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1 Scanning Tunneling Microscopy (STM)

1 Scanning Tunneling Microscopy (STM)

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Microscopy – Nanoscopy

Fig. 2.1 Device with a piezoelectric base plate (1) and three feet (2) allowing the sample to be

approached toward the tip which is mounted on a piezoelectric tripod scanner (3). (Reprinted with

permission from [2.20]. © 1994 Cambridge University Press)

Fig. 2.2 Atomically resolved

image of KBr(001) in contact

AFM mode. The small and

large protrusions are

attributed to K+ and Br−

ions, respectively. (Reprinted

with permission from [2.21].

© 2003 American Physical


(iii) Atomic resolution together with atomic positioning of the tip leads to the

controlled manipulation on the atomic level and the prospects of creating

atomic-scale devices.

Scanning probe microscopes are operated after the following common principles:

A very fine, nanosized probe tip interacts with a specimen surface and is scanned

line by line over this surface. Commonly, the relative movement between tip and

specimen surface is effectuated by piezodrives (see Fig. 2.1). The data registered

by the tip in dependence of the lateral and normal movements are stored in a computer and displayed in a color code on a monitor (see Fig. 2.2). With the scanning

probe microscopy techniques presently available, a wide field of applications in

nanotechnology emerges.

2.1.1 Scanning Units, Electronics, Software

For atomic resolution of a surface, isolation of the microscope against vibrations is

required. Piezoelectric drives can be used for the scanning units operating the 3D tip


Scanning Tunneling Microscopy (STM)


motion (see Fig. 2.1). The bars or tubes with high stiffness offer high resonance frequencies making video scan rates possible without exciting vibrations. This enables

the study of dynamic processes as, e.g., atomic surface diffusion. Furthermore, high

sensitivity, large scan areas, and low thermal drifts are of importance.

By the electronics set-up, a tip bias voltage is supplied giving rise to a tunneling

current which is compared to a preset current level in order to feed the difference

signal into feedback amplifiers in the constant current imaging mode (see below).

The experiments are equipped with computer control and data visualization.

The sensor tip, the most critical component of an STM, should have a small

tip radius and a high-aspect ratio. Sharp tips can be prepared by electrolytical

etching and ion milling [2.20]. Metallic tips can be magnetically modified for highresolution magnetic sensing [2.10]. For chemical sensing on a nanometer scale

carbon nanotube tips have been specifically modified (see Chap. 5.1).

2.1.2 Constant Current Imaging (CCI)

This is a widely used STM mode (see Fig. 2.3). As described earlier [2.20] a

feedback loop adjusts the height of the tip during scanning so that the tunneling

current flowing between tip and specimen is constant. Therefore, the recorded signal Uz Ux , Uy can be translated into a “topography” z (x, y), provided that the

sensitivities of the three piezoelectric drives are known.

In a theoretical treatment of STM the tunneling probability of a 1D contact

can be dealt with in a perturbative time-dependent approach (Bardeen’s transfer

Hamiltonian, see [2.20]). Within Bardeen’s formalism, the tunneling current I can

be evaluated in a first-order time-dependent perturbation theory according to


2π e

f Eμ

1 − f (Eν + eU) − f (Eν + eU) 1 − f Eμ


× Mμν


δ Eν − Eμ

Fig. 2.3 Schematics of the constant current mode of STM operation. (Reprinted with permission

from [2.20]. © 1994 Cambridge University Press)



Microscopy – Nanoscopy

where f (E) is the Fermi function, U is the applied sample bias voltage, Mμν is the

tunneling matrix element between the unperturbed electronic states ψμ of the tip,

and ψν of the sample surface, Eμ (Eν ) is the energy of the state ψμ (ψν ) in the

absence of tunneling, and the delta function describes the conservation of energy

for the case of elastic tunneling. The essential issue is the calculation of the tunneling matrix element Mμν [2.22] which requires explicit expressions for the wave

functions ψμ and ψν of the tip and of the sample surface, respectively. In the simplest model, an s-type tip wave function [2.23] is assumed. Then, the STM images

obtained at low bias voltage in the constant current mode represent contour maps

of constant surface local densities of states (LDOS) at the Fermi energy EF of the

sample surface, provided the s-wave approximation for the tip is justified. In this

model the tunneling current

I ∝ exp (−2κs)

is an exponential function of the distance s between tip and substrate with the decay

rate κ. It should be mentioned that modifications of this model are necessary for the

widely used W or Pt–Ir tips in STM studies because for these materials the density

of states at the Fermi level is dominated by electronic d states rather than s states.

A direct comparison between an experimental constant current scan and a calculated contour of constant local density of states at the Fermi level using the

adatom-on-jellium model was made for the case of xenon atoms adsorbed on a

Ni(110) surface [2.24]. A reasonable agreement appears in Fig. 2.4 because Xe

binds at relatively large distances from metal surfaces with a relatively large size

of the Xe 6s orbital extending further out into the vacuum than the base-surface

wave function.

Fig. 2.4 A comparison of theoretical and experimental normal tip displacement versus lateral tip

displacement for a Xe atom absorbed on a metal surface. (Reprinted with permission from [2.24].

© 1991 American Physical Society)


Scanning Tunneling Microscopy (STM)


The lateral resolution in constant current STM is given by (see [2.20])

L eff = (R + s) /κ


with the geometrical quantities R (tip radius) and s (distance between sample surface

and front end of the tip) rather than by the wavelength of the tunneling electrons.

This is the typical situation of the so-called near-field microscopes which are operated at distances (1.2–12 nm) between probe and sample that are not so large

compared to the electron wavelength (0.3–1.0 nm). STM facilities are operated

under UHV conditions not only at low temperatures but also at elevated pressures

and temperatures [2.25].

2.1.3 Constant-Height Imaging (CHI)

In constant current imaging the data acquisition rate is limited by the timeconsuming feedback loop. This feedback is switched off in the constant-height

imaging (CHI) mode. In this mode the modulation of the tunneling current with

the full sensitivity of the exponential current dependence on the tip-surface spacing

reflects the atomic-scale topography (see Fig. 2.5). In this mode STM images can

be collected at video rates for the observation of dynamic surface processes such as

Fig. 2.5 Schematic of the

constant-height mode of

STM. (Reprinted with

permission from [2.27].

© 1987 American Institute of




Microscopy – Nanoscopy

diffusion [2.26]. However, the CHI mode is preferably used for zooming to selected

smaller surface areas of sufficient flatness.

2.1.4 Synchrotron Radiation Assisted STM (SRSTM)

for Nanoscale Chemical Imaging

With STM, which conventionally is sensitive to conduction electrons, chemical

information on the composition of a surface can be gained by photo-induced secondary electrons that are produced by core–electron excitation under synchrotron

radiation [2.4]. Since the intensity of the secondary electrons emitted from the surface is proportional to the x-ray absorption probability of core–electrons, one can

obtain the chemical “fingerprint” of an element by measuring with the STM the

secondary electron intensities below and above the characteristic x-ray L absorption

edge of, e.g., Ni or Fe (see Fig. 2.6). By this technique, checkerboard-patterned samples of Fe and Ni stripes on a thick Au film formed on Si (001) can be specifically

detected (Fig. 2.6b, c) with a lateral resolution of ∼ 10 nm.

2.1.5 Studying Bulk Properties and Volume Atomic

Defects by STM

The surface-sensitive STM technique can be used to study bulk properties of a

crystal by exploiting the wave nature of electrons, e.g., in copper and study their

interference patterns on the surface caused by scattering centers in the bulk of the

material [2.28, 2.31]. Most solid-state properties can be characterized by the structure of the Fermi surface – the dividing line between the states occupied by an

Fig. 2.6 (a) Schematic of an Fe and Ni checkerboard pattern as observed by synchrotron radiation

assisted scanning tunneling microscopy (SRSTM). (b) Element-specific image of Fe obtained by

dividing a photo-current image taken at the top of the Fe L3 absorption edge (hν = 706 eV) by that

at the bottom of the edge (698 eV). (c) Element-specific image of Ni obtained around the Ni L3

absorption edge (hν = 852 and 843 eV). (Reprinted with permission from [2.4]. © 2009 American

Physical Society)


Scanning Tunneling Microscopy (STM)


Fig. 2.7 (a) A nearly free-electron gas has a spherical Fermi surface. The blue arrows indicate

the direction of electron propagation at the Fermi surface. (b) In the Fermi surface of Cu certain

directions become preferred due to the non-spherical shape of the Fermi surface. The thick arrows

indicate directions of electron focusing. (c) When a scatterer is present under the surface, the electron wave can be reflected. For a spherical Fermi surface this results in a weak interference pattern

at the surface. (d) When the Fermi surface is not spherical, electron focusing is observed along

certain directions which can give rise to a pronounced interference pattern at the surface [2.31]. (e)

Scanning tunneling micrographs (STM) of four Co atoms below the Cu (111) surface (9 by 9 nm).

The right inset shows (4 by 4 nm) the calculated local density of states (LDOS), whereas the

left inset refers to density-functional theory (DFT) calculations. (Reprinted with permission from

[2.28]. © 2009 AAAS)

electron and the empty states. The simplest model for electrons in a solid is the

nearly-free electron gas with a spherical Fermi surface (Fig. 2.7a). A small deviation from a sphere, such as in Cu (Fig. 2.7b), allows to measure the shape of the

bulk Fermi surface which is most frequently measured by quantum oscillations or

photo-emission spectroscopy and calculated with density-functional theory (DFT)

[2.31]. When an electron is injected from the tip of an STM into a sample, it

propagates as a wave and eventually scatters or arrives back at the tip. This wave

behavior of the electrons in the bulk is not visible in most STM images. The situation changes dramatically when a point defect is incorporated under the surface. A

dramatic increase of the surface interference pattern is observed for Co atoms buried

several layers underneath (Fig. 2.7e). This is ascribed to the shape of the Fermi surface: Along certain spatial directions, the amplitude of the scattered wave decays

very slowly (see arrows in Fig. 2.7b). The electrons are scattered along beams of

electron waves, a phenomenon referred to as electron focusing. When these beams



Microscopy – Nanoscopy

intersect the surface of the crystal, a strong and characteristically shaped interference pattern is observed containing information about the propagation of electrons

through the bulk of the material, the shape of the Fermi surface, and the characteristics of the scattering potential below the surface. According to calculations [2.28],

separate interference patterns (Fermi surfaces) should be observed for minority spin

versus majority spin electrons in magnetic materials. Kondo resonances of electron scattering at a magnetic atom on a non-magnetic host were studied earlier

[2.29, 2.30].

2.1.6 Radiofrequency STM

STM with an electronic band width as high as 10 MHz has been demonstrated

[2.32]. This allows for high-sensitivity detection of high-frequency mechanical

motion and is expected to be capable of quantum-limited position measurements

(see Sect. 7.2).

2.2 Atomic Force Microscopy (AFM)

The scanning force microscope or atomic force microscope has been invented by

Binnig et al. [2.33]. As shown in Fig. 2.8 a probetip is mounted on a cantilever type

spring. The force interaction between the sample and the tip after approaching each

other causes the cantilever to deflect according to Hooke’s law



where C denotes the spring constant and z the deflection. The AFM can be operated either in the contact regime or in the non-contact regime where, e.g., small van

der Waals forces may be probed.

The most critical component is the cantilever-type spring with a sharp tip on one

end. For a high sensitivity, a large deflection of a soft spring (with a low spring constant) for a given force is desirable. On the other hand, a high resonance frequency

ω0 = (C/m)1/2

is necessary in order to minimize the influence of mechanical vibrations. Both conditions can be achieved only by keeping the mass, m, and therefore the geometrical

dimensions small so that microfabrication techniques must be employed. Challenges

in receiving atomic resolution and optimization of imaging parameters have been

discussed [2.21].

The applicability of AFM techniques to bulk insulators is of particular importance where electron microscopical, spectroscopical, and STM studies are difficult

because of charging effects.


Atomic Force Microscopy (AFM)


Fig. 2.8 Schematic set-up of an atomic force microscope (AFM) with a four-segment photodiode

for detection of the laser beam deflection due to bending and twisting of the cantilever. (Reprinted

with permission from [2.34]. © 1999 Karlsruher Institut für Technologie)

Mainly optical techniques (see Fig. 2.8) are employed in order to detect the

cantilever deflection. In this set-up a laser beam is reflected from the cantilever

and the cantilever displacement is measured by the detection of the reflected

laser beam using a position-sensitive detector consisting of, e.g., four photoactive segments with eventually sub-Ångström sensitivity. By the four photoactive

cells, vertical and lateral deflections (for, e.g., friction measurements) can be


2.2.1 Topographic Imaging by AFM in Contact Mode

In this mode, where the tip and the sample are in contact, the interaction force causes

the cantilever to deflect. In the constant force imaging (CFI) mode of AFM which

is analogous to the constant current mode in STM, the cantilever deflection is kept

constant by means of a feedback circuit. The output signal of the feedback loop

Uz is recorded as a function of the (x, y) coordinates and can be translated into

the “topography” z (x, y). As equiforce surfaces are measured by AFM we have to

consider the tip-surface interaction forces in the contact regime.

The invention of the AFM has considerably contributed to an increased interest

in the force picture of quantum mechanical systems. The fundamental relationship

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