Springer Handbook of Condensed Matter and Materials Data

Bearbeitet vonWerner Martienssen, Hans Warlimont

1. Auflage 2005. Buch. xviii, 1121 S. HardcoverISBN 978 3 540 44376 6

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1031

Mesoscopic an5.3. Mesoscopic and Nanostructured Materials

This chapter addresses the properties of nanostruc-tured materials considered as statistical ensemblesof nanostructures. Emphasis is put on size andconfinement effects, although enhancements insurface and interface properties are mentioned.After a survey and a summary of basic definitionsand concepts in the introductory Sect. 5.3.1, theproperties associated with electronic confinementare addressed in Sect. 5.3.2. Electronic confine-ment affects the spectral properties, i. e. lightabsorption and luminescence, mainly throughquantum size effects, and the electrical conduc-tion properties through the Coulomb blockade.Both two-dimensional systems (quantum wells)and zero-dimensional systems (quantum dots)are reviewed. Particular attention is drawn tosemiconductor-doped matrices. The effects asso-ciated with confinement of electromagnetic fieldsare treated in Sect. 5.3.3. Numerical relationshipsand data for plasmon excitations of various metalnanoparticles can be found in this section. Mag-netic nanostructures are addressed in Sect. 5.3.4.The two main applications of nanostructuredmagnetic materials, namely spin electronics, orspintronics, and ultrahigh-density data storagemedia, are treated. Finally, we list and briefly de-scribe in Sect. 5.3.5 some generic techniques forthe preparation of nanostructured materials, or-ganized into the following groups of methods:molecular-beam epitaxy (MBE), metal-organicchemical vapor deposition (MOCVD), nanolithogra-phy, nanocrystal growth in matrices, and ex-situsynthesis of clusters.

5.3.1 Introduction and Survey ...................... 10315.3.1.1 Historical Review..................... 10315.3.1.2 Definitions ............................. 10325.3.1.3 Specific Properties ................... 10345.3.1.4 Organization of this Chapter ..... 1034

5.3.2 Electronic Structure and Spectroscopy... 10355.3.2.1 Electronic Quantum Size Effects . 10355.3.2.2 Breakdown of the Momentum

Conservation Rule ................... 10365.3.2.3 Excitons

in Quantum-Confined Systems.. 10365.3.2.4 Vibrational Modes

and Electron–Phonon Coupling. 10405.3.2.5 Electron Transport Phenomena . 1042

5.3.3 Electromagnetic Confinement .............. 10445.3.3.1 Nanoparticle-Doped Materials .. 10445.3.3.2 Periodic

Electromagnetic Lattices........... 1048

5.3.4 Magnetic Nanostructures..................... 10485.3.4.1 Spin Electronics....................... 10495.3.4.2 Ultrahigh-Density Storage

Media in Hard Disk Drives......... 1060

5.3.5 Preparation Techniques ...................... 10635.3.5.1 Molecular-Beam Epitaxy .......... 10635.3.5.2 Metal-Organic Chemical Vapor

Deposition (MOCVD) ................. 10645.3.5.3 Lithography ............................ 10645.3.5.4 Nanocrystals in Matrices........... 10645.3.5.5 Ex Situ Synthesis of Clusters ...... 1065

References .................................................. 1066

5.3.1 Introduction and Survey

5.3.1.1 Historical Review

Except in the life sciences, there are only a few examplesof materials that are naturally structured on scales ofthe order of a few to a few hundred nanometers. One

can cite, however, the natural zeolites, which constitutea group of hydrated crystalline aluminosilicates con-taining regularly shaped pores with sizes from 1 nmto several nanometers. This provides them the abil-ity to reversibly adsorb and desorb specific molecules.

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They were named “zeolite” (“boiling stone”) in 1756 byCronstedt, a Swedish mineralogist, who observed theiremission of water vapor when heated. At the other sizelimit, opals constitute another example of a naturally oc-curring nanostructured material. These gems are madeup mainly of spheres of amorphous silica with sizesranging from 150 nm to 300 nm. In precious opals, thesespheres are of approximately equal size and can thusbe arranged in a three-dimensional periodic lattice. Theoptical interferences produced by this periodic indexmodulation are the origin of the characteristic iridescentcolors (opalescence).

Apart from these few examples, most nanostruc-tured materials are synthetic. Empirical methods for themanufacture of stained glasses have been known forcenturies. It is now well established that these methodsmake use of the diffusion-controlled growth of metalnanoparticles. The geometrical constraints on the elec-tron motion and the electromagnetic field distribution innoble-metal nanoparticles lead to the existence of a par-ticular collective oscillation mode, called the plasmonoscillation, which is responsible for the coloration of thematerial. It has been noticed recently that the beautifultone of Maya blue, a paint often used in Mesoamer-ica, involves simultaneously metal nanoparticles anda superlattice organization [3.1].

The chemistry and color changes of colloidal goldsolutions were observed by Faraday during the 19thcentury [3.2]. These properties were due to highly size-dispersed gold nanoparticles.

Improvements in the diffusion-controlled growthtechnique opened up the possibility of growing nano-crystallites with better-controlled sizes and densitiesand permitted its extension to various semiconduc-tors. The fabrication of colored long-wavelength-passglasses and of photochromic glasses provides well-known examples of commercial technologies based onsuch methods developed decades ago. Various tech-niques for the production and assembly of cluster- andnanoparticle-based materials are currently under intensestudy.

More recently, important technological efforts havebeen made, driven by the increasing needs of the elec-tronics industry, in order to understand and control thegrowth of semiconductors at the atomic level. The de-velopment of molecular-beam epitaxy (MBE) permittedthe control of atomic-layer-by-atomic-layer growth ofsemiconductors. It has become possible to create struc-tures made up of an alternation of different layers,each of which is only a few atomic layers thick. Thefirst observation of the quantization of energy levels in

a quantum well in 1974 [3.3] opened the way to the tai-loring of the electronic wave function in one dimensionon the nanometer scale, leading to the production of newelectronic and also magnetic materials. A new trend insurface science is work aimed at the control of in-planenanostructuring, such as the formation of wire or dotshapes, through self-organization.

In parallel to developments in the field of electron-ics, nanostructured materials have been developed bymaterials scientists and chemists also. The concept ofnanocrystalline structures emerged in the field of ma-terials science, and polycrystals with ultrafine grainsizes in the nanometer range have been produced. These“nanophase materials” have been shown to have sig-nificant modifications of their mechanical propertiescompared with the coarse-grain equivalent materials.The huge surface area of nanoporous materials has at-tracted much attention for applications in chemistry suchas molecular sieves, catalysis, and gas sensing. Thishas motivated intense research aimed at the fabrica-tion of materials with a well-controlled composition andnanoscale structure, such as synthetic zeolites.

The scientific and technological domains of researchon nanostructured materials cover a range of disci-plines, from biology to physics and chemistry. However,their convergent aspects, as well as, to some extent,a common type of approach, have been recognized re-cently in the realm of nanoscience and nanotechnology,under the term “nanostructured materials”, or simply“nanomaterials”.

For an extended review on nanotechnology see therecently published Handbook of Nanotechnology [3.4].

5.3.1.2 Definitions

In their broadest definition, nanostructured materialsshow structural features with sizes in the range from1 nm to a few hundred nanometers in at least one dimen-sion. This very general criterion actually includes verydiverse physical situations.

First, as is apparent from the previous section, eachnanostructured material is associated with a specificnovel property or a significant improvement in a spe-cific property resulting from the nanoscale structuring.As a consequence, the type of nanostructuring usedmust be based on a spatial dependence of some param-eter related to the property under consideration. Thisparameter could be, for example, the material density,transport parameters, or the dielectric constant. Anotherconsequence is that the upper size limit of the structuralfeatures varies depending on the property considered,

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Mesoscopic and Nanostructured Materials 3.1 Introduction and Survey 1033

from a molecular size for molecular-sieve properties upto the wavelength of light for the optical properties.

Second, in addition to the nanometer-scale struc-turing, a larger-scale ordering of the unit patternsmay be necessary for the existence of the propertysought. For example, the particular optical prop-erties of opals mentioned above require the silicananospheres to show a long-range order with a co-herence length well beyond a micron. The sameconsiderations hold for quantum-well superlattices, forexample. In other cases, the nanosized building blocksdo not need long-range order to provide a specificproperty, but still require some degree of short-rangeorganization. For example, an electrical conductiv-ity appears only above a critical percolation densityof conducting particles. Finally, some properties ofnanostructured materials simply reflect a correspond-ing intrinsic property of their individual building blocks.This is the case, for instance, in nanoparticles embed-ded in glass or polymer matrices for optical-filteringapplications.

Two main technological approaches may be defined:

• The top-down manufacturing paradigm consists indownscaling the patterning of materials to nano-meter sizes. This allows the generation of materials

Table 5.3-1 Examples of reduced-dimensional material geometries, and definitions of their dimensionality and of the associatedtype of confinement

L X,Y,Z > L0 No nanostructures No confinement Bulk material

L X,Y > L0 > L Z Two-dimensional (2-D) One-dimensional (1-D) Wells

nanostructures confinement

L X > L0 > LY,Z One-dimensional (1-D) Two-dimensional (2-D) Wiresnanostructures confinement

L0 > L X,Y,Z Zero-dimensional (0-D) Three-dimensional (3-D) Dotsnanostructures confinement

which are coherently and continuously ordered frommacroscopic down to nanoscopic sizes.• The bottom-up paradigm is based on the atomicallyprecise fabrication of entities of increasing size. Itis the domain of macromolecular and supramolecu-lar chemistry (dendrimers, engineered DNA, etc.)and of cluster and surface physics (epitaxy, self-assembly, etc.).

Mesoscopic materials form the subset of nanostruc-tured materials for which the nanoscopic scale is largecompared with the elementary constituents of the mater-ial, i. e. atoms, molecules, or the crystal lattice. For thespecific property under consideration, these materialscan be described in terms of continuous, homogeneousmedia on scales less than that of the nanostructure. Theterm “mesoscopic” is often reserved for electronic trans-port phenomena in systems structured on scales belowthe phase-coherence length ΛΦ of the carriers.

Most of the common nanomaterials can be classifiedin terms of dimensionality, according to the number oforthogonal directions X, Y, Z in which the structural pat-terns referred to above have dimensions L X,Y,Z smallerthan the nanoscopic limit L0. This leads to the classicaldefinitions of dimensionality summarized in Table 5.3-1.However, it should be noted that experimental situations

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1034 Part 5 Special Structures

can be encountered in which the dimensionality maynot be so obviously defined. For instance, the structuralpatterns may be formed by nonrectilinear wires whichoccupy a surface or a volume or may be branched.

The structure of the density of states (DOS) in nano-structures is strongly dependent on the dimensionality.A free 3-D motion yields a band characterized by threewave vectors kx, ky, kz . The corresponding DOS de-pends smoothly on the energy E, as (E − E0)1/2, whereE0 is the energy of the bottom of the band. Confine-ment into a 2-D system splits the band into subbands,and leaves only two continuously varying wave vectorskx, ky in each subband. The DOS for each subband isthen constant above the energy E0

N of its bottom state.The overall DOS is discontinuous, with a stepwise struc-ture that is characteristic of quantum wells (Fig. 5.3-1).Confinement in one additional dimension splits each 2-Dsubband further into a set of 1-D subbands. Each 1-Dsubband is characterized by only one continuously vary-ing wave vector kx , and two quantum numbers N, M.The DOS corresponding to the subband N, M has a vari-ation of the form (E − E0

N,M)−1/2, with a divergence atthe bottom of the subband E0

N,M . The DOS of a quan-tum wire thus has a more pronounced structure thandoes a 2-D well, with a larger number of subbands,each one starting as a peak (Fig. 5.3-1). Finally, con-finement in all three dimensions creates a completelydiscrete, atom-like set of states. The DOS of a quan-

DOS

E

Fig. 5.3-1 Schematic illustration of the density of states for3-D motion of a free electron (dashed line), a 2-D quantumwell (solid line), and a 1-D quantum wire (shaded area) asa function of energy

tum dot thus consists of a series of δ-functions (notrepresented in Fig. 5.3-1). The sharpening of the DOSat specific energies induced by quantum confinement isthe origin of many improvements in the properties ofnanostructured materials compared with bulk materials.This spectral concentration enhances all resonant effectsand increases the energy selectivity. The preservation ofthese effects when one is dealing with an ensemble ofquantum-confined systems requires a high homogeneity.

5.3.1.3 Specific Properties

The specific properties of nanostructured materials canhave two different possible origins:

• Size effects, which result from the spatial confine-ment of a physical entity inside an element of thenanoscale structural pattern. Such an element iscalled a low-dimensional system. An example is theconfinement of electron wave functions inside a re-gion whose size is smaller than the electron meanfree path. This class of effects may give birth tocompletely new properties.• Boundary effects, which are a consequence of thesignificant volume fraction of matter located nearsurfaces, interfaces, or domain walls. Processes thattake place only at such locations may be highlyfavored, and properties specific to structural bound-aries may also be greatly enhanced.

For a recent comprehensive review of the basic prin-ciples of the origin of the properties of nanostructuredmaterials, see [3.5].

5.3.1.4 Organization of this Chapter

Many classification schemes for nanostructured ma-terials exist. These may be based on their chemicalcomposition, on the technique for their manufacture,or on their dimensionality. These schemes, however, areoften suitable only for a subset of materials. Moreover,they generally address only one particular scientific ortechnological approach and its associated communityof specialists. Since, as noted above, most nanostruc-tured materials are associated with a specific property,we have chosen a presentation based on properties. Thisscheme allows us to include all nanostructured materialsand is accessible to the largest possible readership.

Consistently with the materials approach of thischapter and with its limited size, only the proper-ties of statistical ensembles of nanostructures will beconsidered. The specific behaviors of individual nano-

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Mesoscopic and Nanostructured Materials 3.2 Electronic Structure and Spectroscopy 1035

sized objects or devices are not included. Since surfaceand interface properties are treated in another section,emphasis will be put here on size effects. Propertiesrelated to electronic confinement and its consequencesfor spectral properties are addressed in Sect. 5.3.2. Ef-

fects of the confinement of electromagnetic fields aretreated in Sect. 5.3.3. Magnetic size effects are addressedin Sect. 5.3.4. Finally, we list and briefly describe inSect. 5.3.5 some generic methods for preparation ofnanostructured materials.

5.3.2 Electronic Structure and Spectroscopy

5.3.2.1 Electronic Quantum Size Effects

Confined electronic systems are quantum systems inwhich carriers, either electron or holes, are free to moveonly in a restricted number of dimensions. In the con-fined dimension, the sizes of the structural elementsare of the order of a few de Broglie wavelengths ofthe carriers or less. Depending on their dimensionality,these structures can be quantum dots (0-D), quantumwires (1-D), or quantum wells (2-D). Quantum wellsare typically produced by the alternate epitaxial growthof two or more different semiconductors. Quantum wiresare less commonly encountered, since their fabricationprocedures are much more complicated (Sect. 5.3.4).

One of the most dramatic effects, called the quan-tum size effect, consists in a redistribution of the energyspectrum of the system, the density of states becom-ing discrete along the confinement direction. In themost simple “particle in a box” model of a quan-tum well, the energies of the corresponding eigenstatesare

EN,kx ,ky = N2 π2�

2

2md2 +(

k2x + k2

y

)�

2

2m, (3.1)

where m is the effective mass of the carrier, d is theconfinement dimension, and N is a quantum number.The first term appears because of the quantized motionin the z direction, whereas the second term representsthe energy of the free x, y motion, characterized bywave vectors kx, ky. Each value of N defines a semi-infinite subband of energy levels. Although the “particlein a box” model is simplistic compared with real sys-tems, this limiting case is often successful in describingthe essential features of quantum size effects [3.6].

The importance of the quantum size effect is mainlydetermined by the energy differences EN+1 − EN .Quantum size effects become observable when this sep-aration exceeds the thermal energy of the carriers, sothat adjacent subbands are differently populated. Sincethe energy difference EN+1 − EN increases with N ,it could be anticipated that quantization effects would

be more important for processes involving higher sub-bands. However, the practical observation of such effectsin systems with a large Fermi energy (EF � E1), i. e.in metals, is often made difficult because of con-tributions from many levels and the appearance ofcollective phenomena such as plasmon oscillations,which wash out quantization effects. Most of the spec-tral data revealing quantum well states in metal filmsa few monolayers thick have been obtained by angle-resolved photoemission for Cs on Cu(111) [3.7] and forAg on Au(111) [3.8]. The Fabry–Perot-like regularly-spaced spectrum of energy levels appears particularlyclearly in a study of Ag films on Fe(100) for thick-nesses up to more than 100 monolayers (Fig. 5.3-2).The superposition at half-integer coverages (27.5 and42.5 monolayers) of two sets of peaks correspondingto the two closest integer thicknesses emphasizes theextreme sensitivity to surface homogeneity. Quanti-tatively, the characteristic roughness of well barriersmust be much below the de Broglie wavelength ofthe quantum states observed. This is another reasonwhy quantum size effects have been observed mainlyin semiconductor nanostructures, which have largeFermi wavelengths, rather than in metals, which haveFermi wavelengths comparable to a few crystal latticeperiods.

The existence of discrete electronic states of elec-trons confined in a small metal cluster has been observedto influence the thermodynamic stability of the system,in particular during the production of sodium clus-ters in supersonic beams composed of the metal vaporand an inert gas. The statistics of the relative abun-dances of different particle sizes reveal the existenceof “magic numbers” for the number of atoms in thecluster, N = 8, 20, 40, 58, 92, . . . [3.9]. This has beeninterpreted in terms of the existence of degenerate en-ergy levels in a spherical well with infinite-potentialwalls. Particularly stable structures are obtained whenthe number of valence electrons is such that it leadsto a closed-shell electronic structure, i. e. a structurewith a completely filled energy level and an empty up-

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1036 Part 5 Special Structures

2

119

95

71

57

42.5

42

28

27.5

14

12

1 0

Photoemission intensity (arb. units)

Binding energy (eV)

= 16 eVνhAg / Fe (100) Thickness

(ML)

Fig. 5.3-2 Dots: experimental normal photoemission spec-tra for Ag quantum wells deposited on Fe(100), with variousthicknesses. Solid curves: fits and background functions.(After [3.12])

per level. The electronic shell structure induces similarsize dependences in the work function and the electrondensity, through Friedel-like oscillations [3.10]. The se-ries of “magic numbers” is discernible up to N = 1430.For larger particles, the relative abundance of differentsizes is controlled instead by the stability and relativesizes of the various facets of the surface of the par-ticle. It is noteworthy that 2-D quantum well states arealso predicted to produce oscillatory variations of theenergetics of a film as a function of thickness, withsimilar “magic numbers” for the number of depositedmonolayers [3.11].

5.3.2.2 Breakdown of the MomentumConservation Rule

As a result of the Heisenberg uncertainty principle, lo-calization of carriers in a confinement volume spreadstheir wave functions in reciprocal space. The possibleoverlap in k space of electron and hole wave functionsbreaks the rule of conservation of crystal momentum.In other words, the momentum needed for a transi-tion at a different k may be provided by scatteringfrom the boundaries. This consequence of quantumconfinement is particularly meaningful for nanostruc-tures based on indirect-band-gap semiconductors, forwhich luminescence from recombination of the lowest-energy electrons and holes is forbidden in the bulkmaterial, but becomes increasingly possible for sys-tems of decreasing size, with a scaling law of d−6

for dots [3.13]. The observation of bright luminescencefrom nanoporous silicon samples [3.14] was, from thestart, interpreted in terms of quantum confinement intosilicon nanowires [3.14, 15]. This observation triggeredan important research activity motivated by the industrialprospect of being able to incorporate silicon photonicelements into the current silicon technology. Althoughit has been shown that other phenomena such as sur-face effects and phonon modes (discussed later) comeinto the play, and that more complicated geometriesincluding both quantum dots and quantum wires haveto be considered, the role of quantum confinement inthe luminescence of porous silicon is generally con-sidered to be central, at least for the “red” part of theluminescence. The studies of nanostructure-induced lu-minescence have been extended to porous GaP [3.16,17]and SiC [3.18], two other semiconductors with an indi-rect band gap, and the results parallel those for poroussilicon. Quantum-confined luminescence has been ob-served in indirect-gap semiconductor nanostructureswith well-controlled geometries such as silicon andgermanium 2-D wells [3.19] and quantum dots (seee.g. [3.20]), which may possibly be integrated into light-emitting devices [3.21]. The observation of optical gainin silicon nanocrystals [3.22] opens up new prospectsfor the creation of silicon-based lasers [3.23].

5.3.2.3 Excitonsin Quantum-Confined Systems

A very general effect of quantum confinement in semi-conductors is a widening of their optical band gap. Forthe model system of an infinite-barrier 2-D quantumwell, (3.1) shows that the lowest energy (N = 1) of a con-

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Mesoscopic and Nanostructured Materials 3.2 Electronic Structure and Spectroscopy 1037

duction electron is increased compared with the bottomof the conduction band. A similar consideration appliesto the lowest energy of a hole in the valence band. Botheffects contribute to an increase in the minimum ex-citation energy of the system compared with the bulkband gap. This blueshift has a comparable magnitude in2-D and 0-D structures [3.24]. This constitutes the lead-ing contribution to the characteristic blueshifts in theoptical spectra of strongly quantum-confined semicon-ductor systems. However, the confinement of oppositelycharged carriers at reduced separations also has dramaticeffects on the electron–hole Coulomb energy and thuson exciton formation.

Two regimes of exciton confinement must be distin-guished, depending on the confinement size d comparedwith the Bohr radius a∗

0 of the Mott–Wannier exciton inthe bulk semiconductor [3.25]. The weak-confinementregime corresponds to sizes such that d ≥ 4a∗

0. In thisregime, the relative electron–hole motion, and in particu-lar its binding energy, is essentially left unchanged. Theexciton can still be considered as a quasiparticle, but itscenter-of-mass translational motion becomes quantized.A simple model [3.26] of a single-point quasiparticlewith mass MEx equal to the total mass of the exciton,MEx = m∗

e +m∗h, explains the observed frequency shifts.

The translational state with the lowest energy, N = 1,which is the only optically allowed state, has a nonzerokinetic energy. Compared with an infinite-sized system,the lowest excitation energy in the weak-confinementregime is thus increased by

∆EWeak = π2�

2

2MExd2 . (3.2)

Like that for electron states, this shift has comparablemagnitudes for various dimentionalities. In the weak-confinement regime, the exciton wave function stillinvolves combinations of several conduction-band elec-tron states and valence-band hole states, and not only thelowest-energy states. The quantization of carrier statesdoes not change significantly the average energy of allof the states involved in exciton formation. As a con-

Table 5.3-2 1s exciton Bohr radius for various semiconductors

Direct-band-gap semiconductors

Semiconductor CuCl Diamond CdTe CdS GaN CdSe GaAsa∗

B (nm) 0.7 0.85 2.8 2.9 3.6 5.6 12

Indirect-band-gap semiconductors

Semiconductor GaP SiC Si Gea∗

B (nm) 1.17 2.7 4.9 17.7

sequence, in the weak-confinement regime, the excitonenergy is not affected by the band gap increase whichresults from the increase in the energy levels of thelowest electron and hole states discussed above. Theweak-confinement model is very suitable for describingspectral variations in nanoparticles of semiconductorswith low exciton Bohr radii, such as CuCl (Table 5.3-2),as shown in Fig. 5.3-3.

The strong-confinement regime corresponds to theopposite limit, d ≤ 2a∗

0. In that case the relative electron–hole motion is strongly affected by the barriers. In thedirection of restricted motion, the kinetic energies of thelowest-energy electron and hole states determined bythe quantum confinement are larger than the Coulomb

0.0050.01

0.05

0.1

0.5

1.0

510

R/a*B

0 2 4 6 8 10 12 14

Energy shift (E*Ry)

σ = ∞

σ = 1σ = 5

σ = 10

Fig. 5.3-3 Observed values of energy shifts in the lu-minescence peak of CuCl nanocrystals in NaCl (circles)and in the absorption peak of CdS nanocrystals in sili-cate glass (triangles), compared with theoretical models:weak-confinement model (dashed-dotted lines), strongconfinement model (short-dashed line); σ = m∗

h/m∗e is con-

sidered as a fixed parameter. (After [3.25])

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1038 Part 5 Special Structures

attraction. The exciton states are thus formed from un-correlated electron and hole states of the “particle ina box” model in the confinement direction, whereas spa-tially correlated electron–hole bound states can still beformed in the unrestricted directions. This yields 2-D,1-D, and 0-D excitons in quantum wells, quantum wires,and quantum dots, respectively. The binding energy ofa 2-D exciton can be deduced from the two-dimensionalhydrogen atom problem [3.27]. The exciton Rydbergseries changes from E∗

3-D = −R∗/n2 in the 3-D caseto E∗

3-D = −R∗/(n −1/2)2 in the 2-D case, where R∗is the Rydberg constant for the exciton. This effect is op-posed by the increased energy required for the creationof an electron–hole pair owing to the confinement of thecarrier motion. The variation of the excitation energy ofthe first 1s-like exciton state in the regime of strong 1-Dconfinement is then

∆E2-DStrong = π2

�2

2µd2−3R∗ , (3.3)

where µ is the electron–hole reduced mass, such thatµ−1 = m∗

e−1 +m∗

h−1. The first term is larger than the

term due to the weak confinement of exciton motion(3.2) because of the difference between µ and MEx. The0-D case is treated in detail in [3.25]. The variation ofthe minimum excitation energy in the regime of strong3-D confinement is

∆E0-DStrong = π2

�2

2µd2−1.786

e2

4πεd−0.248R∗ . (3.4)

The divergence as d−1 of the second term for small sizesresults from the increased Coulomb interaction in this re-stricted geometry compared with the 2-D case. As couldbe expected, the case of a 1-D exciton in a quantum wireis intermediate between 0-D and 2-D, with a divergentCoulomb interaction which is sublinear in d−1 [3.28].For all dimensionalities, in the strong-confinementregime, the increased kinetic energy of quantum-confined carriers is dominant, and a blueshift of theoptical gap is observed that varies continuously betweenthe weak- and the strong-confinement regimes. How-ever, the considerably increased exciton binding energyin strongly confined systems yields more pronounced ex-citon effects. For the most widely used semiconductors,excitonic effects are not discernible in room tempera-ture spectra without quantum-confinement. However,in strongly confined geometries of any dimensionality,many semiconductors exhibit well-resolved excitonicpeaks since the exciton binding energy can then ex-ceed the thermal excitation energy kBT . Both theblueshift of the spectra and the increasingly pronounced

excitonic absorption are very evident in II–VI semi-conductor nanoparticles, as exemplified in Fig. 5.3-4for CdSe [3.29]. Semiconductor-doped glasses, formedfrom a dispersion of II–VI semiconductor crystallitesin a silicate glass matrix, are the basis for some com-mercially available yellow-to-red long-wavelength-passoptical filters [3.30]. The glasses with a cutoff wave-length in the visible contain CdS1−xSex nanocrystallites,and the glasses used in the infrared filters contain es-sentially CdTe nanocrystallites. Their abrupt absorptionband edge can be tuned by adjusting the composition,the size [3.31], and, as will be discussed later, theconcentration of the particles. In other widely used semi-conductors, such as Si, Ge, and III–V compounds, thevalence bands may have complex features and containlight- and heavy-hole branches. The two correspondingtypes of excitons will have different characteristics, suchas different binding energies.

The second important consequence of the squeez-ing of excitons in the strong-confinement regime isan increase in the optical matrix element associatedwith their excitation. A detailed discussion of this ef-fect can be found in [3.32]. Its origin is the strongeroverlap of electron and hole wave functions in reduced-dimensional excitons. This effect, associated with theconcentration of oscillator strength into a few discretetransitions, has found many applications in optoelec-tronic devices. Certainly the most important is thefabrication of electrically powered multiple-quantum-well (MQW) lasers in InxGa1−xAs and AlxGa1−xAs(infrared), and AlxGayIn1−x−yP (red). These systemsare widely used today in data storage systems, bar codescanners, laser pointers, and printers. The physics andtechnology of MQW lasers are far beyond the scopeof this section. Details may be found in [3.33], for ex-ample. 1-D and 0-D systems are also of interests for lasersystems [3.34]. Laser applications of quantum-confinedsystems exploit the enhanced stimulated-emission coef-ficients that result from the increased transition matrixelements and spectral sharpening in quantum-confinedsystems. Besides MBE-grown devices, optical gain inchemically synthesized CdSe nanocrystal quantum dotshas been achieved [3.35]. The operation of an op-tically pumped solid-state distributed-feedback (DFB)laser based on a CdSe-doped titania matrix gain mediumhas been demonstrated [3.36]. The output color of thislaser can be selected by choosing appropriately sizednanocrystals and tuning the DFB period accordingly (seeFig. 5.3-5).

Another consequence of the large oscillator strengthsassociated with confined-exciton transitions is the

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Mesoscopic and Nanostructured Materials 3.3 Electromagnetic Confinement 1047

2 3 hω (eV) 2 3 hω (eV)

3 5 hω (eV) 2 3 hω (eV) 2 3 hω (eV)

50 70 hω (meV)4 6 hω (eV)

10090807060

50

40

302010

5

1009080706050403020105

2 3 hω (eV)

100908070605040302010

5

1009080706050

40

30

20

10

5

10090807060

50

40

302010

5

7

100908070605040302010

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8

1007050

30

9

105

7

5

3

210.5

b) Silver

Extinction constant

2R (nm): c) Copper

Extinction constant2R (nm):

d) Aluminium

Extinction constant

2R (nm):e) Sodium

Extinction constant

2R (nm):f ) Potassium

Extinction constant

2R (nm):

h) MgO

Extinction constant

2R (µm):g) Silicon

Extinction constant

2R (nm):

a) Gold

Extinction constant2R (nm):

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1048 Part 5 Special Structures

in addition to quantum size effects (Sect. 5.3.2), totune the absorption band edge of semiconductor-dopedglasses.

5.3.3.2 Periodic Electromagnetic Lattices

Coupled Plasmon ModesThe coupling between the plasmon modes of severalclosely packed nanoparticles yields new electromag-netic eigenmodes and spectroscopic properties. Theelectromagnetic eigenmodes of some few-particle sys-tems, such as Ag and Au pairs and triplets with variousgeometries, have been computed, for instance in [3.72,Sect. 2.3.4], and have been observed directly by e-beamexcitation [3.78]. For the lowest eigenmodes, a largefield enhancement is observed in the small gap betweenthe particles.

Coupled plasmon modes have been observed ex-perimentally in regularly spaced linear chains of goldnanoparticles [3.79] and in 2-D hexagonal arrays of sil-ver nanoparticles [3.80]. The controlled propagation ofplasmon excitations in tailored metal nanoparticle struc-

tures is a new domain of application, sometimes called“plasmonics” [3.81].

Opals and Photonic-Band-Gap Materials3-D ordered arrays of nanostructures with periods of theorder of a fraction of the optical wavelength may showintense Bragg diffraction for specific wavelengths anddiffraction angles. This phenomenon is the origin of theiridescent colors (opalescence) of opals. Opals consist ofan fcc-like array of silica nanoparticles with sizes in therange 150–900 nm [3.82], with a size dispersion below5% [3.83].

For nanoscale objects with large scattering strengthsand particular geometries, spectral intervals where nopropagating mode is allowed in any direction appear,thus forming “photonic band gaps”. The idea of ex-ploiting this phenomenon in optoelectronic devices hasbeen suggested [3.84,85]. However, up to now, this phe-nomenon has been realized only in the infrared andmicrowave regions. Application in the visible, whichwould require 3-D nanostructured materials, is still un-der active development.

5.3.4 Magnetic Nanostructures

The driving force for the research on magnetic nano-structures is the possibility of their incorporation intofuture generations of information storage devices. Thiscould lead to a real technological breakthrough, anda huge economic impact is foreseen. As always, the keyquestion is whether any potential benefit of such tech-nology will be worth the production costs. Overall, thecurrent effort in this research field is considerable. Thestudy of the magnetism of nanoscale objects is charac-terized by the closeness between fundamental researchand applications. What is more, a number of magneticdevices are currently in commercial use without a fullunderstanding of the basic magnetic phenomena under-lying them. An instructive example is the following: spinelectronic phenomena have been applied rapidly sincethe first observation of giant magnetoresistance (GMR)was reported in 1988, and magnetic sensors and readheads based on this effect have been available since1994 and 1997, respectively.

Most digital information is stored in the form oftiny magnetized regions or “bits” within thin magneticlayers on disks. The size of a magnetic bit deter-mines the information storage capacity of a magneticdisk drive. The magnetic storage media used in to-day’s commercial hard disks consist of homogeneous

polycrystalline magnetic films. Owing to continuousimprovements in both the magnetic properties of themedia and the read/write heads, the storage densityof hard disk drives has increased considerably duringrecent years, as shown in Fig. 5.3-17. Since 1990, thestorage capacity of disk drives has increased at a 60%

1

0.1

0.01

10–3

1975 1980 1985 1990 1995 2000

Areal density (Gb/in2)

Date of general availability

Inductiveread/write head

21%/ year

Magnetoresistive read head57%/year

Fig. 5.3-17 Evolution of areal storage density of hard diskdrives (data from IBM, Almaden)

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3.4

Mesoscopic and Nanostructured Materials 3.4 Magnetic Nanostructures 1051

–40 –30 –20 –10 0 10 20 30 40

0.8

0.7

0.6

0.5

1 R /R (H = 0)

(Fe 30 Å/Cr 18 Å)30

(Fe 30 Å/Cr 12 Å)35

(Fe 30 Å/Cr 9 Å)40

H3

H3

H3

FeCrFe

Magnetic field (kG)

≈ 80%

Fig. 5.3-19 Magnetoresistance curves at 4.2 K of Fe/Crmultilayers. (After [3.86])

have been reported in a large number of systems com-bining ferromagnetic transition metals or alloys withnonmagnetic metals (for a review, see [3.93]). The mostcommonly used combinations of magnetic and non-magnetic layers are Co/Cu and Fe/Cr, but multilayersbased on permalloy as the magnetic component are alsofrequently used.

The second key ingredient was discovered by Parkinand Mauri [3.94]. These authors discovered that the ori-entation of the magnetic moments of two neighboringmagnetic layers depends on the thickness of the inter-vening nonmagnetic layer. In fact, the orientation ofthe magnetic moments oscillates between parallel andantiparallel as a function of the thickness of the nonmag-netic layer [3.96]. This phenomenon is referred to as anoscillatory exchange coupling. Figure 5.3-20 shows theresults of the original experiment of Parkin and Mauri.Oscillations of the GMR as a function of the Cr thick-ness occur because the magnetoresistive effect is onlymeasurable for those thicknesses of Cr for which the in-terlayer coupling aligns the magnetic moments of all theFe layers so that they are antiparallel.

GMR effects have been obtained in two geometries.In the first one, the current is applied in the plane of thelayer (hereafter denoted by CIP), as in the experimentsfor which results are shown in Figs. 5.3-19 and 5.3-20,while in the second one, the current flows perpendicu-lar to the plane of the layers (hereafter denoted by CPP).The first measurements in the CPP configuration were

30

20

10

00 1 2 3 4 5

GMR (%)

Chromium thickness (nm)

Fig. 5.3-20 Dependence of the GMR ratio of an Fe/Crmultilayer on Cr thickness. (After [3.94])

obtained by sandwiching the multilayer between twosuperconducting Nb layers [3.97]. A CPP-GMR con-figuration has also been obtained in nanowires, namelymultilayers electrodeposited in the pores of a nuclear-track-etched polycarbonate membrane [3.98], and byoblique deposition on a prestructured substrate [3.99].The CPP-GMR effect is definitely larger than the CIP-GMR effect and occurs at much larger thicknesses.

The mechanism of the GMR effect is illustrated inFig. 5.3-21 for α = (ρ↓/ρ↑) > 1, where ρ↓ and ρ↑ are

Parallel configuration

M MNM

Antiparallel configuration

M MNM

+

–

+

–

R+= 1

R–= R

R R

1 1

R

R1

1

R+= (1+R) /2

R–= (R+1)/2

Fig. 5.3-21 Schematic picture of the GMR mechanism.The electron trajectories between two scatterings are rep-resented by straight lines and the scatterings by abruptchanges in the direction. The signs + and − are for spinsSz = 1/2 and Sz = −1/2, respectively. The arrows rep-resent the majority-spin direction in the magnetic layers.M = magnetic, NM = nonmagnetic. (After [3.95])

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1052 Part 5 Special Structures

the resistivities for spins parallel and antiparallel, respec-tively, to the magnetization direction; α > 1 means thatthe resistivity is smaller for the majority spins. In theparallel configuration, the spin+ (up) electrons are al-ways the majority-spin electrons and are always weaklyscattered in all layers, resulting in a resistance r for thischannel that is smaller than the resistance R for the spin−(down) channel. The shorting of the current by this fastelectron channel makes the resistivity low in the paral-lel state (RP = r). In the antiparallel configuration, eachof the spin directions is alternately the majority and theminority one. The resistance is averaged for each chan-nel, and the overall resistance RAP = (r + R)/4 is largerthan in the parallel state. The GMR ratio is then

GMR = RAP − RP

RP = (r − R)2

4rR. (3.15)

This picture holds in both the CIP and the CPP geom-etries.

An antiparallel configuration can also be obtained inmultilayers in which consecutive magnetic layers have

2

0

–2

–200 0 200

–200 0 200

2.5

2.0

1.5

1.0

0.5

0

M (10–3 emu)b)

RTH in plane || EA

∆R/R (%)

H (Oe)

H (Oe)

H in plane || EART

c)

a)

FeMn 10 nm

NiFe 15 nm

Cu 2.6 nm

NiFe 15 nm

Antiferro-magnetic

Ferromagneticpinned

Nonmagnetic

Ferromagneticfree

Substrate

Fig. 5.3-22 (a) Schematic illustration of the spin valve multilayer originally proposed by Dieny et al. (15 nm NiFe/2.6 nmCu/15 nm NiFe/10 nm FeMn). (b) Magnetization curve, and (c) relative change in resistance. The magnetic field is appliedparallel to the exchange anisotropy (EA) field created by the FeMn layer. The current flows perpendicular to this direction.(After [3.100])

different coercivities [3.101], or by combining hard andsoft magnetic layers.

Spin ValvesThe best known structure for obtaining an antiparal-lel arrangement is the spin valve structure, originallyproposed by Dieny et al. [3.100] (Fig. 5.3-22). A spinvalve has two ferromagnetic layers (alloys of Ni, Fe,and Co) sandwiching a thin nonmagnetic metal (usuallyCu), with one of the two magnetic layers being “pinned”,i. e. the magnetization in this layer is relatively insensi-tive to moderate magnetic fields. The other magneticlayer is called the “free layer” and its magnetization canbe changed by application of a relatively small magneticfield.

As the alignment of the magnetizations in the twolayers changes from parallel to antiparallel, the resis-tance of the spin valve typically rises by 5–10%. Thegoal is to obtain the result that the magnetization of thefree layer reverses in a very small field (a few oersteds),while the magnetization of the pinned layer remains

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Mesoscopic and Nanostructured Materials 3.4 Magnetic Nanostructures 1053

fixed. Pinning is usually accomplished by using an an-tiferromagnetic layer, such as FeMn, that is in closecontact with the pinned magnetic layer. The resultantspin valve response is given by ∆R ∝ cos(θ1 − θ2),where θ1 and θ2 are the angles of the magnetiza-tion directions respectively of the free layer and ofthe pinned layer with respect to the direction paral-lel to the plane of the magnetization of the mediumwhose magnetization is being sensed, as shown inFig. 5.3-23.

The discovery of the GMR effect has createdgreat expectations, since this effect has importantapplications, particularly in magnetic information stor-age technology. The use of spin valve multilayers inhard-disk read heads was first proposed by IBM in1994 [3.102]. The principle of operation of a magneticread head will be detailed in the section on ‘Applications’below. Because the GMR effect is so important for indus-trial applications, there have been many improvementsin recent years. The simplest type of pinned layer hasbeen replaced by a synthetic antiferromagnet (two mag-netic layers separated by a very thin (1 nm) nonmagneticconductor, usually ruthenium) [3.94]. The magnetiza-tions in the two magnetic layers are strongly coupledso as to make them antiparallel, and are thus effectivelyimmune to outside magnetic fields. The second innova-tion is the nano-oxide layer (NOL), which is formed onthe outside surface of the soft magnetic layer. This NOLreduces the resistance due to surface scattering, thus re-ducing the background resistance and thereby increasingthe percentage change in the magnetoresistance of thestructure [3.103].

Exchange layer

Spacer

LeadLead

Free layer Pinned layer

y

x

M1

M2

θ1

θ2

Fig. 5.3-23 Schematic illustration of an IBM GMR spinvalve sensor used in read heads. M1 and M2 are magne-tizations,and θ1 and θ2 are angles from the longitudinaldirection. The read head moves perpendicular to thexy plane. (After [3.102])

Magnetic Tunnel JunctionsTunneling belongs to a class of electron transportphenomena known as quantum transport, “quantum”because they cannot be explained unless the wave na-ture of electrons is invoked. In the quantum mechanicalpicture, an electron is associated with a wave function ψ

related to the probability Ψ that the electron can befound in a volume dv: by Ψ = ψψ∗ dv. Quantum the-ory predicts that a particle has a nonzero probability ofpenetrating through a classically forbidden region sep-arating two classically allowed regions of configurationspace, by the process of tunneling.

The concept of tunneling has found applications ina vast number of domains in modern physics and chem-istry; the particular case of interest here is tunelingin heterostructures consisting of metallic and insula-tor films, leading to innovative electronic devices. Ina metal–insulator–metal (M–I–M) heterostructure, thepotential barrier arises from the microscopic interactionsbetween the metals and the insulator layer. By means oftunneling, an electron with an energy lower than the po-tential barrier can be transferred from one metal to theother, under the condition that the thickness of the poten-tial barrier is not too large compared with the electron’swavelength (Fig. 5.3-24).

For a long period, up to the 1970s, the spin ofthe electron was neglected in tunnel transport. In1971, Tedrow and Meservey [3.104] conducted tunnelingmeasurements on junctions between a very thin super-conducting Al film and a ferromagnetic Ni film, throughan Al2O3 barrier, in a high magnetic field. They showed

Insulating layerF1

F2

EF

0

EF

eV

Fig. 5.3-24 One-electron energy diagram for a metal–insulator–metal tunnel junction

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