university research highlights

School of Materials Science
and Engineering
(a) School of Physics
Georgia Institute of Technology
Atlanta GA 30332-0245 USA

Size and shape selected nanocrystals behave like molecular matter that can be used as fundamental building blocks for constructing nanocrystal assembled superlattices. These nanocrystals form a new class of materials that have orders in both atomistic and nanocrystal lengthscales. The nanocrystals are passivated with organic molecules (called thiolates) that not only protect them from coalescence but act as the molecular bonds for forming the superlattice structure. The interparticle distance is adjustable, possibly resulting in tunable electric, optical and transport properties.

Nanophase and nanoparticle materials, as a component of nanotechnology in the twenty-first century, have attracted a great deal of attention in today’s research [I]. The unique properties of nanophase materials are determined not only by their intrinsic atomistic scale structure, but also by interparticle interaction. The role played by particle size is comparable, in some cases, to the particle chemical composition, adding another flexible parameter for designing and controlling their behavior. Size and even shape selected nanocrystals behave like a molecular matter, and are ideal building blocks for two- and three-dimensional cluster self-assembled superlattice structures. The electric, optical, transport and magnetic properties of the structures depend not only on the characteristics of individual nanocrystals, but also on the coupling and interaction among the nanocrystals arranged with long-range translational and even orientational order. Research has successfully fabricated self-assembly passivated nanocrystal superlattices (NCS’s) of metal [2], semiconductor [3] and oxide clusters [4], which are a new form of materials with fundamental interests and technological importance.

Self-assembled arrays involve self-organization into monolayers, thin films, and superlattices of size-selected nanoclusters encapsulated in a protective compact organic coating (Figure 1) [5]. Nanocrystals are the hard cores that preserve the ordering at the atomic scale; the organic molecules adsorbed on their surfaces serve as the interparticle molecular bonds and as protection for the particles in order to avoid direct core contact with a consequence of coalescing. The interparticle interaction can be changed via control over the length of the molecular chains. Quantum transitions and insulator to conductor transition could be introduced, resulting in tunable electronic, optical and transport properties. This is one of the most attractive characteristics of NCS’s.

Figure 1. (a) Atomic structural model of a truncated octahedral nanocrystal.

(b) A schematic model illustrating the ordered self-assembling

of the size and shape selected nanocrystals passivated with organic molecules.

NCS’s are characterized by unprecedented size-uniformity, translation and even orientational order, created through a multistage processing strategy involving synthesis and separation of size selected nanocrystals, reversible passivation. by organic monolayers, and self-assembly. Particles that can be self- assembled usually have sizes smaller than 10 nm, it is in this size range that many exciting and unusual physical properties are enhanced. The nanocrystals are passivated by a monolayer of long-chain organic molecules, such as SR, where R = n-C_nH_2n+l, n = 4, 6, 8, 12 ...,called thiolates.

Research on metallic nanocrystals has had a long history because of their exciting size-dependent optical properties and applications in catalysis. The plasmon resonance frequency of metallic particles depends sensitively on the particle size as well as the interaction among the particles. Controlling the interparticle distance via the choice of length of passivation molecules results in unique optical properties [6]. Figure 2a shows a transmission electron microscopy (TEM) image of monolayer assembling of Ag nanocrystals on a carbon substrate, where the two-dimensional superlattice is apparent. The Ag particles were synthesized using an aerosol technique [7] and passivated with SC₁₂H₂₅. The Ag particles have sizes of 4 ą 0.5 nm and their shapes are dominated by tetrahedral (see the projected triangle shapes in Figure 2b) [8], a four-face polyhedron enclosed by {111} facets.

Figure 2. (a) A transmission electron microscopy image of monolayer
self-assembled Ag nanocrystals with long-range translational symmetry,
but only short-range orientational symmetry.
(b) An enlargement of the image illustrating the projected
tetrahedral shape of the nanocrystals.

Self-assembling of Ag nanocrystals also forms three-dimensional structures, as shown in Figure 3a, where large size platelet sheets of NCS’s are formed. A higher magnification TEM image in Figure 3b clearly illustrates the superlattice structure, where each dark dot is a row of nanocrystals. The particle size is 6 ą 0.5 nm and their shapes are dominated by icosahedra and decahedra [9]. The NCS structure has been determined to be hexagonal close packed. The thickness of the sheets has been measured by atomic force microscopy to be ~ 15 nanocrystal layers. This type of material is an ideal candidate for non-linear optics with tunable second order permittivity [6].

Figure 3. (a) Low magnification and (b) high magnification transmission
electron microscopy images of three-dimensional superlattices
assembled by Ag nanocrystals. The ordered arrangement of the
nanocrystals forms a periodic hexagonal close packed crystalline lattice,
with the [000 1 ] direction parallel to the incident beam direction.

The crystallography of self-assembling of nanocrystals is strongly affected by the shape of the nanocrystals. Self-assembling of truncated octahedral Ag nanocrystals of 6 ą 0.5 nm in core size, enclosed by eight {111} and size {100} facets (see Figure 1 a), forms the face-centered cubic (fcc) superlattice structure [10]. The particles tend to be packed face-to-face to lower the energy, the surface adsorbed molecules are distributed on the facets of the particles and are self-assembled into bundled and interdigitative molecule bonds [ 11 ], which have been found to be extraordinarily strong, stabalizing the NCS to temperatures as high as 500°C.

Synthesis and studies of semiconductor nanocrystals have vital practical importance for many applications in optoelectronics [12]. The most interesting phenomena associated with semiconductors is the quantum-dot effect, surface states and electrical transport properties. The properties of nanocrystals appear to be much different from bulk crystal if their sizes approach the dimension of atomic or ionic diffusion lengths, electronic elastic and inelastic mean free path lengths, or the correlation and screening lengths. The 3-D hexagonal close packed and face- centered cubic assembling of CdSe nanocrystals have been reported [3].

Patterned magnetic nanocrystals are of vital interest both scientifically and technologically because of their potential applications in information storage, color imaging, bioprocessing, magnetic refrigeration, and ferrofluids. In ultra-compact information storage, for example, the size of the domain determines the limit of storage density while the sharpness of the domain boundaries is closely related to the media noise. This issue is critically important in the 300 Gbit/in² information storage density predicted for the 21st century. The noise reduction can be achieved by the segregation of a non-magnetic phase at the grain boundaries, thus, the media are composed of at least two materials. The self-assembly passivated nanocrystal superlattice is a potential candidate for solving this problem, in which the passivated surfactant serves not only as an isolation layer but also as a protection layer for the nano-magnets.

Figure 4. Self-assembling of ferromagnetic Co nanocrystals of sizes ~10-13 nm,
a potential candidate for ultra-high density magnetic data storage.
The inset is an electron diffraction pattern recorded from the Co particles,
proving the face-centered cubic atomic structure of the nanocrystals.

Cobalt nanocrystals were synthesized by chemical decomposition of CO₂(CO)₈ in toluene. Sodium bis(2-ethylhexyl) sulfosuccinate (C₂₀H₃₇O₇SNa, in short, Na(AOT)) was added as a surface active agent. For ultra-high density data storage, the most useful size range is 10-20 nm because the transition from ferromagnetism for large size particles to superparamagnetism for small size particles occurs at ~ 10 nm, and the monolayer self-assembling is the most desirable structure (Figure 4). Monolayer self- assembling of ferromagnetic nanocrystals is difficult experimentally because of the strong agglomeration of magnetic nanocrystals due to their magnetic interaction.

Co ferromagnetic nanocrystals can be separated from the antiferromagnetic CoO and Co₃O₄ nanocrystals by a magnetic phase separation technique. The purified CoO nanocrystals can also form NCS with ordered structure (Figure 5) [13]. CoO particles have a dominant tetrahedral shape of sizes 4 ą 0.5 nm. As illustrated previously in Figure lb, the bonds between nanocrystals are the organic molecules coated on the nanocrystal surfaces. A key question here is about the stability and the phase transformation behavior of the NCS. In-situ TEM studies of CoO and Ag NCS’s have proved the structural stability up to temperatures of ~ 500°C [14].

Figure 5. Monolayer self-assembling of COO nanocrystals passivated with
Na(AOT). The triangle shape of the projected particle shape in TEM
proves the three-dimensional tetrahedral structure (see the inset).

In conclusion, it can be claimed that nanocrystal engineered superlattices are a new class of materials that is different from either a single particle or the bulk materials. This type of material could have significant impact on future electronics, optics and magnetic storage. Most of the current research has been concentrated on synthesis of NCS materials. Novel techniques are required to characterize the physical and chemical properties of individual particles, such as the electric transport measurements of a single carbon nanotube, revealing the so called ballistic conductance [15]. Exploration of the novel physical and chemical properties of NCS’s is the focus of near future research.

[1] See many articles in Nanomaterials: Synthesis, Properties and Applications, edited by A.S. Edelstein and R.C. Cammarata, Institute of Physics Publishing (Bristol and Philadelphia, 1996).

[2] Whetten RL, Khoury JT, Alvarez MM, Murthy M, Vezmar 1, Wang ZL, Cleveland CC, Luedtke WD, and Landman U. Nanocrystal gold molecules. Adv. Materials 8: 428-433, 1996.

[3] Murray CB, Kagan CR and Bawendi MG, Self-organization of CdSe nanocrystallites into three-dimensional quantum dot superlattices. Science 270: 1335-1338, 1995.

[4] Bentzon MD, van Wonterghem J, Morup S, and Thölén A. Ordered aggregates of ultrafine iron oxide particles: ‘super crystals’. Philos. Mag. B 60: 169-178, 1989.

[5] Wang ZL. Structural analysis of self-assembling nanocrystla superlattices. Adv. Mater. 10: 13-30, 1998.

[61 Collier CP, Saykally RJ, Shiang JJ, Henrichs SE, and Heath JR. Reversible tuning of silver quantum dot monolayers through the metal-insulator transition. Science 277: 1978-1981, 1997.

[7] Alvarez MM, Vezmar I, and Whetten RL. On-line sampling and intact mass analysis of nanometer-size aerosols via time-of-flight high-mass spectrometry. J. Aerosol Sci. 29: 115-127, 1998.

[8] Wang ZL, Harfenist SA, Vezmar 1, Whetten RL, Bentley J, Evans ND, and Alexander KB. Superlattices of Self-assembled Tetrahedral Ag Nanocrystals. Adv. Mater., submitted (1998).

[9] Harfenist SA, Wang ZL, Alvarez MM, Vezmar 1, and Whetten RL. Hexagonal close packed thin films of molecular Ag nanocrystal arrays. Adv. Mater. 9: 817-822, 1997.

[10] Harfenist SA, Wang ZL, Alvarez MM, Vezmar I, and Whetten RL. Highly oriented molecular Ag-nanocrystal arrays. J. Phys. Chem. 100: 13904-13909, 1996.

Peter D. Persans
Department of Physics ,
Applied Physics, and Astronomy
Rensselaer Polytechnic Institute
Troy, NY 12180

I review basic ideas, recent optical measurements, and properties of nanometer-size II-VI (CdS, CdSe) crystallites.

By varying the chemical composition in a semiconductor on a scale of nanometers, it is possible to confine some of the electron states to specific regions and create a variety of new quantum effects. The best known examples of this are epitaxially-grown quantum-well superlattices, in which the charge carriers are confined in one dimension to layers often only a few nanometers thick. Many useful devices are based on these materials, including semiconductor lasers, and optical receivers and modulators. Successes such as these as well as interest in fundamental phenomena have stimulated the development of materials in which the electrons are confined in all three dimensions. Such materials are known as “quantum dots”.

In the quantum size limit (less than ~3-5 nm diameter) we expect that the optical absorption spectrum of a semiconductor material will become a series of discrete lines broadened only by lifetime, phonon, and band mixing effects. We might also expect that resonant nonlinear optical coefficients would be enhanced over bulk properties because it is possible to saturate the lowest interband transition with only one electron-hole pair per particle. It is for these reasons that semiconductor nanocrystal systems have been studied as nonlinear optical materials for communications technologies [1].

II-VI (especially Cd chalcogenide) nanocrystals are one of the most extensively studied classes of quantum dot systems. My review here is by no means exhaustive. It focuses on II-VI nanoparticles precipitated in glass because that has been the thrust of my own research. I also include some references to work on powders prepared by colloidal techniques.

In addition to linear optical absorption, properties of quantum dots are studied by a variety of optical techniques including photoluminescence, photoluminescence excitation spectroscopy, pump-probe spectroscopy, two photon absorption [2], Raman scattering [3], and electromodulation spectroscopy. Changing pressure and temperature [4-6] can also inform us on the nature of the optical transitions. Most optical measurements measure the average properties of many particles excited simultaneously, there have been a few reports on the optical properties of individual particles [2].

There have been dozens of studies on the lowest energy optical transition in Cd chalcogenides (references [1, 7-9] are reviews). All studies show a dramatic blue shift of the optical absorption edge with decreasing particle size below 4 nm. In Fig. 1 we show the optical absorption spectra of large and small CdS nanoparticles in glass. The bulk absorption edge is near 2.5 eV. The peak near 3.2 eV has been interpreted as the transition between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) [10-12]. The breadth of the observed peak is mostly due to a distribution of particle sizes in the glass. Raman scattering and XAS confirm that neither composition variation nor strain contribute to the observed shift [3, 12-14]. The absorption spectrum for large particles approaches that expected for small spheres with the properties of bulk CdS embedded in a glass dielectric host.

Simple effective mass theories [11, 15], which quantitatively explain the shift in the HOMO-LUMO transition with size, assume that a single valence band is being quantized. However, three distinct valence bands exist in most semiconductors of interest, including II-VI, III-V, and group IV semiconductors. The valence bands can no longer be considered independently and the excited state spectrum is dramatically altered relative to the single band assumption [16, 17]. Several theoretical studies have addressed improvements on simple effective mass theories for specific systems [16, 18, 19].

Excited states in II-VI nanoparticles in glass have been probed by linear [17] and modulation spectroscopy[20]. An example of electroabsorption results is given in Fig. 2 [20]. Each negative Da peak indicates a discrete electronic transition. Transition A originates from the upper-most valence band and transition B originates from the spin-orbit split-off valence band. The evolution of the excited-states is evident, with peaks shifting, appearing, and disappearing as the particle size decreases.

Figure 2 Electroabsorption spectrum of CdS0.5Se0.5 nanoparticles in glass.
Average particle sizes are given in the figure.

Photoluminescence (PL) is a standard technique for the characterization of semiconducting materials and is complimentary to linear optical absorption. In the absence of configurational relaxation the relationship between PL and absorption is given by the Roosbroeck-Schockley relationship for the spontaneous emission rate [21]. Usually, PL is used in conjunction with linear absorption spectroscopy. Examining the differences between the lowest absorption peak and the PL peak provides information about the nature of the emitting state. Temperature- and intensity-dependent steady-state PL[16, 22, 23] and time-resolved PL measurements [24] yield the energies and lifetimes of the trap states involved in radiative recombination. Particle-size selection is accomplished by tuning the laser in the red edge of the absorption band thereby exciting only the largest particles in the distribution. This technique, called fluorescence-line narrowing, is possible since there is almost always a 20 to 100 meV redshift in the PL peak from the absorption peak in semiconductor nanoparticle composites [25]. Two-photon photoluminescence excitation spectroscopy addresses excitation into states that could not normally be excited by a single photon due to selection rules [2].

Photoluminescence excitation spectroscopy (PLE) is similar to PL except that here a single luminescence band is monitored while the excitation wavelength is varied. PLE can be used to effectively reduce the inhomogeneous width of the transitions by extracting information from a subset of the nanoparticle distribution. Only the smallest crystallites in the sample are probed in PLE when monitoring a narrow spectral region on the blue edge of the luminescence band [26]. PLE is used to probe quantum dot size distribution as well as study higher excited states.[17]

In photoabsorption spectroscopy a light pulse causes a perturbation of the dielectric function by one or both of two possible processes: state filling and photo-induced Stark effect [17, 27]. State filling simply causes a bleaching of the optical transition that is filled upon photoexcitation. The reduction in absorption when a state is filled is used to perform hole-burning spectroscopy. The photo-induced Stark effect is caused by separation of the electron-hole pair when one carrier is trapped in a surface state.[28] In the latter case, the PA spectra resemble EA spectra.[29]

Transient hole burning is useful for measuring electron-hole lifetimes for the lowest as well as the higher excited states. The spectra generally show bleaching (negative Da) peaks at the electronic transition energies. The variable time delay between the pump and probe pulses yields the recovery time of the bleaching and hence the lifetime of the electron-hole pair. Generally, one can pump anywhere in any absorption band and detect photo-induced changes in the entire spectrum. In fact, changes are observed for photon energies higher than the excitation. There have also been many measurements of the nonlinear optical coefficient c⁽³⁾, which is responsible for phase conjugation, in II-VI doped glasses [1]. c⁽³⁾(w, -w, w) has its origin in the electronic response and therefore depends on the nature of the quantized electronic states in semiconductor dots. The peak in c⁽³⁾ occurs at approximately the same wavelength as the peak in absorption. The response time is very fast, of order <10 ps [30] for R=3 nm CdSSe particles and becomes faster when particle size is reduced. Large particles in glass have c⁽³⁾ ť 1x10^-9 esu. Smaller particles have dramatically smaller c⁽³⁾ reflecting the size dependence of the response time [30].

Semiconductor quantum dots provide us with a rich materials system in which optical properties can be tailored by changing particle size and composition. Exciting, related work involves structured nanoparticles in which layers of different composition are fabricated, producing electron confinement in thin shells [31, 32]. Coating semiconductor particles with metal shells allows us to tailor the frequency dependent optical field using the metal plasmon resonance [33]. Much work remains to be done.

[1] C. Flytzanis and J. Hutter, “Nonlinear optics in quantum confined structures,” in Contemporary nonlinear optics, vol. New York: Academic Press, 1992.

[2] S. Blanton, A. Dehestani, P. Lin, and P. Guyot-Sionnest, “Photoluminescence of Single Semiconductor Nanocrystallites by Two-Photon Excitation Microscopy,” Chemical Physics Letters, vol. 229, pp. 317, 1994.

[3] A. Tu and P. D. Persans, “Raman scattering as a compositional probe of II-VI ternary nanocrystals,” Appl. Phys. Lett., vol. 58, pp. 1506-1508, 1991.

[4] H Yükselici and P D Persans, “High Temperature Optical Studies of CdS Nanoparticles”, J Non-Cryst. Sol., vol. 203, 206 (1996).

[5] X. S. Zhao, J. Schroeder, P. Persans, and T. Bilodeau, “Resonant Raman scattering and photoluminescence studies in glass composite and colloidal CdS,” Phys. Rev. B, vol. 43, pp. 12580, 1991.

[6] J. Schroeder and P. D. Persans, “Spectroscopy of II-VI nanocrystals at high pressures and temperatures,” J. Lum., vol. 70, pp. 69-84, 1996.

[7] U. Woggon, Optical Properties of Semiconductor Quantum Dots. New York: Springer, 1997.

[8] P. D. Persans and K. L. Stokes, “Embedded Nanocrystal Spectroscopy” in Handbook of Nanophase Materials ed. A. Goldstein, (Marcel Dekker, New York), 1997.

[9] P. D. Persans, M. Silvestri, G. Mei, E. Lu, H. Yukselici, and J. Schroeder, “Size effects in II-VI semiconductor nanocrystals,” Brazilian J. Phys., vol. 23, pp. 144-150, 1993.

[10] A. I. Ekimov and A. A. Onushchenko, “Quantum size effect in the optical spectra of semiconductor microcrystals,” Sov. Phys. Semicond., vol. 16, pp. 775-778, 1982.

[11] L. E. Brus, “A simple model for the ionization potential, electron affinity, and aqueous redox potentials of small semiconductor cystallites,” J. Chem. Phys., vol. 79, pp. 5566-5571, 1983.

[12] H. Yukselici, P. Persans, and T. Hayes, “Optical studies of the growth of Cd[1-x]Zn[x]S nanocrystals in borosilicate glass,” Phys. Rev. B, vol. 52, pp. 11763, 1995.

[13] P. Persans, A. Tu, M. Lewis, T. Driscoll, and R. Redwing, “Optical Properties of II-VI Semiconductor Doped Glass,” Mat. Res. Soc. Symp. Proc., vol. 164, pp. 105, 1990.

[14] P. Persans, L. B. Lurio, J. Pant, R. Olsson, H. Yukselici, and T. M. Hayes, “X-ray absorption spectroscopy and optical absorption studies of the growth of CdS nanocrystals in glass,” Mat. Res. Soc. Symp. Proc., vol. 358, pp. 225, 1995.

[15] A. I. Ekimov and A. A. Onuschchenko, “Quantum size effect in three-dimensional microscopic semiconductor crystals,” JETP Letters, vol. 34, pp. 345, 1982.

[16] A. I. Ekimov, F. Hache, M. C. Schanne-Klein, D. Richard, C. Flytzanis, I. A. Kudryavtsev, T. V. Yazeva, A. V. Rodina, and A. L. Efros, “Absorption and intensity-dependent photoluminescence measurements on CdSe quantum dots: assignment of the first electronic transitions,” J. Opt. Soc. Am. B, vol. 10, pp. 100-107, 1993.

[17] D. J. Norris, A. Sacra, C. B. Murray, and M. G. Bawendi, “Measurement of the size dependent hole spectrum in CdSe quantum dots,” Phys. Rev. Lett., vol. 72, pp. 2612-2615, 1994.

[18] P. E. Lippens and M. Lanoo, “Calculation of the band gap for small CdS and ZnS crystallites,” Phys. Rev. B, vol. 39, pp. 10935-10942, 1989.

[19] J. B. Xia, “Electronic structure of zero-dimensional qauntum wells,” Phys. Rev. B, vol. 40, pp. 8500-8507, 1989.

[20] K. L. Stokes and P. Persans, “Excited States and Electric Field Response of CdSSe Quantum Dots”, Phys. Rev B 54 1892 (1996).

[21] R. B. Stephens, “Photoluminescence determination of minority-carrier kinetics in semiconductors,” Phys. Rev. B, vol. 29, pp. 3283-3292, 1984.

[22] M. Kull and J.-L. Coutaz, “Intensity-dependent absorption and luminescence in semiconductor-doped glasses,” J. Opt. Soc. Am. B, vol. 7, pp. 1463-1472, 1990.

[23] F. Hache, M. C. Klein, D. Ricard, and C. Flytzanis, “Photoluminescence study of Schott commercial and experimental CdSSe-doped glasses: observation of surface states,” J. Opt. Soc. Am. B, vol. 8, pp. 1802-1806, 1991.

[24] J. Puls, V. Jungnickel, F. Henneberger, and A. Schulzgen, “Carrier dynamics in CdSe quantum dots embedded in glass,” J. Crystal Growth, vol. 138, pp. 1004-1009, 1994.

[25] M. Nirmal, C. B. Murray, D. J. Norris, and M. G. Bawendi, “Size-dependent spectroscopy and photodynamics of some II-VI semiconductors,” Proc. of the SPIE, vol. 1861, pp. 280-284, 1993.

[26] M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, and L. E. Brus, “Electronic structure and photoexcited carrier dynamics in nanometers-size CdSe clusters,” Phys. Rev. Lett., vol. 65, pp. 1623-1626, 1990.

[27] K. L. Stokes and P. D. Persans, “Intensity-dependent electro-modulation spectrum in CdSSe nanocrystals,” Phys. Rev. B, vol. 54, pp. 4460, 1996.

[28] Y. Wang, A. Suna, J. McHugh, E. F. Hilinski, P. A. Lucas, and R. D. Johnson, “Optical transient bleaching of quantum-confined CdS clusters: The effects of surface-trapped electron-hole pairs,” J. Chem. Phys., vol. 92, pp. 6927-6939, 1990.

[29] G. Mei, S. Carpenter, and P. D. Persans, “Steady-state photomodulation mechanisms in CdS_xSe_1-x doped glass,” Solid State Commun., vol. 80, pp. 557-561, 1991.

[30] H. Shinojima, J. Yumoto, and N. Uesugi, “Size dependence of optical nonlinearity of CdSSe microcrystallites doped in glass,” Appl. Phys. Lett., vol. 60, pp. 298-300, 1992.

[31] A. P. Alivisatos, “Semiconductor nanocrystals,” Bull. Mat. Res. Soc., vol. XX, pp. 23-32, 1995.

[32] H. S. Zhou, I. Honma, H. Komiyama, and J. Haus, “Coated semiconductor nanoparticles: The CdS/PbS system’s synthesis and properties,” J. Phys. Chem., vol. 97, pp. 895, 1993.

[33] J. W. Haus, N. Kalyaniwalla, R. Inguva, M. Bloemer, and C. M. Bowden, “Nonlinear optical properties of conductive spheroidal particle composites,” J. Opt. Soc. Am., vol. B6, pp. 797, 1989.

Peter D. Persans
Department of Physics, Applied Physics, and Astronomy
Rensselaer Polytechnic Institute
110 8th Street
Troy NY 12180-3590
Tel: 518-276-2934
FAX: 518-276-6680
email: persap@rpi.edu
web: http://www.rpi.edu/~persap

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