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that the void growth rate will increase for future generation interconnects.

In addition, the volume of the via and line will also be scaled down.

Therefore, the combination of a faster void growth rate and a smaller void

size required to cause failure will reduce chip lifetime in every new gen-

eration. The methods of enhancing Cu electromigration lifetime should

focus on improving the Cu/dielectric interface, for example, by metal

capping or by impurity segregation on the top of the Cu line surface.

Drastic improvement in electromigration lifetimes for chips with metal

caps or impurity-rich surface layers will give exceptional flexibility to cir-

cuit designers and may rule out electromigration as the limiting factor for

use of high currents.

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Chapter-09 11/29/04 6:51 PM Page 488

10 Diffusion in Some Perovskites:

HTSC Cuprates and a

Piezoelectric Ceramic

Devendra Gupta

IBM T. J. Watson Research Center, Yorktown Heights, New York

10.1 Introduction

Understanding of diffusion processes in perovskites, represented

by the high-temperature superconducting (HTSC) cuprates and a

piezoelectric ceramic, of all the constituent elements as well as of

some foreign atomic species, is important for scientific as well as tech-

nological reasons. Self-diffusion of various cations and anion species

in these compounds is a basic material property; it has an impact on

the superconducting properties of the former and the physical response

of the latter to electrical, mechanical, and thermal fields. The interplay

of diffusion with the microstructures ultimately controls the reliability of

the devices in actual applications. One good example is the control of

twin-density and grain refinements accomplished recently through

cation doping, which in some cases alleviates the flux-pinning prob-

lem in the matrix.

[1]

There are many situations in which cation diffu-

sion manifests itself in the fabrication of HTSC elements. In the bulk

production of tapes and wires produced by the oxide-powder-in-tube

(OPIT) method, for example, silver sheath is typically used and the

composite is subjected to severe thermomechanical deformation.

[2]

such a fabrication process, silver sheath may partially dissolve in the

fabrication process and reach the oxide core by diffusion, thereby

reducing the current-carrying capacity of the connectors. Similarly,

contacts to the HTSC and piezoelectric thin-film microelectronic

devices involve metallic electrodes that typically consist of AgPd

alloys. A controlled amount of diffusion would promote adhesion and

strength between the film and the substrate in the fabrication

processes. However, large and uncontrolled diffusion may degrade the

critical superconducting temperature (T

), the critical current (J

), and

other physical characteristics, as has been shown in the substitution

studies of several metals,

[3]

and may also lead to device degradation

due to material reactions. Similarly, degradation of the dielectric con-

stants and Curie temperature may be expected in the piezoelectric

Ch_10.qxd 11/12/04 4:32 PM Page 489

490 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

ceramics, which consist of highly reactive base metals such as Pb, Mg,

Nb, Ni, Ti, Sr, and Zr.

Diffusion of the anion (oxygen) species is also important. Ordering

and stoichiometry of oxygen are directly related to the T

and J

through

the vacancy structure in the basal planes.

[4]

In this chapter it will be shown

that diffusion and stoichiometry of oxygen are themselves related to the

Cu cation self-diffusion kinetics in HTSC. We have use x to denote devi-

ation from the stoichiometry in the YBa

7x

superconductor to avoid

confusion of the usage of d for grain boundary width.

This chapter is largely based on a recent review of diffusion in HTSC

cuprates.

[5]

We first discuss the self-diffusion of all constituent cation

atomic species in the polycrystalline YBa

7x

(YBCO) compound

and its epitaxial thin films grown on (100) SrTiO

from the studies con-

ducted in several laboratories.

[6–9]

In all studies, well-characterized YBCO

specimens showing T

in the high 88 to 90 K range have been used, and

radioactive-tracer diffusion studies have typically been conducted under

an oxygen pressure of 10

Pa (1 bar). From these investigations, a com-

prehensive picture of cation diffusion in YBCO has emerged. Initially, in

Sec. 10.2.1, we discuss the general characteristics of the YBCO bulk and

thin-film specimens. Because thin films are vital for actual applications,

diffusion and interaction between the YBCO thin films and the substrate

are also discussed. This is followed by a description of the atomic mech-

anisms of self-diffusion for the three kinds of constituent cations in

YBCO, which show a marked variation due to their site preference. To a

limited extent, we describe the anisotropy of diffusion in YBCO single

crystals and the perturbations, which are caused by charge variation dur-

ing diffusion of the impurity cations. A comprehensive discussion of

anion (O) diffusion kinetics in a large number of HTSC cuprates is pro-

vided, as well as information on defect equilibria and the underlying

defect mechanisms. While the anion diffusion kinetics seem to vary

widely in the various HTSC cuprates, their overall behavior can be uni-

fied when stoichiometry and ordering of oxygen are taken into account.

From the cation Cu self-diffusion data in the YBCO, it is possible to

obtain lower and upper bounds for the diffusion kinetics for the anion (O)

species as well in the large number of HTSC cuprates examined; the

procedures to obtain them are described. Diffusion of several cations in

the same piezoelectric group of perovskites, such as PbNbNiO

(PNN),

PbTiO

(PT), PbZrO

(PZ), PbMgNbO

(PMN), and SrTiO

, and their

solid solutions, are discussed. Diffusion in the lattice and grain bound-

aries has also been studied recently in some of these materials

[10]

and

compared with the HSTC cuprates. Experimental techniques commonly

used for diffusion measurements are described by Rothman

[11]

and are not

included here.

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DIFFUSION IN SOME PEROVSKITES, GUPTA 491

10.2 Cation Diffusion

10.2.1 Characteristics of YBCO Bulk and Thin-Film

Specimens

In general, diffusion in materials is very sensitive to their microstruc-

ture, as discussed in Chapter 1. Defects such as dislocations and grain

boundaries enhance diffusion by many orders of magnitude. Oxides and

ceramic materials are no exceptions in this respect. In fact, interconnected

sintering porosity, commonly present in this class of sintered materials,

becomes an additional source for acceleration of diffusion. Microstructural

defects manifest themselves in several ways: They increase the depth of

diffusion, lower the activation energy, and distort the diffusion profiles,

causing nonlinearity in the log of the specific activity vs. the penetration-

distance-squared Gaussian plots. Generation of non-Gaussian profiles is

the first indication that the short-circuiting paths in the microstructure

Figure 10.1 Polarized light micrograph of the bulk YBa

7x

showing single-

phase microstructure with more than 96% density in the area imaged. The heat

treatment in O

produced univariant twinning in each grain.

[7]

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