Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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218 Part B Chemical and Microstructural Analysis

collected by the same objective lens and focused again

but now at an exit slit that is placed at the confocal posi-

tion of the entrance aperture. The light passing through

the confocal aperture is detected by a photosensor. The

light from the sample may be luminescence from a sub-

stance at the focal spot. The important point is that light

from points on the sample other than the focal spot are

rejected by the confocal exit aperture, thereby greatly

reducing stray background light. If we scan the sample

laterally with respect to the objective lens, we obtain

a two-dimensional image on the screen. It should be

pointed out that, although the point resolution is limited

to a subwavelength (a few hundred nanometers) due to

the effect of light diffraction, tiny objects much smaller

than the resolution limit may be viewed as bright spots

when they scatter or emit light visible to the human eye

or detectable by a photosensor. This means that signals

from even a single molecule can be detected if their

separation from other molecules is large enough. A dis-

advantage of LSCM is the long image acquisition time

due to its scanning nature.

TIRFM is based on the evanescent waves generated

when light is incident onto an interface between two

optical media of different refractive indices. It uses an

ordinary ﬂuorescence microscope equipped with a sam-

ple illumination system, as shown in Fig. 5.11. Samples

attached to the surface of a glass plate are labeled

by ﬂuorescent molecules (ﬂuorochromes). The back of

the glass surface is illuminated with light at an an-

gle smaller than the critical angle for total internal

reﬂection, so that only ﬂuorochromes within the small

extension distance (< light wavelength) of the evanes-

cent wave are illuminated to induce ﬂuorescence, which

is imaged by the objective lens. The sample may be im-

mersed in a liquid whose refractive index is smaller than

Objective

lens

Water

solution

Fluorescent

molecules

Total reflecting lightIllumination light

Glass

plate

Evanescent wave

Fig. 5.11 The principle of total internal reﬂection ﬂuores-

cence microscopy

that of glass, so the magniﬁcation can be increased up

to ×100 by immersion, and biomolecules can be inves-

tigated in vivo in water solutions. TIRFM is superior to

LSCM in its high speed of image acquisition.

Transmission Electron Microscopy (TEM) [5.14]

Electrons interact so strongly with solids that they

cannot penetrate thick solids. Figure 5.12 shows the de-

pendence of the electronic absorption cross section on

the electron energy. Electrons lose their energy most ef-

ﬁciently by exciting plasmons in the low energy range

(10–30 eV), but the cross section governed by electronic

excitations decreases with increasing kinetic energy of

electrons except at core excitation edges that are speciﬁc

to the elements contained in the sample until it increases

due to the start of Bremsstrahlung radiation loss. There-

fore, if the sample thickness is smaller than ≈ 1 μm,

electrons of energies higher than ≈ 100 keV can pene-

trate the ﬁlm sample to some extent. A key issue for

TEM studies is how to prepare samples thin enough

for observation. The most common method is chem-

ical thinning by using a chemical etchant after a prior

mechanical thinning process, though a suitable etchant

cannot always be found. The advent of the ion milling

method using an accelerated Ga ion beam for sputtering,

however, has relieved the common difﬁculty in sample

preparation and so widens the range of materials that

may be studied by TEM.

A great advantage of TEM over other microscopic

techniques is its ability to switch operation between

the imaging and diffraction modes very easily, thereby

investigating in situ the crystallographic properties of

a speciﬁc sample area just being observed in the image.

smaller

logσ

logE (eV)

Plasmon loss

Bremsstrahlung

radiation loss

Heavy elements

Light elements

Core loss

(ionization loss)

≈ 0.05nm

Fig. 5.12 Energy dependence of the absorption cross sec-

tion of electrons

Part B 5.1

Nanoscopic Architecture and Microstructure 5.1 Fundamentals 219

Figure 5.13 illustrates the electron optics of ordinary

TEM in the two modes. Essentially, in the imaging

mode, the image in the real space formed on the im-

age plane of the objective lens is projected onto the

ﬂuorescence screen, whereas in the diffraction mode

the diffraction pattern formed on the back focal plane

is projected onto the screen just by changing the focal

length of the intermediate electromagnetic lens. Usu-

ally, for observations of inhomogeneities in samples, to

obtain an image arising from a speciﬁc diffraction an

(objective) aperture is inserted at the back focal plane

where a diffraction pattern is being formed. To ob-

tain a diffraction pattern from a speciﬁc area of the

sample, an aperture for selected area diffraction (SAD)

is inserted at the image plane of the objective lens.

Usually the objective aperture selects only the direct

beam, so the images obtained generally look bright

(contrasted against a gray background due to absorp-

tion) with varying contrast due to inhomogeneities, and

are therefore called bright-ﬁeld (BF) images. Occa-

sionally, a diffracted beam can be selected to brighten

the images of the imperfections responsible for the

diffraction against the dark background, leading to

a dark-ﬁeld (DF)image.

In most cases, a TEM image is an interference pat-

tern of the electron waves diffracted by a crystalline

sample. Therefore, no correct interpretation of a TEM

image is possible until one carefully compares images

acquired under various diffraction conditions. Although

the quantitatively precise interpretation of TEM images

requires the dynamical theory, the images in many cases

can be understood rather intuitively in the framework of

the kinematical theory. Nevertheless, in some important

cases, dynamical effects or multiple reﬂection effects

must be taken into account. As illustrated in Fig. 5.14,

a) b)

Wedge sample

Direct Diffrac-

ted

Direct Diffrac-

ted

–1

eff

≈ξ

–1

Fig. 5.14a,b Periodic exchange of electron energy be-

tween direct and diffracted waves.

(a) kinematical case

|ξ

−1

|s| and (b) dynamical case |ξ

−1

|s|≈0. Af-

ter [5.16]

a) b)

Specimen

Remove aperture

SAD aperture

Intermediate

image 1

Variable

focus

length

Fixed

focus

length

Second

intermediate

‘image’

Fixed

Objective lens

Objective

aperture (back

focal plane)

Remove aperture

Intermediate

lens

Projector

lens

Final image

Screen

Diffrac-

tion

pattern

Fig. 5.13a,b Electron optics of transmission electron microscope in

the diffraction mode A and in the imaging mode B. After [5.15,

p. 144]

a beam incident with a Bragg angle of θ

onto a set

of net planes is reﬂected to give rise to a diffraction

beam which may be reﬂected again by the reverse side

of the same net planes returning to the primary beam di-

rection. If the crystal is thick, this process is repeated

with the electron energy being interchanged periodi-

cally between the direct beam and the diffracted beam.

When only one diffraction g is excited, a detailed analy-

sis [5.16] shows that the intensity of the direct wave and

that of the diffracted wave emanating from a sample of

thickness t are given by

=cos

(πs

eff





eff



−1





πt



sin

(πs

eff

(

πs

eff

)

(5.10)

and



πt



sin

(πs

eff

(πs

eff

, (5.11)

respectively, where ξ

, the so-called extinction distance

(The terms extinction distance or extinction effects of-

ten used in textbooks originate from the fact that, due to

the diffraction effect, within the distance ξ

the primary

beam intensity decays, or is extinguished, more rapidly

Part B 5.1

220 Part B Chemical and Microstructural Analysis

than expected from the energy absorption effect), is de-

ﬁned as

≡

πΩ cos θ

λF

, (5.12)

where Ω is the volume of the unit cell, θ

is the Bragg

angle, λ is the electron wavelength, and F

is the struc-

ture factor for g. The parameter s

eff

≡



+ξ

−2

, (5.13)

where s denotes the deviation from the Bragg condition

in reciprocal space. Figure 5.14 shows schematically

how the two intensities vary with the thickness of

a wedge-shaped sample. When



−1



(Fig. 5.14a)

or t  ξ

, we could apply the kinematical theory, in

which the thickness dependence is determined by s.

On the other hand, when



−1



≈0(Fig.5.14b)

or t >ξ

, the transmission intensity must be treated

rigorously by the dynamical theory, where s

eff

→ ξ

−1

and the two beams exchange their intensities, alternat-

ing with a period of ξ

, not s

−1

. One should note that

=1 throughout the sample. For its resemblance

to the behavior of two coupled pendulums, this effect

that gives rise to thickness fringes is referred to as

Pendellösung, which forms the basis of similar fringe

contrasts not only in TEM but also in x-ray topography.

In imperfect crystals, the argument is modiﬁed by intro-

ducing an additional phase shift due to the presence of

defects. The consequence is described in Sect. 5.3.

The Pendellösung effect embodies the presence of

two dispersion branches at the zone boundary corres-

ponding to the Bragg diffraction at K = g.Itmaybe

regarded as a consequence of beating between the two

Bloch waves on the two branches. They have amplitudes

Branch 1 Branch 2

Atomic columns

Fig. 5.15a,b Bloch waves on two dispersion branches.

Waves

(a) and (b) are absorbed less and more, respectively

at different column positions as shown in Fig. 5.15:

The wave (a) has its amplitude in between the atomic

columns whereas the wave (b) along the columns. Since

the interaction of the waves with the atoms is weak in

(a) but strong in (b), the waves (a) and (b) are absorbed

by the crystal to a lesser and greater extent, respec-

tively. This causes the effects of anomalous absorption

(Kikuchi patterns in electron diffraction, Sect. 5.5.1)

or anomalous transmission (Electron channeling,

Sect. 5.5.1) for electrons and the Borrmann effect for

x-rays, Sect. 5.3.2) propagating in particular directions.

The Ewald sphere in the diffraction of TEM elec-

trons of energy ≈ 100 keV is large compared with the

reciprocal lattice parameter. The reciprocal lattice points

are broadened perpendicular to the sample surface due

to the small thickness of the sample in TEM. As a con-

sequence, if the thickness is smaller than ≈100 nm, the

electron diffractions practically occur in many g vectors,

asshowninFig.5.16. This makes it possible to form

an image by collecting many diffraction beams, includ-

ing those of large

values that contain information

of small-scale structures in the sample. This is the ba-

sis of high-resolution transmission electron microscopy

(HRTEM) which is now a standard installation in mod-

ern TEM microscopes owingto the technological progress

in the improvement of spherical aberration of the objec-

tive lens. Under a special defocusing condition, called

Ewald sphere

|k|=|k

2π

Fig. 5.16 Ewald construction of electron diffraction in

TEM. The reciprocal lattice points are elongated normal

to the surface of thin specimens, so that many diffractions

can be excited

Part B 5.1

Nanoscopic Architecture and Microstructure 5.1 Fundamentals 221

a) b)

Fig. 5.17a,b The principle of high-resolution TEM. (a)

A perspective view of a schematic crystal along an axis

along which the electron beam is incident to obtain a sym-

metric diffraction pattern, as schematically shown in (b).

Diffracted beams with large wave numbers are collected to

form a high-resolution TEM image that represents, under

the Scherzer defocus condition, approximately the projec-

tion of the atomic columns viewed along the direct beam

the Scherzer defocus, the HRTEM images represent ap-

proximately the arrangement of atomic rows viewed

along the direction of the electron beam, as illustrated in

Fig. 5.17. HRTEM images depend sensitively on the de-

focus condition, the sample thickness, and the depth of

the object in the ﬁlms. The true atomic arrangements can

be deduced only by careful comparison of experimen-

tal images taken under various defocusing conditions

other than the Scherzer defocus and theoretical images

simulated for model structures using the dynamical the-

ory. The routine resolution (point resolution) of HRTEM

is ≈0.2nm.

X-Ray Topography (XRT)

As with transmission electron microscopy, x-ray

diffraction may be used to image crystallographic

inhomogeneities in crystalline samples. A signifcant

difference from TEM, however, is the lack of good

lenses for x-rays so images cannot easily be magniﬁed

as in OM and TEM. The best resolution is determined

by the particle size of the emulsion in x-ray ﬁlms, typi-

cally around 2–3 μm, which may be reduced to ≈1 μm

by the use of synchrotron radiation. The simplest setup

for x-ray topography (XRT) is one devised by Lang

shown in Fig. 5.18. A version using reﬂected beams for

imaging (the Berg–Barrett method) is also used, par-

ticularly when the sample is not transparent to x-rays.

XRT images are obtained by recording diffracted beams

of a certain g vector, equivalent to dark-ﬁeld images

in TEM. An advantage of XRT over TEM is that it

can examine rather bulky samples in a gaseous atmo-

X-ray beam

Translator

Sample crystal

Beam stopper

X-ray film

Fig. 5.18 Lang camera for transmission x-ray topography.

The crystal and the x-ray ﬁlm are simultaneously trans-

lated to record a topographic image consisting of sample

sections

sphere. Owing to this fact. together with the higher

accuracy in the detection of strains, XRT is suitable for

studies of phenomena in which the stress state is of pri-

mary importance (e.g., fracture). A judicious choice of

diffraction geometry as well as x-ray wavelength and

sample thickness allows high topographic contrast. Ap-

plications of XRT are described in Sect. 5.3.2.

High-Angle Annular Dark-Field STEM

(HAADF-STEM)

In scanning transmission electron microscopy (STEM),

an electron beam focused to a small size is raster

scanned in parallel across a sample surface and a detec-

tor collects some signal arising from the interaction of

the electrons with the sample solid. The signal intensity,

which may vary over the sample position depending on

the crystal structure, orientation, composition, etc., is

used to construct two-dimensional maps of the material

properties in each pixel. The spatial resolution of STEM

is limited by the size of the focused probe beam. The

advantage of STEM is that it does not need imaging

lenses that inevitably have some chromatic aberration

and limit the resolution of TEM images, and the sam-

ple thickness may be relatively thick in comparison with

TEM samples. A demerit of STEM is the lower speed

of image acquisition (seconds to minutes for a single

image) due to the serial recording of the signal.

Part B 5.1

222 Part B Chemical and Microstructural Analysis

In bright-ﬁeld (BF) STEM, the signal collected is

the directly transmitted electrons that are not diffracted

by the crystallographic sample. Similarly, dark-ﬁeld

(DF) STEM images can be obtained by collecting only

diffracted electrons. Although the imaging principle of

STEM is different from that of TEM, the two micro-

scopic techniques could be viewed as equivalent if one

regards the electron detector in STEM as the objective

aperture in TEM, both of which are (not physically as

for the detector in STEM) placed at the back focal plane

of the objective lens.

High-angle annular dark-ﬁeld STEM (HAADF-

STEM) allows one to observe STEM images with

higher resolution and compositional information. As

shown in Fig. 5.19, HAADF-STEM images are formed

by collecting high-angle scattered electrons with an an-

nular dark-ﬁeld detector placed at the back focal plane

of the objective lens. The image formation mecha-

nism is based on the fact that a fraction of electrons

incident on a crystalline sample along a channeling

direction are diffusely scattered by thermal vibrations

of atoms at relatively high angles ( 70 mrad) when

the beam scans over the atomic columns. Therefore, in

HAADF-STM images, the positions of atoms are ob-

served as bright contrasts depending strongly on the

average atomic number of the atoms in the column.

Owing to this feature, HAADF-STM, otherwise called

Z-contrast imaging, is a powerful technique for compo-

sition analysis especially for elements of large atomic

numbers. The spatial resolution in HAADF-STEM is

limited by the size of the focused probe beam as in or-

Focused electron beam

Convergent angle

≈ 10 mrad

Probe size & 0.2 nm

Beam scan

Scan

circuit

Raster scan

2-D

Map

Small Z

Large Z

Scattering angle

& 70 mrad

Annular detector

Collected current

Fig. 5.19 Setup of high-angle annular dark-ﬁeld scanning

transmission electron microscopy (HAADF-STEM). Elec-

trons diffusely scattered by thermal vibrations of atoms

with relatively high angles are collected by an annular de-

tector to form a scan image

dinary STEM. Under good conditions, an atomic-level

spatial resolution can be achieved, although such sam-

ples must be thin enough (usually thinner than several

tens of nanometers) for beam broadening to be avoided.

The advantage of HAADF-STM over HRTEM is the in-

sensitivity to focusing conditions and sample thickness

variations, both of which very substantially affect the

phase sensitive contrast of HRTEM images.

Scanning Electron Microscopy (SEM). The representa-

tive microscope of the scanning type is the scanning

electron microscope (SEM)[5.17], in which the scan-

ning probe is a ﬁnely focused electron beam. Fig-

ure 5.20 shows various forms of signals generated by

incidence of electrons onto solid samples. Some of the

incident electrons lose most of their initial energy and

are emitted from the surface with a low energy (≈afew

tens of eV). These electrons are called secondary elec-

trons, which can escape only from very shallow depths

of the solid due to their large absorption cross section

(Fig. 5.12). Without losing much energy, other electrons

are either reﬂected backward as back-scattered elec-

trons or absorbed into the solid as a drain current. On

the loss of electron energy, x-ray ﬂuorescence or Auger

electron emission occur, which are very useful for elem-

ent analysis. In semiconductor samples, the electron

energy may be converted to a luminescence (cathodo-

luminescence, CL) or an electron-beam-induced current

(EBIC) when an electric ﬁeld separating electron–hole

pairs is built up in the surface layer. Depending on the

detected signal, SEM has several operation modes. The

most common mode is secondary electron SEM (SEM-

SE), in which the difference in the escape probability of

secondary electrons depending on the direction relative

to the surface normal produces surface roughness con-

trast observed from an oblique angle when the electron

detector is placed as shown in Fig. 5.21.

Finely focused beam scan

X-ray fluorescence

Cathodoluminescence

Secondary electrons

Backward scattered

electrons

Auger electrons

Electron beam induced current

Sample

Fig. 5.20 Signals generated in scanning electron micro-

scopy

Part B 5.1

Nanoscopic Architecture and Microstructure 5.1 Fundamentals 223

Secondary

electron detector

Fig. 5.21 Escape probability of secondary electrons (SE)

with its maximum in the surface normal direction render-

ing the morphological contrasts in SEM-SE

Electron

probe beam

Escape depth of

secondary electrons

≤1nm

Spread range

of injected

electrons

≥

Generation

range of

secondary

electrons

Diffusion range

of minority carriers

(semiconductors)

≤ a few μm

≤1nm

Fig. 5.22 Factors governing the spatial resolution in SEM

The spatial resolution depends on what signal is

used and how large the signal is. As illustrated in

Fig. 5.22, incident electrons are spread by a random

walk on the nanometer range that increases in depth

with increasing acceleration voltage. For the primary

beam size to dominate the resolution in SEM-SE,we

should choose an accelerating voltage at a medium

value to reduce the lateral spreading of electrons. In

commercial SEM-SE operated at 5 keV, subnanometer

resolution is achievable by the use of a ﬁeld emission

gun, the high brightness of which allows extremely ﬁne

focusing of the probe beam. The resolution in SEM-SE

is determined by the spread range, while the resolution

in SEM-CL and SEM-EBIC is worsened by the dif-

fusion of the carriers generated by the electrons. The

samples for SEM observations must be more or less

electrically conductive to avoid charging effects. If they

are not metals or semiconductors, precoating the sam-

ples with Au ﬁlms may work.

For samples which are too thin for the fast electrons

to excite secondary electrons for SEM-SE observations,

the use of low-energy electrons (< 1keV)orinactive

light He

ions for the probe beam enables studies for

such samples as single-walled carbon nanotubes.

Scanning Probe Microscopy. Since the advent of scan-

ning tunneling microscopy (STM)[5.18–20], the use of

extremely sharp tips controlled by a piezo-actuator as

showninFig.5.23 opened fascinating opportunities to

study materials on the nanometer scale. To date, many

schemes of scanning probe (tip) microscopy (SPM)

have been devised, though some of them are still under

development at present.

Scanning Tunneling Microscopy (STM). The STM is

based on the fact that a quantum mechanical tunnel-

ing current ﬂows between two electrically conductive

solids closely spaced within a distance of ≈1 nm under

an electric bias voltage, with a very sensitive depen-

dence on the separation. Figure 5.24a–c illustrates the

situation for a combination of metallic tip and a semi-

conductor sample. If the probe tip, usually an electro-

chemically etched tungsten needle, is sharp enough, the

tunneling current is conﬁned to a very narrow region

Tip Piezo-actuator

–V

Fig. 5.23 Piezo-actuator (tube scanner) for tip scanning

Part B 5.1

224 Part B Chemical and Microstructural Analysis

a) b) c) d)

a) b) c)

(Tip)

(Sample)

LDOS

Metal tip

Vacuum

gap

Sample

(Tip)

(Sample)

LDOS

Vacuum

gap

Sample

(Tip)

(Sample)

LDOS

Vacuum

gap

Sample

Metal tip Metal tip

(Sample)

/dV

LDOS

Fig. 5.24a–d Vacuum tunneling between a metallic tip and a semiconducting sample, also illustrating the principle of

scanning tunneling spectroscopy

(< 0.1 nm) beneath the tip. Scanning a sample surface

with such a sharp tip and recording as a signal the volt-

age applied to the piezo-actuator that acts to keep the

tip–sample distance (more precisely the tunneling cur-

rent) constant, we can obtain a two-dimensional image

of the surface topography, as shown in Fig. 5.25.

STM images generally reﬂect very strongly the lo-

cal density of states (LDOS) of surface electrons on

which the tunneling current is also dependent. This fact

provides a unique method, scanning tunneling spec-

troscopy (STS), for the assessment of local electronic

properties of the samples. Figure 5.24 illustrates the

principle of STS, which is based on the fact that most of

the external bias voltage is applied across the vacuum

gap and that electron tunneling occurs from electronic

ﬁlled states to empty states conserving energy. The tun-

neling current I

varies with the bias voltage V

as in

Fig. 5.24d with its derivative with respect to V

approx-

imately representing the LDOS.

In principle, STM experiments could be conducted

in ambient environments as long as the current is con-

ﬁned beneath the tip, but in most cases clean surfaces

are investigated in ultra-high vacuum to obtain re-

producible results. Preferably, the surface should be

atomically ﬂat with steps in atomic heights; otherwise

in rough surfaces, the tip shape is convoluted with the

image giving a spurious surface morphology.

Atomic Force Microscopy (AFM). Atomic force micro-

scopy (AFM) uses a sharp probe tip mounted on

a cantilever, as shown in Fig. 5.26 [5.21, 22]. When the

sample and the tip are close enough, the sample exerts

a short-range force on the cantilever, an attractive force

originating from the van der Waals interaction, a re-

pulsive force due to the Pauli exclusion principle, and

a variable force of chemical origin. The force may also

15nm

18nm

Fig. 5.25 STM image of Si(111)–7 × 7 surface

be long-ranged, arising from a Coulombic interaction.

The simplest AFM with the tip in mechanical contact

with the sample surface detects a force-induced devia-

tion of the cantilever by an optical or electronic method.

Recently, noncontact AFM has made great progress in

imaging solid surfaces at atomic resolution comparable

with STM. The common technique used for the de-

tection of atomic force is to measure the shift of the

resonance frequency of the cantilever that is caused by

a nonlinear force operating between the sample and

the tip (Fig. 5.26). In the current state-of-the-art instru-

ments, the lateral and vertical resolutions are 10 pm

and one to several pm, respectively. Figure 5.27 shows

a set of noncontact AFM images of a GaAs surface.

An atomic resolution is achieved when the closest dis-

tance z between the sample and the cantilever tip is

shorter than ≈ 0.1 nm (b and c). The blurred contrast

in (a), obtained at a slighty large closest approach, is

considered to indicate the presence of charged defects

beneath the sample surface.

Part B 5.1

Nanoscopic Architecture and Microstructure 5.1 Fundamentals 225

X-Y-Z

Piezo-actuator

Laser beam

Position-sensitive

detector

Cantilever

Probe tip

Sample

Oscillation amplitude

Oscillation frequency

Frequency shift

Tip–sample distance

Tip–sample

interaction

Potential felt

by the cantilever

Fig. 5.26a–c The principle of noncontact atomic force mi-

croscopy (AFM). (a) The sample exerts a force on the

probe tip on top of a cantilever whose deﬂection is de-

tected, in this case, by an optical lever method. The

cantilever is forced to oscillate at the resonance frequency

(b) which changes with the tip–sample distance due to the

nonlinear interaction between the tip and the sample (c)

Scanning Near-Field Optical Microscopy (SNOM).

Scanning near-ﬁeld optical microscopy (SNOM)[5.23]

overcomes the diffraction-imposed resolution limit of

OM by exploiting an evanescent ﬁeld that is gener-

ated and/or detected by a probe tip that is brought

very close to the sample. Usually, the tip is made of

metal-coated optical ﬁber with a tiny aperture at the

apex. The tip–sample distance may be controlled by

the same technique used in STM and AFM. There are

many SNOM schemes, only two of which are illus-

trated in Fig. 5.28.InFig.5.28a, the light guided by an

optical ﬁber illuminates the sample in a region that is

highly localized by the aperture, and the light scattered

or emitted by the object is collected by the probe itself

or detected as a far-ﬁeld light by a photosensor. In the

setup in Fig. 5.28b, the sample on an optically ﬂat glass

is illuminated with an evanescent wave of a total inter-

nal reﬂecting light. The probe collects secondary light,

or a photodetector senses a change to the total reﬂected

light intensity caused by the presence of the tip in close

vicinity to the object. More recently, attempts at aper-

tureless SNOM using a metallic tip illuminated with

a macroscopic light to exploit the metal–tip-enhanced

optical ﬁeld have been reported. In any case, the spatial

resolution at present is limited to tens of nanometers.

SNOM is a rapidly growing technique because of the

wide applicability to materials, regardless of sample

properties such as electrical conductivity, and the ﬂexi-

ble test environments. Interested readers should refer to

most contemporary articles for the latest progress.

Field Ion Microscopy (FIM). The ﬁeld ion microscope

(FIM)[5.24] is a type of microscope based on a prin-

ciple completely different from those described so far.

In the basic setup, illustrated in Fig. 5.29, the sample is

a metallic needle the apex of which is atomically sharp-

ened with an end radius of 50–100 nm so that an electric

ﬁeld applied to the sample is concentrated on the atomic

step edges. The sample faces a phosphor screen placed

at a distance of ≈ 5 cm from the needle tip. To ob-

tain images, a small amount (≈ 10

−3

Pa) of an inert

gas, usually helium, is introduced into the ultra-high-

vacuum chamber in which the sample and the screen

are accommodated, and a positive (with respect to the

screen) bias voltage is then applied to the sample. The

inert gas atoms polarized by the electric ﬁeld are elec-

trostatically attracted to the tip and migrate further to

the step edges where a high electric ﬁeld is concen-

trated. When the bias voltage is high enough (a few

tens of V/nm), an electron in the inert gas atom tun-

nels quantum mechanically to the tip resulting in the

formation of a positively charged ion at the step edges.

The ion formed is immediately repelled by the strong

electric ﬁeld present between the sample and the screen,

and starts to be accelerated towards the screen along the

direction of the electric ﬁeld. Since the electric ﬁeld em-

anates radially from the tip apex, the distribution of the

ion impinging spots on the screen, as shown in Fig. 5.30,

represents a highly magniﬁed image of the atoms at the

step edges on the sample tip. Usually, a multichannel

plate is placed in front of the phosphor screen for sig-

nal enhancement. The sample may be cooled to a low

temperature to suppress thermal atomic motion on the

Part B 5.1

226 Part B Chemical and Microstructural Analysis

11.5 nm 11.5 nm 11.5 nm

12.2 Hz

c)b)a)

4.57 Hz1.9 Hz

z ~ 0.4 nm

Δ Δ Δv = –31Hz

z ~ 0.10 nm

v = –62Hz

z ~ 0.08 nm

v = –70Hz

Fig. 5.27a–c Noncontact AFM images of a p-GaAs(110) surface. z denotes the closest distance between the sample and

the tip, and Δν the shift of the cantilever resonance frequency. p-GaAs(110) N

=1.4×10

−3

(after [5.25])

surface. FIM is useful for three-dimensional microanal-

ysis of element distribution if combined with an atom

probe method (Sect. 5.5.3).

5.1.3 Spectroscopy

Optical Spectroscopy

The physical property of primary importance in optical

spectroscopy is the energy of the photons. Figure 5.31

summarizes the main optical spectroscopic methods ar-

ranged according to the range of photon energies, and

the corresponding wavelengths and frequencies. Al-

though electromagnetic waves in general range from

radio frequency (RF)wavestoγ -rays, we ﬁrst con-

ﬁne ourselves in traditional optical spectroscopy, which

is usually limited to a range from infrared to ultra-

violet light (It should be noted that, owing to the

development of more intense light sources and more

sensitive light detectors, the techniques now mostly

applied to this range are being extended, based on es-

sentially the same principle, to regions down to THz

waves and up to x-rays. For recent development in

the range of extreme violet (30–250 eV) to soft x-rays

(250 eV–several keV) see [5.26]). The interaction of

light in this range of photon energies with matter

has different origins depending on which quasiparti-

cles (quanta) are excited: electronic, vibrational, or

both coupled (vibronic). In the bottom of Fig. 5.31,

the quanta that can be studied are shown. In this

section, we touch only on matters relevant to this

chapter.

Infrared Absorption Spectroscopy (IRAS)

Fourier transform (FT) spectroscopy has advantages

over spectroscopic measurements using a dispersive

Optical fiber

Photo-

detector

Photo-

detector

Metal

coat

a) b)

Fig. 5.28a,b Two representative setups of scanning near-

ﬁeld optical microscopy (SNOM) using evanescent waves

(a) from an optical ﬁber tip and (b) from the surface of

a glass plate internally total reﬂecting light

Part B 5.1

Nanoscopic Architecture and Microstructure 5.1 Fundamentals 227

monochromator (e.g., a grating monochromator), in

which spectral signals are detected sequentially with

a single detector, under certain conditions. For FT mea-

surements we use, instead of a dispersive monochroma-

tor, an interferometer such as a Michelson-type device

shown in Fig. 5.32. The output of the interferometer

fed with light of wavelength λ and intensity I

is vari-

able depending on Δx, the displacement of the movable

Fig. 5.30 FIM Image of a W tip (Courtesy of Dr. K. Hono)

Frequency

Wavelength

Photon

Energy

Spectroscopic

methods

Quanta

studied

1GHz 1THz 1PHz 1EHz 1ZHz

1m 1mm 1μm 1nm 1pm

1μeV 1 meV 1eV 1keV 1MeV

Microwave Far-IR

Visible Soft x-rays

UV hard x-rays γ-rays

NMR ESR FT-IR

IRAS

Absorption

Reflection

Raman

Absorption

UPS

XAFS

XPS

PAC

PAS

Nuclear spin Electronic spin

Rotation phonon

Valence electron

Core electron

Valence electron

core electron

nuclear spin

Near-IRInfrared

Fig. 5.31 The energy of photons used for optical spectroscopic measurements of various quanta

Imaging gas Multichannel plate

Phosphor

screen

Ionized atom

Sample tip

Fig. 5.29 The principle of ﬁeld ion microscopy (FIM). Inert imag-

ing gas atoms arriving at the ﬁeld-concentrated atoms at step edges

are ionized and repelled towards a phosphor screen to project the

atomic image at high resolution

mirror, through

(Δx) = I

sin



2π

2Δx



. (5.14)

If the movable mirror is displaced at a constant ve-

locity v,thenΔx = vt at time t, and hence

(t) = I

sin



4πv



= I

sin

(

)

. (5.15)

Equation (5.15) indicates that light of intensity I

is sinusoidally modulated at a frequency given by

Part B 5.1