Hawkes P.W., Spence J.C.H. (Eds.) Science of Microscopy. V.1 and 2

Подождите немного. Документ загружается.

1010 P. Sutter

measured Schottky barrier height were detected, emphasizing the

need for high-resolution maps of interfacial transport.

Carrier transport in BEEM is affected by all stages of the injection

pathway: (1) tunneling from the tip into the metal base layer, (2) hot

carrier transport through the base, (3) transmission across the metal–

semiconductor interface, and (4) transport in the semiconductor, includ-

ing transmission through additional heterostructure interfaces. In

addition to local Schottky barrier heights, the technique is therefore

sensitive to a number of factors, e.g., surface topography, elastic or

inelastic scattering in the different layers or at interfaces, and the band

structures of the junction partners, which affect not only interface

transmission probabilities but also the spatial resolution obtainable in

BEEM via metal band structure-induced focusing or defocusing.

BEEM current maps can be acquired simultaneously with constant-

current STM images by measuring I

spatially resolved during a con-

stant-current scan. Figure 15–31 shows STM and BEEM current images

obtained on 2.5 nm epitaxial CoSi

/Si(111) (Sirringhaus et al., 1994). The

lattice mismatch of 1.2% between the metallic silicide and the Si sub-

strate is accommodated by an interfacial dislocation network. In STM

topography, the location of these line defects is detected via their elastic

strain ﬁ eld at the CoSi

surface. Strikingly, the defects are mapped in

BEEM as sharply localized regions with increased collector current

with a width of only 0.8 nm, as expected for ballistic transport of car-

riers with a strongly forward focused tunneling momentum distribu-

tion, i.e., k

∼ 0. While the Schottky barrier was found to be uniform,

as expected for an epitaxial interface, the sharp local increase in trans-

missivity of the CoSi

/Si interface was explained by a signiﬁ cant

increase in in-plane momentum due to scattering by the dislocation

core, facilitating the transmission into the Si conduction band

minima.

Figure 15–31. (a) Constant-current

STM image and (b) corresponding

BEEM image obtained on epitaxial

2.5 nm CoSi

/Si(111). A dislocation

network at the silicide/silicon inter-

face is indicate by dashed lines. In

the BEEM image brighter areas

indicate regions of higher collector

current. Hot electron scattering at

the interfacial dislocations causes a

sharply localized increase in collec-

tor current.

Chapter 15 Scanning Tunneling Microscopy in Surface Science 1011

In experiments such as those on CoSi

/Si(111), growth and probing

of the entire heterostructure in the same UHV environment is critical

to achieve ordered interfaces and reliable measurements on reactive

metal surfaces. For the microscopy itself, low temperatures have several

practical advantages, such as improved energy resolution due to

reduced thermal broadening of the tunneling distribution, and reduced

thermal drift of the STM. An additional beneﬁ t is a lower thermal noise

due to a reduction of thermionic emission across interfacial barriers,

which allows shallower potential barriers to be probed. As a result,

semiconductor band offsets, resonant transport in semiconductor het-

erostructures, and interfacial barriers between an organic layer and a

metal base (Troadec et al., 2005) can be measured successfully by low-

temperature BEEM. Examples are embedded self-assembled quantum

dots (Rubin et al., 1996), lithographically patterned quantum wires

(Eder et al., 1996), double-barrier resonant tunneling structures (Sajoto

et al., 1995), and superlattices (Heer et al., 1998). Figure 15–32 shows

the band proﬁ le for carrier injection into an individual InAs quantum

dots in GaAs (Rubin et al., 1996). Also shown are STM and BEEM

images, as well as BEEM spectra obtained with the tip positioned on

top and next to the dot. The semiconductor heterostructure was coated

with a polycrystalline Au base layer, whose morphology largely domi-

nates the contrast in STM. A strong enhancement in BEEM current in

a circular region with 30 nm diameter is associated with carrier trans-

port through a single InAs quantum dot. A comparison of BEEM

spectra obtained on and between dots shows signatures of transport

through two zero-dimensional states of the dot.

Ballistic carrier transport and scattering can, in principle, be used

to probe a wide variety of other systems, beyond Schottky barriers

and semiconductor heterostructures. Examples are metal–insulator–

semiconductor structures (Cuberes et al., 1994) or magnetic multilayers

(Rippard and Buhrmann, 2000). In the latter, an Au/Si(111) Schottky

barrier is used as an analyzer for spin-dependent scattering of carriers

Figure 15–32. BEEM on self-assembled quantum dots. (a) STM and BEEM images of an individual

InAs/GaAs quantum dot under a polycrystalline Au base. (b) Comparison of BEEM spectra obtained

by ballistic electron injection into an InAs dot and into the wetting layer between dots. (Reprinted

1012 P. Sutter

in a Co/Cu/Co trilayer structure, used in spin-valve devices, inte-

grated on top of the Au base layer. Unpolarized carriers injected from

an STM tip into this magnetic multilayer base will undergo spin-

dependent scattering in the ferromagnetic Co layers. In areas in which

the Co layers couple ferromagnetically, only one spin component will

be scattered heavily and a large fraction of unscattered carriers is

transmitted across the Au/Si interface. If the magnetization direction

of the two Co layers is misaligned, both spin components are strongly

attenuated by scattering, causing a sharp drop in collector current.

5.2 Probing Buried Interfaces (II)—Quantum Size Effects

In BEEM hot carriers, locally injected into a metal/semiconductor het-

erostructure, are used to measure the transmitted current across a

buried interface. Instead, carriers that impinge with energies below

threshold and are reﬂ ected back into the metal ﬁ lm can also be con-

sidered. Due to the long mean free path, these carriers can set up

standing waves in the metal ﬁ lm. An STM tip, probing the evanescent

tails into the vacuum, can then be used to image fringes due to inter-

ference of these electrons. The concept of electron interference in metal

ﬁ lms dates back to Jaklevic et al. (1971), and interference effects have

been observed by angle-resolved photoemission, low-energy electron

diffraction and low-energy electron microscopy.

An implementation of an STM experiment to probe interference

effects in the system Pb/Si(111) is shown in Figure 15–33. Pb evapo-

rated onto a stepped Si(111) substrate forms (111)-oriented islands

whose surface is atomically ﬂ at. Due to the substrate vicinality, the Pb

Figure 15–33. Electron interference in a Pb “quantum wedge” on Si(111). (Left) Geometry of the

Pb wedge on a stepped Si(111) substrate. The Pb thickness varies in increments of roughly one Si(111)

step height, giving rise to electron interference fringes in the direction of the substrate steps. (Right)

Constant-current STM images (730 nm × 110 0 n m) at −5 V (a) and +5 V (b) sample bias. The image

obtained at positive bias shows apparent height changes at the surface of the wedge due to electron

Physical Society.)

Chapter 15 Scanning Tunneling Microscopy in Surface Science 1013

island is wedge shaped, with a thickness that changes in integer mul-

tiples of the Si(111) step height from one substrate terrace to the next.

While STM at positive sample bias, i.e., injection of electrons from the

tip, images the atomically smooth Pb surface, STM images at opposite

bias show bands of apparent terraces and steps, aligned with steps of

the Si substrate, at the surface of the Pb wedge. These images, and

associated tunneling spectra, are interpreted as signatures of quantum

well states in the Pb wedge (Altfeder et al., 1997), and can be used to

determine the position of subsurface steps as well as the position-

dependent absolute thickness of the Pb ﬁ lm. Bands with constructive

and destructive interference alternate with a thickness change d

of one

Pb(111) monolayer if d

≈ λ

/4, where λ

denotes the Fermi wavelength.

Similar interference effects were also observed by STM for epitaxial

silicide layers, such as CoSi

/Si(111) (Lee et al., 1994) and NiSi

/Si(111)

(Kubby and Greene, 1992).

Strikingly, electron interference can even be used to image interfacial

atomic structures buried under as much as 10 nm of metal. In the Pb/

Si(111) system, the (7 × 7) reconstruction of the Si(111) surface remains

essentially intact upon low temperature evaporation of Pb, except for

some intermixing by replacing Si adatoms by Pb (Altfeder et al., 1998).

Due to the topology of the Fermi surface of Pb, in particular a large

mismatch between the electron effective mass in in-plane and normal

directions, the quantized electron states in the Pb ﬁ lm can be used to

map interfacial structure with a resolution of 0.6 nm for overlayer thick-

nesses exceeding 10 nm, or roughly 10 times the Fermi wavelength in

the metal.

5.3 Imaging Buried Heterostructures—Cross-Sectional STM

The strong interest in low-dimensional semiconductor structures—

quantum wells, wires, and dots—has stimulated widespread activity

in nanoscale imaging of electronic materials with reduced dimension-

ality. Recent efforts have focused on self-assembled quantum dots,

generated by lattice mismatched heteroepitaxial growth. Semiconduc-

tor quantum dots with lateral size in the 10–100 nm range are readily

imaged by STM if they are exposed as islands on a free surface. Con-

sequently, a large number of studies have been devoted to studying

epitaxial growth and quantum dot self-assembly by conventional STM

imaging. However, almost any technological applications of self-

assembled quantum dots require embedding in a matrix, often consist-

ing of the substrate material. The embedding process causes signiﬁ cant

modiﬁ cations to the dots that include segregation and intermixing,

shape changes, dopant redistribution, and adjustments to the local

strain ﬁ eld in the dot and in the surrounding material. All these

factors make it desirable to image embedded rather than exposed

nanostructures.

Cross-sectional STM (X-STM), originally demonstrated by Feenstra

et al. (1987) for imaging and spectroscopy on (110) surfaces of III–V

compound semiconductors, offers an elegant solution to this chal-

lenge. Semiconductors that cleave easily, as most III–V compounds do,

1014 P. Sutter

are used as a substrate for the growth of embedded self-assembled

quantum dots. A sample is then cleaved in UHV, and STM imaging is

performed on the cleavage face, typically a nonpolar (110) plane, which

provides large step-free areas for atomic resolution imaging. In this

geometry, X-STM gives access to subsurface structures over the entire

thickness of the epitaxial layer and the underlying substrate.

X-STM has been used to image a variety of buried semiconductor

heterostructures, such as superlattice structures in GaAs/AlGaAs

(Salemink and Albrektsen, 1991), InAs/GaSb (Feenstra et al., 1994), and

GaN/GaAs (Goldman et al., 1996), showing atomic-scale composition

ﬂ uctuations, interface roughness, lateral stain variations, and phase

separation in these systems. The technique has seen a strongly revived

interest with the advent of self-assembled quantum dots and quantum

dot superlattices (Legrand et al., 1998). Speciﬁ cally for the imaging of

quantum dots, X-STM relies on the fact that the dots are small and form

rather dense populations. Hence, a random cleavage will cut through

a large number of these nanostructures and provide a cross-sectional

view of their atomic structure on the cleavage plane (Figure 15–34).

Much of the power of X-STM imaging derives from the fact that bias-

dependent imaging provides chemical contrast on (110) cleavage faces

of III–V compounds (Feenstra et al., 1987). Empty-state imaging gives

atomically resolved maps of the cation sublattice and allows a direct

identiﬁ cation of atomic species, e.g., indium atoms in a GaAs matrix

(Pﬁ ster et al., 1995). This electronic structure effect not only provides

strong contrast to determine the shape of individual buried InAs

quantum dots and their stacking in multilayer structures, but can also

be used to quantify interface roughness, intermixing, and surface seg-

regation, near the dots and the wetting layer, with atomic precision.

To access this information in high-resolution images, a background

subtraction has to be performed to remove topographic contrast of the

Figure 15–34. Cross-sectional STM on self-assembled quantum dots. (Left) Illustration of the possible

apparent geometries observed due to cleavage at random positions through quantum dots with pyra-

midal and truncated pyramidal shape. (Right) Filled-state constant-current STM of an InAs quantum

dot embedded in GaAs. Part of the image in (a) is treated by a local mean equalization ﬁ lter to accen-

tuate the atomic corrugations in the dot and the surrounding GaAs matrix, as shown in (b). (Reprinted

Chapter 15 Scanning Tunneling Microscopy in Surface Science 1015

pronounced local deformation of the cleavage plane due to the relax-

ation of the strained dots and matrix (Davies et al., 2002). Conversely,

when combined with modeling, the elastic relaxation at the free cleav-

age surface itself can be used to quantitatively determine the strain

ﬁ eld in and around individual dots.

Apart from the imaging of buried semiconductor quantum struc-

tures, an application of X-STM that has been receiving increasing atten-

tion is the mapping of electronic dopants for electronics (Figure 15–35)

and, more recently, of magnetic dopants for spintronics applications.

Buried substitutional Zn and Be acceptors in p-GaAs have been imaged

as protrusions in ﬁ lled-state constant-current STM via a contrast mech-

anism assigned to an increased local state density directly above a

dopant (Johnson et al., 1993). Si donors at Ga sites (Si

) in GaAs have

been imaged on GaAs(110) as protrusions, a few nanometers in size

and with discrete values of apparent height, superimposed on the

background lattice. The observed contrast in ﬁ lled-state constant

current STM was attributed to a local perturbation of the near-surface

band bending by the Coulomb potential of the Si

. The discrete appar-

ent heights were interpreted as a consequence of a distribution of the

donor atoms over ﬁ ve subsurface layers beneath the cleavage surface

(Zheng et al., 1994).

Deep acceptor states due to magnetic impurities in III–V semicon-

ductors, such as substitutional Mn

in GaAs, are expected to play an

important role in the hole-mediated coupling between magnetic impu-

Figure 15–35. Imaging of individual dopants by X-STM. (a) Filled-state constant-current STM image

(V = −1.6 V) of cleaved GaAs(110). Individual Si

substitutional donors appear as protrusions of dif-

ferent apparent height. (b) Band diagram illustrating the electron tunneling process between a metal

tip and the GaAs(110) surface in the presence of tip-induced band bending. The Coulomb potential of

a donor ion locally alters the band bending, causing an increase in tunneling current above the donor.

1016 P. Sutter

rities, and thus determine the magnetic properties of hole-mediated

ferromagnetic semiconductors such as Ga

1−x

As, important for

emerging spintronics applications. X-STM at room temperature was

used to map the wave function of the hole bound to an individual Mn

acceptor in GaAs (Yakunin et al., 2004). Via bias-induced changes to

the local band bending, the acceptor could be imaged in both the

neutral (U

= +0.6 V) and ionized state (U

= −0.7 V). The acceptor

ground state has a highly anisotropic structure due to a signiﬁ cant

contribution of d-wave envelope functions, which is well-reproduced

by simulated images based on a tight-binding model of the Mn accep-

tor structure (Tang and Flatté, 2004).

6 STM Image Simulation

Although STM is a very powerful experimental technique in its own

right, geometric and spectroscopic contrast tend to be difﬁ cult to sepa-

rate, as discussed previously. In many cases, the unequivocal identiﬁ -

cation of surface structures or of adsorption geometries requires a

comparison of experimental STM images with contrast simulations.

The conventional approach to STM image simulations follows a two-

step process. Relaxed atomic positions of candidate surface structures

are calculated by ab initio theoretical methods, such as density func-

tional theory. The actual STM contrast is then computed using the

Tersoff–Hamann theory of STM (Tersoff and Hamann, 1983, 1985).

By combining bias-dependent atomic-resolution STM images with

simulated images for various candidate structures, even completely

unknown surface structures can in principle be “solved” on the basis

of STM imaging alone. The difﬁ culty lies less with the microscopy than

with the identiﬁ cation of plausible candidate surface structures. In the

past, this key step has typically been approached intuitively, i.e., by

guessing structures based on minimizing the density of dangling

bonds, starting from a truncated bulk structure. Recently developed

systematic techniques, based on stochastic optimization, for generating

comprehensive sets of candidate structures promise to become a pow-

erful tool for solving a wide range of surface structures by STM imaging

and image simulation (Ciobanu and Predescu, 2004).

The Tersoff–Hamann theory, the basis of most STM image simula-

tions to date, provides a transfer matrix formalism to calculate the

tunneling matrix element and tunneling current for realistic conﬁ gura-

tions of tip and sample. For values of tip–sample separation typical in

STM imaging (∼1 nm), the coupling between tip and sample wave func-

tions is weak, and the tunneling process can be treated by ﬁ rst-order

perturbation theory. Within this framework the tunneling current is

given by

fE fE M E V E

(

)

−

(

)

[]

+−

(

)

≈

∑

µν

µν ν µ



MMEEEE

FFµν µ ν

µν

δδ

−

(

)

−

(

)

∑

(7)

Chapter 15 Scanning Tunneling Microscopy in Surface Science 1017

where f(E) is the Fermi function, V denotes the tunneling bias, M

µv

the

tunneling matrix element between a tip state ψ

and a sample state ψ

and E

µ(v)

the energy of state ψ

µ(v)

. In the second line, the Fermi function

was replaced by a step function (zero-T approximation), and the limit

of low tunneling bias has been assumed. If, after Bardeen (1961), the

tunneling matrix element is written as a surface integral, and the

sample and tip wavefunctions are expanded in plane waves, one

obtains

dabe e

=−

∫

−

⋅



(8)

Here q is the Fourier wavevector and a

, b

are expansion coefﬁ cients

in the plane wave expansion of the sample and tip wavefunctions, x

and z

denote the lateral and vertical tip position, and κ

is the decay

constant. Given the wavefunctions of sample and tip, this expression

provides the tunneling matrix element, from which the tunneling

current can be calculated via Eq. (7).

In practice, a difﬁ culty arises from the fact that the atomic-scale

geometry and chemical composition of the tip are unknown. Thus,

assumptions have to be made as to the tip wavefunctions (i.e., b

). For

an s-wavefunction of the tip (as for an ideal “point”–tip), the tunneling

current is

IEEE∝

()

−

(

)

≡

()

∑

ψδ ρ

vF F

(9)

i.e., is proportional to the local density of states of the sample at the

Fermi energy, a property of the sample surface alone! For ﬁ nite tun-

neling bias, V, the tunneling current can be written as an integral over

the energy range between the Fermi energy E

and E

+ V:

IEEeVTEeVdEt

()

−

()()

∫

ρρ

, (10)

and the tunneling conductance at bias V is proportional to the posi-

tion-dependent density of states of the sample at energy eV from the

Fermi energy

eV T eV V

(

)

≈

()()( )

ρρ

(11)

Contrast calculations thus involve the computation of the position- and

energy-dependent sample DOS to obtain simulated maps of tunneling

conductance dI/dV(x,y) or tunneling current I(x,y).

Although originally derived for small voltages, as used for STM

imaging on metals, with this extension the Tersoff–Hamann formalism

can be applied to simulate images at higher bias as well, and has

proven a powerful simulation tools for a wide range of imaging sce-

narios. Tromp et al. (1986) were the ﬁ rst to show that it could be applied

to semiconductor surfaces, as demonstrated by their successful contrast

simulation for the Si(111)-(7 × 7) reconstruction. The systems simulated

since then include surface structures of semiconductors (Fujikawa

et al., 2002; Klijn et al., 2003), ultrathin insulators (Olsson et al., 2005),

1018 P. Sutter

as well as adsorbed atoms (Repp et al., 2004) and molecules (Olsson et

al., 2003; Kühnle et al., 2002).

Figures 15–36 and 15–37 illustrate two of the numerous examples of

this approach in the literature.

Shallow Ge quantum dots self-assembled during heteroepitaxy on

Si(001) invariably have surface termination by (105) facets, with surface

normal just 11° away from [001]. These (105) facets appear extremely

stable, likely due to a low density of dangling bonds and additional

strain stabilization by surface strain compensating for some of the 4%

lattice mismatch strain between the Ge overlayer and the Si substrate.

To calculate the surface energy, and thus explain the stability of the

facet, a detailed knowledge of the surface structure is necessary. Dual

bias constant-current STM combined with STM contrast calculations

was used to identify a best match with one of two proposed structures

of the (105) surface: “paired dimer” (Structure A) and “rebonded step”

(Structure B) (Fujikawa et al., 2002). The STM contrast is clearly identi-

ﬁ ed as that of a “rebonded step” structure, the structure that not only

has the lowest dangling bond density but also causes tensile surface

strain, key to the strain stabilization of the (105) facet.

Figure 15–36. Identiﬁ cation of the surface structure of Ge(105). Empty- and

ﬁ lled-state constant-current STM images are compared with two candidate

structures, the paired dimer Structure A and rebonded step Structure B (c and

d). A Tersoff–Hamann calculation of the STM contrast for these two structures

clearly shows that the experimental STM images arise from the rebonded step

American Physical Society.)

Chapter 15 Scanning Tunneling Microscopy in Surface Science 1019

Simulations of STM contrast of adsorbed molecules pose a somewhat

different problem than simulations of surface structures. For solid

surfaces, the combination of STM imaging with image simulation can

discriminate between several candidate structures, as discussed in the

previous example. For molecules, the structure is typically well known.

However, the adsorption geometry (site, orientation) as well as the

conformation for larger, more ﬂ exible molecules enter as unknowns

into the simulation. A relatively simple example is the stiff molecular

cage structure of fullerene C

(Hou et al., 1999; Pascual et al., 2000; Lu

et al., 2003). In this case, the structure and conformation are well

known, and the only parameter of the contrast calculation is the ori-

entation. A more complex system, Cu-tetra(3,5-di-tert butyl phenyl)

porphyrin (Cu-DTBPP) on Cu(211), is illustrated in Figure 15–37.

Cu-DTBPP consists of a central porphyrin ring with four symmet-

rically attached di-tert-butyl phenyl (DTBP) groups (Figure 15–37a).

These four bulky groups determine the shape of the molecule, which

is imaged in STM as a four-leaf clover structure, and deﬁ ne the interac-

tion with the metal substrate (Jung et al., 1996). The orientation of the

side groups is the main parameter that needs to be optimized to deter-

mine the conformation of the adsorbed molecule, and to simulate the

experimental STM images. Figure 15–37 shows several candidate con-

formations, with leg angles of 60° (b), 45° (c), 30° (d), and the optimized

angle of 10° relative to the substrate (e), which was found to best repro-

duce the experimental STM image of the molecule.

Figure 15–37. Identiﬁ cation of the molecular conformation of Cu-DTBPP on

Cu(211). (a) Molecular model of Cu-DTBPP, with the four-lobed pattern

observed by STM marked in yellow. (b–e) STM contrast calculation for differ-

ent angles between the four legs and the substrate: (b) 60°, (c) 45°, (d) 30°, and

(e) 10°. (f) Experimental STM image of the molecule. (Reprinted from Moresco