Nanostructured Multilayers

Another kind of bulk nanostructure consists of periodic layers of nanometer thickness of different materials such as alternating layers of and These layered materials are fabricated by various vapor-phase methods such as sputter deposition and chemical vapor-phase deposition. They can also be made by electrochemical deposition, which is discussed in Section The materials have very large interface area densities. This means that the density of atoms on the planar boundary between two layers is very high. For example, a square centimeter of a multilayer film having layers of thickness has an interface area of 1000 Since the material has a density of about 6.5 the interface area density is comparable to that of typical heterogeneous catalysts (see Chapter 10). The interfacial regions have a strong influence on the properties of these materials. These layered materials have very high hardness,

200 150 100 3 50 0 0 5 10 15 20 25 30 Strain Strain

Figure 6.10. Stress-strain curve of nanostructured copper prepared by electrodeposition. [Adapted from L. Lu et Mater. Res. 15, 270

39 37 29 Z I 0 50 100 150 200 250 300 BILAYER PERIOD (nm)

Figure 6.11. Plot of the hardness of multilayer materials as a function of the thickness of the layers. (Adapted from B. M. Clemens, MRS Bulletin, Feb. 1999, p. 20.)

which depends on the thickness of the layers, and good wear resistance. Hardness is

measured using an indentation load depth sensing apparatus which is commercially available, and is called a nanoindenter. A pyramidal diamond indenter is pressed into the surface of the material with a load, and the displacement of the tip is measured. Hardness is defined as where is the area of the indentation. Typically measurements are made at a constant load rate of -20

Figure 6.1 1 shows a plot of the hardness of a nanomultilayered structure as a of the bilayer period (or thickness) of the layers, showing that as the layers get thinner in the nanometer range there is a significant en- hancement of the hardness until where it appears to level off and become constant. It has been found that a mismatch of the crystal structures between the layers actually enhances the hardness. The compounds and both have the same rock salt or structure with the respective lattice constants 0.4235 and 0.5151 nm, so the mismatch between them is relatively large, as is the hardness. Harder materials have been found to have greater differences between the shear modulus of the layers. Interestingly, multilayers in which the alternating layers have different crystal structures were found to be even harder. In this case dislocations moved less easily between the layers, and essentially became confined in the layers, resulting in an increased hardness.

Electrical Properties

For a collection of nanoparticles to be a conductive medium, the particles must be in electrical contact. One form of a bulk nanostructured material that is conducting consists of gold nanoparticles connected to each other by long molecules. This

6.1. SOLID DISORDERED NANOSTRUCTURES 143

network is made by taking the gold particles in the form of an aerosol spray and subjecting them to a fine mist of a thiol such as dodecanethiol RSH, where R is These alkyl thiols have an end group -SH that can attach to a methyl and a methylene chain 8-12 units long that provides steric repulsion between the chains. The chainlike molecules radiate out from the particle. The encapsulated gold particles are stable in aliphatic solvents such as hexane. However, the addition of a small amount of dithiol to the solution causes the formation of a three- dimensional cluster network that precipitates out of the solution. Clusters of particles can also be deposited on flat surfaces once the colloidal solution of encapsulated nanoparticles has been formed. In-plane electronic conduction has been measured in two-dimensional arrays of 500-nm gold nanoparticles connected or linked to each other by conjugated organic molecules. A lithographically fabricated device allow- ing electrical measurements of such an array is illustrated in Fig. 6.12. Figure 6.13

gives a measurement of the current versus voltage for a chain without (line a) and with (line b) linkage by a conjugated molecule. Figure 6.14 gives the results of a measurement of a linked cluster at a number of different temperatures. The conductance G, which is defined as the ratio of the current I , to the voltage is the reciprocal of the resistance: R = The data in Fig. 6.13 show that linking the gold nanoparticles substantially increases the conductance. The tempera- ture dependence of the low-voltage conductance is given by

where E is the activation energy. The conduction process for this system can be modeled by a hexagonal array of single-crystal gold clusters linked by resistors, which are the connecting molecules, as illustrated in Fig. 6.15. The mechanism of

Cluster array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _{. . .} . . . _{. . .} . . . _{. . .} ... _... . . . . . . : : : : : I . . . . . . _{. . .} . . . _{. . .} . . . . . . _{. . .} . . . _{. . .}

Figure 6.12. Cross-sectional view of a lithographically fabricated device to measure the electrical conductivity in a two-dimensional array of gold nanoparticles linked by molecules. (With permission from R. P Andres et al., in Handbook of Materials and Nanotechnology, H. S. Nalwa, ed., Academic Press, San 2000, Vol. 3, Chapter 4, 217.

Figure 6.13. Room-temperature current-voltage relationship for a two-dimensional cluster array: without linkage (line a) and with the particles linked by a molecule (line b). [Adapted from D. James et 18, 275

2 1.8 1 . 6 1.4 1.2 0.8 0.6 0.4 0.2 0 0 1 2 3 4 VOLTAGE

Figure 6.14. Measured current-voltage relationship for a two-dimensional linked cluster array at the temperatures of 85, 140, and [Adapted from D. James et Superlaff.

6.1. SOLID DISORDERED NANOSTRUCTURES 145

Figure 6.15. Sketch of a model to explain the electrical conductivity in an ideal hexagonal array of single-crystal gold clusters with uniform intercluster resistive linkage provided by resistors connecting the molecules. (With permission from R. P. Andres et in Handbook of

Materials and Nanotechnology, H. S. Nalwa, ed., Academic Press, San 2000,

Vol. 3, Chapter 4, p. 221

conduction is electron tunneling from one metal cluster to the next. Section 9.5 (of Chapter 9) discusses a similar case for smaller gold nanoparticles.

The tunneling process is a quantum-mechanical phenomenon where an electron can pass through an energy larger than the kinetic energy of the electron. Thus, if a sandwich is constructed consisting of two similar metals separated by a thin insulating as shown in Fig. under certain conditions an electron can pass from one metal to the other. For the electron to tunnel from one side of the junction to the other, there must be available unoccupied electronic states on the other side. For two identical metals at 0 K, the Fermi will be at the same level, and there will be no states available, as shown in Fig. and tunneling cannot occur. The application of a voltage across the junction increases the electronic energy of one metal with respect to the other by shifting one level relative to the other. The number of electrons that can then move across the

T = O . . . . . . . . T = O

Figure 6.16. (a) junction; (b) density of states of occupied levels and Fermi level before a voltage is applied to the junction; (c) density of states and Fermi level after application of a voltage. Panels (b) and (c) plot the energy vertically and the density of states horizontally, as indicated at the bottom of the figure. Levels above the Fermi level that are not occupied by electrons are not shown.

junction from left to right (Fig. in an energy interval is proportional to the number of occupied states on the left and the number of unoccupied states on the right, which is

where is the density of states in metal I , is the density of states in metal 2, and is the distribution of states over energy, which is plotted in Fig. 9.8. The net flow of current across the junction is the difference between the currents flowing to the right and the left, which is

= K - -

where K is the matrix element, which gives the probability of tunneling through the barrier. The current across the junction will depend linearly on the voltage. If the

SOLID DISORDERED NANOSTRUCTURES 147 density of states is assumed constant over an energy-range (electron volt), then for small V and low we obtain

= which can be rewritten in the form

I = where

and is identified as the conductance. The junction, in effect, behaves in an ohmic manner, that is, with the current proportional to the voltage.