−x,y (x ⬍ y) x supr. T c 90 y semi. + supr. T c 85 K YBa 2Cu 3O 7−x (ceramics) supr. T c 90 K x = 0 supr. T c 80 K x = 0.5 supr. T c 60 K x ⬎ 0.5 semi. YBa 2Cu 3O 7−x (ceramics) x = 0.06 supr. T c 90 K x = 0.50 supr. T c 45 K x = 0.66 semi.

I m/I s

W (eV)

Reference 7

4.6 4.3 2.5

9.3 9.1 9.0

5.5 3.7

9.8 9.0

— 4.9 2.0

— 9.5 9.0

3.2 6.9

9.1 9.7

2.0 3.8 9.4 —

8.8 9.3 9.9 11

2.4 3.1 3.5

8.9 9.1 9.4

7

33

33 7

30

32

electronic structure of materials without radiation damage in most cases. Fig. 3 shows the energy loss structures ranging from 5 to 30 eV relative to the zero loss line for both LiNbO 3 and LiTaO 3· [8]. The most intense and best resolved line is the O1s. The energy loss structure is the same for the remaining core lines within the experimental uncertainty. No change in the energy loss structure was observed when the electron takeoff angle relative to the surface was varied from 90 to 20 degrees for examination of the surface effect. The effective sampling depth decreases to 1/3 with the decrease of the take-off angle. The observed energy loss structure reflects both the surface and bulk energy loss functions of LiNbO 3 and LiTaO 3. As shown in Fig. 3 the energy loss structures can be approximated by a sum of four components; three peaks are relatively narrow (P1, P2 and P3) and one is broad (P4). The relevant parameters and possible assignments for the loss structure are listed in Table 2. The loss structure in XPS for LiNbO 3 agrees fairly well with that in the EELS [34], though the energy resolution of the XPS is better than that of reported EELS.

Fig. 2. The separation and intensity ratio of main to satellite peaks. In the upper panel the experimental relations are plotted. Proper superconductivity for each system was realized in the shaded regions [7].

Interband transitions from valence band to conduction band are caused by a traveling electron with sufficient energy and give rise to an energetically discrete structure in the energy loss structure. X a molecular orbital calculation for LiNbO 3 revealed that the valence band maximum departs by 3.65 eV from the conduction band minimum, and the conduction band splits into the lower conduction band (2.19 eV wide) consisting of an Nb 4d band and the upper conduction band consisting of Nb 5s and 5p bands [35]. The width of the valence band observed experimentally was about 5 eV which agrees with that of the density of states (DOS) calculated by the first-principles orthogonalized linear combination of atomic orbitals method in the local density approximation and self energy correction [36]. The valence band of 5.3 eV

129

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131 Table 2 Energy loss structure in LiNbO 3 and LiTaO 3 (eV) a Peak

LiNbO 3

LiTaO 3

Assignment

P1 P2 P3 P4

7.0 12.0 14.5 21.8

8.0 13.4 15.8 22.6

VB to lower CB VB to upper CB VB to upper CB Plasmon

a

Fig. 3. Electron energy structures of LiNbO 3 and LiTaO 3 by XPS. Surface and bulk loss functions for LiNbO 3 and LiTaO 3 calculated by Mamedov et al. [40] are also reproduced for convenience in comparison.

width is derived from the hybridized O 2p and Nb 4d orbitals. It is separated from the lower conduction band by a gap of 3.56 eV which is comparable to the optical band gap (3.78 eV) [37]. The lower conduction band consists of the Nb 4d orbitals and is about 2.3 eV wide. It is separated from the upper conduction band (about 7 eV wide) by a gap of about 2.0 eV. The observed width of the valence band (FWHM:5 eV) agrees fairly well with the band structure calculated by the full potential linearized augmented plane-wave method [38]. The band structure of LiTaO 3 is completely analogous to that of LiNbO 3 except for the difference in the band gap (E g). The

The values of separation is relative to the zero loss line. VB, valence band; CB, conduction band.

calculated E g of LiTaO 3 is larger by 1 eV than that of LiNbO 3. The analogy of the band structures seems to be reasonable since the crystal symmetries of LiNbO 3 and LiTaO 3 are identical and the ionic radii of Ta and ˚ , and that of O is about 1.4 A ˚, Nb are about 0.6 A making the sum of each pair (Ta–O and Nb–O) ˚ . The electronic structure calculation about 2.0 A [38] suggests that the narrow peaks labeled P1, P2 and P3 with an energy less than 20 eV can be ascribed to interband transitions. As listed in Table 2, the peaks P1 (E loss = 7.0 eV for LiNbO 3 and 8.0 eV for LiTaO 3), P2 (E loss = 12.0 eV for LiNbO 3 and 13.4 eV for LiTaO 3) and P3 (E loss = 14.5 eV for LiNbO 3 and 15.8 eV for LiTaO 3) correspond to the excitation from the valence band to the lower and upper conduction bands, respectively. In some semiconducting and insulating materials valence electrons form a plasmon peak in a higher energy region within 10–30 eV than an interband transition peak [39]. The electron energy loss function is expressed as Im(−1/␧) = ␧ 2/(␧21 + ␧22 ). The condition ␧ 1 = 0 determines the plasma frequency of the free electron gas where ␧ 2 is small and monotonous. Mamedov et al. [40] measured the optical reflectivity of LiNbO 3 and LiTaO 3 in the energy range of 0.1–35 eV using synchrotron radiation as a light source. They clarified that the imaginary part ␧ 2 of the dielectric function ␧ in the high energy region of ⬎ 15 eV is small and monotonous, and has no evident peaks which indicate interband transition, though ␧ 1 is not zero. Therefore, we identify peak P4, separated by 21.8 eV for LiNbO 3 and 22.6 eV for LiTaO 3, to be plasma oscillation. For LiNbO 3 this plasmon energy is consistent with that reported by Barner et al. (about 21.5 eV) [41], but it is smaller than the reported optical plasmon energy of 25.5 eV [40]. The plasmon energy of 22.6 eV for LiTaO 3 is also smaller than the reported optical plasmon energy of 25.3 eV [40]. Optical measurement

130

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131

usually yields bulk optical constants (e.g. a bulk plasmon). However, it is well known that photoelectrons undergo surface excitation (e.g. a surface plasmon). Present loss structures by XPS significantly include the contribution of the surface loss function Im[ − 1/(␧ + 1)] which shifts the plasmon energy to a lower energy. Mamedov et al. [40] calculated both the surface and bulk loss functions for LiNbO 3 and LiTaO 3. As it seen in Fig. 3, the peaks at around 22 eV by XPS correspond to those in the surface loss functions. For LiNbO 3 and LiTaO 3 similar energy loss structures appeared on the lower kinetic energy side of the core lines in XPS as shown in Fig. 3. The peak separations of the interband transitions for LiTaO 3 are larger by about 1 eV than those for LiNbO 3 as listed in Table 2, and this difference is consistent with that in the calculated band gap between LiNbO 3and LiTaO 3. The loss structures by XPS include significant contributions of the surface loss function.

5. Summary The Auger parameter is valid for determining the change in the extra-atomic relaxation energy which is equivalent to the polarization energy by Mott et al. as demonstrated in Section 2. Using the Auger parameter in XPS is a powerful and excellent method to determine the dielectric constant at the surface of solids since the electron escape depth is very ˚ ). small (⯝ 20 A As demonstrated in Section 3, for the Bi 2Sr 2Ca xCu 1+xO 6+2x (x = 0,1,2) and La 2−xSr xCuO 4 (x = 0,0.13) systems, proper high-T c superconductivity was realized by increasing the transfer integral and the interaction strength of the Cu–O bond of the crystal determined the superconducting properties. However, for the ErBa 2Cu 3O 7−x and YBa 2Cu 3O 7−x systems, 90 K superconductivity was realized by increasing the charge transfer energy. The extended valence state including the Cu, Ba and O valence states in the crystal determined the superconducting properties of the ErBa 2Cu 3O 7−x and YBa 2Cu 3O 7−x systems. As demonstrated in Section 4, the energy loss structures below 30 eV for both LiNbO 3 and LiTaO 3 can be partitioned into four components. These were due to interband transitions from the valence band to the

separated lower and upper conduction bands and excitation of a plasma oscillation of the valence electrons. The energy of the interband transitions reflected the difference in the band gap and empty conduction bands. The energy loss structures by XPS include significantly the contribution of the surface loss function. Relaxation of core-hole state reflects the electronic state of the system. The parameters of the many-body effects such as extra-atomic relaxation energy, effective Coulomb energy, transfer integral, charge transfer energy, the energy of interband transition and plasmon excitation are informative to design, synthesis and characterization of solids.

Acknowledgements This paper was published in the Special Issue of Spectrochimica Acta Part B, Instrumentation Chemistry, dedicated to Y. Gohshi.

References [1] C.N. Berglund, W.E. Spicer, Phys. Rev 136 (1964) A1030. [2] J.W. Gadzuk, in: B.Feuerbacher, B. Fitton, R.F. Willis (Eds.), Photoemission and The Electronic Properties of Surfaces, Wiley, Chichester, 1978. [3] S.P. Kowalczyk, L. Ley, F.R. McFeely, R.A. Pollak, D.A. Shirley, Phys. Rev. B9 (1974) 381. [4] C.D. Wagner, Faraday Discuss. Chem. Soc. 60 (1975) 291. [5] S. Kohiki, S. Ikeda, Phys. Rev. B34 (1986) 3786. [6] S. Kohiki, S. Ozaki, T. Hamada, K. Taniguchi, Appl. Surf. Sci. 28 (1987) 103. [7] S. Kohiki, M. Sakai, K. Mizuno, S. Hayashi, A. Enokihara, K. Setsune, S. Fukushima, Y. Gohshi, J. Appl. Phys. 74 (1992) 7410. [8] S. Kohiki, S. Fukushima, H. Yoshikawa, M. Arai, Jpn. J. Appl. Phys. 36 (1997) 2856. [9] C.D. Wagner, Faraday Discuss. Chem. Soc. 60 (1975) 291. [10] C.D. Wagner, L.H. Gale, R.H. Raymond, Anal. Chem. 51 (1979) 466. [11] C.D. Wagner, in: D. Briggs, M.P. Seah (Eds.), Practical Surface Analysis, Wiley, Chichester, 1983, p. 477. [12] S.P. Kowalwyk, L. Ley, F.R. McFeely, R.A. Pollak, D.A. Shirley, Phys. Rev. B9 (1974) 381. [13] D.A. Shirley, in: M. Cardona, L. Ley (Eds.), Photoemission in Solids, vol. 1, Springer, Berlin, 1978, p. 177. [14] D.A. Shirley, Phys. Rev. A7 (1973) 1520. [15] L. Hedin, G. Johansson, J. Phys. B2 (1969) 1336. [16] S.P. Kowalczyk, R.A. Pollak, F.R. McFeely, L. Ley, D.A. Shirley, Phys. Rev. B8 (1973) 2387.

S. Kohiki / Spectrochimica Acta Part B 54 (1999) 123–131 [17] W.N. Asaad, E.H.S. Burhop, Proc. Phys. Soc. (London) 71 (1958) 369. [18] E.U. Condon, G.H. Shortley, in: The Theory of Atomic Spectra, Cambridge University Press, London, 1970. [19] J.B. Mann, in: Atomic Structure Calculations 1, Los Alamos Scientific Report no. LASL-3690, 1967. [20] K. Hubner, A. Lehmann, Phys. Status Solidi A46 (1978) 451. [21] N.F. Mott, R.W. Gurney, Electronic Processes in Ionic Crystals, Clarendon, Oxford, 1948. [22] S. Kohiki, J. Kawai, S. Hayashi, H. Adachi, S. Hatta, K. Setsune, K. Wasa, J. Appl. Phys. 68 (1990) 1229. [23] K. Okada, A. Kotani, J. Phys. Soc. Jpn 58 (1989) 2578. [24] J. Ghijsen, L.H. Tjeng, J. van Elp, H. Eskes, J. Westernik, G.A. Sawatzky, M.T. Czyzyk, Phys. Rev. B38 (1988) 11322. [25] G. van der Laan, C. Westra, C. Hass, G.A. Sawatzky, Phys. Rev. B23 (1981) 4369. [26] A.K. McMahan, R.M. Martin, S. Satpathy, Phys. Rev. B38 (1988) 6650. [27] S. Kohiki, S. Hatta, K. Setsune, K. Wasa, M. Sakai, S. Fukushima, Y. Gohshi, J. Appl. Phys. 70 (1991) 6945. [28] D.E. Ramaker, N.H. Turner, J.S. Murday, L.E. Toth, M.F.L. Hutson, Phys. Rev. B36 (1987) 5672.

131

[29] D.E. Ramaker, J. Electron Spectrosc. 52 (1990) 341. [30] J.J. Yeh, I. Lindau, J.Z. Sun, K. Char, N. Missert, A. Kapitulnik, T.H. Geballe, M.R. Beasley, Phys. Rev. B42 (1990) 8044. [31] J.J. Yeh, Phys. Rev. B45 (1992) 10816. [32] C.N.R. Rao, A.K. Santra, D.D. Sarma, Phys. Rev. B45 (1992) 10814. [33] S. Kohiki, S. Hayashi, H. Adachi, S. Hatta, K. Setsune, K. Wasa, J. Phys. Soc. Jpn. 58 (1989) 4139. [34] P. Steiner, H. Hochst, Z. Phys. B35 (1979) 51. [35] L. Hafid, F.M. Michel-Calendini, J. Phys. C: Solid State Phys. 19 (1986) 2907. [36] W.Y. Ching, Z.Q. Gu, Y.N. Xu, Phys. Rev. B50 (1994) 1992. [37] A. Dhar, A. Mansingh, J. Appl. Phys. 68 (1990) 5804. [38] I. Inbar, R.E. Cohen, Phys. Rev. B53 (1996) 1193. [39] D. Pines, P. Nozieres, The Theory of Quantum Liquids, vol. 1, chap. 4, Benjamin, New York, 1966. [40] A.M. Mamedov, M.A. Osman, L.C. Hajieva, Appl. Phys. A34 (1984) 189. [41] K. Barner, R. Braunstein, H.A. Weakliem, Phys. Status Solidi B68 (1975) 525.