Chemical approaches to semiconductor nanocrystals

J Phy

PII: SOO22-3697(97)00201-l

Pergamon

CHEMICAL

APPROACHES

TO SEMICONDUCTOR

Chem Solrds Vol59. No. 4. pp 459-465. 1998 0 1998 Elsewer Science Ltd Prmted m Great Britnn All right9 reserved 0022-3697/98 $19.00 + 0.00

NANOCRYSTALS

LOUIS BRUS Chemistry Department, Columbia University, New York, NY 10027, USA Abstract-I discuss the chemistry and physics of semiconductor nanocrystals. Variousphysical size regimes ate outlined in both spectroscopic and kinetic properties. There is a solvation effect on electron transport kinetics due to the electric field of the moving carrier. The importance of chemical synthesis is emphasized with regard to both single nanocrystals, and self-assembled ‘supercrystals’ of nanocrystals. The potential metastability of nanocrystals at standard temperature and pressure (STP), in unusual crystal structures thermodynamically stable only at high pressure, is suggested. 0 1998 Elsevier Science Ltd. All rights reserved. Keywords: A. nanostructures, B. chemical synthesis, D. high pressure 1. INTRODUCTION Currently there is a flourishing world-wide

2. NANOCRYSTAL PROPERTIES ‘nanoscience’

research effort, drawing ideas and methods from chemistry, physics, materials science, and engineering. Nanoscience attempts to make and organize objects on the l-10 nm length scale, and also to understand the evolution of the bulk properties from the molecular properties in this region. Nanoscience is presently in a discovery phase. The key technological issue is understanding and thus control of the natural processes to organize nanometer components in useful ways. Such a ‘self-assembly’ is likely to be a major area of research in the coming century. In this article, some aspects of semiconductor nanocrystal science are discussed. As a material’s characteristic size approaches the molecular regime, one might suspect that chemical methods might become quite useful (synthesis, characterization, and organization). Chemical synthesis can be extremely powerful. For example, Fenske and coworkers in 1993 synthesized, and crystalized from solution, a three-dimensional ‘supercrystal’ composed of monodisperse, organically capped nanocrystais Cu1&e7s(PPh3)30, each a 2 nm by 4 nm tiny fragment of the layered semimetal Cu2Se [I]. The best developed semiconductor ‘nanocrystal’ synthesis is that of CdSe, which in the bulk is a I .7 eV direct gap material with sps tetrahedral (wurtzite) bonding. In 1988 we first reported an inverse micelle method to make pure and stable powders of organically capped CdSe nanocyrstals [2]. Organic capping passivates broken surface bonds and prevents spontaneous aggregation. An improved, high temperature synthesis in trioctyl phosphine oxide liquid solvent has recently been found [3]. By separating nucleation from growth, followed by a size selective precipitation process, gram amounts of nearly monodisperse CdSe nanocrystals can now be made.

An extensive effort over the last decade has led to an understanding of the various physical size regimes in structural, spectroscopic, and kinetic properties as shown in Fig. 1 [4-61. With respect to spectroscopy and structure, very small clusters are essentially molecules with chemical bonding different from that in the bulk. As a cluster grows, it will at some size adopt the unit cell and bonding of the bulk lattice. Such particles are nanocrystals, sometimes termed quantum dots. Nanocrystals have discrete excited electronic states and an increased band gap in comparison with the bulk material. Bulk electronic properties appear asymptotically as their size increases. Nanocyrstals are weakly coupled to the electromagnetic field, as are molecules. As a nanocrystal grows, the bulk band gap forms, and the electromagnetic interaction increases and must be included in zero order. At this point the nanocrystal modifies the spatial distribution and intensity of the electromagnetic field. This is the polariton regime. Perhaps the most dramatic property of semiconductor nanocyrstals is the size evolution of the optical absorption spectra shown in Fig. 2. The discrete excited states of small CdSe nanocyrstals shift to the red and merge with each other, with increasing size, forming the continuous absorption characteristic of the bulk. The lowest excited state asymptotically approaches the near IR bulk band gap. The excited states can be assigned using an effective mass theory that takes into account three dimensional quantum confinement of the bulk Bloch electronic wavefunctions. Of the many possible optical transitions, only a few are allowed under dipole selection rules. These allowed, atomic-like transitions have been extensively characterized in absorption and emission [7, 81. Fig. 3 shows a schematic correlation diagram relating the discrete states of nanoclusters to the continuous bulk bands. The quantized electronic states have maximum 459

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probability density inside the nanocyrstal, with a node on

the surface in simple approximation. In the language of molecular spectrocopy, the band gap transition is the HOMO-LUMO transition. If the surface passivation is

CdSe Nanocrystals

400

500 500 Wavelength (nm)

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Fig. 2. 23’C optical absorption spectra of CdSe nanocyrstals in solution as a function of size (adapted from ref. [3]).

incomplete, then there can also be surface local&d states at energies within the nanocrystal band gap. In indirect gap semiconductors such as Si [6,9, lo] and rocksalt CdSe nanocrystals formed at high pressure, the optical spectra appear continuous, even though the band gap increases and the individual valence and conduction band eigenstates are discrete. This happens because many overlapping discrete transitions appear to be present with roughly equal intensity via vibronic electron-phonon interaction. With respect to kinetic properties a large nanocrystal with a bandgap close to the bulk value often contains several electron hole pairs under typical electric or optical excitation conditions. At 23°C these pairs are not bound with respect to kT, and they dissociate. Carrier recombination is then a many-body kinetic problem, as in the bulk. However, in very small nanocyrstals normally just one electron hole pair is present. The pair cannot dissociate since the electron and hole are confined by the size and shape of the nanocyrstal. They interact with each other via Coulomb forces, exchange forces, and via polarization of the lattice vibrations. This is essentially a molecular excited state which decays by unimolecular processes. This kinetic evolution is shown schematically on the right hand side of Fig. 1. If impurities are present in the bulk semiconductor, at modest concentration, then very small nanocyrstals will tend to have few or no impurities. If impurities dominate the kinetics, then nanocyrstals without impurities will have completely different kinetics. This is an impurity size exclusion effect on the kinetics. In silicon nanocyrstals, quantum confinement causes a kinetic enhancement of the luminescence quantum yield, as well as an increase of the band gap. In individual Si

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nanocyrstals, and in the closely related material porous silicon [ 1 1 - 141, luminescence increases by many orders of magnitude with respect to indirect gap bulk silicon. It was initially suggested that silicon nanocrystals might be partially ‘direct gap’ like, as an explanation for increased luminescence. Fig. 4 shows a simplified Si band diagram. The electron momentum k is not a good quantum number

Fig. 4. Si band struture and nanocrystal Fourier superstition (adapted from ref. [9]).

because of its finite size. In order to localize a carrier inside the nanocrystal, in real space, it must be a Fourier superposition in k-space within the Brillouin Zone, as shown in the figure. The band gap transition should become weakly allowed. However, a detailed study of radiative rates, photoluminescence excitation spectra, and size selective luminescence spectra, shows that Si nanocrystals remain essentially indirect gap, with a vibronically induced band gap optical transition, down to the smallest sizes studied (1.2- 1.5 nm in diameter) [6]. Instead of an increase in the radiative rate in nanocrystals, the nonradiative rate decreases in nanocrystals; this is the cause of the high luminescence quantum yield in Si nanocyrstals and in porous Si [6]. In bulk Si the recombination kinetics are dominated by nonradiative three body Auger processes, and also nonradiative recombination is catalysed by defects and impurities. Both these processes are significantly decreased in nanocrystals because electron-hole pairs are isolated in individual nanocrystals and are not mobile. Thus the quantum yield increases with respect to bulk wafer Si. Very similar size dependent changes occur in indirect gap AgBr [ 151. Chemical methods are useful for processing Si nanocrystals. Fig. 5 shows a broad luminescence in the rear IR from a wide distibution (A) of Si nanocrystals. If the distribution is separated into two fractions by size selective precipitation, then the two fractions (B) and (C) have sharper spectra. This experiment shows the luminescence does shift to the blue region as size decreases. Note also that size is determined by a

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chemical method here-high graphy (HPLC).

pressure liquid chromato-

3. ELECTRON HOPPING TRANSPORT KINETICS The fact that the Coulomb interaction between electron and hole is screened in bulk semiconductors (for example, es, = 11.8) necessarily implies that an extra electron in a nanocrystal has a size dependent dielectric polarization energy [16, 171. For example, Fig. 6 shows

the electrostatic potential energy in Si nanocrystals embedded in SiOr [ 181. There is an image potential force pulling the electron to the nanocrystal center, which is the point of greatest dielectric stabalization. At the center, the energy is shifted higher than the conduction band of bulk Si due to the net loss of dielectric polarization energy. The nanocyrstal electron affinity decreases by an amount AA AA=KE(d)+(lSIP(r)llS)

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Semiconductornanocrystals The first term is the electron kinetic energy, and the second term is loss of the dielectric polarization with respect to the bulk. The second term is quite large in vacuum, or media with a low dielectric constant. The fact that the electric field interacts with the outside medium modifies the electron transfer kinetics as well as the electrostatic energy levels. This is important in the electroluminescence of porous silicon. Porous Si is a microns thick thin film grown on Si wafers by electrochemical etching. It is composed of an open, irregular network of Si wires of undulating diameter, and touching Si nanocyrstals. In 80% porous films, the average Si nanocyrstal size is l-3 nm, with band gaps near 2.0 eV because of quantum confinement [ 11- 131.In dry porous Si diodes, made with solid state contacts, the resistivity is very high and electroluminescence occurs with very low quantum yield. However in aqueous liquid junction diodes, the quantum yield of luminescence increases significantly [ 141. An important, perhaps rate limiting step is hole injection from one nanocyrstal into a touching nanocyrstal containing an electron, to create an electron-hole pair which then emits. In the Marcus formalism for transfer kinetics, the hole is coupled to both the external water medium, if it is present, and the vibrations of the Si nanocrystals. The Marcus theory was originally developed for electron transfer in protiens and solvated molecules. When applied in Si nanocrystals, the hole coupling to the covalent Si vibrations is found to be weak, and the coupling to the polar water is in fact about 20-fold stronger [ 181. An external aqueous medium completely dominates the kinetics. Fig. 7 is a plot of the log(base 10) of the activation factor in the transfer rate, versus the size

463

of the accepting nanocrystal, for a fixed hole donor of 2 nm diameter. As acceptor size increases above 2 nm, the transfer becomes more exothermic. In water the transfer rate is fast for all sizes, as the water coupling energy is of the same magnitude as the transfer exothermicity. In vacuum, however, the activation energy is very high except for those acceptor sizes where there is electronic resonance with an excited state of the hole, such as transfer to the 3S state at 4 nm acceptor size. In vacuum porous silicon behaves like a resonant tunneling device with weak coupling to phonons, while in water porous Si shows fast exothermic transfer that is similar to that of solvated molecules and proteins. As porous Si is composed of a wide distribution of sizes this calcaulation helps to explain why electroluminescence is better in wet porous Si. This example shows how one could tune electron transfer kinetics in a nanocrystal material via the polarity of the enviroment.

4. SUPERCRYSTALSOF NANOCRYSTALS If the size distribution is narrow in a colloidal system, it may be possible to slowly and reversibly crystallize the particles from solution. Such collidal crystals, or supercrystals, have been reported for Fe203 and CdSe, as well as Curse as mentioned in the introduction [19, 201. Natural opal gemstones are infact analogous supercrystals of round silica particles in the 0.1 to 0.5 micron range [21]. Normal opals are simple close packed structures made from particles of one size. However, a remarkable superlattice opal crystal (shown in Fig. 8) has been descibed by Sanders [22]. It is composed of diameter

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Fig. 8. SEM image of a superlatticeopal crystal (adaptedfrom ref. [22a]).

entropically driven. Theory indicates different diameter ratios favor different structures [22]. This body of work offers a glimpse of new possibilities in creation of crystalline materials composed of nanocrystals. One might create layers of large CdSe nanocrystals separated by electrically insulating layers of small SiOl particles. This material should show anisotropic conduction. The electrical connection from one nanocrystal to the next could be influenced through the polarity of the interstitial medium and the nature of the surface capping molecules. Thus, the width of the bands could be varied independently of the size of the nanocrystals. This, in future, should be a rich area of materials science.

5. SOLID-SOLID PHASE TRANSITIONS AND METASTABLITY OF HIGH PBESSURE PHASES Tetrahedral semiconductors have rich temperaturepressure phase diagrams. At high pressure, four coordinate sp3 hybridized semiconductors undergo first order transitions into dense, six coordinate phases. For example, wurtzite CdSe transforms into a rock-salt phase, and diamond lattice Si transforms into a tin phase. In bulk single crystals, the transformation is apparently always nu eated at defects and shows substantial hysteresis due (7 to a\very large kinetic barrier. Study of phase transitions in nanocrystals provides insight into the fundamental science of these processes [23]. Only one nucleation event per nanocyrstal is observed: a single nanocrystal of one phase transforms into a single nanocrystal of the other phase. As a result, the nanocrystal shape changes to accommodate the unit cell change. For example, Fig. 9 shows how a nearly spherical Si diamond cubic particle is thought to transform into an oblate spheroid beta-tin phase nanocrystal. Correspondingly, a prolate spheroid cubic Si nanocrystal transforms into a nearly spherical beta-tin phase nanocrystal. Evidence for such shape changes has recently been observed in 50 nm Si particles with a thin oxide surface coating [24].

A simple model for this process assumes that a nanocrystal thermally fluctuates from one phase into the other, along the coherent transformation coordinate that simultaneously transforms all unit cells [25]. In Fig. 10, this transformation is shown for beta-tin Si particles of two different initial shapes. The energy surface has both surface and volume contributions. For large particles, the volume contribution dominates and the activation energy rapidly increases with increasing size. For small particles, the shape dependent surface energy is quite important. Yet for nanocrystals larger than 2 nm the activation energy is sufficiently large that the high pressure phase nanocrystal should be me&table, with a lifetime of many years at STP (standard temperature and pressure). These ideas suggest that it may be possible to synthesize a wide variety of semiconductor nanocrystals in high pressure phases, as well as in the normal sp3 phases. High pressure phase structures should be metastable at STP if the nanocrystals can be made as perfect single crystallites with well passivated surfaces. Because of the extra degree of freedom offered by the surface,

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known [26]. Acknowledgements-I thank M. Nirmal for his useful comments on this manuscript. Present nanocrystal research at Columbia is partially supported by the Joint Services Electronics Program in the Columbia Radiation Labatory. Much of the work described here was performed over the past decade at AT&T (now Lucent Technologies) Bell laboratories in Murray Hill, NJ. I express deep appreciation to former post-doctoral students A.P Alivisatos, M.G. Bawendi, K.A. Littau and J. Macklin, and to many collaborators at Bell Labs: M.L. Steigerwald, T.D. Harris, A. Muller, A.R. Kortan, Alex Harris, DC. Douglass, R.L. Opila, P.J. Carroll, P.J. Szajowski, P.H. Citrin, W.L. Wilson, L. Rothberg, F.H. Stillinger. J. Trautman, J. Tully and R.H. Laudise. This article is adapted from a related chapter in the proceedings of the R.A. Welch Foundation Symposium on Nanophase Chemistry (1996).

REFERENCES I. Krautscheid,

H., Fenske, D., Baum, G. and Semmelman, M., Angew. Chem. Int. Ed. Engl., 1993,32, 1303. 2. (a) Steigenvald, M.L: Alivisatos, A.P; Douglass, DC; and Brus, L.E, J. Am. Chem. Sot. 110,3046(1988). (b) Kortan, AR Hull, R; Opila, R.L; Bawendi, M.G; Steigerwald, M.L; Carroll, P.J, Brus,L.E, J. Am.Chem. Sot. 112,1327.(1990). 3. Murray, C.B., Norris, D.J. and Bawendi, M.G., J. Am. Chem. Sot., 1993,115,8706. 4. Efros, A1.L. and Efros, A.L., Sov. Phys. Semicond., 1982.16,

1209. 5. Brus. L.J., J. Phys. Chem., 1986,%,

2555.

nanocrystals

465

6. Brus, L., Szajowski P., Wilson, W., Harris, T., Schuppler, S. and Citrin. P., J. Am. Chem. Sot.. 1995. 117. 2915. 7. Bawendi, M.G., Wilson, W.L., Rothberg, L: Rothberg, L., Carroll, P.J., Jedju, T.M.. Steigerwald, M.L. and Brus, L.E., J. Chem. Phys. Rev. Lett., 1990, 65, 1623; (b) Bawendi, M.G., Carroll, P.J., Wilson, W. and Brus, LE., J. Chem. Phys., 1992, 96, 946. 8. (a) Norris, D.J., Sacra, A., Murray, C.B. and Bawendi, M. G., Phys. Rev. Lett. 1994,72,2612-2615; (b) Effros, A1.L.. Rosen, M., Kuno, M., Nirmall, M., Norris, D. and Bawendi. M.G., Phys. Rev., 1996, B54.4843. 9. (a) Littau, K.A., Szajowski, P.F., Muller, A.J.. Kortan, R. F. and Brus, L.E., J. Phys. Chem., 1993.97, 1224; (b) Wilson, W.L., Szajowoski, P.F. and Brus, L.E., Science, 1993,262, 1242; (c) Brus. L., J. Phys. Chem., 1994,98, 3575. 10. (a) Schuppler, S., etal., Phys. Rev. Let?., 1994.72.2648; (b) Schupplkr, S., ef al., Phys..Rev., 1995, B52, 4910. 11. Canham, L.T.. AL&. Phvs. Lerr.. 1990.57. 1046. 12. Koyama, H., A&, M.: Yamamoyo. Y. and Koshida, N., Jpn. J. Appl. Phys., 1991.30, 3606. 13. Lehmann, V. and Gosele, U., Appl. Phys. Letr.. 1991, 58, 856. 14. (a) Bsiesy, A., Muller, F., Ligeon, M . Gaspard, F., Henno. R., Romestain, R. and Vial, J., Phys. Rev. Letr., 1993, 71, 637; (b) Bsiesy, A., Muller, F., Ligeon, M., Gaspard, F., Herino, R., Romenstain, R. and Vial. J., Appl. Phys. Left.. 1994,65,337 I. 15. (a) Johansson, K.P., McLendon, G.P. and Marchetti. A. P.. Chem. Phys. Let!., 1991, 179, 321; (b) Johansson, K.P.: Marchetti, A.P. and McLendon, G.P.. J. Phys. Chem., 1992. 96, 2873; (cl Marchetti, A.P.. Johansson. K.P. and McLendon, G.P..‘ bhys. Rev., 1993, B47, 4268; (d) Chen, W., McLendon, G., Marchetti, A., Rehm, J.M., Freedhoff, M. and Meyers, C.. J. Am. Chem. Sot., 1994, 116, 1585, (e) Kanzaki, H. and Tadakuma, Y., Sol. St. Commun.. 1991.80. 33. 16. BNS, L., Chem. J. Phys., 1983,79,5566and J. Chem. Phys.. 1984,80,4403. 17. (a) Babic, D., Tsu, R. and Greene, R.F., Phys. Rev., 1992, B45, 14150; (b) Tsu, R. and Babic. D., Appl. Phys. L&t., 1994.64, 1806; (c) Delerue, C., Allan, G. and Lannoo, M., Phys. Rev., 1993, B48, 11024; (d) Lannoo, M., Delerue, C. and Allan, G., Phys. Rev. Lea, 1995.74, 3415; (e) Chazalvie], J., Ozanam, F., and Dublin. V., J. Phys. I Frunce. 1994. 4, 1325. 18. Brus, L., Phys. Rev., 1996, B53, 4649. 19. Bentzon, M., van Wonterghem, J., Morup, S., Tholen, A. and Koch, C., Phil. Msg., 1989, B60, 169. 20. Murray, C., Kagan. C. and Bawendi, M., Science, 1995,270. 1335. 21. (a) Sanders, J.,Acra Crystall.. 1968, A24.427; (b) Pieranski. P., Comp. Phys., 1983.24, 25. 22. (a) Sanders, J., Phil. Msg., 1980, A42, 705; (b) Bartlett, P. and Pusev, P., Phvsica A, 1993.194.415. 23. Tolbert, S. and Alivisatos, A.P., Annu. Rev. Phys. Chem., 1995,46,595. 24. Tolbert. S.. Herhold, A., Brus, L. and Ahvisatos, A.P , Phys Rev. Lett., 1996, 76, 4384. 25. Brus, L., Harkless, J. and Stillinger, F., J. Am. Chem. Sot.. 1996, 118.4384. 26. (a) Vollstadt, H., Ito, E., Akaishi, M.. Akimoto, S. and Fukunaga, 0.. Proc. Jpn. Acad. Ser. E, 1990, 66, 7: (b) Lin, J.. Cates, E. and Bianconi, P.. J. Am. Chem. Sot., 1994. 116, 4738; (c) Xie, Y., Qian, Y., Zhang. S. and Wang, Y., Appl. Len., 1996, 69, 334.