i

Materials Science and

Engineering Laboratory

Nanometrology:

FY 2003 Program and

Selected Accomplishments

MSEL

Clare Allocca

Senior Scientific Advisor to the Director, MSEL

Stephen Freiman

Deputy Director, MSEL

NISTIR 7074

January 2004

National Institute of

Standards and Technology

Arden L. Bement, Jr.

Director

Technology

Administration

Phillip J. Bond

Undersecretary of

Commerce for Technology

U.S. Department

of Commerce

Donald L. Evans

Secretary
ii

Certain commercial entities, equipment, or materials may be identified in this document

in order to describe an experimental procedure or concept adequately. Such identification

is not intended to imply recommendation or endorsement by the National Institute of

Standards and Technology, nor is it intended to imply that the entities, materials, or

equipment are necessarily the best available for the purpose.
iii

Table of Contents

Table of Contents

Nanometrology Program ........................................................................................................ 1

Nanomechanics

Metrology for Nanoscale Properties:

Nanoscale Mechanical Properties ....................................................................................... 3

Nanoscale Measurement of the Amount of Complex

Hydrocarbon Molecules on Magnetic Hard Disks.............................................................. 4

Physical Properties of Thin Films and Nanostructures:

Mechanical Properties of Thin Films ................................................................................... 6

Physical Properties of Thin Films and Nanostructures:

Mechanical Properties of Low-κ Dielectric Films .............................................................. 7

Physical Properties of Thin Films and Nanostructures:

Green’s Function Methods ................................................................................................... 8

Micrometer-Scale Reliability:

Bridging Length Scales ........................................................................................................ 9

Nanocharacterization

Critical Dimension Metrology of Nanoscale Structures with

Small Angle X-ray Scattering ............................................................................................. 10

Elastic Flow Instability in Polymer-Dispersed Carbon Nanotubes ................................... 12

Multiscale Modeling of a Gold Nanoisland in a

Million-Atom Copper Crystallite ........................................................................................ 14

Gradient Combinatorial Reference Specimens for

Advanced Scanned Probe Microscopy .............................................................................16

Bridging Length Scales in Theory and Modeling:

Microstructure Evolution and Material Mechanics ........................................................... 18

Particle Metrology and Standards ...................................................................................... 19

Metrology for Nanoscale Properties:

Conductive AFM Using Carbon Nanotubes...................................................................... 20

Metrology for Nanoscale Properties:

Brillouin Light Scattering .................................................................................................... 21

The NIST Center for Neutron Research (NCNR) ..........................................................22

Nanoelectronics

Pore Size Distributions in Low-κ Dielectric Thin Films

from SANS Porosimetry .................................................................................................... 24

Advanced Metallizations for Sub-100 nm Electronics ...................................................... 26
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Nanomagnetics

Modeling Dynamics, Damping and Defects for

Perpendicular Magnetic Recording Media ........................................................................ 28

Magnetic Properties of Nanostructured Materials............................................................ 30

Nanomagnetodynamics ...................................................................................................... 31

Anomalously Large Low Temperature Intermixing in Metallic Thin Films...................... 32

Detecting Magnetic Nano-Twists in Hard-Disk Reading Heads

Using Polarized Neutron Scattering ..................................................................................33

Nanomanufacturing

Nanomanufacturing ............................................................................................................ 34

Process Monitoring of Polymer Clay Nanocomposites .................................................... 35

Electrochemical Processing of Nanoscale Materials ........................................................ 36

Organizational Charts ........................................................................................................... 37

Table of Contents
1

Nanometrology Program

Nanometrology Program

The emphasis on nanotechnology around the world is

leading to the development and commercialization of

unique products based upon significantly smaller devices

and material ensembles. Materials at the nanoscale in

three dimensions (NEMS, MEMS), two dimensions

(ultrathin films), and one dimension (carbon nanotubes)

are growing in importance. Within the next few years

novel devices at the micro- and nanoscale are expected

to play key roles in a spectrum of industry sectors,

including manufacturing, information technology,

electronics, and healthcare. Nanometrology,

i.e., the measurement of dimensions, characterization

of materials, and elucidation of structures of new and

novel materials at the nanoscale, will be critical to the

commercial development of this exciting new field.

The objective of the MSEL Nanotechnology Program

is the development of metrology at the nanoscale for

bulk and surface material properties as well as process

monitoring. The Program encompasses metals, ceramics,

and polymers in various forms — particles, thin films,

nanotubes, and self-assembled structures. The Program

is divided into five categories: Nanomechanics,

Nanocharacterization, Nanoelectronics,

Nanomagnetics, and Nanomanufacturing.

This report contains short descriptions of selected

accomplishments in these five areas.

A primary focus of nanomechanics is the measurement

and understanding of mechanical properties of materials

at the nanoscale, as well as prediction of nanomechanical

properties based upon those in bulk materials. As one

example, four methods for the determination of the

elastic properties of thin films — atomic force acoustic

microscopy, surface acoustic wave spectroscopy,

Brillouin light scattering, and nanoindentation — are

being compared using common sets of specimens.

This study should lead to a better understanding of the

complementary nature of these techniques for measuring

a fundamental property of nanostructured materials and

their combined use to determine supplementary properties

such as film thickness or density. Reference materials

for use in nanoindentation are being developed in

collaboration with other National Measurement Institutes.

Another aspect of mechanical properties at the nanoscale

is that of nanotribology, the study of nanoscale friction

and wear. Friction and stiction have been identified as

key issues in the implementation of new devices based

upon nanoelectromechanical technology, i.e., NEMS.

Recent work has involved the study of lubrication

of magnetic hard discs.

One of the projects in nanoelectronics involves the

quantitative determination of nanometer-size pore

distributions in low dielectric constant films using

small angle neutron scattering. This work has revealed

subtle material characteristics hitherto unrecognized

by other techniques. A second project encompasses

the development of models and the accompanying

verification of advanced metallization techniques for

sub-100 nm electronics. This work is focused on the

development of processes for superfill of fine features

in electronic devices and extends already developed

models for such mechanisms. Finally, small angle

x-ray scattering is being employed to measure the

critical dimensions in pattern sizes for the

semiconductor industry.

In the broad area of nanocharacterization, a number

of topics are under investigation. New measurement

procedures and reference materials for determining size

distributions for nanoparticles (< 500 nm) are being

addressed. Another exciting area of nanotechnology is

the use of carbon nanotubes in ultra-stiff and strong

composites, as electronic components, and as probes

for use in scanned probe microscopy. During this

past year, MSEL, in partnership with NASA and other

NIST Laboratories, held a workshop whose goal

was to identify the crucial measurement issues with

respect to purity and dispersion of carbon nanotubes.

Measurement protocols and conclusions emerging

from this workshop will be published in the Journal

of Nanoscience and Nanotechnology. A second such

workshop is being planned for September of 2004.

MSEL has considerable experience in the measurement

of parameters critical to nanomagnetics. For example,

the shift to perpendicular magnetic recording presents

issues in the dynamics, damping, and defects in

recording media. MSEL is conducting modeling and

measurements of ferromagnetic resonance on these

materials. Work is also being carried out in the

determination of the magnetic properties of

nanostructured materials using a magneto-optic

indicator film technique.

As an aid to carrying out nanomanufacturing processes,

measurement procedures are being developed to measure

flow properties of fluids at the nanoscale. Also, sensors

are being investigated that can be used to monitor

processing of polymer-clay nanocomposites.

Finally, MSEL supports several unique measurement

instruments including the NIST Center for Neutron

Research, and synchrotron x-ray beamlines at

both the National Synchrotron Light Source at the

Brookhaven National Laboratory and the Advanced

Photon Source at the Argonne National Laboratory.

Each of the facilities has developed instrumentation

to be able to measure features of nanometer

dimensions. In addition, combinatorial materials

synthesis procedures are being addressed as part of

a multiclient consortium. Details of this consortium

can be accessed at www.nist.gov/combi.
2
3

Metrology for Nanoscale Properties:

Nanoscale Mechanical Properties

We are developing AFM-based techniques

to measure nanoscale mechanical properties in

situ. Atomic force acoustic microscopy enables

quantitative point measurements of elastic

modulus as well as images of relative stiffness.

The information obtained furthers our understanding

of the nanomechanical properties of surfaces and

thin-film structures.

Donna Hurley

The accelerating race towards the nanoscale presents

a serious challenge for materials characterization.

Tools that can assess properties with submicrometer

spatial resolution must be developed. Specifically, the

need exists for nanoscale mechanical-property information.

Knowledge of properties like elastic modulus or stiffness

and interfacial quality (defects, adhesion, strain) is critical

to successful development of new film materials and

nanoscale assemblies. Likewise, such information could

help assess integrity or reliability in applications ranging

from microelectronics to biotechnology.

To fill this need, we are developing tools that exploit

the spatial resolution of atomic force microscopy (AFM).

Our approach, called atomic force acoustic microscopy,

(AFAM), involves exciting mechanical resonances of

the AFM cantilever when in contact with a sample. By

comparing spectra for the unknown (test) material and a

reference sample with known properties, the indentation

modulus M can be measured. The small tip diameter

(~ 20–100 nm) means that we can obtain in situ elastic

stiffness images with nanoscale spatial resolution.

In FY03, we continued developing AFAM techniques

for quantitative measurements. We examined a thin Nb

film with two reference samples and two cantilevers. Two

analysis methods were used: an analytical model for the

dynamics of a uniform rectangular beam, and a finite

element method (FEM) that allowed for a variable

cantilever cross-section. By averaging the results from

both reference materials, values for M were in very good

agreement (5 % different) with those obtained by SAW

spectroscopy and nanoindentation. For a cantilever that

approximated a rectangular beam, the analysis methods

yielded very similar values for M. For cantilevers with a

nonuniform cross-section, viscoelastic damping had to

be included in the FEM analysis. Results from the two

cantilevers were equal within measurement uncertainty.

We also examined a hydrogenated silicon carbide film

using two reference samples. Values for M with either

reference material alone were the same (M = 70 ±3 GPa)

within measurement uncertainty as those obtained from

SAW spectroscopy and nanoindentation. From these

results and those on the Nb film, we concluded that AFAM

results are more accurate when the modulus ratio

Mtest /Mreference is ~ 0.9–1.1. We are closely scrutinizing

the measurement approach and its contact mechanics to

better understand this requirement. Nonetheless, these

results demonstrate our ability to reliably and accurately

measure elastic properties at the nanoscale.

Figure 1: Specimen for AFAM RH studies. Circles indicate data

points along a line scan. Green areas show how minimum

contrast to RH sensitivity is determined. (M. Fasolka, NIST)

Potential relative humidity (RH) effects on AFAM

measurements were revealed in experiments on a film of

fluorinated silica glass. Values for M correlated roughly

with outside RH and increased as the RH increased. We

believe that the contact stiffness measurements were

affected by a variable water layer between the tip and

sample. We are working on laboratory RH control in

order to investigate the effect systematically. Samples

for these experiments, obtained in a collaboration with

Polymers Division, will contain controlled variations in

moisture sensitivity as shown in Figure 1. To interpret

the experimental results, we are refining our data analysis

models to include the effects of the water layer.

The work described above involved measurements

of the flexural resonances of the AFM cantilever only. In

upcoming months, we will extend our AFAM methods to

examine torsional resonances as well. This information

will allow us to investigate other nanoscale mechanical

properties such as Poisson’s ratio or friction.

Contributors and Collaborators

P. Rice (Materials Reliability Division, NIST);

A. Kos (Magnetics Division, NIST); M. Fasolka,

P. McGuiggan (Polymers Division, NIST); K. Shen,

J. Turner (University of Nebraska); N. Jennett (NPL,

UK); A. Rar, G. Pharr (University of Tennessee, ORNL);

M. Kopycinska–Mueller, U. Rabe, W. Arnold (IZFP,

Germany)

Nanomechanics
4

Nanomechanics

Nanoscale Measurement of the Amount of Complex

Hydrocarbon Molecules on Magnetic Hard Disks

The requirement for protection in the head-disk

interface is rising. In order to reach 1 Terabit/in2

areal density and double the data transfer rate,

the spacing between the head and disk is shrinking

to 3.5 nm at a flying speed approaching 40 m/s.

Occasional contacts will test the shear strength

of the molecular layer on top of the carbon

overcoat. Current lubricant molecules are alcoholfunctionalized perfluoropolyether which are inert

and oxidatively resistant but lack solubility and

surface bonding strength. Alternative molecules

such as multiply alkylated cyclopentanes are being

considered to improve protection. In order for

any alternate molecules to be used, the average

molecular thickness on a hard disk surface needs

to be measured accurately at 10Å ± 1Å. We have

developed a unique master calibration technique

that, for the first time, is able to accurately determine

the average molecular thickness of a complex

hydrocarbon mixture on magnetic hard disks.

Richard Gates, Charles Ying, and Stephen Hsu

The Information Storage Industry Consortium

(INSIC) has set a goal of reaching 1Tbit/in2 areal

density by 2006 with a concurrent increase in data

transfer rate approaching 100 Gbit/s. This translates

to an extraordinarily ambitious technical goal of a

10-fold increase in capacity in four years. To reach

that goal, the flight height and the carbon overcoat

thickness need to be reduced to 3.5 nm and 1 nm

respectively. Since the disk is protected by the

thickness of the carbon overcoat and 10Å of lubricant

molecules, alternative carbons and lubricant molecules

are needed to provide the same degree of protection

with one-fifth the amount of lubricant and overcoat.

Under the proposed new design, head-disk interface

contacts are inevitable due to reduced flight height,

waviness of the disk, and rotational wobble. One of

the key characteristics that has been identified for

protective molecules is the adhesive strength to resist

high shearing action. A typical solution in this case

would be to add strongly surface-bonding molecules to

the lubricant as additives. The current disk lubricant, a

functionalized perfluoroalkyl ether, has limited solubility.

Therefore, hydrocarbon molecules with extremely low

volatility characteristics are needed. Multiply alkylated

cyclopentane is one such molecule.

Current industrial practice of measuring the thickness

of perfluoroalkyl ether on a hard disk surface (tip to valley

distance from 15 Å to 25 Å) relies on a cross calibration

between fourier transform infrared spectroscopy (FTIR)

and x-ray photoelectron spectroscopy (XPS) on CF2

bonds which is symmetrical and sharp. For complex

hydrocarbons, there are multiple peaks interrelated at

different frequencies, and there is no established technique

for such measurement.

The measurement of “average film thickness” needs

to be defined. The lubricant molecules are a complex

mixture of isomers with different molecular weights.

The surface is atomically rough, and the coverage is

below the full “monolayer” level. Nano- and microscale

aggregations undoubtedly take place, and the distribution

of molecules across the surface hills and valleys is not

known. Recent data from UC Davis tend to support

this observation. High-frequency modulation atomic

force microscopy (AFM) was used to image the

surface, and from these data, elasticity information can

be extracted. Figure 1 relates the topographic image

with elasticity of a hydrocarbon covered hard disk

surface. The bottoms of the valleys show higher

hardness suggesting that the hydrocarbon molecules

do not reside at the bottom of the valleys.

Figure 1: AFM topographic images and elasticity data.

Detection and measurement of a one nanometer

thick complex molecular layer on a rough surface taxes

the detection limits of analytical instrumentation. We first

used FTIR and a modified XPS technique. The modified

XPS technique scanned the surface twice: once without

lubricant coverage and once with lubricant coverage.

The decrease of x-ray photoelectron signal intensity

from the molecule coverage was used to estimate

film thickness. Unfortunately, the carbon overcoat

thickness was found to vary along the radial direction

of the disk. Depending on the specific batch of disks

tested, the variation could be as much as 5 %–10 % from

the inside radius to the outer edge of the disk. Hence,

this measurement technique is insufficient to measure

the “molecular thickness” as required by industry to

control the process.
5

Nanomechanics

We tried various techniques such as AFM

scratching, ellipsometry, and x-ray reflectivity (XRR).

The latter technique has difficulty with surface

roughness and the fact that the average film thickness

is below the peak-to-valley distance. For AFM, the

molecules wet the tip. Ellipsometry data at this range

have large scatter. So the conclusion is there is no

acceptable technique to measure such “film thickness”

of a complex hydrocarbon molecular mixture to the

industrial specification of 10 Å ± 1 Å.

To develop a solution to this industrially important

issue, we created a master calibration sample approach.

Basically we deposit a known (gravimetrically) solution

on a disk with a barrier film surrounding a known area

and allow the solvent to evaporate under controlled

conditions. The resulting “film thickness” can then be

used to calibrate various instruments. The challenges

are uniform distribution of molecules across the area,

containment of fluid, meniscus forces, and evaporation

rate control.

Figure 2: Confined lubricant solution on a hard disk.

Figure 3: Calibration curve relating FTIR signal to known

hydrocarbon film thickness determined gravimetrically. Error

bars are one standard deviation.

Figure 4: XPS signal calibration for known hydrocarbon film

thickness. Error bars are one standard deviation.

A calibration method for nanometer-scale complex

hydrocarbon films on an engineering surface has been

developed. The method is based on gravimetric solution

preparations and utilizes a novel freeze-evaporation

technique to extract the carrier solvent while leaving a

uniform film of complex hydrocarbon on the surface.

The method can be applied to a variety of surfaces

and offers the potential for calibrating many different

analytical techniques for their ability to measure

thickness of complex hydrocarbons.

For More Information on this Topic

S. Hsu (Ceramics Division, NIST)

Initially, this approach was attempted with liquid–phase

samples; however, under these conditions, evaporation

and meniscus forces lead to uncontrolled lubricant film

uniformity. This was solved by evaporating the solvent

from the mixture while it is in the solid state. The solution

is placed within the barrier (Figure 2) and rapidly frozen

using liquid nitrogen. Then the solvent is slowly removed

by evaporation into an inert gas at –10 °C.

By controlled slow evaporation of solvent directly

from a solid frozen state, we avoid the meniscus and

surface tension forces which tend to create non-uniformity

of the liquid mass. A pseudo “sublimation” process is

created. In this way, uniform signal detection by FTIR

confirms that the distribution of molecules across the area

is less than 5 % at less than full monolayer coverage.

Using this new technique, a series of “film thickness

calibration standards” was created (see Figure 3).

A series of three master calibration samples

was prepared and submitted for XPS photoelectron

attenuation analysis. The very small variation of XPS

intensity across the disk surface indicated that film

uniformity was quite good, varying by less than 5 %.

A correlation plot of XPS estimated thickness versus

master calibration target thickness (Figure 4) yielded a

straight line, but the slope was not 1.0 (referenced in

red). This indicates that the XPS attenuation technique

has an inherent bias due to inaccurate assumptions in

the model used in the analysis. The observation that the

slope of the XPS versus target thickness correlation is

0.6 indicates that the initial XPS attenuation technique

was underestimating the hydrocarbon film thickness

by about 40 %. The effect has been attributed to the

difference in density between the hydrocarbon and

carbon overcoat. Utilizing this information, the model

was refined to accommodate this effect.
6

Physical Properties of Thin Films and Nanostructures:

Mechanical Properties of Thin Films

We develop and apply noncontact, nondestructive

tools to measure thin-film mechanical properties

such as elastic modulus and residual stress.

Optical methods are used to determine the

frequency dependence of the velocity of surface

acoustic waves. The information obtained can

assist in developing new film materials. It is

also valuable for predicting the reliability and

performance of thin-film components.

Donna Hurley and Vinod Tewary

To successfully develop a new thin-film material,

knowledge of its mechanical properties is often

needed: to estimate surface residual stresses, to predict

reliability or performance, or to assess film-substrate

adhesion. Yet methods are generally limited to

destructive tests or even “try it and see.” Also, film

properties usually cannot be extrapolated from those

of bulk samples — if they exist.

We are developing nondestructive methods to quantify

thin-film properties. We aim to relate physical properties

like elastic moduli, residual stress, or adhesion to film

microstructure, quality or performance. The approach

exploits the behavior of surface acoustic waves (SAWs).

The SAW velocity varies with frequency and depends on

the film and substrate properties (Young’s modulus E,

Poisson ratio, density, and film thickness). We use

laser ultrasonic methods to generate and detect

SAWs over a broad frequency range. The SAW

velocity-versus-frequency data are interpreted with a

Green’s function method to determine the film properties.

In FY03, we implemented a second SAW apparatus.

Silicon and other materials are not opaque to infrared light

and thus are ill-suited to the infrared detector in the original

apparatus. The new apparatus uses a green laser in its

interferometer, extending capabilities to a wider range of

materials. In addition, a pulsed ultraviolet laser improves

generation efficiency in polymer and other films. The

apparatus is quite user-friendly, increasing accessibility

to postdocs and visitors. This setup frees up our first

apparatus for speculative experiments requiring more

frequent reconfiguring of optical components.

Analysis capabilities were improved by extending the

anisotropic Green’s function inversion software to two

layers. TiN films were analyzed with three different

models: one elastically isotropic layer, one anisotropic

layer, and two layers (isotropic TiN over hexagonal Ti).

SEM images such as that in Figure 1 show a thin Ti

interlayer, but, until now, we could not model two separate

layers. Of the three models, the velocities predicted by

the two-layer model agreed best with experimental values.

The nanoindentation and two-layer SAW values for E were

virtually identical for the thickest film. Discrepancies

in other films may be due to acoustoelastic effects or

indentation substrate effects.

The two-layer model proved valuable in other cases.

In a mini round-robin project for VAMAS TWA 22 begun

this year, we examined oxide films (TiO2 and SiO2) on

glass. SAW measurements on these transparent samples

required the addition of a Cr topcoat. The Cr properties

were fixed in the two-layer model using results from a

sample with a single Cr layer. Preliminary nanoindentation

results were in excellent agreement with the SAW results.

Also, low-k dielectric films containing secondary capping

layers were evaluated with this model (described in detail

on the next page of this report).

Although nanoindentation is in widespread use, absolute

validation by independent means is needed. The VAMAS

project above is one example of our efforts to carefully

compare SAW and nanoindentation results. We also

performed similar comparisons on a Nb film. In that case,

SAW data were obtained at both NIST and another

laboratory on the same sample. By combining SAW and

nanoindentation information so as to exploit the different

sensitivity of each method to different parameters, we

obtained a more consistent and complete set of values

than possible with either method alone. We will pursue

these and related issues (e.g., ultimate uncertainty) during

the visit of a guest scientist in late FY03.

Contributors and Collaborators

C. Flannery (Materials Reliability Division, NIST);

D. Smith (Ceramics Division, NIST); N. Jennett (NPL,

UK); U. Beck (BAM, Germany); D. Fei (Caterpillar)

Figure 1: SEM micrograph of TiN film showing preferential

crystallite orientation and adhesive Ti interlayer (R. Geiss, NIST).

Nanomechanics
7

Physical Properties of Thin Films and Nanostructures:

Mechanical Properties of Low-κ Dielectric Films

Although crucial to the microelectronics industry,

implementation of low-dielectric-constant (low-κ)

films presents serious materials challenges.

We apply different optical methods to these

films to evaluate their critical properties:

density/porosity, Young’s modulus, and Poisson’s

ratio. The techniques provide complementary

data and allow measurement of properties that

are otherwise difficult to obtain.

Colm Flannery and Donna Hurley

Miniaturization in the microelectronics industry

 requires lowering the resistance-capacitance (RC)

factor in order to achieve faster device switching. This

requires replacing standard silica dielectrics with materials

of a lower dielectric constant (κ). The most promising

way to achieve this is to introduce nanometer-sized pores

that reduce κ as porosity increases. An unwanted byproduct is a drastic reduction of mechanical properties.

The very low Young’s modulus of porous low-κ films

lessens the chance of their surviving the microelectronic

chemical-mechanical polishing process and affects

process reliability. Accurate values of film modulus must

therefore be known. However, few tools are available to

characterize such relevant thin-film properties and their

dependence on porosity. Nanoindentation, a standard

industry technique, is challenging on such soft films

and generally tends to overestimate stiffness significantly.

As an alternative, we are developing optical techniques

to enable non-contact property measurement.

Brillouin light scattering (BLS) relies on a

photon–phonon collision process where incident photons

collide with ambient thermal phonons in the material. The

frequency shift of the scattered photons, detected by a

scanning Fabry–Perot interferometer, is characteristic

of the acoustic phonon modes in the film. With BLS,

we examined a series of methylsilsesquioxane (MSSQ)

polymer films of varying porosity. We could detect both

longitudinal and surface acoustic wave modes and, thus,

could determine values for both Poisson’s ratio ν and

Young’s modulus E. Figure 1, which plots the values

of ν obtained in these films vs. porosity, reveals that ν

decreases as porosity increases. This is important since

the dependence of n on porosity is not well understood.

Very few techniques have been able to provide

experimental data to address this issue. BLS appears to

be a very promising tool with which to explore this area.

Figure 1: Poisson’s ratio vs. porosity for MSSQ films.

Figure 2: Young’s modulus determined by SAWS and BLS.

 In addition to BLS, frequency-dependent dispersion

of laser-generated surface acoustic waves can yield

accurate measurements of the density and Young’s

modulus of thin films. In FY03, we implemented a new

SAWS apparatus optimized to inspect thin films on silicon

and paid special attention to developing a robust data

analysis procedure. Figure 2 compares values of E

obtained by BLS and SAWS for a range of low-κ films.

The results show a clear correlation but with a systematic

difference between the techniques of 10–15 %. Reasons

for this small discrepancy are being investigated. (SAWS

density values have also been verified by x-ray reflectivity

measurements).

We are also characterizing two-layer samples (low-κ

film with a thin capping layer), interpreted using our

newly-developed two-layer Green’s function analysis

code. Preliminary results show that SAWS is sensitive

to the presence of capping layers as thin as 50 nm.

Work in the coming year will concentrate on extending

SAWS and BLS measurements to multilayer samples,

analyzing measurement uncertainties, and developing a

standard SAW thin-film data analysis procedure.

Contributors and Collaborators

S. Kim, V. Tewary (Materials Reliability Division,

NIST); W. Wu (Polymers Division, NIST);

J. Wetzel (Tokyo Electron America)

Nanomechanics
8

Physical Properties of Thin Films and Nanostructures:

Green’s Function Methods

We have developed computationally efficient

techniques and computer codes for calculating

elastic Green’s functions with virtual forces and

boundary-element method for application to

a variety of elastostatic and elastodynamic

problems in advanced materials systems such as

semiconductor and metal substrates containing

thin layers and nanoinclusions. Many of these

codes are available from our library of Green’s

functions at the NIST website on the Internet.

Vinod Tewary and Bo Yang

Technical Description

Mathematical modeling of the elastic response of

 anisotropic materials is required for interpretation

and design of experiments leading to industrial

applications of advanced materials system such as

metals and semiconductors with multilayer coatings

or quantum nano-inclusions. The elastodynamic and

elastostatic Green’s functions (GFs) are used for

modeling the propagation of elastic waves, and for

calculations of stresses and strains.

We are developing a new defect GF method for elastic

response of composite material systems such as thin layers

on a substrate or nanoinclusions in a host solid. The defect

GF method is well known in discrete lattice statics but is

new in continuum mechanics. The traditional technique

for solving elastic problems in composite materials consists

of solving the equations of elastic equilibrium in different

regions and then coupling them with appropriate continuity

conditions. We define the defect GF that gives the

response of the composite system and seems to be

computationally more convenient. The defect GF, denoted

by G*, is related to G; the GF of the host solid through

the Dyson integral equation as follows:

G* = L*–1 = (L – ∆L)–1 = G + G ∆L G*,

where L* and L denote respectively the Christoffel

operators of the composite and the host solid, and ∆L

denotes the change in L in different regions.

We have extended our earlier GF method for calculating

surface acoustic wave (SAW) velocities to multilayered

substrates to account for imperfect bonding between the

film A and the substrate B by modifying the continuity

conditions at the interface as follows:

uA = μ uB,

where u denotes the displacement at the interface and

μ is the mismatch tensor (assumed to be diagonal),

and the subscripts A and B refer to solids A and B.

Accomplishments

We have applied our methods to study the formation

of surface quantum dots, static response of an anisotropic

multilayered piezoelectric structure, steady-state motion

of defects in semi-infinite solids and bimaterials, elastic

fields due to inclusions in anisotropic half space,

and SAW propagation in a TiN film on silicon with a

defective interfacial bonding. Computer codes for GF

and boundary-element method for a variety of material

systems are available for download from our Library of

Green’s functions at www.ctcms.nist.gov/gf. Finally,

we have actively collaborated with the formation of the

Digital Library of Green’s functions in the National Science

Digital Library project that was formally launched in

December 2002 by the NSF.

Contributors and Collaborators

D. Hurley, R.R. Keller (Materials Reliability Division,

NIST); L. Bartlolo (Kent State University); A. Powell

(M.I.T.); E. Pan (Akron University)

Figure 2: SAW velocity in TiN for μi = 0.75 (upper curve), μi = 1

(middle curve) and μi

 = 1.25 (lower curve).

Figure 1: Response to a unit point force normal to the surface of

a multilayered piezoelectric solid (InN/AlN). Vertical lines indicate

interfaces between adjacent layers.

Nanomechanics
9

Figure 1: Interaction energy (eV) between a vacancy and the free

surface in Cu (h in units of a=1.807 Å).

Figure 2: Strains at the free surface due to a gold nanoisland in Cu.

Micrometer-Scale Reliability:

Bridging Length Scales

We have developed a multiscale model for

nanostructures in solids. The model relates the

physical processes at the interatomic level to

measurable lattice distortions at the nanometer

level and macroscopic stresses and strains.

The model links the subnano (interatomic),

nano (nanostructures), and macro length scales

by integrating the powerful techniques of

molecular dynamics, lattice-statics Green’s

function, and continuum Green’s functions.

David Read and Vinod Tewary

Technical Description

Mathematical modeling is a very important tool

 for understanding the mechanical behavior of

nanomaterials and for research and design of devices

based upon nanostructures. A nanostructure needs to

be modeled at the following scales: (i) the core region

of the nanostructure (sub nanometer) where the

nonlinear effects may be significant; (ii) the region of

the host solid around the nanostructure (nanometer);

and (iii) free surfaces and interfaces in the host solid

(macro). A nanostructure causes lattice distortion in the

host solid that manifests as strain throughout the solid.

The strain is essentially a continuum-model parameter

whereas the lattice distortions are discrete variables that

must be calculated by using a discrete lattice theory.

Hence, one needs a multiscale model that relates the

discrete lattice distortions at the microscopic scale to

a measurable macroscopic parameter such as strain.

Conventional models of nanostructures are based

upon either the continuum theory, which is not valid

close to the defect, or molecular dynamics (MD) that

is CPU intensive and usually limited to small crystallites,

which may introduce spurious size effects. We need

a computationally efficient multiscale model that links

the length scales from subnano to macro and can be

used on an ordinary desktop. Such a model will be a

valuable tool for research and engineering designs.

 Our model is based upon the lattice-statics Green’s

function (LSGF) that reduces asymptotically to the

continuum Green’s function (CGF). However, the

response of the solid containing a nanostructure is given

by the defect GF that does not reduce to the CGF.

The defect GF (G*) is related to the perfect LSGF (G)

through the Dyson integral equation:

G* = G + G∆ΦG*.

Using the Dyson equation, we can write the response

of the defect lattice as a product of an effective Kanzaki

force and G,which links the perfect LSGF and the CGF.

Accomplishments

We have developed a multiscale Green’s-function

(MSGF) method that integrates LSGF and CGF and applied

it to model point defects in metals and semiconductors.

This method is suitable for a weak defect such as a

vacancy. For modeling nanostructures and other strong

defects, we have integrated this method with modified

MD in the core of the nanostructure. This integration

makes our model truly multiscale by seamlessly linking

length scales ranging from the subnano to the macro.

Our model accounts for the nonlinear effects in the core

of the nanostructure, and it provides a fast algorithm for

modeling a large crystallite. It takes only a few CPU

seconds to calculate the LSGF for a million-atom model

on a standard 3 GHz desktop.

Contributors and Collaborators

R.R. Keller, B. Yang (Materials Reliability Division,

NIST); E. Pan (Akron University)

Nanomechanics
10

Nanocharacterization

Critical Dimension Metrology of Nanoscale Structures with

Small Angle X-ray Scattering

The continued reduction in pattern sizes

throughout the semiconductor industry will

soon require new metrologies capable of high

throughput non-destructive measurements

of dense, high-aspect ratio patterns with

sub-nanometer resolution. In collaboration with

industrial partners, we are developing a metrology

based on Small Angle X-ray Scattering (SAXS)

to quickly, quantitatively, and non-destructively

measure the smallest, or “critical,” dimensions

expected in the next two technology nodes with

sub-nanometer precision. Quantities of interest

include critical dimension, pattern sidewall

angle, statistical deviations across large areas,

and quantitative measures of pattern sidewall

roughness. These efforts are driving toward the

specification of a laboratory scale device capable

of providing pattern dimensions during routine

tests of fabrication processes.

Ronald L. Jones and Wen-li Wu

The drive to reduce feature size to the sub-100 nm

 regime continues to challenge traditional metrology

techniques for pattern characterization. Determination

of the quality of the patterning process currently

depends on the production of test patterns, such as line

gratings, and evaluating dimensional control and the

number of defects. As pattern sizes decrease, existing

metrologies based on scanning electron microscopy

and light scatterometry face significant technical

hurdles in quantifying pattern dimensions and defects

in dense, high-aspect ratio patterns used in modern

semiconductor circuitry. There are currently no clear

solutions to pattern quality measurement for future

technology nodes with dimensions on the order of

30 nm and dimensional control to less than a nanometer.

To address these issues, NIST is developing a

transmission x-ray scattering-based method capable

of angstrom level precision in critical dimension

evaluation over large, (50 x 50) μm, arrays of nanoscale

periodic structures. In contrast to light scatterometry,

Small Angle X-ray Scattering (SAXS) is performed

in transmission using a sub-Angstrom wavelength.

With a wavelength more than an order of magnitude

smaller than the pattern size, the patterns can be

analyzed using methods traditionally employed in

crystallographic diffraction. The high energy of the

x-ray beam allows the beam to pass through production

quality silicon wafers without requiring a specialized

sample environment (ultrahigh vacuum). While current

measurements utilize the flexibility and wide array of

instrumentation available at a synchotron source, initial

results and the commercial availability of x-ray sources

and detectors suggests the technique is portable to a

laboratory scale device.

As shown in the schematic below, the

patterned sample is placed in an x-ray beam where

the transmitted intensity is measured as a function

of the scattering angle, 2θ, on a 2-D detector.

The intensity is then fit to models describing the

average pattern shape. To save valuable space

within the total patterned area, industrial test patterns

are typically smaller than (50 x 50) μm. Using a

monochromator to define the wavelength and two

sets of beam-defining slits, beam footprints of

approximately (40 x 40) μm have been successfully

demonstrated. In contrast to 1-D techniques such as

light scatterometry, the use of a 2-D detector allows

the simultaneous characterization of all dimensions

for patterns such as vias (arrays of cylinders standing

perpendicular to the surface) and via pads (arrays

of rectangles). In addition to measuring the pattern

dimensions along the substrate plane, measurements

at varying sample rotation angles, ω, can be used to

reconstruct the average 3-dimensional pattern shape.

In collaboration with International SEMATECH,

recent SAXS measurements of line gratings have

demonstrated the capability of SAXS to measure

fabricated patterns of thermally grown oxide with

overall dimensions designed for current metrologies.

The resulting detector image is a series of diffraction

peaks along a single diffraction axis perpendicular

to the orientation of the grating. The number of

observable diffraction orders is in part determined by

the pattern quality. The observation of over 30 orders

of diffraction suggests the relatively high quality

of these patterns and provides ample data for

Figure 1: Schematic of SAXS geometry, showing incident and

scattered beams (red lines), sample with pattern oriented at

rotation angle ω and 2-D detector (right).
11

Nanocharacterization

high-precision analysis. In addition, the number of

observable diffraction orders serves as an immediate

measure of pattern quality, termed a SAXS “fingerprint.”

With a measurement time on the order of a second,

dose exposure matrices commonly used to evaluate

optical imaging conditions can potentially be evaluated

in a matter of minutes.

In addition to the SAXS “fingerprint,” quantitative

information is obtained through model fitting of the

data. In contrast to reflection-based techniques, the

models used here are relatively simple. Quantitative

measures of the pattern repeat period and the line width

are therefore obtained rapidly and precisely. For these

samples, SAXS data have provided sub-nanometer

precision in both average repeat distance and average

line width. The precision of this measurement is in

part dictated by the number of observable diffraction

orders, which is in turn limited by the instrumental

resolution and pattern quality. Ongoing studies will

compare these results with measurements from light

scatterometry, atomic force microscopy, and scanning

electron microscopy.

In collaboration with the IBM T.J. Watson

Research Center, the effects of specific types of

defects in patterns on the resulting SAXS image are

being explored. Shown in Figure 2, a simple model

of an ideal line grating captures the main features of

the diffraction spots; however, additional information

is observed in the 2-D image perpendicular to the

diffraction axis. Streaks of intensity emanating

from diffraction peaks are visible near the beamstop.

These streaks are indicative of deviations from the

ideal grating and may provide information about

defects such as long wavelength line edge roughness.

Figure 2: Top down SEM image (top left) of a photoresist

grating on a silicon wafer compared to the resulting 2-D

SAXS image (top right). Also shown are the intensities of

the diffraction peaks as a function of scattering vector,

q (=4π /λ sin θ, where λ is the x-ray wavelength) fit with

a simple model (solid blue line).

Figure 3: Schematic of via-pad patterns (a), where the blue

rectangles represent etched regions in a low-k film, and

(b) the resulting SAXS detector image.

In addition to precisely measuring dense patterns

of etched silicon oxide, the application of SAXS has

been demonstrated for a wide range of materials that

are currently used or are being explored for use in

the microelectronics industry. We demonstrated the

capabilities of SAXS on dense patterns of organic

photoresist, silicon oxide, and nanoporous low-k

samples (detector image from 2-D array of via pads

shown in Figure 3). Additionally, measurements on

samples of copper-filled, low-k patterns demonstrate

the capability to probe multiple component and metallic

patterns. Finally, the transmission geometry allows

the probing of densely packed structures, whether

buried or exposed, providing a potential to measure

other nanoscale 3-D structures being explored for

future microelectronic devices and photonic crystals.

Continuing efforts will focus on developing

quantitative measures of line edge and sidewall roughness,

isolating specific types of long-range order defects

arising from masks, and reconstructing an average 3-D

pattern shape. In addition, further investigations will

provide precise specifications for a laboratory scale

device capable of similar measurements.

For More Information on this Topic

R. Jones, T. Hu, W. Wu, E. Lin (Polymers Division,

NIST); G. Orji, T. Vorburger (Precision Engineering

Division, NIST); A. Mahorowala (T.J. Watson Research

Center, IBM); G. Barclay (Shipley Co.); D. Casa

(Advanced Photon Source, Argonne National Laborotory)

R.L. Jones, T.J. Hu, E.K. Lin, W.-L. Wu, D.M. Casa,

N.G. Orji, T.V. Vorburger, P.J. Bolton, G.G. Barclay,

Proc. SPIE 5038, 191 (2003).
12

Nanocharacterization

Elastic Flow Instability in Polymer-Dispersed Carbon Nanotubes

Novel composites engineered from polymers

and carbon nanotubes offer the promise of

plastics with enhanced thermal, electronic, and

mechanical properties, but the ability to control

and quantify particle dispersion in such materials

is an unresolved issue of fundamental importance.

Of particular interest is how processing flows

influence tube dispersion and orientation.

We are developing metrologies and methods that

directly address the fundamental nature of elastic

flow instabilities in polymer-dispersed carbon

nanotubes, enabling better control of dispersion

during flow processing of melts and suspensions.

Erik K. Hobbie

The clustering of small spherical particles has been

 studied extensively in a broad range of systems.

In contrast, relatively little is known about the

flocculation of asymmetrical particles, such as

platelets, rods, or fibers. Given the current interest in

dispersing anisotropic nanoparticles in organic materials

to enhance physical properties, a deeper understanding

seems warranted. An almost universal aspect of

aggregation is inter-particle attraction, but external

hydrodynamic forces, often used to disperse such

particles, can alone induce clustering in highly

anisotropic suspensions, creating unique challenges and

issues relating to the flow processing of such materials.

We recently observed an elastic instability associated

with flow-induced clustering in polymer dispersed

carbon nanotubes. Kinetic measurements under varied

confinements and shear stresses were compared with

simulations of flocculation in flowing fiber suspensions,

and we found an intriguing rheological signature consistent

with highly elastic domains. Small-amplitude oscillatory

shear measurements reveal this extraordinary elasticity,

with homogenized semi-dilute suspensions showing

gel-like behavior at long time scales. The data suggest

that the underlying instability may in fact be universal

to a number of flowing complex fluids, with important

implications for the flow processing of polymer-carbon

nanotube composites.

Multi-walled carbon nanotubes (MWNTs) were

grown via chemical vapor deposition. A typical electron

micrograph is shown in the inset to Figure 1(a). Based

on such measurements, the mean diameter is d ≈ 50 nm.

Due to their length and optical contrast, individual

MWNTs are discernable in optical micrographs of 25x

or higher, and from 200x images of thin-film dispersions,

the mean length is L ≈ 12 μm. The suspending

polyisobutylene fluid (PIB) is Newtonian over a broad

range of shear rates, with a shear viscosity of 10 Pa-s

at 25 oC. Dispersions are prepared by dissolving the

PIB in sonicated MWNT-toluene suspensions, which

are stirred continuously as the solvent is removed.

Suspensions of primary interest contain 1.7 x 10–3

mass-fraction MWNT in PIB and are semi-dilute,

with nL3 ≈ 45 and nL2d ≈ 0.19, where n is the

number of tubes per unit volume. The tubes in PIB

are non-sedimenting over the time scales in question.

Figure 1: (a) Optical micrograph of MWNTs in a quiescent PIB

dispersion. The inset (width = 1.3 μm) is a SEM image of the

MWNTs before dispersion in PIB. (b) Optical micrograph 30 min

after quenching the mixture to a shear rate of γo = 0.03 s–1.

The flow (x) direction is horizontal. (c) Optical micrograph 2 h

after the quench. (d) Optical micrograph 15 min after quenching

the sample in (c) to γm= 10 s–1.

.

.

Optical microscopy (5x to 25x) is used to observe

the motion of MWNTs and the formation of aggregates

under shear, with flow along the x-axis, a constant

velocity gradient along the y-axis, and vorticity along the

z-axis. Measurements are taken in the x–z plane. The

sample is confined between two parallel quartz plates

separated by a variable gap, h. The upper plate rotates

at an angular speed that sets the shear rate, γ = ∂νx /∂y,

at a fixed point of observation in the middle of the

plates. A controlled-strain rheometer in cone-and-plate

and parallel-plate configurations provides steady

and oscillatory shear measurements of the rheology.

All measurements were performed at 25 oC.

The aggregates have “melted” and the redispersed

tubes broadly orient with the direction of flow, as

evident in the light-scattering pattern (inset Figure 1(d),

scale bar = 1 μm–1). The scale bar is 10 μm and the

gap (h) is 70 μm.

.
13

Nanocharacterization

Figure 2: Evolution of a confined dispersion (upper), where

the micrographs have been converted to binary images.

The lower images are the corresponding c(r). The flow direction

is horizontal, the vorticity axis is vertical, and the red scale bar

(125 μm) applies to all six images. As in Figure 2, h = 70 μm.

The inset to the lower left image is its FFT (width = 1.2 μm–1),

which gives the ubiquitous “butterfly” pattern.

coefficient of friction. Our measurements are in

agreement with simulation. With an elastic bending

modulus 103 times larger than that of a typical fiber,

the MWNTs are flexible enough to exhibit shape

deformation, yet they readily entangle and interlock to

form large coherent structures under weak shear. Held

together by elastic forces, the diffuse clusters store

sizeable energy, which we infer from linear viscoelastic

measurements of the storage modulus, G′(ω), as a

function of n. Other unusual features, such as a

negative first normal stress difference, are currently

under in-depth investigation.

We have observed the early-time domain pattern

[Figure 2 (left), weak minima in c(x)] in a host of

flowing complex fluids, including polymer blends,

semi-dilute polymer solutions, physical polymer–clay

gels, and thixotropic clay gels, all of which fall within

the simple paradigm of weakly interacting elastic

domains suspended in a less viscous fluid. The

homogenized semi-dilute dispersions also exhibit

solid-like behavior at long timescales, suggesting

the presence of a weak “network” or gel, further

reminiscent of other systems that exhibit this type

of flow-induced macrostructure. The role of

confinement in the growth of periodic structures

in these systems is intriguing and merits detailed

computational consideration. We expect that

these issues will have direct consequences for

the processing of nanocomposite melts, and we

are currently extending these measurements to

single-walled carbon nanotubes.

For More Information on this Topic

E.K. Hobbie, S. Lin–Gibson, J. Pathak (Polymers

Division, NIST); H. Wang (Michigan Tech); E. Grulke

(University of Kentucky)

Figure 3: The measured late-t “pattern diagram” in the h – γ

plane for the semi-dilute, non-Brownian MWNT-PIB suspensions

of interest, with homogeneous (H), aggregated (A), and

“striped” (S) regions as indicated.

.

Under weak shear, the tubes form macroscopic

domains consisting of diffuse MWNT networks.

Figure 1 shows optical micrographs of (a) a quiescent

dispersion, (b & c) aggregation at γo = 0.03 s–1,

and (d) redispersed MWNTs after dissolution at

γm = 10 s–1, where light scattering reveals a

steady-state distribution of orientations broadly peaked

around x. In simple shear, the long axis of an isolated

rod rotates around z with a period, τ, that scales as γ –1.

In semi-dilute suspensions, hydrodynamic interactions

determine the distribution of such orbits. The Peclet

number is less than 10–4, implying that hydrodynamic

forces overwhelm Brownian forces.

.

.

8

8 .

By varying h, we observe the transition from bulk

to confined growth. To quantify the latter, we convert

micrographs into binary images in which the clusters

are black and the surrounding fluid white (upper images,

Figure 2), defining a coarse composition field ψ(r).

Ensembles at each annealing time, t, are used

to compute the two-point correlation function,

c(r) = 〈ψ(r)ψ(0)〉 (lower images, Figure 2), and

the steady-state morphology diagram in the h – γ plane

is shown in Figure 3. In region A, moderate aspect

ratio domains exhibit broad vorticity alignment. 

In region S, these domains coarsen along z into

macroscopic striped patterns. The dashed curve

marks a region of “metastability” in which the striped

pattern is transient.

Recent simulations of flow-induced flocculation

in non-Brownian fiber suspensions suggest that interparticle friction leads to aggregation in the absence of

attractive interactions, particularly at low-shear stress

and high-fiber stiffness. The MWNT bending modulus

can be compared with values for typical organic fibers,

as can the shape of the inter-particle potential and

.

8
14

Multiscale Modeling of a Gold Nanoisland in a

Million-Atom Copper Crystallite

Modeling and simulation are playing key roles in

the discovery and interpretation of nanoscale and

atomic-scale phenomena. Multiscale modeling

is the most efficient way to include surfaces

accessible for measurements in models of

atomic-scale phenomena. The brute-force

approach would require treating millions or

even billions of atoms explicitly. A copper

cluster of 1 billion atoms has a side of only

0.23 micrometers, so the desirability of the

multiscale approach is clear.

Vinod Tewary and David Read

Our multiscale modeling approach combines

molecular dynamics (MD) with a recent

extension of Green’s function (GF) analysis. We divide

the physical system to be analyzed into a core, where

the strong, non-linear interactions of interest occur,

and an outer core, a shell and a host solid, where the

atomic interactions become progressively more linear

(termed “harmonic”) and the strains decrease to elastic

levels. Harmonic behavior can be treated with much

less effort, and much less computer power, than

nonlinear atomic interactions. In the core, MD is used

to maintain the capability to treat strongly nonlinear

interactions. The outer core is the region where all the

atoms are near their perfect-lattice positions. The core

atoms are contained by the shell atoms, which are

shared between the MD and GF models, but controlled

by the harmonic interactions described by the GF.

Outside the shell, the atoms blend into the continuum.

Surfaces, with associated strains and displacements,

can be placed in the harmonic-lattice or continuum

GF regions.

We selected the vacancy in copper as our initial

problem to develop and test the method; then we

applied the method to a gold nanoisland in a copper

matrix. The energy of the vacancy turns out to

depend only very weakly on the size of the crystallite

considered, so problems in the multiscale approach

would have shown up clearly. Even as late as the

1960s, the energy of formation of a vacancy had not

yet been calculated accurately. Damask and Dienes,

writing in 1963, list values from 0.81 to 1.2 eV.

The latest experimental value is given by Wollenberger

to be 1.28 ± 0.05 eV. The energy of formation of

the vacancy could not be evaluated properly using

the pairwise atomic interactions developed during the

1970s and 1980s. However, in the late 1980s and early

1990s, workable many-body potentials were developed.

These potentials, fitted to experimental elastic

constants, produced accurate vacancy energy values.

Here we use a “second moment–tight binding” potential

reported by Cleri and Rosato in 1993. It is a very

long-range potential, out to fifth neighbors, and

parameters were given for mixtures of gold and

copper, as well as for the elements individually.

The MD method can evaluate the formation energy

of the vacancy; of course, the result depends on the

parameters of the MD model used, and the vacancy

energy is often considered in fixing the parameters.

Both the MD and GF models can calculate the

displacements that occur when an atom is removed

from a crystallite to create a vacancy. We carried

out such calculations with the MD and GF models

separately, and they agreed. Then we combined them

in the multiscale approach. The multiscale calculation

for 216,000 atoms converged after only one iteration.

Figure 1 shows the relaxation, and also shows that

the strains caused by the vacancy are concentrated in

the 100 or so atoms nearest the vacancy. The energy

of formation of the vacancy includes these deviations

from the perfect-crystal energy.

The MD and GF models cooperate closely in the

multiscale calculation. The MD model controls the

core atoms, and calculates forces on the shared atoms,

which are regarded as fixed within the MD calculation.

The GF model, in turn, calculates displacements for the

shared and outer-core atoms. Because the potential is

Figure 1: Multiscale model evaluation of the energy of a vacancy

in a copper lattice. The vacancy is created, then the configuration

relaxes iteratively to its minimum energy configuration. The MD

core contribution to the energy is the largest, because it includes

the missing interatomic bonds. Strains in the outer core and the

host add to the energy. The latest published experimental result

is 1.28 ± 0.05 eV.

Nanocharacterization
15

many-body, the force on an atom depends on

the position of all its neighbors. This dependence

is especially pronounced in the fifth neighbor

Cleri–Rosato potential used here. The key

mathematical “trick” of our multiscale approach is

that the many-body force contributions from the host

atoms, which are not included in the MD model but

are required to get the forces on the shell atoms

correct, are evaluated using the equilibrium conditions

enforced by the GF model for the outer core, shell,

and host regions. As the minimum energy condition

is approached, the atomic displacements are smaller

so that eventually these forces become constant and

the iteration converges.

By replacing 63 atoms within a million-atom copper

lattice with gold atoms, we created a gold nanoisland

within the copper matrix. Gold’s face-centered-cubic

(fcc) unit cell is 13 % larger than that of copper; the

unknowns were how much the expansion of the gold

island would be restrained by the surrounding copper,

and what form of the strain and displacement fields

around the gold island would be. These turned out

to be surprisingly complex. Because the GF model

includes the capability to account for a free surface,

these strains and displacements are experimentally

accessible using, for example, scanned probe

microscopy (SPM) or local x-ray diffraction (XRD).

This simulation required a larger MD core and shell

than the vacancy. We placed 10,156 atoms in the shell

and 5,356 in the outer core. Figure 2 shows the initial

and final positions of atoms on a section through the

gold nanoisland.

The gold nanoisland was placed near a surface to

calculate surface strains and displacements. Figure 3

shows the out-of-plane displacements. The largest

displacement does not occur directly above the

nanoisland. Rather, the displacement peaks at the

same distance out from the center as the nanoisland is

beneath the surface. That the displacement is upwards

above the nanoisland is consistent with the larger lattice

parameter of gold, compared to copper.

Figure 2: Section through gold nanoisland in copper after

partial relaxation. The red circles indicate the original positions

of the copper lattice sites. Note the short range of the displacement

field around the nanoisland. The copper nearest-neighbor

distance is 2.55 Å.

Figure 3: Out-of-plane surface displacements above an

8 Å-wide gold nanoisland located 38 Å beneath the surface of

a million-atom copper lattice. The maximum height is 0.02 Å.

Figure 4: Surface strains above an 8 Å-wide gold nanoisland

located 38 Å beneath the surface of a million-atom copper lattice.

 Figure 4 shows the surface strains above the

island. The surface strains above the nanoisland are

even more complex than the displacements because of

the elastic anisotropy of the copper elastic constants.

For More Information on This Topic

V. Tewary, D.T. Read (Materials Reliability Division,

NIST)

Nanocharacterization
16

Gradient Combinatorial Reference Specimens for

Advanced Scanned Probe Microscopy

Engineering of nanomaterials, biomaterials

and NEMS hinges on characterization techniques

that image complex nano-scale structures. In this

respect, new Scanned Probe Microscopy (SPM)

methods promise to provide nano-scale mapping

of chemical, mechanical, and electro-optical

properties. However, emerging SPM techniques

generally offer qualitative information since

probe fabrication is inconsistent and since

probe/sample interactions are not understood.

Through a suite of reference specimens fabricated

with a combinatorial design, we aim to gauge

probe quality and calibrate advanced SPM image

contrast, thereby advancing these promising

tools for nanometrology.

M.J. Fasolka, D. Julthongpiput, and

P.M. McGuiggan

Introduction

Scanned Probe Microscopy (SPM) techniques

promise micrographs that map specimen properties

with nanometer scale resolution. While current SPM

images generally afford qualitative information, some

progress has been made in quantifying SPM data.

A prime example in this regard is AFM topography

data. In this case, two factors, scanning piezo

non-linearity and unknown probe tip shape, hamper

precision measurements of specimen surface features.

Now, linearized/calibrated piezo systems ensure

micrograph dimensions. In addition, specialized

substrates with ultra sharp features can measure tip

geometry so that, in principle, tip-shape effects on

topographic data can be removed. Indeed, such

reference specimens are now available commercially.

In recent years, a new generation of SPM

techniques, which intend to measure chemical,

mechanical, and electro/optical properties on the

nanoscale, have been developed. Based upon

sample/probe interactions that are more complex

than in AFM, contrast in these new SPM images is

difficult to quantify. In particular, the development

of quantitative SPM techniques requires methods to

gauge the following factors:

■ Resolution and Sensitivity: The lateral resolution,

measurement volume, and sensitivity to measured

properties must be determined.

■ Probe Quality: Many new SPM techniques depend

upon custom-made probes, the fabrication of

which often is not reliable or uniform. Accordingly,

convenient means to characterize these probes

are needed.

■ Combination Effects: SPM measurements of,

for example, chemical properties are convoluted

with local mechanical, topographic, and other effects.

Effective reference specimens would serve to

separate the impact of these “combined” effects

on image contrast.

In response to these needs, a new research effort

initiated by the NIST Combinatorial Methods Center

(NCMC) aims to provide a suite of reference specimens

useful for the quantification of next-generation

SPM data. By design, these specimens gauge

the quality of SPM probes, calibrate SPM image

contrast through “traditional” surface measurements

(e.g., spectroscopy, contact angle), and provide

information useful for modeling complex probe/sample

interactions. The design and production of these

specimens uses bench-top microfabrication routes,

used in conjunction with the combinatorial gradientspecimen fabrication toolbox developed by the NCMC.

Here, the use of combinatorial methods is key, since

these approaches can fabricate specimens that vary

properties expected to govern SPM image contrast in

a gradual and independent manner.

Reference Specimen Design

Nanocharacterization

An example reference specimen design is

illustrated in Figure 1. Such a specimen would be

useful for quantifying chemically sensitive SPM

techniques such as friction-force AFM or Chemical

Force Microscopy (CFM), which employs a chemically

Figure 1: Schematic of gradient reference specimen for gauging

tip quality, for calibrating image contrast, and for determining

sensitivity in chemically-sensitive SPM techniques. Chemical

contrast in the patterned area is gauged via traditional measures

along the calibration areas.
17

functionalized AFM probe. The reference specimen

includes a pattern of micron-scale lines that gradually

change in their chemical contrast (e.g., surface energy)

with respect to a constant matrix. Wide “calibration”

fields, which bound the patterned area, directly

reflect the changing (or static) chemistry of the lines

(or matrix); so traditional measurements along the

calibration fields gauge chemical differences in the

gradient micro-pattern. Accordingly, for SPM

micrographs acquired along the patterned region,

the specimen calibrates the image contrast and

illuminates the sensitivity (minimum contrast) with

respect to traditional measures. In addition, for

techniques like CFM this specimen serves as a tool

for comparing the quality of tip-functionalization.

Example Route

For Specimen Fabrication

Fabrication of gradient-pattern specimens

requires soft-lithography of appropriate SAM

molecules onto a planar substrate. A composite

stamp, which has both flat and corrugated areas,

allows printing of the micropatterned strip with

the adjacent solid calibration field. Next, a graded

UV-ozonolysis (UVO), gradually modifies the

chemistry of the patterned SAM (and calibration field)

along one direction. For example, methyl-terminated

alkyl chain monolayers (hydrophobic) can be gradually

converted into carboxylic acid terminated (hydrophilic)

chains. Subsequent “filling” with a hydrophilic SAM

completes the “matrix” of the specimen. To test this

design and process, traditional micro-contact printing

of thiol-SAM “inks” onto gold substrates followed by

gradient UVO provided quality specimen prototypes.

While this validated the specimen design, ultimately

the use of delicate gold /thiol chemistry will not result

in specimens that can be stored, cleaned, and reused.

Accordingly, the next generation of reference

specimens will be fabricated using more robust

substrates and chemistries, thereby making them

viable candidates for applications such as NIST

Standard Reference Materials.

In the beginning stages of this project, we will

demonstrate novel routes for the graded patterning of

monochlorosilane (MCS) SAMs on SiO2-terminated

silicon substrates; and we will discuss the fabrication

and testing of reference specimens created through

these new fabrication approaches. The utility of these

specimens will be demonstrated with respect to

emerging SPM techniques such as CFM and Atomic

Force Acoustic Microscopy. In addition, we will show

how graded pattern specimens can be useful for the

high-throughput analysis of surface-directed behavior

in thin films of homopolymers, polymer blends and

block copolymers.

For more information on NCMC SPM research

and combinatorial methods in MSEL, see

www.nist.gov/combi.

Contributors and Collaborators

D. Hurley (Materials Reliability Division, NIST);

B. Huey (Ceramics Division, NIST); T. Nguyen, X. Gu

(Materials and Construction Research Division, NIST)

Nanocharacterization
18

Bridging Length Scales in Theory and Modeling:

Microstructure Evolution and Material Mechanics

The performance of many structural and

functional materials depends on the distribution of

composition, phases, grain orientations, internal

stresses, and microstructure on length scales from

nanometers to meters. Industry needs predictive

models to reduce the enormous costs and

development times involved in designing and

inserting new materials into state-of-the art products.

To address these needs, we are developing phase

field models of solidification and solid-state

transformations, with coupling to stress, grain

orientation and solute/vacancy dynamics.

James A. Warren and William J. Boettinger

I

n order to model the complex interfacial shapes that

 produce real microstructures, the phase field method

has become the technique of choice for computational

materials scientists.

Modeling of microstructures produced by processing

of materials involves solution of mathematical equations

for heat flow, deformation /fluid flow, and /or solute

diffusion. Boundary conditions on external surfaces

reflect the macroscopic processing conditions that

can be externally controlled. In classical models of

materials processing, boundary conditions on internal

interfaces corresponding to the liquid–crystal (grain),

grain–grain and/or phase–phase interfaces reflect

material thermodynamic and kinetic conditions. For

solid–solid transformations, stress effects also become

significant, and surface stresses become particularly

important in nanoscale microstructures. Phase field

models finesse the difficult numerical task of tracking

moving internal interfaces by the introduction of a new

variable, the phase field.

Research in phase field modeling conducted in the

Metallurgy Division is also supported by the NIST

Center for Theoretical and Computational Materials

Science. Recent efforts have focused on bringing

together many of the disparate efforts in phase field

modeling to create a unified picture of materials

processing with a single set of equations governing

microstructure evolution. In the past year we have:

■ Developed a model of a stressed system containing a

curved interface between two phases with different

elastic properties. This model has been applied to a

liquid (zero shear modulus)–solid system.

■ Simulated 3-D fault dynamics in directionally

solidified binary eutectics.

■ Combined phase field models of eutectic colony

growth with polycrystalline structures. This approach

readily deals with complex interface shapes and

topology changes (see Figure 1).

■ Simulated the growth of dendrites in polymers where

crystallographic rotation of the growth direction

occurs, “dizzy dendrites” (with the Polymers Division).

■ Prepared an overview of phase field modeling of

polycrystalline growth and coarsening (Acta

Materialia, in press).

Figure 1: A simulation of eutectic colony growth. The colors

indicate crystal orientation. The solid phase can be distinguished

as large regions of a single color while the liquid appears

essentially random in orientation at the smallest scales.

While this research is ambitious in its scale, the

successes so far suggest that the goals are within

reach. Work to be done includes joining the stress

models with existing models of polycrystalline growth,

the addition of vacancies to all of these models in a

thermodynamically consistent manner, the extension of

the grain boundary model to three dimensions, and the

coupling of all of these effects to fluid flow.

Contributors and Collaborators

J. Warren, W. Boettinger, D. Lewis, J. Guyer,

R.F Sekerka (Metallurgy Division, NIST); J. Douglas

(Polymers Division, NIST); J. McFadden (Mathematical

and Computational Sciences Division, NIST); J. Slutkser,

A. Roytburd (University of Maryland); R. Kobayashi

(Hokkaido University, Japan); L. Granasy (RISSPO,

Hungary)

Nanocharacterization
19

Particle Metrology and Standards

As technology migrates toward smaller physical

dimensions, new analytical approaches are

required to characterize material properties

and to investigate scientifically important issues.

In particle technology, these needs become

critical in the nanosize regime. Industrial

processes involving nanoparticle technology

include advanced device manufacture and

the development and production of functional

materials for microelectronic, pharmaceutical,

and biotechnology applications. Our goal

is to improve existing metrology and develop

new methods and standards for measuring the

physical and interfacial properties of nanosize

and nanostructured particle systems.

Vincent A. Hackley and James Kelly

Standard reference materials (SRMs) are critical

 for calibrating instruments used for nanoparticle

characterization. Primary customers for nanoparticle

SRMs are quality control laboratories in the ceramic and

pharmaceutical industries. This year, we have initiated

the production of a 100 nm to 500 nm particle size

distribution (PSD) SRM, the first of its kind (inorganic

material system with a broad size distribution), to fulfill

a pressing need in the sub-micrometer size range.

Interest in this TiO2-based standard has been

expressed from a wide range of industries. The SRM

will be certified for PSD using electron microscopy

and by X-ray disc centrifuge methods. Additionally,

certification of SRM 1021 was completed. This

SRM is intended for the evaluation and calibration of

equipment used to measure PSDs in the 2 μm to 12 μm

diameter range. The size range of this SRM follows

that of the coarser beads of existing SRM 1003c.

Another activity involves ultra-small angle x-ray

scattering (USAXS) of nanoparticle suspensions and

partially-gelled systems. Objectives are to develop

sensitive metrological techniques for characterizing

metastable and unstable nanoparticle suspensions and

to gain new insights into mechanisms influencing their

agglomeration and stabilization. Systems of interest

include SiO2, TiO2, and ZrO2, studied after stabilization

at pH values representing states close to and far from

the isoelectric point. For example, Figure 1 shows

discrete particle doublets (right-hand peak) in SiO2

suspensions that form only at the isoelectric pH.

USAXS allows such phenomena to be quantified to

an unprecedented level. A flow cell for in situ,

real-time USAXS studies of unstable suspensions

is under development.

This year, a new activity was initiated on interfacial

property measurements of nanostructured particulates.

The goal is to develop the measurement methodology

to obtain reliable data to establish a clear relationship

between charge development and particle size,

crystallinity and interparticle structure. Metal oxides

exposed to an aqueous phase develop charge via

protonation of surface hydroxyl sites. Surface charge

and surface site reactivity play key roles in dissolution,

precipitation and growth, corrosion, aggregation, and

sorption processes. As particle size shrinks into the

low nano-regime (< 10 nm), charge development

and reactivity are predicted to exhibit size dependent

behavior. Preliminary results indicate some potentially

important findings.

■ A systematic decrease in the isoelectric point of

TiO2 with decreasing crystallite size was observed;

data will be incorporated into modeling efforts by

NSF-funded researchers to account for proton-induced

charge formation as a function of crystal size.

■ Zeta potential measurements indicate that adducts

formed between nanocrystalline MgO and molecular

halogen species are more stable in an aqueous medium

than had been previously predicted; this has important

implications for their use as microbial biocides.

■ Small-angle neutron scattering experiments suggest

MgO may be capable of localized expansion around

individual crystallites in response to an aqueous

intrusion, without fully disrupting the assembly

structure; this would represent a unique attribute

not typically associated with inorganic particles.

Contributors and Collaborators

A. Allen, A. Jillavenkatesa, L. Lum (Ceramics

Division, NIST); L. Sung, C. Ferraris (Materials &

Construction Research Division, NIST); D. Ho (Center

for Neutron Research, NIST); K. Klabunde (Kansas State

University); U. Paik (Hanyang University); M. Ridley

(Texas Tech University); M. Machesky (Illinois State

Figure 1: Volume fraction PSD for SiO Water Survey); P. Jemian (University of Illinois) 2 at the isoelectric point.

Nanocharacterization
20

Metrology for Nanoscale Properties:

Conductive AFM Using Carbon Nanotubes

The latest integrated electrical circuits, as well as

microelectical mechanical devices, are dependent

on sub-micron features with very high aspect

ratios. We are developing a technique using

carbon nanotubes mounted to atomic force

microscope tips to probe the surface conductivity

of these devices with nanometer resolution.

The development of these tips also leads to

probing high-frequency electronic circuitry and

the electrical properties of biological specimens.

Paul Rice

We are mounting carbon nanotubes on the end

of conductive atomic force microscope (AFM)

tips to probe the surface electrical properties of

various samples with nanometer resolution. Using

these tips, we are attempting to map the sample surface

conductivity and also to probe local electric fields on

high-frequency circuits.

Carbon nanotubes have qualities that make

them very desirable as AFM probes. They can be

micrometers long and only nanometers in diameter

allowing for probing devices with deep narrow

features such as microelectrical and mechanical

systems (MEMS). In addition, there are a variety of

types of nanotubes that can have different electrical

transport properties. A nanotube can be a ballistic

conductor with very low resistance, a metallic conductor,

or a semiconductor. The nanotubes are also very

durable and can withstand multiple crashes while

imaging. For example, we have found that a nanotube

we mounted to an AFM tip will spring back after being

bent back upon itself and still provide good quality images.

We are currently developing expertise in

mounting nanotubes to AFM tips using the SEM.

Figure 1 shows an AFM image taken with a nanotube

attached to the AFM tip using our in-house technique.

The image resolution is comparable to an image taken

with a commercial AFM tip. Also, in this application,

the nanotube provides extended capabilities for

high-aspect-ratio probing, tip durability, and

electrical conductance.

Figure 1: The image above shows a topographic atomic force

microscope image of sputter deposited thin-film niobium. The

inset is a SEM micrograph of the AFM tip, fabricated at NIST,

which took the AFM image. Attached to the end of the AFM tip

is the carbon nanotube that actually probed the sample surface.

This image demonstrates the resolution and durability of a carbon

nanotube as used for AFM imaging.

Figure 2: Resistance versus voltage behavior of a multiwalled

nanotube connected to an Au thin-film test structure using electron

beam assisted deposition of carbon in the SEM.

We are also testing the electrical properties of

the nanotubes and their subsequent interconnects.

Shown in Figure 2 is the resistance versus voltage

behavior of a nanotube plus the effects of its

interconnects. The resistance response to temperature

indicates semiconductive behavior, while the voltage

response indicates nonlinear effects possibly due to

the interconnects.

Contributors and Collaborators

S.E. Russek (Magnetic Technology Division, NIST);

P. Kabos (Radio Frequency Technology Division, NIST);

D.S. Finch (Materials Reliability Division, NIST)

Nanocharacterization
21

Metrology for Nanoscale Properties:

Brillouin Light Scattering

A Brillouin-light-scattering facility is being

developed for characterizing phonons and

magnons at gigahertz frequencies in thin-film

materials. The current focus of research is on

providing information about the interactions

between magnetic modes and thermal phonons,

which play a central role in determining the

switching times of magnetic-storage devices,

spin-valve sensors, and other thin-film magnetic

devices.

Ward Johnson and Sudook Kim

Technical Description

Methods that employ Brillouin light scattering (BLS)

 for the characterization of materials measure the

intensity of spectral components of light that is inelastically

scattered by acoustic waves (phonons) or spin waves

(magnons). Fabry–Perot interferometric techniques

are used to acquire accumulated spectra through

repeated mechanical sweeping of the etalon spacing.

In this division, research employing BLS is focused

primarily on interactions of magnons and phonons in

ferromagnetic thin films. This subject is important with

respect to maximizing the speed of magnetic-storage

devices, spin-valve sensors, and other thin-film magnetic

devices because the coupling of spin waves to thermal

phonons determines the settling time of the magnetization

during a switching event. BLS has the potential of

becoming a particularly powerful tool for probing these

interactions because it can detect both magnons and

phonons at gigahertz frequencies. The aim of our research

is to characterize changes in the populations of magnons

and phonons induced by ferromagnetic resonant excitation.

Accomplishments

We have implemented techniques for

electromagnetically pumping magnons during BLS

measurements. As represented in Figure 1, an oscillating

magnetic field B′ at gigahertz frequencies is superimposed

on a constant magnetic field B0 to drive spins into uniform

precession (excite magnons with a wavevector of zero).

Scattered light undergoes a frequency shift ∆ω and a

change in direction ∆θ relative to the specular reflection,

as a result of interactions with acoustic or magnetic waves

in the film.

Figure 1: Scattering of light off waves in a thin film in the

presence of static and dynamic magnetic fields.

Figure 2: Backscattered BLS spectrum showing 8.8 GHz pumped

magnons in a film of Ni81Fe19 (0.9 % Tb).

This implementation of magnon pumping in a

backscattered configuration enables measurements

on opaque films, which cannot be studied using

forward-scattering techniques. Ongoing measurements

are focused on permalloy (Ni81Fe19) thin films

doped with Tb, which affects magnetic relaxation.

An example of a pumped-magnon spectrum from a

50 nm film of Ni81Fe19 (0.9 % Tb) is shown in

Figure 2. Counts in the range between –2 GHz and

2 GHz arise from a direct reference beam. Strong

magnon peaks appear at the 8.8 GHz pumping frequency.

Contributors and Collaborators

P. Kabos (Radio-Frequency Technology Division,

NIST); S. Russek (Magnetic Technology Division,

NIST)

(This project was partially funded by the National

Nanotechnology Initiative.)

Nanocharacterization
22

The NIST Center for Neutron Research (NCNR)

Growth in nanotechnology requires a means by

which the structure and dynamical properties of

novel nanoscale materials can be characterized.

One of the most effective techniques for this

purpose is that of neutron scattering. The NIST

Center for Neutron Research (NCNR) provides

the nation’s scientific community with a broad

suite of unique and state-of-the-art neutron

measurement capabilities, which are currently

used to characterize nanomaterials in many

different areas ranging from physics and

chemistry, to biology.

J. Michael Rowe and Patrick D. Gallagher

The NIST Center for Neutron Research (NCNR)

neutron source provides intense beams of neutrons

that are used for the characterization of novel nanoscale

materials. Neutrons reveal properties of materials that

are not available to other probes. They can behave

like microscopic magnets, diffract like waves, or set

atoms into motion as they recoil from their impact.

The wavelengths of the neutrons can be readily varied

to cover a range from less than 0.1 nm to 10 nm.

Thus neutrons can provide structural information on

the nanometer scale. At the same time, the neutrons

carry energies of order 1 meV, which is the same

order as that of motions of atoms in solids, waves

in magnetic materials, or the vibrations in molecules.

Because of this fortuitous combination of wavelength

and energy, neutrons can provide unique information

about the geometry and dynamics of nanoscale objects.

In addition to the thermal energy neutron beams,

which emanate from the heavy water or graphite

moderators, the NCNR has a large area liquid hydrogen

moderator, or cold source, that provides intense

neutron beams for the only cold neutron facility

presently operating in the United States. There are

currently 29 experiment stations located at the NCNR:

six provide high neutron flux positions for irradiation,

and 23 are beam facilities, most of which are used

for neutron scattering research. The figure provided

here shows a view of the instruments located within

the NCNR guide hall, all of which view the NCNR

cold source.

The NCNR supports important NIST research

needs, but it also operates as a major national user

facility with merit-based access made available to the

entire U.S. technological community. Each year, over

1900 research participants from all areas of the country,

from industry, academia, and government, use the

facility for measurements. Roughly 350 papers are

either published or in press each year as a result of

the research conducted at the NCNR.

Beam time for research to be published in the open

literature is without cost to the user, but full operating

costs are recovered for proprietary research. Access

is gained mainly through a peer-reviewed, web-based

proposal system with beam time allocated by a Program

Advisory Committee twice a year. For details, see

www.ncnr.nist.gov/beamtime.html. The National

Science Foundation and NIST co-fund the Center

for High Resolution Neutron Scattering (CHRNS)

that operates six of the world’s most advanced

instruments. Time on CHRNS instruments is made

available through the proposal system. Some access

to beam time for collaborative measurements with

the NIST science staff can also be arranged on

other instruments.

Nanocharacterization

Figure 1: Instruments in the cold neutron guide hall.
23
24

Nanoelectronics

Pore Size Distributions in Low-κ Dielectric Thin Films

from SANS Porosimetry

The microelectronics industry is testing a wide

variety of porous low-dielectric constant (“low-κ”)

materials for future use in integrated circuits.

To understand low-κ thin film properties, a

quantitative analysis of pore size distribution

is vital. The Electronics Materials group has

developed a new approach to this challenging

problem based on a small angle neutron scattering

(SANS) porosimetry technique. The new technique

quantifies pore size distribution and reveals subtle

material characteristics inaccessible to other

measurement techniques.

Barry J. Bauer and Ronald C. Hedden

As feature size on integrated circuits decreases to

 below 100 nm, electrical crosstalk, or interference

between interconnects, becomes a major obstacle to

device performance. A need has arisen to develop

improved electrical insulating materials for the next

generation of microelectronic devices. Silicon dioxide

and fluorosilicate glass, the insulators used in today’s

devices, have dielectric constants (κ) of about 4.2 and

3.7 respectively, but materials with dielectric constants

of 2.2 or lower will be needed by 2007. However, it

has proven difficult to improve existing materials by

changing their chemical structure.

Much of the recent developmental efforts in

low-κ dielectrics involve production of nanoporous

thin films. By introducing tiny air-filled pores into

the material, the bulk dielectric constant is lowered

because air has a dielectric constant of 1.0. The

microelectronics industry is testing a wide variety of

porous low-dielectric constant (“low-κ”) materials,

including both organosilicate and organic polymer

types. To understand the basis for their physical

properties, detailed structural characterization is

essential. Specifically, quantitative characterization

of the pore size distribution is a critical issue because

pore size impacts mechanical, thermal, and barrier

properties of the films. Because pore size is very small

(< 10 nm) and pore volume fraction is high (0.1 to 0.5),

microscopy techniques are generally insufficient for

evaluation of pore size distribution.

A new approach to pore size determination

combines the established science of capillary

porosimetry with a powerful analytical technique,

small angle neutron scattering (SANS). Capillary

porosimetry is an established experimental technique

applicable to determination of pore size distributions.

The porous material is exposed to the vapor of a “probe

solvent,” and pores fill with liquid solvent by capillary

condensation. An adsorption isotherm is constructed

by measuring solvent uptake as a function of partial

pressure. In general, filling of the pores with solvent

is size-dependent; the smallest pores fill first as solvent

partial pressure is increased. Alternatively, the sample

temperature may be varied while solvent partial

pressure is held constant. Optical, x-ray, or gravimetric

techniques may be employed to measure solvent uptake.

Figure 1 shows solvent adsorption curves obtained by

specular x-ray reflectivity (SXR) for an organosilicate

type low-κ material.

A limitation of capillary porosimetry is that pore

size is usually not directly measured but is calculated

by applying a physical model to the adsorption

data. Serious ambiguities result when hysteresis

phenomena are observed, which is normally the case

for nanoporous materials. In addition, physical models

for adsorption may fail when pores are very small, as in

the low-κ dielectrics. Conventional analysis of capillary

porosimetry data, therefore, can provide only qualitative

comparisons between low-κ materials, not quantitative

pore size distributions. However, a great improvement

to the technique is possible by using small angle neutron

Figure 1: Solvent adsorption data for an organosilicate low-κ

dielectric measured by x-ray reflectivity. Porosimetry is conducted

by two methods: under isothermal conditions while varying

solvent partial pressure in a carrier gas (green, black), or in a

saturated solvent atmosphere while varying sample temperature

(red, blue).
25

Nanoelectronics

scattering (SANS) to observe the adsorption process.

By monitoring the pore filling and unfilling with SANS,

important characteristics of the pore size distribution

can be quantified irrespective of hysteresis phenomena.

To facilitate SANS porosimetry experiments,

a programmable atmospheric control device was

constructed that uses mass flow controllers to deliver

solvent vapor in air to a flow-through sample cell.

The partial pressure P of the solvent can be varied

from 0.0 (pure air) to P* (saturated solvent vapor).

The sample may also be exposed to solvent vapor at

a constant partial pressure P while sample temperature

is varied, effectively changing P*.

The first stage of neutron porosimetry is a

“contrast match point” determination. The pores

are filled with solvent mixtures of variable neutron

scattering length density (SLD). The solvent SLD is

varied by mixing hydrogen- and deuterium-containing

analogs of the solvent. The scattered intensity I(q)

from the solvent-filled, porous material depends on

the difference in SLD or “contrast” between the

solvent and the matrix. The solvent SLD is varied

systematically, and the scattered intensity I(q) is

measured at each composition. If the material is

homogeneous in atomic composition and all of the

pores fill with solvent, a contrast match solvent

composition exists for which I(q) becomes zero over

all q. If the material has inhomogeneities in its atomic

composition, or if some of the pores are not filled by

solvent (“closed pores”), a contrast match point will not

be observed. SANS porosimetry is more applicable to

samples with a true contrast match point, as subsequent

data analysis is complicated by inhomogeneities.

The second stage of the measurements is

porosimetry using solvent vapor of the contrast match

composition. SANS data are collected as the partial

pressure of the probe solvent is increased (sorption)

and decreased (desorption). When pores fill with the

contrast match liquid, their SLD matches the sample

matrix, so the SANS measurement yields the size of

only the “empty” pores. Thus, as solvent partial

pressure is increased, pore size is measured for

sub-populations of pores of increasingly large size.

If the volume fraction of the solvent in the film

is also measured as a function of partial pressure,

then average pore size and pore volume fraction are

simultaneously known. X-ray reflectivity porosimetry

allows such measurement with high precision and

is a powerful complement to SANS porosimetry.

Figure 2 shows combined results from both techniques:

pore size from SANS is plotted vs. empty pore

volume fraction from SXR. The data are essentially

unaffected by hysteresis phenomena within the limits

of uncertainty of the experiment. When all pores are

empty, the SANS measurement gives the average pore

size for the entire distribution. As pores are filled,

the upper end of the pore size distribution is probed

because only the larger pores are empty and contribute

to I(q) from SANS. For the sample shown in Figure 2,

the average pore size is about 60 Å, but the sample

contains some pores of 80 Å or larger. By using

capillary porosimetry to isolate the scattering from the

largest pores, sub-populations of large pores within a

low-κ material can be readily identified, provided their

concentration is high enough to make a measurable

change in the scattering. Such information is valuable

to the low-κ integration effort because large pores are

a leading cause of device failure.

Figure 2: Size information (average chord length) from SANS

porosimetry plotted vs. volume fraction empty pores from x-ray

reflectivity. The scattering data contain size information related to

the average size of only the empty portion of the pores. As solvent

partial pressure is increased from P/P*= 0.0 to P/P*= 1.0

(saturated solvent vapor), pores fill with liquid solvent in order

from smallest to largest. As P/P* approaches 1.0, the scattering

from the largest pores is probed.

The SANS porosimetry technique allows

characterization of pore size distribution without a need

for a physical model for adsorption. SANS porosimetry

is perhaps the most quantitative technique available

today for characterizing pore size distribution in

nanoporous low-κ thin films.

For More Information on this Topic

B. Bauer, H. Lee (Polymers Division, NIST);

R. Hedden (Department of Materials Science and

Engineering, The Pennsylvania State University)
26

Nanoelectronics

Advanced Metallizations for Sub-100 nm Electronics

for the first time. In this process, the catalyst is

adsorbed on the patterned wafer prior to metal

deposition; in traditional copper processing, a single

electrolyte contains both the catalyst and the metal ions.

As explained by the CEAC mechanism, this process

offers the possibility of improved filling of finer features

with higher aspect ratios through minimization of the

conformal “incubation” period of growth. In addition,

the plating bath requires fewer components and is thus

easier to maintain under industrial conditions.

In a review of NIST research by International

Sematech in November 2000, Aaron Frank, Program

Manager for Copper Deposition, requested that we also

examine a growing problem for on-chip interconnects:

poor deposition of seed layers as features shrink.

In response to this request, we demonstrated in

FY 2003 that superconformal electrodeposition

directly on ruthenium barrier layers on patterned

substrates eliminates the difficulties associated with

sputter-depositing copper seeds on tantalum and

titanium nitride barriers, again allowing filling of finer

features with higher aspect ratios (See Figure 1).

Figure 1: Bottom-up copper fill during electrodeposition in

50 nm wide trenches with no copper seed is visible in the top

image. The patterned dielectric with the ruthenium barrier alone

is visible in the bottom image.

Computer codes, that quantitatively predict

superconformal deposition in fine features through the

CEAC mechanism, evaluate concentration fields in the

electrolyte as well as surface coverage of adsorbed

catalyst on a moving boundary. Our closed-form solution

for fixed initial coverage of catalyst can be used to assess

the accuracy of these codes, increasing the reliability of

Electrodeposited copper is rapidly replacing

aluminum for on-chip “wiring” because of its

lower electrical resistivity, superior electromigration

behavior, and the ability to fill fine features

without the formation of seams or voids. As

feature dimensions go below 100 nm, difficulties

in maintaining performance are anticipated. We

are addressing these issues through a combination

of modeling and experimental efforts. In FY2003,

we have pushed the quantitative limits of the

Curvature Enhanced Accelerator Coverage (CEAC)

mechanism developed in the Metallurgy Division

of NIST. Exploration of the mechanism has yielded

new electrochemical processing routes for improved

metallization and is guiding the development of

advanced metallizations beyond copper as well

as new processing routes such as ruthenium

barriers for seedless electrodeposition of copper.

Thomas P. Moffat and Daniel Josell

This project is meeting the microelectronics

industry’s need for improved device metallizations

by exploring advanced materials and process models

for superconformal film growth. In FY2003 we have:

■ Developed a two-step process for obtaining superfill

during silver electrodeposition;

■ Demonstrated superconformal feature filling using

ruthenium barriers without copper seeds;

■ Described an exact solution for feature filling under

conditions of fixed total catalyst coverage;

■ Extended the CEAC mechanism to explain surface

stabilization of planar deposits during deposition of

metals in electrolytes containing surfactant additives;

■ Quantified consumption of adsorbed catalyst

(neglected in previous CEAC models) which can

substantially affect feature filling under certain

deposition conditions.

Technical Details

Filling of trenches and vias with silver and copper

is quantitatively explained by the Curvature Enhanced

Accelerator Coverage Mechanism (CEAC) developed at

NIST. Our current measurement and modeling effort

is focused on copper and silver metallizations, the latter

metal having the lowest resistivity of any element and,

thus, having potential on-chip applications.

A two-step process for superfill of high aspect

ratio features during silver deposition was demonstrated
27

Nanoelectronics

Electrochemical and surface analytical measurements

on planar substrates were used in FY2003 to establish

rates of catalyst consumption that affect both feature

filling and, quite likely, the microstructure of the metal

deposits. Previous CEAC-based models have discounted

such consumption, and this work demonstrates the

reasonableness of such assumptions for the previously

studied conditions. It also extends the understanding

of CEAC mechanism operation to the less than ideal

deposition conditions for which catalyst consumption

is significant.

D. Josell, D. Wheeler, C. Witt, and T.P. Moffat.

“Seedless Superfill: Copper Electrodeposition in

Trenches with Ruthenium Barriers.” Electrical and

Solid-State Letters, (in press).

G.B. McFadden, S.R. Coriell, T.P. Moffat,

D. Josell, D. Wheeler, W. Schwarzacher, and J. Mallett.

“A Mechanism for Brightening: Linear Stability Analysis

of the Curvature Enhanced Accelerator Coverage Model.”

J. Electrochem. Soc., (in press).

D. Josell, S. Kim, D. Wheeler, T.P. Moffat, and

S.G. Pyo. “Interconnect Fabrication by Superconformal

Iodine-Catalyzed Chemical Vapor Deposition of Copper.”

J. Electrochem. Soc., 150 (5), C368–C373 (2003).

D. Wheeler, D. Josell, and T.P. Moffat. “Modeling

Superconformal Electrodeposition Using the Level Set

Method.” J. Electrochem. Soc., 150 (5), C302–C310

(2003).

B.C. Baker, C. Witt, D. Wheeler, D. Josell, and

T.P. Moffat. “Superconformal Silver Deposition Using

KSeCN Derivitized Substrates.” Electrochemical and

Solid-State Letters, 6 (5), C67–C69 (2003).

T.P. Moffat, B. Baker, D. Wheeler, and D. Josell.

“Accelerator Aging Effects During Copper

Electrodeposition.” Electrochemical and Solid-State

Letters, 6 (4), C59–C62 (2003).

S.G. Pyo, S. Kim, D. Wheeler, T.P. Moffat, and

D. Josell. “Seam-Free Fabrication of Sub-Micrometer

Copper Interconnects by Iodine-Catalyzed Chemical Vapor

Deposition.” J. Appl. Phys., 93 (2), 1257–1261 (2003).

B.C. Baker, M. Freeman, B. Melnick, D. Wheeler,

D. Josell, and T.P. Moffat. “Superconformal

Electrodeposition of Silver from a KAg(CN)2-KCNKSeCN Electrolyte.” J. Electrochem. Soc., 150 (2),

C61–C66 (2003).

T.P. Moffat, D. Wheeler, C. Witt, and D. Josell.

“Superconformal Electrodeposition Using Derivitized

Substrates.” Electrochemical and Solid-State Letters,

5 (12), C110–C112 (2002).

D. Josell, B. Baker, C. Witt, D. Wheeler, and

T.P. Moffat. “Via Filling by Electrodeposition:

Superconformal Silver and Copper and Conformal Nickel.”

J. Electrochem. Soc., 149 (12), C637–C641 (2002).

Our findings have also been conveyed to the U.S.

microelectronics industry, academia, and other national

laboratories through more than 15 external presentations

in the last year, including an invited presentation at

Intel’s Portland, Oregon facility. Project publications

generated 100+ citations in the past year.

For More Information on this Topic

D. Josell, D. Wheeler, T.P. Moffat (Metallurgy

Division, NIST)

their predictions when applied to more complex conditions

including catalyst accumulation and consumption.

In a development with application far beyond the

microelectronics industry, our recent publication on

the CEAC mechanism of brightening is the first to

quantitatively explain the impact of adsorbed catalyst

on surface stabilization during growth. This work is

possibly the most significant advance in understanding

surface stabilization since the growth of surface

perturbations due to concentration gradients was

first described. It is as significant to creating shiny

electrodeposits of metal on a car bumper as it is to

reducing defect-inducing surface roughness in feature

filling for microelectronics.

Figure 2: The geometry used to define the exact solution for

the superconformal filling of a trench. The metal deposits at the

bottom corners of the trench have met in the middle where a new,

even more rapidly moving, growth front emanates.

Selected Project Publications for FY2003

D. Josell, T.P. Moffat, and D. Wheeler. “An Exact,

Algebraic Solution for the Incubation Period of Superfill,”

J. Electrochem. Soc., (in press).
28

Modeling Dynamics, Damping and Defects for

Perpendicular Magnetic Recording Media

In its accelerating march toward ever higher

recording densities, the hard disk drive industry

is moving toward perpendicular recording,

where the magnetization of the written bits is

directed perpendicular to the disk surface. One

of the metrology needs generated by the shift to

perpendicular recording is the characterization

of inhomogeneity in the media. This article

describes our development of models that enable

measurement of inhomogeneity in perpendicular

media by ferromagnetic resonance.

Robert D. McMichael

One of the growing metrology needs of the hard

 drive industry is the ability to characterize the new

generation of perpendicular recording media, where

the information is stored as magnetic bits magnetized

perpendicular to the disk surface. To store these bits,

it is desirable to have media with small, nearly decoupled

grains with strong, uniform anisotropy and easy axes

directed along the disk normal. Typical grain sizes in

the new media are approximately 10 nm.

Characterization of the average properties of

perpendicular media is routinely accomplished by

magnetometry. However, there is a significant need for

information about the inhomogeneity of perpendicular

media, particularly the angular easy axis distribution

and the distribution of anisotropy fields. Inhomogeneity

of the media impacts the bit writing process, analysis

of bit stability, and media noise in the read process.

Information about the dispersion of the

crystallographic axes can be obtained from x-ray

diffraction, but magnetic coupling may force two

crystallographically distinct grains to behave as a single

magnetic grain, so a purely magnetic measurement of

the dispersion angle would be more closely related to

the performance of the media.

For variations in the anisotropy field, the only

estimates currently available are based on TEM

compositional analysis coupled with anisotropy studies

on bulk materials. Here again, a direct, purely magnetic

measurement would give a clearer indication of the

magnetic performance of the media.

The new perpendicular media, with aligned

anisotropy axes, is much better suited to ferromagnetic

resonance measurements than longitudinal media.

Ferromagnetic resonance is a peak in the transverse

susceptibility at a frequency that corresponds to

precession of the magnetization about its equilibrium

orientation. The width of the ferromagnetic resonance

peak, or “line width,” is the combined effect of damping

and inhomogeneity. While there are well-established

models for damping, better models of inhomogeneity

were needed for interpretation of line width data.

Through our modeling the dynamics of

inhomogeneous films, we have laid the theoretical

support needed for interpretation of line width data to

obtain inhomogeneity information on magnetic thin films.

Previously, there were two known models

of ferromagnetic resonance line broadening by

inhomogeneity: the “local resonance” model and

the “two-magnon” model. The local resonance

model assumes that interactions are not important,

and the line width is therefore a direct measure of the

inhomogeneity strength. The “two-magnon” model

includes interactions but, because it is a result of

perturbation theory, is limited to weak inhomogeneity.

The two-magnon linewidth depends quadratically

on the inhomogeneity strength. The models give very

different results, but both models have been successfully

used to describe separate sets of linewidth data.

Figure 1: In the absence of interactions, inhomogeneity leads

to local resonances at a distribution of frequencies, leading to

a broadened resonance line. Interactions cause narrowing of

the envelope peak described by the two-magnon model.

To understand the relationship between the local

resonance and two-magnon models of line width, we

modeled a series of inhomogeneous films with different

grain sizes and different levels of inhomogeneity, and

we computed the eigenmodes of the magnetization

Nanomagnetics
29

approximation to the line width, but for larger values of

inhomogeneity, the two magnon results will exceed the

local resonance values and the local resonance results

would be valid.

Figure 2: Line widths as a function of grain size in a Permalloy

film calculated by eigenmode analysis for three random field

strengths Hp. (Open and closed symbols are for two methods of

computing line width from the eigenmode spectrum.) The line

width transitions smoothly from the local resonance model for

large grains (weak interactions) to the two-magnon model when

grains are small. The pink line indicates where interactions and

inhomogeneity are roughly equal.

The full eigenmode analysis takes a significant

amount of computation time, making it a poorly

suited technique for data fitting. However, the results

in Figure 2 suggest a simple first approximation;

for a given combination of microstructure and

inhomogeneity, the lesser of the two-magnon model

and the local resonance model is likely to be valid,

except in the range where they are similar.

Figures 3 and 4 show two-magnon and local

resonance line width calculations for perpendicular

media with thickness 15 nm and grain size 10 nm

with an average anisotropy field of 1.4 T (14 kOe).

In these figures, the top diagram portrays the local

resonance result, the green curve is the two-magnon

model with dipolar interactions only, and the blue

and pink curves are for fractional and full exchange

coupling. For the given inhomogeneity strengths, the

two magnon model results are expected to be a good

Figure 3: Local resonance and two-magnon line widths resulting

from tilting of the easy axis directions in perpendicular recording

media with 10 nm grains. Two magnon results are calculated for

three values of exchange coupling.

Figure 4: Local resonance and two-magnon line widths resulting

from anisotropy variations in perpendicular recording media

with 10 nm grains. Two magnon results are calculated for three

values of exchange coupling.

These results show that the ferromagnetic

resonance line width can be a sensitive probe of

inhomogeneity in perpendicular recording media with

the ability to differentiate damping, c-axis dispersion,

and anisotropy variations. For weak inhomogeneity,

the two-magnon model becomes valid, and the line

width can also provide information about exchange

coupling.

A ferromagnetic resonance apparatus with the

frequency and field ranges necessary to measure

perpendicular media is in the design phase.

For More Information on this Topic

R.D. McMichael, W.F. Egelhoff, Jr. (Metallurgy

Division, NIST)

R.D. McMichael, D.J. Twisselmann, A. Kunz,

Phys. Rev. Lett. 90, Art. No. 227601 (2003).

motion (Figure 1). We found that the behavior of

the magnetization dynamics depends on the relative

strengths of the interactions and the inhomogeneity.

For a uniform film, the eigenmodes are spin

waves (“magnons” in quantum mechanics), and

inhomogeneities or strong interactions cause mixing

of the spin wave modes in agreement with the two

magnon model. For strong inhomogeneities relative to

interactions, the dynamics were localized on individual

grains in agreement with the local resonance model.

These results are summarized in Figure 2, where

small grain sizes correspond to strong intergranular

interactions, and large grains correspond to weak

interactions. These results unify the local resonance

and two-magnon models.

Nanomagnetics
30

Magnetic Properties of Nanostructured Materials

In the past 10 to 15 years, there has been a

remarkable improvement in the technology for

materials preparation, resulting in today’s

capability of controlling morphology and features

at the nanometer level. In magnetic materials,

such control allows the fabrication of nm-thick

(or separated) composite materials of dissimilar

magnetism, leading to materials with novel

magnetic character and unusual property

combinations. We provide the understanding

and metrology that allows U.S. industry to take

advantage of these new materials.

Alexander J. Shapiro and Robert D. Shull

Present day high-density data storage is possible

due to the giant magnetoresistance (GMR) spin

valve, which is now used as the read head in magnetic

disc drives. This structure is composed of two

ferromagnetic (FM) layers separated by a thin

non-magnetic layer. When an external magnetic field

reverses the magnetization of one of the FM layers, the

resistance of the composite changes. Consequently,

one FM layer must maintain a constant magnetization

during this process, usually accomplished by placing

an antiferromagnetic (AF) layer adjacent to it so as

to “exchange-bias” that FM layer. This results in a

hysteresis loop that is shifted along the field axis

as shown in Figure 1(a). Unfortunately, this

exchange-biasing is not well understood.

Neel temperature of the AF but below the Curie point

of the FM (Figure 1b). Application of the alternating

field at elevated temperatures formed a demagnetized

FM composed of striped domains with alternating

magnetization vectors, shown in Figures 1(b) and 2(a),

on top of coincident AF domains. When a field was

applied to this bilayer to saturate the FM [Figures 2(c),

(f)], there still remained a remnant image of the original

domain pattern (Figure 2a), indicating the AF wall

below the FM has not moved.

Figure 1: Hysteresis loops for a NiFe /FeMn bilayer cooled

under (a) constant and (b) alternating field conditions.

Several years ago, we found we could elucidate

some of the basics of the magnetization reversal

process in such systems [V.I. Nikitenko, et. al., PRB

57, R8111 (1998)] by using the magneto-optic indicator

film technique (MOIF) developed in our laboratory.

This domain imaging technique enabled us to show

for the first time that, contrary to popular thought, the

two sides of the hysteresis loop are not symmetrical

but are each governed by different mechanisms. This

year, we have answered another key question regarding

exchanged bias systems: do the domain walls in the AF

move when the FM reverses its magnetization? MOIF

observations were made of a NiFe (FM) / FeMn (AF)

bilayer which had been ac-demagnetized above the

Figure 2: MOIF images of domains in the FM at the conditions

specified by the positions designated in Figure 1(b).

Some AF spins in the region of the AF/FM interface,

however, are changing during the FM reversal, as

attested to by the fact that Figures 2(e) and (g) only

show domain activity in the same areas for both field

application and removal respectively, contrary to that

for a normal ferromagnet. Similar observations have

also been made on a different AF/FM bilayer, FeMn/

Fe76Mn6C18, wherein the initial coincident domain

structure in the FM and AF was created by elevated

temperature preparation under a low applied field.

As a result of these measurements, theoretical

models may now be improved, and industry should

now be able to better tailor spin valve processing to

obtain improved reproducibility. In the past year,

over 40 % of all papers on exchange-biasing have

referenced our MOIF results.

Contributors and Collaborators

V. Nikitenko, V. Gornakov (Russian Academy

of Sciences); C.L. Chien (Johns Hopkins University);

H.-W. Zhao (Chinese Academy of Sciences)

Nanomagnetics
31

Nanomagnetics

Nanomagnetodynamics

This project provides the magnetic information

storage industry with metrology for magnetization

damping and magnetic inhomogeneity in thin film

ferromagnets. Damping is expected to become a

critical issue for magnetic information storage at

GHz data rates, and inhomogeneity on the scale

of 10 nm in recording media is important for

increased storage density in the new generation

of disk drives, which will use perpendicular

magnetic recording.

Robert D. McMichael

The central issue in interpretation of ferromagnetic

resonance line width data is the determination of

how much of the ferromagnetic resonance line width is

due to damping and how much is due to inhomogeneity.

Ferromagnetic resonance is observed as a peak in

the transverse susceptibility that occurs when the

frequency of the driving field is close to the frequency

of precession. The peak position can be used to

determine sample average properties, but the width

of the resonance peak, or “line width,” is a combined

effect of damping and inhomogeneity.

Existing simple models describe the contribution of

damping to the line width. We have provided reliable

models of inhomogeneity that are key to interpretation

of line width data. These models describe the line

width behavior as a function of frequency and applied

field orientation for different types of inhomogeneity.

 Neglecting the exchange and dipolar interactions

that are characteristic of ferromagnets, local variations

in magnetic properties would be expected to result

in a distribution of local precession frequencies and a

broadened resonance peak. However, interactions tend

to synchronize the precession in neighboring regions,

effectively “smoothing” the inhomogeneity, and

reducing its effect on the line width.

Significant accomplishments in FY03 include:

■ Development of a unified model of inhomogeneous

line broadening in thin films. This model covers

the full range of inhomogeneity and interaction

strengths but is computationally too expensive to use

for fitting. This model established that the transition

from local to collective behavior is governed by

the relative magnitudes of the inhomogeneity and

the region-to-region coupling. See R.D. McMichael,

D.J. Twisselmann, and Andrew Kunz, Phys. Rev.

Lett., 90, Art. No. 277601 (2003).

■ An approximation to the full calculation of

inhomogeneous line broadening using the “two

magnon” model in the strong coupling/weak

inhomogeneity limit and local resonances in the

weak coupling/strong inhomogeneity limit.

■ Useful analytical approximations for the “two

magnon” model for ultra thin films in the limit of

zero damping.

■ Measurement of the damping properties of Cr

in proximity to Permalloy (Figure 1). These

experiments imply that ferromagnetic resonance

measurements in CoCr based hard drive recording

media will not be hindered by excessive damping.

■ Modeling of ferromagnetic resonance line widths in

perpendicular recording media under development

in industry.

Contributors and Collaborators

D.J. Twisselmann, W.F. Egelhoff, Jr., A.P. Chen

(Metallurgy Division, NIST); Andrew Kunz (Lawrence

University); H. Nakamura, M.E. McHenry (CMU);

S. Rezende (Recife, Brazil); G.S.D. Beach,

A.E. Berkowitz (UCSD)

Figure 1: Ferromagnetic resonance linewidth for a

Cr/Permalloy/Cr trilayer as a function of applied field angle.

This plot illustrates the ability to separate the linewidth into a

damping component (pink line) and an inhomogeneous component

(blue line) corresponding to 7 % variations in the effective

magnetization.
32

Anomalously Large Low Temperature Intermixing in

Metallic Thin Films

The objective of this program is to provide

assistance to U.S. companies in the ultra-high

density data storage industry, which includes such

products as hard disk drives and magneto-resistive

random access memory chips. Our work provides

U.S. companies with significant competitive help

by investigating the scientific issues underlying

the manufacturing process. Often, this scientific

understanding will point the way to improved

manufacturing processes.

William F. Egelhoff, Jr.

As the scale of microelectronic devices shrinks,

 surfaces and interfaces play increasingly important

roles as they become a larger fraction of the total

device volume. Interfaces are especially important

for the metallic thin films so common in layered device

structures. Interfaces between thin films may appear

to be abrupt at macroscopic length scales but diffuse

at atomic length scales. Fortunately, when metallic thin

films are deposited on one another at room temperature,

there is generally little intermixing at the interface.

Typically, if there is any intermixing, it is limited to one

or two atomic layers. However, recent collaborative

studies by NIST and the University of Durham have

shown that such low-temperature intermixing can be

far more extensive when Al and a transition metal (TM)

are involved.

Thin film samples of the type “Al on TM” and

“TM on Al” were prepared at the NIST Magnetic

Engineering Research Facility and analyzed by

grazing-incidence x-ray reflectometry (GIXR)

at Durham. GIXR is an ideal technique for these

studies since it is extremely sensitive to intermixing

at interfaces. We find the intermixing profile

perpendicular to the interface is usually well described

by a Gaussian distribution, as expected, since diffusion

processes often follow Fick’s Law. The results are

displayed in Table 1 as the full-width-at-half-maximum

(FWHM) of the intermixed region. The FWHM results

span the range from 0.1 nm for Al on W to 16.8 nm

for Cu on Al. This Cu-on-Al result corresponds to

approximately 100 atomic layers of intermixing.

Such results are a great surprise to researchers in

the field. For example, electronic properties for a thin

film structure consisting of 2 nm Cu /1 nm Al/2 nm Cu

were recently reported and analyzed as if the interfaces

were atomically sharp. In fact, the sample must have

been essentially a random alloy!

Among other combinations showing large

intermixing were Mn on Al with 15.1 nm and V on Al

with 9.4 nm. These surprising results suggest that the

heat of alloying is driving much more extensive chemical

reactions at the interface than had heretofore been

known. These results have important implications for

many microelectronic devices incorporating Al films.

For example, problems in magnetic-tunnel-junction

devices may be directly attributed to such phenomena.

NIST is also developing solutions to such problems

based on oxide barriers to suppress the intermixing.

Table 1: The intermixing FWHM (in nanometers)

for thin films of Al on transition metals and

transition metals on Al

TM Element Al on TM TM on Al

Ti 1.7 5.0

V 2.6 9.4

Cr 0.5 3.3

Mn 10.4 15.1

Fe 0.9 2.1

Co 0.8 6.8

Ni 1.4 7.9

Cu 2.8 16.8

Zr 1.0 5.1

Nb 0.8 3.6

Mo 1.3 3.4

Ru 0.8 5.2

Rh 0.4 4.7

Pd 4.8 5.6

Ag 2.5 4.5

Hf 2.0 4.4

Ta 0.1 0.9

W 0.1 3.5

Re 2.1 8.6

Os 0.1 7.1

Ir 0.2 5.4

Pt 1.9 4.5

Au 5.2 6.3

Contributors and Collaborators

R.D. McMichael (Metallurgy Division, NIST);

M.D. Stiles (Electron and Optical Physics Division, NIST);

C.J. Powell (Surface and Microanalysis Science Division,

NIST); Readrite Corporation; Seagate Corporation;

J.D.R. Buchanan (Durham, UK); J. Moodera (MIT)

Nanomagnetics
33

Detecting Magnetic Nano-Twists in Hard-Disk Reading Heads

Using Polarized Neutron Scattering

The nanoscale magnetic films in magnetic

reading heads have multiple magnetically active

layers. Some of these layers track the varying

magnetization of the storage medium, and others

stay constant, thus providing a known reference

layer. It is anticipated that some of these mobile

layers change their magnetization by producing

a magnetic twist. Confirming this behavior

is difficult using conventional techniques.

We have developed a technique which greatly

simplifies this metrological challenge.

Kevin V. O’Donovan and Julie A. Borchers

The magnetic recording industry has been steadily

increasing the density of storage in computer

hard disks. Reading the stored data depends critically

on the well-characterized and predictable behavior

of nanoscale magnetic films in the reading head.

It is thought that some of the layers which track

the data change their magnetization by producing a

magnetic twist.

NIST researchers working at the NIST Center

for Neutron Research have developed an extension

of polarized neutron reflectometry (PNR) to enhance

its sensitivity to buried magnetic twists. Techniques

other than PNR typically measure only the average

orientation of the magnetic spins. Earlier techniques

of measuring PNR provide depth sensitivity to most

magnetic structures but cannot readily distinguish a

twist in these materials from a magnetic structure in

which all the layers are aligned. PNR measurements

can now exhibit enhanced contrast for magnetic twists

by simply measuring the reflectivity from the front

and back of the sample. Key features in the data

Now a new collaboration with researchers at

Hitachi is applying this PNR technique to the basic

components of an advanced reading head for hard

disk drives. Figure 1 shows the results of the new

scattering technique applied to an CoFe10|CoFe2O4

spin valve. In the absence of a twist, the figure should

be nearly symmetrical about the center. However, the

strong asymmetry in the spinflip reflectivity at the q’s

labeled 0.2 nm–1 indicates a twisted magnetic structure.

The structure fit to the data was determined to be

that shown in Figure 2. The twist was expected to

be confined to depths colored blue through purple.

This new measurement identified an unexpected twist

in the depths colored green through powder blue.

References

1 K.V. O’Donovan, J.A. Borchers, C.F. Majkrzak,

O. Hellwig, and E.E. Fullerton. Physical Review Letters

88, 067201 (2002).

2 K.V. O’Donovan, J.A. Borchers, C.F. Majkrzak,

O. Hellwig, and E.E. Fullerton. Applied Physics A 74,

S1544 (2002).

3 K.V. O’Donovan, J.A. Borchers, S. Maat,

M.J. Carey, B.A. Gurney. Accepted by Journal of

Applied Physics (2004).

Contributors and Collaborators

C. Majkrzak (NIST Center for Neutron Research);

S. Maat, M. Carey, E. Fullerton, B. Gurney (Hitachi

Global Storage Technologies); O. Hellwig (BESSY)

Figure 1: Polarized neutron reflectivity and fits of a spin valve

measured at 47 mT after saturating at –700 mT. The insets show

the scattering geometry from each surface

Figure 2: Magnetic structure derived from fit in Figure 1, as well as

its projection into the xy plane. The color coding shows the angle of

the magnetization with respect to the applied magnetic field.

Nanomagnetics

immediately indicate the presence of a twist, as

demonstrated in a collaboration with researchers

from IBM.1,2
34

Nanomanufacturing

In nanoscale manufacturing, knowledge of

inherent and process-induced properties is crucial.

In new realms of nanoscale manufacturing,

nanomaterials will be manufactured in nanoliter

volumes, combining so-called top-down and

bottom-up or self-assembly approaches. Miniature

tools to characterize such materials and processes

are needed. We are developing devices that can

impose a wide variety of process flows and

measure flow-induced properties at transient

and persistent conditions.

Steven Hudson and Frederick Phelan, Jr.

The four-roll mill is a macroscopic flow device

that has played a critical role in elucidating the

interactions between flow and material response. In

the microscale regime, an analogous device is needed

to efficiently characterize fluids. Merely scaling

down the four-roll mill to microscopic dimensions is

inherently problematic due to the rotating components.

Instead, we are developing a device which uses

pressure-generated flow to achieve the same flow

types as a four-roll mill, but is miniaturizable, and has

greater control over the flow. It is also integrable

into high power microscopes and scattering devices.

in the channels. The relative amount of rotation and its

direction can also be adjusted. Figure 2 illustrates the

flow streamlines for conditions that yield extensional

and shear flow.

To evaluate various candidate geometries for a

pressure-driven microchannel device, flow generated

in these devices was calculated in the (Stokes) limit

of low Reynolds number by the finite element method.

Although a variety of geometries produce highly

extensional flow, shear flow is produced at the

stagnation point only when opposing channels are offset

laterally. A suitable geometry is shown in Figure 1.

A wide range of flow type, including pure shear, is

possible in this device by adjusting the relative flow rate

Figure 1: a) Design of a microchannel analog of the 4-roll mill.

b) Flow type as a function of pressure ratio p1/p2. Flow type

values equal to –1, 0, and 1 correspond to pure rotation, shear

and extension, respectively.

Figure 2: 2D Stokes calculations of pressure-driven flow in

microchannels. Streamlines are shown for a) extensional and

b) shear flow conditions.

Figure 3: Images of drops in a computer-controlled

cross-channel extensional flow device. Image analysis control

feedback adjusts the flow to keep the drop(s) at the stable

stagnation point of the device during deformation (shown at left)

and collision experiments (series at right).

A computer control system, with image analysis

feedback, has been developed. Experiments with

immiscible polymeric fluids have demonstrated that, by

using this device, drops can be moved into the device,

placed at the stagnation point, deformed, and broken

(Figure 3). Drops were then caused to collide and

coalesce. Surface tension-driven relaxation of drop

deformation has been measured. Based on these

results, a focused project to measure interfacial tension,

with partner companies in the NIST Combinatorial

Methods Center (NCMC), was established.

Contributors and Collaborators

J.T. Cabral, J.A. Pathak (Polymers Division, NIST);

NIST Combinatorial Methods Center Focused Project

(with member companies) to measure interfacial tension.

Nanomanufacturing
35

Nanomanufacturing

Process Monitoring of Polymer Clay Nanocomposites

Real-time, on-line measurements of polymer

composite materials properties are desirable

not only because they preempt the need for

post-processing characterization but also because

they can be used to monitor resin conditions, to

detect problems with processing parameters, to

control the process, and to predict performance

of the final product. In this project, we have

developed measurement techniques based on

optical, dielectric, and rheological techniques.

NIST has filled an industry need by designing and

constructing process sensors and by collaborating

with industry partners in the application of new

sensor technology to process monitoring.

Anthony J. Bur

The state of microstructure that forms during the

compounding of polymer and clay nanocomposites

determines their performance properties. On-line,

real-time measurements that are sensitive to

microstructure conformation yield a database that can

improve efficiency and productivity by giving processors

immediate knowledge of the microstructure state.

Real-time measurements can potentially minimize the

extent of off-line microstructure determinations using

x-ray and Transmission Electron Microscopy (TEM)

observations. The on-line instrumentation that we

have developed is a multifunctional device that contains

dielectric, pressure, optical, and ultrasonics sensor ports.

The instrument is designed to attach to the end of a

twin-screw extruder. The resin flow through the sensor

conforms to a slit that is 2 mm high by 28 mm wide,

and the sensors are aligned to interrogate the resin in the

slit region. The extrudate, shown in the picture below,

consists of a strip of material that can be cut into pieces

for off-line measurements.

Nylon 6, when compounded with certain clays

containing polar organo modifiers, can form a

nanocomposite consisting of exfoliated silicate platelets

that are a few nanometers thick by tens of nanometers

in diameter. On the other hand, if the organo modifier

is nonpolar, then the clay particle remains in its

aggregate condition of a micrometer size particulate

when compounded with nylon 6. When the composite

is subjected to an alternating electric field, the

dielectric contrast between particle and resin forms

a resistance–capacitance network that expresses a

dielectric relaxation known as a Maxwell–Wagner

(MW) relaxation. The characteristic relaxation time of

the resin/nano-platelete combination is longer than that

of the resin/aggregate because the nanosize silicate

platelet has a high, effective capacitance.

The table shows characteristic relaxation times and

dielectric relaxation strengths ∆ε for three compounded

nylons: neat, exfoliated clay nanocomposite, and

aggregate clay composite. The measurements were

carried out at processing temperature, 240 oC. After

correcting the data for DC conductivity and electrode

polarization effects, we observed only one dielectric

relaxation in the neat polymer, but two relaxations were

observed in the composites. The single relaxation of

the neat is associated with the α relaxation (log f = 2.40)

of the macromolecule, and the two relaxations of the

composites are the α relaxation (log f = 2.70 and 2.46)

and the MW relaxation at log f = 1.98 and 1.33 for

which the exfoliated microstructure displays the lowest

characteristic frequency. Large ∆ε is characteristic of

MW relaxation.

NY 6/clay NY 6/clay

NY 6 neat aggregate exfoliated

Log f1 2.40 2.70 2.46

Log f2 1.98 1.33

∆ε1 441 1700 2200

∆ε2 18,200 18,400

Contributors and Collaborators

C. Snyder, Y. Lee, N. Noda, S. Roth, V. Prabhu,

P. Start, S. Hudson, J. Obrzut (Polymers Division,

NIST); D. Ho, C. Glinka (NIST Center for Neutron

Research); M. McBrearty (Chemical ElectroPhysics)
36

Electrochemical Processing of Nanoscale Materials

Precise temporal control of supersaturation

provided by electrochemical methods holds

promise for the synthesis and characterization of

materials and structures of very small dimensions

— nanomaterials. Variation of the electrochemical

potential leads not only to changes in the metal

deposition rate but also effects the adsorption of

surfactants and segregation phenomena which

exert a strong influence on the morphological

evolution and stability.

Thomas P. Moffat and Jon Mallett

Electrochemical synthesis has become an important

 tool in the fabrication of nanoscale devices and

structures. Modulation of the electrode potential can

be used to create films with a corresponding variation

in composition and /or structure. This allows materials,

such as multilayers and nanocontacts, to be engineered

with submonolayer precision. Likewise, knowledge of

the stability and reliability of these finite size structures

will be central to any technical application.

 In the last year, we have continued using scanning

probe microscopy to characterize the structure and

stability of immersed surfaces. This work ranges

from atomically resolved STM studies of adsorbate

dynamics to AFM measurements of roughness evolution

during electrodeposition. The focus of this activity is

strengthening our knowledge of the connection between

atomistic processes and morphological evolution

observed at larger length scales.

A new aspect of our program this year is the study

of nanocontacts formed by electrodeposition between

two electrodes. Physical property measurements of

these junctions have revealed a variety of effects such

as quantized conductance, ballastic magnetoresistance,

and adsorbate-influenced surface scattering. Many

investigations use electrodeposited contacts, yet limited

techniques are available for growing and maintaining

such junctions at a fixed or predetermined conductance.

At NIST, we have combined a bipotentiostat with

a STM-like feedback circuit in order to form

electrodeposited metal contacts of predetermined

fixed resistance.

Figure 1: A high resolution STM image of a c(2x2) chloride

adlayer on Cu(100) in 0.01 mol/L HCl. The image was collected

at –0.150 V SCE as shown on the inset voltammogram.

Figure 2: Schematic of control circuit used for forming and

maintaining contacts of fixed conductance.

Figure 3: Controlled step in nanocontact resistance.

The junction conductance measured with a

lock-in-amplifier is compared with a preset value,

and the electrochemical potential of the two working

electrodes is adjusted to either deposit or etch material

to obtain the specified conductance value. Figure 3

shows a controlled transition in contact resistance

between 778 Ω and 369 Ω. Careful choice of the

feedback control parameters resulted in transients

with only one damped oscillation. Stable contacts

have been grown between 800 Ω and 2 Ω.

In the coming year, the measurements outlined

above will be extended towards problems relevant to

micro- and molecular electronics.

Contributors and Collaborators

W.F. Egelhoff, H. Ettedgui, E.B. Svedberg,

J.E. Bonevich, R.D. McMichael (Metallurgy Division,

NIST)

Nanomanufacturing
37

Organizational Charts

Organizational Charts

Materials Science and Engineering Laboratory

Polymers

E.J. Amis, Chief

C.R. Snyder, Deputy

Metallurgy

C.A. Handwerker, Chief

F.W. Gayle, Deputy

Ceramics

D.L. Kaiser, Chief

D.R. Black, Deputy

Materials Reliability

A.F. Clark, Chief

T.A. Siewert, Deputy

NIST Center for

Neutron Research

J.M. Rowe, Director

Director

Deputy Director

National Institute of Standards and Technology

Director

Boulder Laboratories

Baldrige National Quality

Program

Director for

Administration

& Chief Financial

Officer

Technology

Services

Advanced

Technology

Program

Manufacturing

Extension

Partnership

Manufacturing

Engineering

Laboratory

Chemical Science

and Technology

Laboratory

Materials Science

and Engineering

Laboratory

Electronics and

Electrical Engineering

Laboratory

Information

Technology

Laboratory

Physics

Laboratory

Building and

Fire Research

Laboratory

L.E. Smith, Director

S.W. Freiman, Deputy Director
38