Optical properties of nanocrystalline ceria

Liu Fangxin, Wang Chengyun, Su Qingde, Zhao Tianpeng, and Zhao Guiwen

We believe that, for the first time, the UV-visible optical reflectivity of nanocrystalline ceria with variousparticle sizes has been measured, and their optical absorption characteristics have been studied byKramers–Kronig transformation. The wide absorption band in the 200–480-nm range consisted of twonarrow bands. This wide band was designated as the charge transfer of O2p–Ce4f while both narrowbands, which overlapped in this wide band, were due to the well-known 2F5y2–

2F7y2 spin-orbit splittingof the Ce 4f1 state. With a decrease in the particle sizes of the samples, the bandwidth expandeddistinctly and a red shift in the wide band was observed. On the other hand, the band gap between thenarrow bands showed a remarkable increase. All of these phenomena resulted from the effects ofquantum size and the interface of nanostructured materials. © 1997 Optical Society of America

Key words: Optical properties, nanocrystalline ceria.

The preparation and study of nanostructured mate-rials is a fascinating research area not only for phys-icists but also for chemists.1,2 As the diameter of thefunctional material approaches the nanometer scale,some new properties may appear that do not exist inthe original material.3 Insight into these propertiesis quite important for the application of these nano-structed materials.Cerium and its compounds have many unique

characteristics owing to the extension characteristicsof its 4f electrons, which has resulted in a continuingcontroversy over the electronic structure of ceria.Because the insulator and nonmagnetic properties ofceria can be successfully elucidated by a 4f0 Ce ionand a filled O2p band, until recently Ce has beenthought to be a typical covalent insulator. However,results of experiments such as photoemission, x-rayabsorption, and optical reflectivity show that a 4f1

electron exists in ceria even in the ground state.Therefore significant theoretical and experimentalresearch has been carried out on the electronic struc-ture of ceria, particularly the valence state of Ce inceria. The optical reflectivity of single-crystal ceriahas been measured by Marabelli and Wachter,4 andthe absorption bands in the optical reflectivity havebeen elucidated. But the optical reflectivity spectra

The authors are with the Department of Applied Chemistry,University of Science and Technology of China, Hefei, Anhui,230026 China.Received 13 June 1996.0003-6935y97y132796-03$10.00y0© 1997 Optical Society of America

2796 APPLIED OPTICS y Vol. 36, No. 13 y 1 May 1997

of nanocrystalline ceria powders have not been re-ported. We have measured the ultraviolet-visible~UV-VIS! optical reflectivity of nanocrystalline ceriawith various particle sizes and analyzed the mecha-nism of the absorption band in the optical reflectivityto provide distinct evidence that ceria has trivalent~4f1! characteristics in the ground state. We havealso studied the quantum size effect of nanocrystal-line ceria.Nanocrystalline ceria was prepared by the hydro-

thermal technique. The as-prepared nanocrystal-line ceria was annealed at various temperatures toobtain samples with different particle sizes, labeledA, B, and C. X-ray-diffraction analysis was con-ducted with a Japanese Rigaku Dymax gA rotatinganode x-ray diffractometer with high-intensity Cu Ka

radiation. All the peaks could be indexed to the cu-bic phase of ceria with a fluorite structure. Particlesizes and the morphology of nanocrystalline ceriawere determinedwith anHitachi H-800 transmissionelectron microscope ~TEM!. TEM micrographsshowed the spherical morphology of the particles anda narrow-size distribution range. Both x-ray diffrac-tion results and TEM images showed that the parti-cle sizes were;3, 15, and 30 nm for samples A, B, andC, respectively.The optical reflectivity of nanocrystalline ceria was

measured with a Shimadzu UV-240 UV-VIS spectro-photometer at room temperature in the wavelengthrange from 200 to 800 nm, corresponding to photonenergy varying from 6.19 to 1.55 eV, as shown in Fig.1. An interband transition existed in the range from200 to 480 nm, and both reflectivity peaks in thisband displayed a fine structure.

To gain insight into the electronic process causingthese spectral features, the optical constants n and kwere determined from a Kramers–Kronig analysis ofthe reflectance data. This analysis requires an in-tegration of reflectance to the infinite photon energyto determine the phase change on reflection. Henceextrapolations are required for spectral regions out-side the range of experimental data. We used thereflectance data from Ref. 4, below 1.55 eV in theanalysis. For energies greater than 6 eV and lessthan 18 eV, the reflectivity has been assumed to dropoff as v22 and as v24 for still higher energies. Op-tical functions of more direct physical interest werecalculated by using n and k values thus obtained.The spectral dependence of the real ~ε1! and imagi-nary ~ε2! parts of the dielectric functions is shown inFig. 2. The x-ray photoelectron spectroscopy-bremsstrahlung isochromat spectroscopy ~XPS-BIS!spectrum of single-crystal ceria5 is shown in Fig. 3 aswell as the imaginary parts of the dielectric functions~ε2! for both single-crystal ceria and 3-nm ceria. Forcomparison, the XPS-BIS spectrum of single-crystalceria is drawn on the same energy scale as the ε2spectrum.First, let us discuss the spectral features of the ε2

as shown in Fig. 3. Koelling et al.6 carried out theself-consistent-field band calculation and predictedthat the band-gap energy between the valence bandof O2p character and the Ce5d conduction band is ;6eV, with a Ce4f narrow band lying within the bandgap. The XPS-BIS spectrum reveals rather local-ized 4f states at ;4.5 eV above the topmost valenceband as shown in Fig. 3. We can therefore assignthe resonancelike peak centered at 4.2 eV to the tran-sition from the O2p valence band to the localized Ce4fstate above the Fermi level. This transition could bedescribed as p6 ~oxygen!–p5~oxygen!4f1~Ce! in refer-ence to the electronic configuration. As far as inter-

Fig. 1. Optical reflectivity of nanocrystalline ceria with variousparticle sizes: A, 3 nm; B, 15 nm; C, 30 nm.

atomic transitions are concerned, such a p–ftransition will be in principle dipole forbidden.However, in the current case, owing to the smalloverlap between the O2p and the Ce4fwave functions,the O2p–Ce4f transition, i.e., a charge transition, isallowed.Note that the 4f1 peak in the ε2 spectrum of single-

crystal ceria is shifted by 0.6 eV toward lower ener-gies comparedwith that in the BIS spectrumwhereasin nanocrystalline ceria the 4f1 peak is shifted by;0.4 eV. To understand the energy shift, it is im-portant to consider the difference in the excitationprocesses associated with the two spectra. The BISprocess is a one-electron addition into empty states,whereas optical reflection and absorption processesare excitations of electrons from occupied states to

Fig. 2. Dielectric function ε of 3-nm ceria: ε1, the real part of ε;ε2, the imaginary part of ε.

Fig. 3. Comparison of εwith the XPS-BIS spectrum: a, XPS-BISspectrum of single-crystal ceria; b, ε2 of single-crystal ceria; c, ε2 of3-nm ceria.

1 May 1997 y Vol. 36, No. 13 y APPLIED OPTICS 2797

empty states, resulting in an electron hole being leftbehind in the initially occupied states. In the cur-rent case a valence band hole is created in the opticalexcitation process. This suggests that the loweringof the 4f1 position in the ε2 spectrum is due to theexistence of the Coulomb potential by the valencehole that is an excitonic effect. An energy separationof;0.6 eV is then considered to be the binding energyof the exciton, which consists of a valence hole and anextra 4f electron at Ce ion sites. To explain the dif-ference between the two shifts in energy, we note thatthe original band gap would increase by DE ~excitonenergy! resulting from the quantum size effect whenthe particle sizes approached the nanometer scale.By assuming that the energy band is parabolic nearthe band gap, that is, the effective mass approxima-tion, the size-dependent shift with respect to the bulkband gap in the exciton energy of nanocrystallineceria can be derived as

DE 5\2p2

2R2 S 1me1

1mh

D 21.786e2

εR2 0.248ERy*,

where R is the particle size of nanocrystalline ceriaand ERy* is the effective Rydberg energy. The firstterm represents the particle-in-a-box quantum local-ization energy and has a single 1yR2 dependence.The second term represents the Coulomb energy witha 1yR dependence, whereas the third term is a resultof the spatial correlation effect. This last size-independent term is usually small but can becomesignificant for semiconductors with small dielectricconstants. Therefore the optical reflectivities ofnanostructured materials are affected not only by theCoulomb energy of exciton but also by the quantumlocalization energy. Furthermore all three energymodifications were dependent on the particle size ofsamples. When the particle sizes are decreasedenough to approach the nanometer scale, DE ismainly affected by the Coulomb energy. Therefore itis only the quantum size effect that results in a de-crease in the energy shift of the nanocrystalline ceriacompared with that of single-crystal ceria.The ε2 spectrum of single-crystal ceria presents a

well-defined structure at 3.9 eV with a bandwidth of;3.2 eV,4 as shown in Fig. 3, while the ε2 spectrum ofnanocrystalline ceria with a particle size of ;3 nmhas a peak at 4 eV with a bandwidth of ;4 eV. Ob-viously, a gap of ;0.8 eV exists between the band-widths. Furthermore this wide band consisted oftwo narrow bands, and the band gap was ;1 eV,which is much larger than that of single-crystal ceria,whose band gap is only 0.28 eV. These two narrowbands could be designated as the 2F5y2–

2F7y2 spin-orbit splitting of the Ce 4f1 state. On the otherhand, with a decrease in the particle size of thenanocrystalline ceria, the bandwidth of the 4-eV peakincreased, and the band gap between these two nar-row bands increased simultaneously with the wave-

2798 APPLIED OPTICS y Vol. 36, No. 13 y 1 May 1997

length of the center of the band shifting red, as shownin Fig. 1.It is well known that nanocrystalline particles con-

sist of two constituent parts: one is the interior,whose structure is similar to that of a single crystal;the second is the surface layer, where the atomicarrangements differ distinctly from those in singlecrystals. A distribution of the crystal field is pro-duced in the nanocrystalline particles; the crystalfield is weak in the surface layer, whereas it is ratherstrong in the interior. Therefore the gap betweenthe energy levels has a distribution range that leadsto an expansion in the bandwidth. The smaller theparticle size of the nanocrystalline particles, thelarger the ratio of the surface atoms to total atomsand the greater the increase in bandwidth. We ob-served this phenomenon in our experiments. Thered shift of the reflection peak of nanocrystalline ce-ria with a decrease in particle size can be understoodfrom the equation mentioned above. The calcula-tion showed that DE is mainly affected by the Cou-lomb energy in nanocrystalline ceria. The Coulombenergy decreased simultaneously with a decrease inthe particle size, R, leading to a red shift in the re-flection peak.In conclusion, we have measured the UV-VIS op-

tical reflectivity of nanocrystalline ceria with variousparticle sizes and obtained the optical constants of ε1and ε2 by Kramers–Kronig analysis. The spectralcharacteristics can be elucidated with charge and in-terband transitions. The resonantlike wide band at4.1 eV was designated to be a charge transition fromthe O2p valence band to the Ce4f localization band,while both narrow bands overlapped in this wideband owing to the 2F5y2–

2F7y2 spin-orbit splitting ofthe Ce 4f1 state. With a decrease in particle size,the bandwidth increased remarkably and the centerof this wide band shifted to the red, while the bandgap between the two narrow bands increased simul-taneously. Both the red shift and expansion can beexplained by the quantum size effect.

References1. Y. Wang and N. Herron, “Nanometer-sized semiconductor clus-

ters: materials synthesis, quantum size effects, and photo-physical properties,” J. Phys. Chem. 95, 525–532 ~1991!.

2. L. Zhang and J. M. Mou, Nanostructured Materials ~LiaolingScience Press, Shengyang, 1994!, p. 26.

3. T. He, P. Wang, X. Zhang, and F. Liu, “The quantum size effectsof AgBr semiconductor ultrafine particles,” Chinese J. Chem.Phys. 8~1!, 23–27 ~1995!.

4. F. Marabelli and P. Wachter, “Covalent insulator CeO2: op-tical reflectivity measurements,” Phys. Rev. B 36, 1238–1243~1987!.

5. E. Wuilloud, B. Delley, W. D. Schneider, and Y. Baer, “Spectro-scopic evidence for localized and extended f-symmetry states inCeO2,” Phys. Rev. Lett. 53, 202–205 ~1984!.

6. D. D. Koelling, A. M. Boring, and J. H. Wood, “The electronicstructure of CeO2 and PrO2,” Solid State Commun. 47, 227–232~1983!.