Electronic properties of crystalline and amorphous SiO2 investigated via all-electron calculations and photoemission spectroscopy

Solid State Communications,Vol. 95, No. 5, pp. 313-317, 1995 Elsevier Scicw Ltd Printedin Gmat Britain 0038.1098(95)00266-9 0038-1098/95 $9.50+.00

Pergamon

ELECTRONIC INVESTIGATED

PROPERTIES

VIA ALLELECTRON

OF CRYSTALLINE CALCULATIONS

AND AMORPHOUS

AND PHOTOEMISSION

A. Di Pomponio, A. Continenza, L. Lozzi, M. Passacantsndo,

SiOr SPECTROSCOPY

S. Santucci and P. Picoszi

Dipartimento di Fisica, Universith de L’Aquila, I-67010 Coppito (AQ), Italy

(Received 16 February 1995 by E. Molinari) The electronic properties of silicon dioxide at sero pressure are investigated by means of full-potential linearized augmented-plane-wave calculations and of x-ray and ultraviolet photoemission spectroscopies. The comparison between our theoretical and experimental results regarding the valence band structure of a-quarts (the crystalline polymorph of silica stable at normal conditions) shows that the main features at lower binding energies (mainly the 0 2p bonding and nonbonding states) are well reproduced, while the binding energy of the 0 25 semicore states is underestimated by theory, due to local-density approximation. In addition, photoemission measurements on amorphous SiOs show that the overall structure of the valence band is very similar to that of the ordered phase. Nevertheless, some minor features are observed in o-quarts spectra, due to long-range order of the crystalline structure. Keywords: A. insulators, D. electronic states, E. photoelectron spectroscopy

1. Introduction

metry. Its trigonal structure is defined by six parameters: two lattice constants and four fractional coordinates [S]. We analyse the electronic properties of the structure at zero pressure which corresponds to the minimum of the I%-Y curve. Further details of this calculation and structural data obtained as a function of pressure are reported in Hef. [8]. Our ab initio calculations are based on full-potential linear&d augmented-plane-wave (FLAPW) method [9], within local-density approximation (LDA), as pararneteri~ by Hedin and Lundqvist [lo]. For an accurate description of the electronic density of states (DOS) and the energy distribution of the joint density of states (EDJDOS), the Hamiltonian was diagonalised at 100 k points in the IBZ within the linear tetrahedron method [ll].

Silicon dioxide is a compound of relevant importance in modern technology: due to its peculiar properties it is widely used in electronic devices and in glass manufactures. Thii general interest explains the great effort devoted to study both crystalline and amorphous SiOr over the past years. In particular, the electronic structure has been investigated by means of experimental measurements based on x-ray emission [l], optical method [2], x-ray, ultraviolet photoelectron and electron-energy-loss spectroscopies [3,4]. Up to now, there have been few a6 initio calculations of the electronic properties of silicon dioxide [5], because of the relatively complex structure of all its polymorphs [S]. Only very recently, there has been a flurry of theoretical activity bssed on powerful first principles methods to study the properties of silica polytypes and its behavior under pressure [7,8]. In spite of numerous experimental and theoretical studies on the SiOr systems, some aspects in the electronic structure can be further investigated in order to obtain a deeper understanding. In the present paper we present a detailed study of the electronic properties of cr-quarts, based on all-electron calculations and x-ray photoemission measurements (XPS). In addition, x-ray and ultraviolet photoemimion (UPS) spectra of amorphous SiOs (&iOs) are presented and compared with the results concerning the crystalline phase. a-quarts is the stable form of silica at ambient temperature and at pressures below 3 GPa. It is a 42 coordiiated crystal, where each silicon atom is surrounded by four oxygen neighbors in a tetrahedral configuration. On the other hand, the amorphous phase presents small bond-length and bond-angle diitortions (about 1% and lo%, respectively), while a larger freedom for the values of the interpolyhedral angles is oteerved. Our aim is to dii the theoreticrd and experimental Sndings in order to p-t a detailed band picture of the ekctronic structure of a-quarts. The description of the crystalline SiOr (&iOs) allows us to understand the main features of electronic properties of &?iiOs 2. Computational

Experimental The XPS and UPS experiments have been performed in an ultra-high vacuum (UHV) chamber, at a pressure of about 5~10-~ Pa. The apparatus is equipped with Al K, (1486.6 eV) and Mg Ka (1253.8 eV) unmonochromated x-ray sources, a Hcdiiarge lamp (21.2 and 40.8 eV photon energy) and a spherical analyzer with a multichannel detector. The overall resolution (source and analyzer) is about 1 and 0.2 eV for XPS and UPS measurements, respectively. The samples were an aquarts crystal and a SiOs film (-100 A thick)deposited on a Si substrate. During the measurements care was taken to control charging effects of the samples. Using core-level spectroscopy, we were able to check that the degree of surface contamination was low enough not to affect noticeably the valence band structure.

3. Hesults and Discussion Electronic Properties of a-quarts The calculated density of states of &quarts is reported in Fig. 1 (solid lime) and compared to the XPS spectrnm of the v+ lence band and shallow core levels lltateaobtained using the Mg K,x-rayrraurce(d~edline).Thevduwr~edge~tdrmas

and Experimental Details

the sero of the energy scde. The background has not beensub tracted from the experimental XPS spectmm. Theoretical data have been convoluted with a Gatumiaw bmadeamg fnnethm with a full rsidth at half maximum of 0.5 eV. The intemity of the XPS

Calculations The unit cell of a-quarts hss nine atoms (three Si and six 0): Only one siheon and one oxygen atom are independent for sym-

313

314

ELECTRONIC PROPERTIES OF SiO,

25

Vol. 95, No. 5

2.5

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(a

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8 Energy(eV) Figure 1: Calculated XPS spectrum from lence band maximum intensity of the XPS

density of states (solid line) of a-quartz and Mg Ko, x-ray source (dashed line). The vais taken as the zero of the energy scale. The data is in arbitrary units.

data is in arbitrary units. Since XPS spectra from Mg and Al Km are very similar, we do not report the latter in Fig. 1. Three main groups of peaks are observed in the DOS; they can be related to the following states: 0 2s semicore-like states (lowest peaks, from about -20.0 to -16.5 eV; label A in Fig. l), 0 2p Si (35, 3p) bonding states (intermediate peaks, from -10.0 to -4.3 eV; label B) and 0 2p nonbonding states (upper part, between -4.0 eV and the top of the valence band; label C’). This decomposition of the valence band (VB) in orbital states is clear by inspection of Fig. 2, where the projected densities of states (PDOS) per atomic and per each angular momentum components are reported. Let us look now at the major features of experimental spectrum in Fig. 1, in order to compare photoemission and theoretical data. The XPS 0 2s peak is located at -20 eV below the top of the valence band, and it is about 2 eV lower than the correspending theoretical peak: This discrepancy in the binding energy (about 10%) is related to LDA and the consequent underestimate of the exchange-correlation energy in confined states. However, it is interesting to note that the slight asymmetry of the 0 2s pho toemission peak is well reproduced in the global shape of the corresponding DOS peak. The XPS spectrum shows a wide valence band region from about -11 to 0 eV (about 1 eV larger than the corresponding DOS range), split in two groups related to bonding and nonbonding orbit&. The photoemission intensity in this region is lower with respect to the 0 2s peak, due to the energydependent transition probability which weights in a different way the spectrum components. The broad VB region in the energy range between -11.0 and -4.5 eV (corresponding to B peaks in the DOS) derives from Si-0 bonding states: The main component is represented by 0 2p orbitals, spatially oriented along the Si-0 bonding direction. The photoelectron spectrum shows only two main peaks in this energy range; in fact, experimental resolution (1 eV) smooths out most of the minor features exhibited by the DOS. Moreover, if we focus on the intensity of the XPS data in the region -11.0 up to -4.5 eV we find a different trend from the corresponding theoretical results as a function of the energy. This is related to the photoionization cross-section [12], which depends on the x-ray sources used and on the kind of orbit& involved in the transition. In fact, from inspection of Fig. 2(d), Si (I and p like orbitals contribute differently to the total DOS in this region: orbitals with Si s dominant character are localized between -10.0

:,

A,,A,,;,:.1

-24 -20 -18 -12 -8.\-4 0

4

8

Enemy WI Figure 2: Projected density of states (PDOS) of o-quartz. Total 0 contribution [panel (a)]; 0 s (long dashed line) and p (solid line) (b); total Si contribution (c); Si s (long dashed line), p (solid line) and d (short dashed line) [panel (d)].

to -7.5 eV, while three with Si p character are confined in the lower binding energy region (-7.5 to -4.3 eV). Recalling that the ratio of the s to p orbitals photoelectric cross-section is about 5 to 1 [12], we find that the intensity of the transitions involving *like states is noticeably enhanced compared to those involving glike states and this gives a semi-quantitative explanation of the different intensity trend between calculated DOS and XPS spectrum. The highest part of the VB (labeled C) is made of 0 2p nonbonding orbitals, spatially localized on the atomic sites and oriented transversally with respect to the bonding Si-0 direction. Furthermore, there is a tendency in the XPS data to fill in the forbidden energy range between bonding (B) and nonbonding (CJ DOS peaks: the smooth experimental dip is located at a slightly higher binding energy than theory (about 0.3 eV). We can ah observe a slight XPS tailing of states into the band gap, which is lacking in the DOS curve. Tbii effect is most probably due to surface and defect [13] levels, which give rise also to a broadening of the spectrum at the top of the VB. In the photoemission spectrum we note the presence of a small peak at -13 eV, not related to 0 or Si states: it has been identified as a 3p peak of potassium, present in the quartz sample as a chemical impurity [4]. The lowest empty states of the DOS have 0 s-p and Si s-p character; in particular the bottom of the conduction band is determined prevalently by 0 and Si s states (Fig. 2). The indirect

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ELECTRONIC PROPERTIES OF SiO,

KU-F, LDA gap value is E9 = 5.8 eV. The extremum of the VB at M is slightly lower (~0,04 eV) than the value at K, while at the other high-symmetry point8 in the Brillouin zone the valence band maximum is a few tenths of eV lower than at K (e.g., the top of the VB at F is 0.35 eV lower). As expected from LDA calculations, the theoretical band gap underestimates the real optical gap (about 8.9 eV) [2], measured via photoconductivity experiments on amorphous silica. Let us look now at the charge density contour maps, which further highlight the features of Si-0 bond. In Fig. 3(a) we plot the valence charge density, projected on the Si-0-Si bonding plane. We can observe that most of the electron charge density is localized in the interatomic region between Si and 0, corresponding to the formation of the bond, mainly due to the p state8 of silicon and oxygen, a8 already pointed out. The charge accumulation localized at the oxygen site, pointing away from silicon, corre sponds to 0 p nonbonding orbitala. In Figs. 3(b) and (c) electronic charge density corresponding to the intermediate states (label B in Fig. l), and the highest region (C) of the valence band, respectively, are shown. We stress the different shapes of the charge density in these plots: the bonding character of the 0 p orbitala, oriented along Si-0 direction [Fig. 3(b)], and the nonbonding nature of oxygen p states [Fig. 3(c)], well localized on the atomic site and oriented transversally with respect to the bonding direction. Electronic

Properties

of Amorphous

SiOz

The photoelectron spectrum of the valence band of the amorphous phase is expected to be very similar to that of the corresponding crystalline state. This is generally true, since the gross feature8 of photoemission data are determined by the va-

lence etatea which, in turn, depend mainly on short-range chemical bonds of the constituent atom8 (141. The lack of long-range order only results in the roundoff of the sharp features in the spectrum of the crystalline phase. In Fig. 4 XPS spectra of a-quartz (solid line) and amorphous silicon dioxide (dashed line) from Al K, x-ray source are shown. At first glance, photoemission spectra of c- and o-SiO8 appear to be quite similar, as already pointed out: location8 and global shape of major peak8 are the same for both solids. XPS 0 28 peak is indistinguishable in the two phases: topological disorder doe8 not aITect the features of these states, which have an atomic-like nature. The lack of the translational symmetry and possible fluctuations in the short-range order smear out some finer structures in the photoemission spectra. For instance, in the intermediate energy range (from about -11.0 to -5.0 eV) the minor peak in the crystalline XPS data (centered at w-6.0 eV) is substituted by a small shoulder in the amorphous c8se. Moreover, the dip between bonding and nonbonding states (at about -5.0 eV) is leas pronounced in the disordered phase. This is an important different feature, which is partially hidden by the presence of the background of secondary electrons in both spectra. In the inset we show XPS data limited to the energy range from -12.0 eV to the top of the VB, after the subtraction of the background: the different depth of the dip between bonding and nonbonding states in the ordered and disordered casea is enhanced. This confirm8 that the lack of the forbidden energy range in the amorphous silica is an actual effect, due to the hybridization between the 0 2p bonding orbital8 and the 0 lone pair. These mixed states are related to the local topological disorder: fluctuations in the short-range order, such as bond-angle distortions, and bonds dimerization give rise to these states in amorphous SiOz. Further insights can be obtained analyzing the He II (40.8 eV photon energy) UPS spectrum of uSiOz, reported in Fig. 5(a) (dashed line) and compared with calculated DOS of a-quartz (solid line). The larger sensibility and resolution of the ultravio let with respect to the x-ray photoemiagion spectrcecopy permit to achieve more detailed informations. We would like to stress that the observed close similarity between XPS spectra of c- and o-SiOz allow us to compare experimental and theoretical data of amorphous and crystalline SiOz, respectively.

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I

I

-24 -20 -16 -12

-8

-4

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-8

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Energy (eV) Figure 3: Charge density corresponding to all valence states [panel (a)], to the intermediatestates [panel (b)] (-10.0 to -4.3eV, label B, Fig. I) and to the highest valence state8 [panel (c)] (-4.0 to 0.0 eV, label C, Fig. 1). Charge densities are projected in the Si-0-Si bonding plane. Lines of equal value are separated by Be/(unit cell volume).

Figure 4: XPS spectra of a-quartz (solid line) and amorphous SiOz (dashed line), from Al K, x-ray source. The intensity of the XPS data ia in arbitrary units. The inset is an enlargement of the photoemission spectra limited to the energy range from -12.0 eV to the valence band maximum, after the subtraction of the secondary electrons background.

Vol. 95, No. 5

ELECTRONIC PROPERTIES OF SQ

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unlike the XPS data, UPS spectrum showw the came trend of the DOS curve in the energy interval from -10.0 to -4.3 eV. Thir is because Si 8 and p photoeleotron cmm-mctione at 40.8 photon energy have approximatively the came value [12]: therefore the different contribution from silicon a and plike orbitaln in thb energy range, ae already pointed out previously, is directly m&ted in the global UPS intensity tread. We should note that all the major featuren of experimental and theoretical data are in very good agreement. Thin mndt indicates further the close similarity between the overali ehztronic states of crystalline and amorphoue phaaea Again, the lack of the forbidden energy range between bonding and nonhonding atatu in the UPS data eeerm to be the most important di%rence of the disordered silica with respect to a-quarta. In Fig. 5(b) we compare the He II UPS spectrum (duhed line) with the calculated energy dietribution of the joint den&y of statea (solid line), in the framework of the threa&ep model [15]. The EDJDGS reprwenb the fir&order approximation of the spectrum of photoexcited electrons, aawnning that the dipole matrix element between occupied and empty etatee in corurtant. The major differences with reap& to the DOS curve am repra sented by some sharp features in the energy range -4.0 to 0.0 eV, and lees pronounced structures between -9.5 to -6.5 eV: thin in related to the modulation of the valence DOS produced by the conduction DOS. Moreover, the lower lying band edge is higher in EDJDOS (-9.0 eV) with respect to the DOS (-10.0 eV). The agreement between UPS spectrum and EDJDGS is ftily good, except for the above mentioned featurea (from -4.0 to 0.0 eV), as expected. We should note that, unlike the DOS diagram, the EDJDOS curve well reproducee the UPS intensity ratio (~1.5) of the nonbonding to the bonding major peaks. In addition it is interesting to note that the inter&y of the featurw locatai between -10 and -6 eV in the DOS diagram ia noticeabIy reduced in the EDJDOS curve, in agreement with the experimental data. 4. ConcIueiom

-2

0

:

Figure 5: Calculated density of statee of a-quarts (solid line) and UPS spectrum of amorphous SiOl (dashed line), obtained with 40.8 eV photon energy [psael (a)]. Calculated energy diitribution of the joint density of statca of a-quarts (solid line) and He II UPS spectrum of &iOr (dashed line) Lpanel (b)]. The valence band maximum is taken aa the zero of the energy e&e. The intensity of the UPS and EDJDOS data are in arbitrary unita. The secondary electrona background has been eubtracted from UPS data.

The UPS intensity correapondiig to the bonding states (-10.0 to -4.3 eV) ia roughly l.btimw lower than the value related to the nonbonding statee (-4.0 to 0.0 eV). This feature is &etantiaIly due to the diierent number of oxygen p dates, which have a dominant character in these energy regiona: looking at the Fig. 2(b) we observe that the major nonbonding peak is approximatively 1.5 tima, higher than the major bonding peak at w-5.5 eV. On the other hand, the Si r-p orbital do not inRuence thin result, became of the small photoionbation crabsection with respect to the corresponding value of 0 2p orbitala (-20-timea lower). Moreover,

We presented theoreticaI and experimentd reeulta concerning the electronic propertiee of c- and *SiOa. A fairly good w ment haa been obtained between XPS and DGS data related to a-qua& polymorph: aI the major experimental featurea (except 0 2s peak) are well reproduced by the calculations. We were able also to explain the XPS trend intensity-energy, taking into account the photoionization crom-eection vaiuea. We dii in some detailn XPS measurements of both c- and &iOa; the moot important difference in represented by the clceing of the forbidden energy range between the bonding and nonbonding 0 rtatea, due to the hybridiiion between thare w as a rat& of the topological disorder. This distii feature of the amorpholu phase is comirmed by the UPS dab: the Iarger etal mrolution of the ultraviolet photoemhmion spectrum enhanthi important result. Finally, we preamted the caIcuIated energy dib tribution of the joint density of stateu of a-quarm, detamiDcd within the thne-step model: an improved sgaunent with expariment ia obtained, expecially ae far as the trend of the mtauity versus energy is concerned.

Acknowledgments - Work supported by Grant No. 923-102-7 Cineca. The authors acknowledge 0. Spinolo for supplying the SiOs earnplea

References [l] G. Wiech and E. 2. Zurmaev, J. Phys. C 18, 4393 (1985); V. J. Nithiammdam and S. E.

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ELECTRONIC PROPERTIES OF SiO,

[4] B. Fischer, R. A. Pollak, T. H. DiStefaao, and W. D. Grotman, Phys. Rev. B 16, 3193 (1977), and refe-rencea therein. [5] J. R. Chelikowsky and M. schliiter, Phys. Rev. B 15, 4020 (1977); B. silvi, P. D’Arco, and hi. Cau& J. Chem. Phys. 93,7225 (1990); R. Nada, C. R. A. Catlow, R. Dove& and C. Pi, Phys. Chem. Miner. 17,353 (1990); D. C. Allan and M. P. T&r, Phys. Rev. Lett. 59, 1136 (1987); Y.-N. Xu snd W. Y. Ching, Phys. Rev. B 44, 11048 (lQQl), and references therein. [S] H. D. Megaw, CrystolStructure: A Wo&ing Appmod (Saunders, Philadelphia, 1973); P. Villars and L. D. Calve& Pearnod Handbook of &‘rvskrlloomfic Data for IntermetaL lit Phaaea (American Society for Metals, Metals Park, Ohio, 1989). [7] K. T. Park, K. Terakura, and Y. Mat&, Nature 336, 670 (1988); J. R. Chelikowsky, N. Troullier, J. L. Martins, and H. E. King, Jr., Phys. Rev. B 44, 489 (1991); N. Binggeli, N. ‘Itoullier, J. L. Martins, and J. R. Chelikowsky, ibid. 44, 4771 (lQQ1); N. Binggeli and J. R. Chelikowsky, Phys. Rev. Lett. 69, 2220 (1992).

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[g] A. Di Pomponio and A. Continenra, Phys. Rev. B 49,12558 (1993); S9,5950 (1994). [Q] H. J. F. Jansen and A. J. Freeman, Phys. Rev. B 39, 561 (1984). [lo] L. Hedin and B. I. Lundqvist, J. Phys. C 4,2064 (1971). [ll] J. Rath and A. J. Freeman, Phys. Rev. B 11,210Q (1975). [12] J. J. Yeh and I. Lindau, Atomic Data and Nudear Data ?‘ables 32, 1 (1985). [13] F. Bart, M. Gautier, F. Jollet, and J. P. Dmaud, Surf. Sci. 396,342 (1994). [14] M. F. Thorpe and D. Weain, Phys. Rev. B 4,3518 (1971). [15] M. Cardona and L. Ley, Photoemission in Sdids i (SpringerVerlag, Berlin, 1978).