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

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980 P. Sutter

Ge/Si(001) epitaxy (Qin and Lagally, 1997). Classic theories of nucle-

ation in thin ﬁ lm growth are based on the notion of a “critical nucleus,”

deﬁ ned as the structural entity for which the addition of one more atom

will for the ﬁ rst time reduce the free energy. Employing very low Ge

coverages and high-resolution dual bias STM imaging to uncover the

link between monomer adsorption and initial 2D growth islands, this

study shows that island formation may not involve a “critical nucleus,”

but instead may proceed via a family of metastable structures of

varying size, with signiﬁ cant consequences on many growth models

that are based on nucleation and require the size of a critical nucleus

as input.

More recently, interest has concentrated on strained layer heteroepi-

taxial growth, e.g., of Si

1−x

alloys on Si(001), as an elegant way of

producing large arrays of nanostructures. Si and Ge are miscible over

the entire composition range, and the lattice mismatch in the Si

1−x

Si(001) system can be tuned between 0 and 4% by alloying. Over a wide

range of compositions, Si

1−x

alloys initially wet the Si substrate, and

at higher coverage develop coherent (i.e., dislocation free) faceted three-

dimensional (3D) islands that lower the free energy by relaxing part

of the lattice mismatch strain. Potentially useful in electronics or opto-

electronics, these faceted nanostructures have shown a strikingly

complex array of growth phenomena, which make them interesting for

fundamental growth studies.

Constant current STM images with atomic resolution typically

encompass ﬁ elds of view of few tens of nanometers. Combining a drift-

stable microscope with state-of-the-art control electronics, substantially

larger atom-resolved images have become feasible. The ability to obtain

image sizes in excess of 1 µm

with high resolution is potentially pow-

erful for imaging growth processes, since it provides access to all rele-

vant length scales as well as image statistics far superior to that of

conventional small scans. Figure 15–7 illustrates this capability with

an STM image of 1.5 monolayers Ge on Si(111) with a ﬁ eld of view of

0.75 µm and 0.05 nm pixel size. The large scan provides an excellent

overview of the step and island structures resulting from monolayer

Ge deposition. At progressive zoom into the image, individual terraces,

and, ultimately, single surface defects and reconstruction domains

(here coexisting 7 × 7 and 5 × 5 domains) can be examined.

Figure 15–8 gives an example in which the superior statistics result-

ing from large atom-resolved images was used successfully to pinpoint

the mechanism of periodic surface roughening in Ge/Si(001) growth

(Sutter et al., 2003a). Via a sequence of “quench-and-look” experiments

at different Ge coverages, short-range interactions between surface

steps and vacancy lines, periodic arrays of linear chains of dimer

vacancies, are shown to cause a highly correlated surface roughness in

the form of anisotropic 2D islands with progressively higher aspect

ratio (a–c). Finally, images obtained at a critical Ge coverage of four

atomic layers (d) show the transition from 2D to 3D growth by forma-

tion of the ﬁ rst faceted islands on the rough wetting layer, and identify

the atomic-scale pathway of the 2D–3D transition.

Chapter 15 Scanning Tunneling Microscopy in Surface Science 981

Figure 15–7. Large-area atom-resolved STM. (a) STM image with 0.75-µm

ﬁ eld of view and 0.05-nm pixel size, showing the surface morphology of Si(111)

after deposition of 1.5 ML Ge at 550°C. An array of parallel steps, running

diagonally from the upper left to lower right, coexists with islands nucleated

during Ge deposition. (b) Zoomed-in view (50 nm) of the area marked by a

square in (a), showing one of the islands. (c) Further zoom-in (10 nm), showing

the coexistence of (7 × 7) and (5 × 5) reconstructed domains in the area marked

in (b).

Figure 15–8. Transition from 2D to 3D morphology in the growth of Ge on Si(001). Large-area atom-

resolved STM images (250 nm × 125 nm sections are shown here) illustrate the surface morphology at

(a) 1.5 ML, (b) 2.3 ML, (c) 3.5 ML, and (d) 4.0 ML Ge coverage. The transition to 3D growth is preceded

by the formation of highly correlated, anisotropic surface roughness. With the superior statistics of

large-area high-resolution images, the repulsive interaction between surface steps and defects (dimer

vacancy lines) was identiﬁ ed as the origin of the ordering of this surface roughness. (Reprinted with

982 P. Sutter

Initial 3D islands with shallow facets, such as those shown in Figure

15–8d, evolve into more complex shapes involving steeper facets, which

give rise to more efﬁ cient strain relaxation (Figure 15–9). For Si

1−x

epitaxy on Si(001), the facets bounding the islands identiﬁ ed by STM

are to a large extent major stable facets of Si and Ge (Figure 15–9a). At

early stages of 3D growth, shallow (105) faceted “huts” are invariably

observed (Figure 15–9b; Mo et al., 1990). These islands then undergo a

shape transformation to become multifaceted “domes” (Figure 15–9c;

Medeiros-Ribeiro et al., 1998). At later stages in the shape evolution,

elastic strain relaxation increasingly competes with plastic relaxation

via dislocations. For Ge/Si(001) dislocations are introduced before the

“dome” shape can transform further by introducing additional steeper

facets. By reducing the Ge concentration of Si

1−x

alloys, and thus

lowering the lattice mismatch strain, the coherent shape evolution has

been extended beyond the “dome” shape to the end-point in the

stereographic triangle, where steep (111) facets are introduced (Sutter

et al., 2004).

3 Tunneling Spectroscopy

Equation (1) gives an expression for the tunneling current I in the WKB

approximation for planar tunneling. In this approximation the tunnel-

ing current is an integral, over the energy range of width |eV| in which

tunneling can occur, of a product of the densities of states (DOS) of tip

[ρ

(E)] and sample [ρ

(E)] multiplied by the transmission probability,

T(E, eV). While this simple approximation cannot address the high

spatial resolution of STM—a more elaborate theory capable of address-

ing this aspect will be discussed in Section 6—it demonstrates that the

tunneling current is affected by the electronic structure of both the tip

and the sample. In a large number of applications it would be desirable

to merely map the atomic scale “topography” of a sample. The sensitiv-

ity of the tunneling current to the DOS can then be a disadvantage,

since it often prevents a simple interpretation of a tunneling image as

Figure 15–9. Shapes of coherent (i.e., dislocation-free) 3D islands induced by lattice mismatch strain

during Si

1−x

/Si(001) heteroepitaxy. (a) Unit stereographic triangle for Si, showing the major and

minor stable facets (Gai et al., 1998). (b) STM top view, showing a shallow (105) faceted “hut.” (c) Mul-

tifaceted “dome” shape, terminated by (105), (113), and (15 3 23) facets. (d) “Barn”-shaped 3D island,

observed for low-misﬁ t Si

1−x

alloys on Si(001), transformed from a “dome” by introduction of addi-

Physics.).

Chapter 15 Scanning Tunneling Microscopy in Surface Science 983

a “topographic” map. For many metals with small variations in the

DOS near the Fermi energy such a simple interpretation is often pos-

sible, i.e., height maxima in a constant current STM image are corre-

lated with atomic positions. However, for semiconductors with strongly

varying DOS near E

, the simple picture frequently breaks down.

An example is the (001) surface of Si. Geometrically, this surface

consists of Si dimers, in which each atom is bonded to two atoms in

the second layer and to its dimer partner. Constant-current STM images

obtained on Si(001) at positive sample bias indeed show two maxima

in each dimer (Figure 15–10B), which could be interpreted as the

“atomic positions.” At negative sample bias, however, only a single

broader bean-shaped structure is observed (Figure 15–10A), which

extends across each dimer. In fact, the tunneling current in empty-state

STM (positive sample bias) reﬂ ects the charge distribution in a π* anti-

bonding state just above the Fermi energy, whose wave function has a

node at the center of the dimer. Even in this case in which the STM

image shows two maxima per dimer, these maxima do not reﬂ ect the

atomic positions in the dimer. Worse yet, in ﬁ lled-state STM (negative

sample bias) a π bonding state is imaged whose charge density peaks

at the center of the dimer bond, thus giving rise to a single “topo-

graphic” maximum at that position.

The sensitivity to the electronic structure of tip and sample, however,

is not merely a complication in STM imaging. It is also one of the major

strengths of the technique, since it allows measuring and mapping

surface electronic structure with very high spatial resolution well

below 1 nm. While most other techniques, such as ultraviolet or x-ray

photoelectron spectroscopy or Auger electron spectroscopy, average

over macroscopic sample areas, recently developed spectromicroscopy

techniques, such as synchrotron photoelectron emission micro-

scopy, provide spectroscopic imaging with 10 nm spatial resolution (see

Chapter 8, this volume). However, measurements of surface electronic

Figure 15–10. Constant-current STM images of Si(001) at negative [V = −1.6 V

(A)] and positive [V = +1.6 V, (B)]. The (2 × 1) unit cell is outlined, and the loca-

tions of the dimers are shown in the center. (Reprinted with permission from

Reviews www.annualreviews.org.)

984 P. Sutter

structure “atom-by-atom,” summarized under the term scanning tun-

neling spectroscopy, are feasible only by STM.

3.1 Bias-Dependent Imaging

The simplest scenario for gathering electronic structure information

involves the successive measurement of constant-current STM images

at different sample bias. As discussed in Section 1, the tunneling trans-

mission probability is generally highest at the Fermi energy of the

negatively biased electrode, and falls off exponentially at lower ener-

gies. For positive sample bias, i.e., empty-state STM, elastic tunneling

occurs mainly from states near the tip Fermi energy into unoccupied

sample states. In this polarity, varying the bias voltage probes different

surface states of the sample, particularly if the electronic structure of

the tip varies slowly in the energy range deﬁ ned by the bias voltages

used. A series of constant-current STM images at different bias can

thus be used to map the spatial distribution of unoccupied surface

states of the sample.

For negative voltages applied to the sample, i.e., ﬁ lled-state STM, the

situation is not as fortunate. The tunneling current is now dominated

by states near the Fermi level of the sample. As a result, the occupied

sample state with highest energy is invariably imaged preferentially

(Becker et al., 1989). Even if lower-lying surface states exist, as indicated

schematically in Figure 15–11, constant-current STM imaging is rather

insensitive to those states.

As a possible solution to this problem in bias-dependent ﬁ lled-state

imaging it has been suggested that metal probe tips with smoothly

varying density of states near the Fermi energy could be replaced by

a semiconductor tip with a strongly modulated DOS. Band structure

effects have long been recognized in the interaction of low-energy

electrons with metal surfaces (Bauer, 1994). As an example, the high

normal incidence reﬂ ectivity on W(110) at low electron energies is due

to a (110) projected band gap extending over 5 eV, i.e., a lack of extended

bulk states in the energy range of this gap. For W(100), such a gap does

Figure 15–11. Band diagrams illustrating the bias-dependent tunneling

between tip (T) and sample (S). Sample bias V > 0: empty-state STM. V < 0:

ﬁ lled-state STM. T(E) shows schematically the transmission probability as a

function of energy for states participating in the tunneling process.

Chapter 15 Scanning Tunneling Microscopy in Surface Science 985

not exist. Low-energy electrons can propagate into extended states, and

the reﬂ ectivity in the same energy range is low. Similarly, it can be

expected that a lack of ﬁ nal states due to projected band gaps in the

STM tip material can signiﬁ cantly affect the tunneling probability in

the energy range spanned by such gaps. This modulation of the trans-

mission probability could be used for efﬁ cient energy ﬁ ltering of the

tunneling current in constant-current STM, speciﬁ cally in ﬁ lled-state

imaging.

Calculations by density functional theory (DFT) show a number of

gaps in the [111]-projected band structure of III–V compound semicon-

ductors such as InAs. III–V compound semiconductors cleave easily at

(110) planes, and cleavage corners bounded by {110} and (100) planes

are sufﬁ ciently sharp for atomic-resolution STM (Nunes and Amer,

1993). In addition, InAs(110) has the advantage of an unpinned surface

with minimal band bending and slight electron accumulation. The

feasibility of energy-ﬁ ltered STM has been demonstrated by using a

cleaved InAs tip to selectively image different occupied surface states

on Si(111)-(7 × 7) (Sutter et al., 2003b). In these experiments, summa-

rized in Figure 15–12, a [111]-projected gap in the InAs conduction

band, centered at Γ and about 2.6 eV wide, is used to modulate the

tunneling current in ﬁ lled-state constant current STM. The “adatom”

state (“a”) on Si(111)-(7 × 7), which lies only 0.35 eV below the Fermi

energy and is imaged by STM using a metal tip, dominates the tunnel-

ing current at low tip–sample bias. At higher bias, this state aligns with

a projected gap in the InAs conduction bands and its tunneling

probability is reduced sharply. Under these conditions the “rest atom”

Figure 15–12. Energy-ﬁ ltered STM. (a) Bulk band structure of monocrystalline InAs probe tips, pro-

jected along the (111) zone axis parallel to the tunneling direction. E

denotes a projected gap in the

bulk conduction band. (b) Band diagram and STM image for low-bias ﬁ lled state STM with InAs tips,

demonstrating preferential imaging of the adatom state on Si(111)-(7 × 7). (c) High-bias ﬁ lled state

InAs-tip STM on Si(111)-(7 × 7): alignment of the adatom state with the projected tip gap reduces its

contribution to the tunneling current, giving rise to preferential imaging of the energetically lower

Society).

986 P. Sutter

state (“r”), a surface state 0.8 eV below E

that is not accessible in con-

ventional STM imaging, contributes a majority of the tunneling current

and can be imaged selectively. Importantly, these results suggest that

robust bulk band structure effects, which are independent of the atomic

structure of the tip, can be used to modulate the transmission probabil-

ity in vacuum tunneling. Once developed into a routine imaging tech-

nique, energy-ﬁ ltered STM has the potential to provide rich spectroscopic

contrast within the relatively simple framework of bias-dependent

constant current STM.

A classic example of a scenario in which conventional bias-

dependent imaging provides directly interpretable spectroscopic infor-

mation is imaging of cation and anion sites on (110) cleavage planes of

compound semiconductors such as GaAs (Feenstra et al., 1987) or InP

(Ebert et al., 1992) (Figure 15–13). For (110) surfaces of compound semi-

conductors, such as GaAs, the occupied state density (imaged at nega-

tive sample voltage) is localized on the anions (As, P), while the

unoccupied state density (positive sample voltage) is localized on

the cations (Ga, In). As a result, bias-dependent STM imaging can be used

to selectively image the cation and anion sublattices on these surfaces.

3.2 Local I-V Measurements and Current Imaging

Tunneling Spect roscopy

In many instances, a complete electronic structure map is not required,

but one would like to determine, at one or several positions on a

sample, the surface density of states in an interval of a few eV around

the Fermi energy. Such local measurements can, for example, serve

to determine if a speciﬁ c surface reconstruction or a small cluster is

semiconducting or metallic, to measure the band gap at the surface

of semiconductor samples, and to determine for a given location the

energies of surface states.

Figure 15–13. (a) Bias-dependent STM on GaAs(110): selective imaging of Ga and As sublattices at

by the Armeucion Physics Socuity). (b) Compound STM image of the InP(110) surface, assembled from

Elsevier). (See color plate.)

Chapter 15 Scanning Tunneling Microscopy in Surface Science 987

Local current–voltage [I(V)] spectra serve this purpose. The basic

information content of a tunneling I(V) spectrum can be demonstrated

by differentiating Eq. (1) [V > 0]:

eeV TeVeV e E E eV T E

(

)

(

)

(

)

(

)

−

(

)

∂ρρ ρρ

0, ,,/

deV e E E eVTEeV dE

(

)

[

(

)

−

(

)

′

−

(

)

(

)

]

∫

ρρ

(4)

For a given energy eV, the tunneling conductance dI/dV reﬂ ects the

density of states of the sample at that energy, ρ

(eV).

Feenstra et al. (1987) noted difﬁ culties with conductance spectros-

copy, resulting from the fact that the expression for dI/dV diverges

exponentially both in voltage (V) and separation (z). These divergences

can be eliminated by normalizing dI/dV by the conductance of the

tunneling junction, [dI/dV]/[I/V] ≈ d(lnI)/d(lnV). In this form, spe-

ctra obtained at different tip–sample separation z can be compared

directly.

Local spectroscopy is quite simple to perform. The STM tip is posi-

tioned and stabilized over a chosen point on the sample. The feedback

loop is switched off while the sample voltage is varied over the desired

values, and a local measurement of tunneling current as a function of

bias voltage, I(V), is performed. As an alternative, the tunneling con-

ductance, dI(V)/dV, can be measured by ramping the bias voltage with

a small ac voltage added, and measuring the ac component of the tun-

neling current at the modulation frequency of the ac part by lock-in

techniques. After the I(V) or dI(V)/dV spectrum is recorded, the tip

feedback is reactivated, and STM imaging can resume.

Figure 15–14a shows tunneling conductance spectra obtained on p-

and n-type GaAs(110) (Feenstra et al., 1987), which provide a measure

Figure 15–14. (a) Local normalized conductance spectra obtained on n- and p-doped GaAs(110),

showing three peaks (V, D, C) originating from surface states (Feenstra et al., 1987). (b) Normalized

conductance spectra obtained on InP(110), illustrating the valence and conduction band edges delimit-

ing the bulk bandgap (1.4 eV), and the A

and C

surface states deﬁ ning the surface gap (1.9 eV)

988 P. Sutter

of the surface state density. The spectra show three distinct peaks

associated with surface states. Peak C is related to a state in the GaAs

conduction band, localized on the Ga atoms, while peak V stems from

a valence state localized on the As anions. Peak D is associated with

tunneling of dopant-induced carriers within the bulk band gap. The

separation between the leading edges of the C and V peaks is close to

the bulk band gap of GaAs (E

= 1.43 eV), i.e., in this system tunneling

spectroscopy can be used to determine the band gap. Figure 15–14b)

shows tunneling conductance spectra on the (110) cleavage surface of

another III–V compound, InP. Also for InP, the band gap (∼1.4 eV) is

evident from sharp onsets of signiﬁ cant state density at the valence

and conduction band edges. However, for this system it was argued

that a wider surface band gap (∼1.9 eV) is indirect, delimited by a

surface state C

at the edge of the surface Brillouin zone and a broad-

ened state A5 at the zone center.

A natural, albeit experimentally much more complex extension of

local I(V) spectroscopy is the measurement of tunneling spectra, as

discussed above, at each image pixel of a constant-current STM scan.

This measuring scheme is called current-imaging tunneling spectro-

scopy (CITS). Since complete I(V) spectra are obtained at each image

point, the corresponding data sets can provide a full range of spectro-

scopic information. As an example, current maps I(x, y) at ﬁ xed tip–

sample bias can be produced. Instead, the voltage dependent tunneling

conductance dI(V)/dV can be calculated numerically and mapped as a

function of sample position. If the chosen voltage corresponds to the

energy of a surface state of the sample, conductance maps will provide

a direct image of the spatial distribution of that state. Due to the com-

plexity of the data acquisition, the experimental requirements for CITS

are quite stringent. Since complete I(V) curves are measured at each

image pixel, requiring the stopping of a scan and deactivation of the

feedback loop for a fraction of a second per spectrum, a very high sta-

bility of the tunneling gap and low lateral drift of the tip relative to

the sample are of key importance. These conditions are more easily

fulﬁ lled at cryogenic temperatures, where a z-stability of the order of

1 pm and lateral drift velocities of the order of few Å/hour are possible.

Low temperatures also reduce the thermal broadening of the tunneling

transmission coefﬁ cient T(E), and thus narrow the linewidth of fea-

tures in the tunneling spectra.

A classic example of the application of CITS, the measurement of the

electronic structure of Si(111)-(7 × 7), is shown in Figure 15–15 (Hamers

et al., 1986). Shown are a constant current image of the surface at +2 V

sample bias (a), as well as current images acquired during the same

scan at bias voltages of +1.45 V and −1.45 V, showing spatial maps of

unoccupied (+)/occupied (−) sample states at energies up to 1.45 eV

above/below the Fermi energy. CITS difference images, a precursor to

modern dI/dV maps, discussed below, calculated by numerically sub-

tracting current images at energies bracketing those of speciﬁ c surface

states, allowed the mapping of the adatom state, dangling bond, and

backbond state on this complex reconstructed surface.

Chapter 15 Scanning Tunneling Microscopy in Surface Science 989

More recently, this complex data acquisition mode has been used,

for example, to map modiﬁ cations in the electronic structure of indi-

vidual carbon nanotubes arising with the supramolecular assembly of

molecules inside the hollow tube to form nanotube “peapods”

(Hornbaker et al., 2002). dI/dV spectra obtained along the symmetry

axis of C nanotubes show distinct peaks in the density of unoccupied

states with a spatial periodicity corresponding to the average spacing

of embedded C

molecules observed by transmission electron micros-

copy, suggesting that the insertion of C

causes a signiﬁ cant modula-

tion of the electronic structure. A control measurement was constructed

by using the STM tip to push the C

away, and remeasuring dI/dV

spectra along the same nanotube section without embedded C

. The

empty tube obtained in this way shows small and smooth variations

in the density of states along the nanotube axis. Qualitatively, the elec-

tronic structure of the peapods was explained by the single wall C-

nanotube acting as a conduit that enhances the coupling between C

molecules nested inside it, and the Bragg scattering of nanotube states

due to the periodic arrangement of the C

. Calculations of the peapod

electronic structure conﬁ rm the formation of a hybrid electronic band,

which derives its character from both the nanotube states and the C

molecular orbitals (Figure 15–16).

3.3 Differential Conductance (dI/dV) Mapping

For a given energy eV, the tunneling conductance dI/dV reﬂ ects the

density of states of the sample at that energy, ρ

(eV). As a result, it can

be expected that high-resolution maps of tunneling conductance can

provide detailed information on spatial variations in sample electronic

structure. For example, by plotting dI/dV at an energy corresponding

to a localized state at the sample surface, the spatial distribution of that

sample state can be mapped.

In a typical experiment a constant current image, at a speciﬁ c bias

voltage and tunneling current used to stabilize the tunneling gap, is

Figure 15–15. Current-imaging tunneling spectroscopy on Si(111)-(7 × 7) (Hames et al., 1986). (a)

Constant-current STM image (V = +2 V), with one (7 × 7) unit cell outlined (F, faulted; U, unfaulted

half). (b and c) Current images obtained at +1.45 V and −1.45 V, respectively. Note the strong similarity

between the rest-atom contrast in the current image (c), and the contrast obtained in rest-atom imaging

by energy-ﬁ ltered constant-current STM (Figure 15–12).