Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

Подождите немного. Документ загружается.

86 Thin ﬁlm growth

PTcda (fendrich and Krug, 2007). for a sample at room temperature these

step-edge barriers are large compared to k

T so that crossing a step-edge is

comparatively slow. depending on the height of the barrier, the time for an

atom to move down to the layer underneath (the inverse of the rate constant

for crossing a step) can then range from 10 ps to 1 s, the large spread being

due to the exponential dependence on the barrier height (see fig. 5.1). in

general the diffusion and step-edge barriers depend on the orientation of

the underlying crystal and, unlike homoepitaxy, for thin lm growth the

ehrlich–Schwöbel barrier can also be layer dependent, e.g. due to strain

(Zhang et al., 2009, Krause et al., 2004a).

Through rate limiting steps, such as step-edge diffusion or nucleation,

which at moderate temperatures are very slow or even completely frozen

out, fast processes can be slowed down to relatively long timescales (see

Fig. 5.1). Apart from such material-specic, intrinsic effects, extrinsic

parameters start to play a role for slower processes. The most important

extrinsic parameter regarding timescales is the growth rate, which is the net

ux of atoms/molecules onto a surface. The growth rate determines the time

to form a monolayer and therefore is the reference timescale for real-time

experiments. This monolayer formation time can range from milliseconds

for technological production processes up to many seconds or even hours

in research. Such slow rates are mostly employed in fundamental research,

as production processes have to be optimized for high throughput, so that

also fast time-resolved experimental techniques are necessary or have to be

developed for production monitoring. further, the structure and morphology

of the growing thin lm itself can depend strongly on the growth rate, as fast

kinetic growth can result in structures far from thermodynamic equilibrium

if the formation of the lowest energy structure is slow.

in conclusion, growth phenomena span an extremely wide range of

timescales, so far inaccessible to any single theory or experiment. Ultra-fast

studies are used to determine the basic atomistic processes and calibrate rate

constants used in theory. experiments at slower timescales are very important

to identify the growth scenario and follow the structure formation, strain, and

morphology. it is remarkable how experiments on the second time-scale can

help to deduce information on atomistic processes on the surface. further,

real-time experiments are also important technologically, because growth

–15

–13

–11

–9

–7

–5

–3

–1

Fast growth

of one ML

Slow growth

of one ML

De-wetting

of a ML

Time to cross Ehrlich–Schwöbel

barrier (interlayer transport)

Hopping to nearest lattice

site (diffusion)

Seconds

Vibrations

5.1 Simpliﬁed scheme of timescales for processes occurring during

growth.

ThinFilm-Zexian-05.indd 86 7/1/11 9:40:41 AM



87Modelling thin ﬁlm deposition processes

monitoring greatly facilitates or even enables growth of complicated nano- or

hetero-structures which could not be grown without direct process control.

5.3 Experimental techniques for real-time and

in-situ studies

experimental techniques for real-time and in-situ studies face several

challenges. ideally, a wide range of timescales has to be studied, structural

details have to be resolved on atomic length scales in the growth direction

and on the length scale of growing islands in the in-plane direction, the

observation should not interfere with growth itself, and the techniques have

to be surface sensitive, that is they have to discern the small surface signal

of a (monolayer) thin lm from the substrate signal. Currently, no single

technique is able to follow individual atomic movements on both ultra-fast

and slow timescales. correspondingly, several experimental techniques are

necessary to study different time- and length scales. without claiming to

be exhaustive, fig. 5.2 gives an overview of different techniques used for

real-time measurements.

a distinction has to be made between ensemble averaging measurements

and individual measurements both in space and time. in the spatial domain,

ensemble measurements such as X-ray scattering provide atomic detail

Time

Space

Non-repeating process,

continuous measurement

Repeating processes, pump-

probe and spectroscopy

Individual details,

microscopy

X-ray microscopy

LEEM, PEEM

Space averaging,

ensemble and

diffraction

measurements

TEM, SEM

AFM, STM

optical microscopy

Raman spectro-

microscopy

X-ray growth oscillations

helium-atom scattering

RHEED, LEED

Pump-probe

absorption sum

frequency generation

Reﬂection spectroscopy

5.2 Simpliﬁed overview of techniques for real-time growth

observation. The boundaries are, of course, not always necessarily

sharp. Details of the techniques shown can be found in technique

oriented chapters in this book and Lüth (2001) and Michely and Krug

(2004).

ThinFilm-Zexian-05.indd 87 7/1/11 9:40:41 AM



88 Thin ﬁlm growth

averaged over a certain sample area, while microscopy techniques are able to

resolve individual atomic or molecular details, albeit usually at slower time

resolution. Similarly, in the time domain it is possible to distinguish between

continuous real-time measurements that resolve single congurations of an

on-going process on the one hand, and pump-probe or spectroscopy techniques

which average over many repetitions of an ultra-fast/oscillatory process on

the other (note that the data acquisition time is much longer than the process

under study). Growth processes in general are non-repetitive and hard to reset

or trigger by external stimuli (an exception being pulsed laser deposition;

ferguson et al., 2009; Tischler et al., 2006), so that pump-probe techniques

do not easily lend themselves to in-situ growth studies. Therefore, ultra-fast

time resolution is hard to achieve in growth studies, because a continuous

measurement is limited by the read out speed of electronics, and, even more

severely, by the time needed to acquire sufcient measurement statistics

without averaging. despite a continuous measurement on slow timescales,

absorption or raman spectroscopy also contain spectroscopic information

on ultra-fast vibrational timescales of damped oscillatory processes.

in the following we will not discuss ultra-fast techniques but focus on

methods that can be used for real-time measurements during growth without

temporal averaging. Microscopy techniques have started to become fast enough

for real-time observation and examples of leeM (Meyer Zu Heringdorf

et al., 2001) or STM microscopy (rost, 2007) show the potential of spatially

resolved measurements. nevertheless, most real-time experiments in process

monitoring and basic research average over a representative sample area.

widespread techniques in both engineering and research environments are

real-time reectance/ellipsometry measurements and reection high-energy

electron diffraction (rHeed) oscillations, because of the comparative

simplicity of the setup. real-time X-ray scattering and real-time helium

atom scattering are more complex experimental setups, but yield different

information. The latter techniques can also be applied to different types

of samples such as molecular materials, which may get damaged by high-

energy electrons. in the following we will give an overview of spectroscopic

and microscopic techniques for growth monitoring, and then discuss and

compare helium atom, electron and X-ray scattering. we will focus on the

issues conceptually relevant in the context of real-time observations and

their modelling. we will not attempt to explain the implications in terms of

experimental technology and rather refer to the works of forker and fritz

(2009), lüth (2001) and Poelsema and comsa (1989).

5.3.1 Optical spectroscopy techniques

optical spectroscopy techniques can detect sub-monolayers of molecular/atomic

adsorbates on substrates (forker and fritz, 2009; Heinemeyer et al., 2010).

ThinFilm-Zexian-05.indd 88 7/1/11 9:40:41 AM



89Modelling thin ﬁ lm deposition processes

In differential re ectance spectroscopy (DRS), spectroscopic information is

gathered by acquiring the re ectivity R of the substrate before and during

deposition of a thin  lm usually at normal incidence. The time dependent

drS signal is then calculated according to

()

St()St

()

Rt()Rt

–

(

Rt( Rt

= 0)

(

Rt( Rt

= 0)

[5.4]

where R(t = 0) corresponds to the re ectivity of the bare substrate and R(t)

to the re ectivity at time t of the deposition when the substrate is covered by

the  lm with thickness d. As a high photon  ux measurement the detector

sensitivity and dark count rate is often less crucial than high dynamic range

and fast read-out speeds (typically ~10 ms). a typical time resolution is

below 10 s, taking into account averaging of multiple spectra to obtain low

coverage sensitivity. At normal incidence and for very thin  lms (i.e. for

d/l << 1) on a transparent substrate with refractive index n the drS signal

can be related directly to the imaginary part e

of the dielectric function

according to Mcintyre and aspnes (1971):

()

St()St

·(

1 –

)

[5.5]

This approximation simpli es the analysis greatly, although it is not possible

to determine e

. For thicker  lms, the complete dielectric function (e

)

can be modelled by matrix method based software. The experimental set up

for in-situ drS is shown in fig. 5.3.

Expanding the capabilities of DRS, re ection anisotropy spectroscopy

(RAS) measures the re ectance at normal incidence for two perpendicular

polarisations of light and therefore can also resolve in-plane anisotropies

of the optical constants (weightman et al., 2005; Hartell et al., 2001).

Spectroscopic ellipsometry (arwin and aspnes, 1984; aspnes et al., 1990)

 nally expands polarisation sensitive measurements to a range of different

incidence angles and therefore can also determine  lm thicknesses in the

nm range, that is far below the wavelength of light.

Light source

Optical ﬁ ber

CCD

detector

Lens

Sample

UHV chamber

5.3 Experimental setup for in-situ DRS (Heinemeyer, 2009).

ThinFilm-Zexian-05.indd 89 7/1/11 9:40:42 AM



90 Thin ﬁlm growth

Typical information that can be obtained from real-time optical

spectroscopy is the lm thickness evolution, and spectral changes due to

different structures that form during growth. The structural information

is only indirectly inferred from models that describe the excited states in

the thin lm. Therefore structural probes such as scattering techniques are

sometimes preferable as a direct measurement technique (lazzari et al.,

2009; Hosokai et al., 2010). nevertheless, ellipsometry, drS and raS can

be used as a ngerprint technique if the connection between structure and

spectral features is known. further, optical functional properties such as the

optical bandgap can be determined and correlated with the changes in thin

lm structure during growth.

5.3.2 Microscopy

Microscopy techniques are a direct way to measure the real-space structure

of a growing thin lm, but at the same time most microscopy setups also

severely restrict the growth environment so that they are not commonly

used as standard process characterisation tools. Usually, a trade-off between

temporal resolution and spatial resolution has to be found in particular for

scanning microscopy techniques. nevertheless, they combine desirable

experimental properties such as observation of individual sample features

in both space and time.

Scanning probe microscopy (SPM)

Scanning probe techniques have enjoyed tremendous popularity in thin

lm studies due to their atomic resolution capabilities and compatibility

with vacuum, gas, and liquid environments. an advantage of SPM is the

imaging of growth morphologies in real space, in particular island shapes,

nucleation sites and nucleation densities (rabe and Buchholz, 1991; fischer

et al., 1999; rusponi et al., 1997, Kneppe et al., 2000). Growth studies have

been performed for solution deposition (e.g., Hyde et al., 2002; rabe and

Buchholz, 1991) with a time resolution down to video rate (~30 ms). Great

care has to be taken that the atomic force microscopy (afM) tip does not

disturb growth nuclei, for example by avoiding contact mode and scanning

in tapping mode.

STM measurements with, in principle, atomic resolution have also been

used for in-situ growth studies on moderately well conducting substrates. au

deposition from an evaporation source in vacuum has been studied by rost

(2007) and atomic-height steps could be imaged with a lateral resolution of

1 nm in a eld of view of 500 ¥ 500 nm. Such a real-time dataset giving

microscopic insight into growth with atomic resolution makes it possible to

watch growth modes such as step ow and nucleation at dislocations directly.

ThinFilm-Zexian-05.indd 90 7/1/11 9:40:42 AM



91Modelling thin ﬁlm deposition processes

Great care has to be taken to avoid a disturbance of the growth, for example

by shadowing the atomic ux with the tip, or coating of the tip itself with

the evaporation material, which may either inuence the shape of the tip or

also lead to atoms diffusing from the tip onto the surface.

in conclusion, real-time STM studies are slightly challenging but gaining

popularity due to technical advances. Since the focus in this chapter is on

scattering techniques, for an in-depth discussion the reader is referred to

Hofer et al. (2003) and references therein.

Electron microscopy

Electron microscopy combines good spatial resolution and a wide eld of

view for acquiring some surface statistics with video rate (30 ms) real-time

capabilities. The best spatial resolution is obtained in transmission electron

microscopy (TeM), albeit at the expense of restricting the sample to very thin

substrates in the range of several 10 nm and requiring the growth apparatus

to t in the microscope. Examples of real-time TEM studies include growth

of cu on au in a liquid cell from solution studied at 5 nm lateral resolution

(williamson et al., 2003) and formation of Pt nanoparticles in solution at sub-

nm resolution (Zheng et al., 2009). achieving not only structural resolution

but also chemical imaging is highly desirable and X-ray uorescence in

TeM can provide additional, local chemical information but also imaging

of photoelectrons gives a material-specic contrast. In-situ photoelectron

emission microscopy (PeeM) at a time resolution of 60 s has been used to

study growth of the molecular semiconductor pentacene. Using PeeM to

study pentacene growth the diffusion limited dendritic growth of individual

monolayers could be resolved down to 125 nm (Meyer Zu Heringdorf et al.,

2001).

5.3.3 Scattering methods

elastic X-ray scattering, atom scattering and electron scattering are particularly

useful for real-time observation of thin lms, because they give structural

information on the atomic length scale with a time resolution suited to growth

dynamics. They are compatible with typical vacuum growth environments

and, in particular, X-rays with their large penetrating power can be used

to perform experiments in a wide range of sample environments such as

vacuum, gas and liquid environments. all three scattering techniques measure

an ensemble average where usually:

beam footprint on sample >> coherence length of structural

features

but the spatial resolution, which is given by the (de Broglie) wavelength, can

ThinFilm-Zexian-05.indd 91 7/1/11 9:40:42 AM



92 Thin ﬁlm growth

be on an atomic length scale (for a more precise discussion of resolution,

see fenter, 2002) so that area averaged microscopic properties are sampled.

Spreading the X-ray or particle ux over a macroscopic area reduces the

likelihood of beam damage while at the same time providing enough ux

for obtaining sufcient counting statistics with a time resolution in the sub-

second range.

We will rst point out common characteristics of real-time measurements

with X-ray, He-atoms, and electrons before individually discussing their

unique properties. in general, a part of the incident beam changes the

propagation direction, and the two wave vectors k

of the incident and k

out

of the scattered beam dene the scattering plane (see Fig. 5.4). The wave

vector transfer q = k

out

– k

points in the direction in which the periodicity

d of the thin lm is sampled, and strong reections occur when the Bragg

condition q = n2p/d is fullled for an integer n. Both the in-plane structure

to the substrate surface, fig. 5.4b) and out-of-plane structure (q

the sample surface along the growth direction, fig. 5.4a) can be measured

during growth. an example for following the in-plane structure is given

in Section 5.4 and an observation of the in-plane reections has been used

for example in Schreiber et al. (1998), Schreiber (2000) and Kowarik et al.

(2006) to follow the growth of self-assembled monolayers and other systems.

There are several approaches for real-time structure analysis by scattering

techniques. for instance, one can measure the (monotonous)increase or shift

of a diffraction feature. another approach is recording an oscillatory signal

due to the lling of individual layers.

Oscillating signals that vary with the number of lattice planes lled during

growth are of particular interest and most commonly used, because details

about the growth mode can be obtained with sub-monolayer resolution. for

||x

||y

out

(a) (b)

5.4 (a) Specular reﬂectivity measurement: incoming and outgoing

beams enclose the same angle with the substrate surface, and

therefore the wave vector transfer q is directed along the surface

normal. (b) Grazing incidence diffraction (GIXD) and non-specular

scattering involves a momentum transfer parallel to the surface.

ThinFilm-Zexian-05.indd 92 7/1/11 9:40:42 AM



93Modelling thin ﬁ lm deposition processes

all three scattering techniques oscillations are primarily, but not exclusively,

measured by observing the specular re ection, that is the scattered beam is

detected for ‘mirror-like’ re ection (q

perpendicular to sample surface). for

the purpose of the following discussion, here we want to distinguish two

basic scattering mechanisms, which in uence the specular re ection signal

during growth and may lead to intensity oscillations:

(a) out-of-phase interference between the scattering from successively

growing atomic monolayers (no change in in-plane momentum q

= 0)

(see fig. 5.5a).

(b) loss of specular intensity into diffuse scattering ‘sideways’ of the

specular beam due to surface corrugation that oscillates during growth

≠ 0) (see Fig. 5.5b).

in (a) the oscillations involve interference between atomic layers in different

depths scattering out-of-phase, that is q

must not ful l the Bragg condition.

Then the successive  lling of atomic layers will cause the specular re ectivity

to oscillate according to:

()

It()It

= |

()

At()At

eA +eA

eA eA

()

te()te

te · te

ubs

eASeA

iiqi

[5.6]

This equation adds the scattering amplitudes A

substrate

and A

of both the

substrate and all the n adlayers, taking into account the correct relative phase

j = q

between the substrate and the adlayers due to d

(bonding distance

between substrate and  rst adlayer) as well as the phase shift between adlayers

separated by a distance of n times the lattice constant d. The oscillations

can be most readily understood for q

= p/d where the exponential factor

in the sum alternates between –1 and 1, that is adjacent layers alternate

between adding to/subtracting from the scattering amplitude. note, that

this mechanism only redistributes intensity between the re ected beam and

5.5 Specular scattering with a change in q

and diffuse scattering

with a change in q

and q

ÍÍ

||x

||y

Specular reﬂ ection

no change in q

Diffuse scattering

change in q

Diffuse

Specular

(a)

(b)

ThinFilm-Zexian-05.indd 93 7/1/11 9:40:43 AM



94 Thin ﬁlm growth

the transmitted (and eventually absorbed) beam, because the in-plane wave

vector is not changed – no in-plane periodicity is probed in this oscillation

mechanism. Therefore in elastic scattering where momentum is conserved

the only choice for q is being normal to the surface for the reected beam

or zero for the transmitted beam.

in (b) the mechanism of intensity change during growth (monotonous

or oscillatory) is distinctly different as it involves momentum transfer not

only perpendicular but also parallel to the sample surface. in case of a

periodicity within the surface non-specular scattering can lead, inter alia, to

in-plane Bragg reections, while a non-periodic corrugated surface results

in broad, diffuse scattering in many directions. while the surface changes

during growth also the specularly and diffusely scattered signal change in

a characteristic fashion. for all three techniques of X-ray, He, and electron

scattering a changing surface corrugation – for example smooth Æ rough

(upon nucleation of islands in a new layer) Æ smooth (upon layer completion)

– leads to an oscillation in the diffuse scattered intensity (integrated over

all q) with oscillating roughness (fuoss et al., 1992; eres et al., 2002).

The specular reection intensity changes inversely to the diffuse intensity,

because beam intensity which is scattered diffusely is missing in the specular

reectivity.

it is important to note that in X-ray scattering also buried layers including

the substrate contribute to the scattering, that is A

is proportional to q

with q

being the coverage of the n-th layer. in contrast, for surface sensitive helium

atom scattering, only the exposed layers contribute to the scattering, that is

the scattering amplitudes A

of buried layers vanish and A

is proportional

to the uncovered fraction (q

– q

n–1

) of the n-th layer which also inuences

the oscillation period,

The underlying reasons (a) and (b) for growth oscillations are similar

in all three techniques, but there are also important differences between

the three probe types. Most importantly, the scattering cross-section and

penetration depth varies greatly (see fig. 5.6). due to these different interaction

X-ray scattering

He-atom

scattering

Electron

scattering

5.6 X-ray scattering penetrates the sample so that scattering occurs

also from buried layers, while He-scattering is exclusively surface

sensitive. Electron scattering occurs in the ﬁrst few atomic layers and

multiple scattering events can occur as shown.

ThinFilm-Zexian-05.indd 94 7/1/11 9:40:43 AM



95Modelling thin ﬁ lm deposition processes

mechanisms there are a range of differences in the real-time data which are

discussed separately in the following sections.

X-ray scattering

X-ray scattering is usually performed at X-ray energies around 10 keV

where the elastic scattering cross section is large and the wavelength of

around 1 Å  ts to studies of thin  lm growth on atomic length scales. It is

worth noting that chemically selective scattering can be achieved by tuning

the X-ray energy to speci c atomic transitions where the scattering cross

section is enhanced by anomalous scattering. in general, X-rays have great

penetrating power so that not only the top surface is sampled, but also bulk

lattice constants and buried interfaces are accessible.

Surface speci city can nevertheless be improved by using a grazing angle

of incidence, so that the beam undergoes total external re ection and the

X-ray intensity of the evanescent wave decays exponentially on a length

scale of around 10–100 Å (depending on the  lm electron density) thereby

reducing bulk sensitivity. This grazing incidence X-ray diffraction (GiXd)

is used to determine in-plane lattice constants by scanning q

, and it can

also be used to determine the thin  lm unit cell if so called rod scans are

performed, that is the scattering vector is chosen to have components both in

and q

. GiXd has been performed in real time during growth of organic

molecular semiconductors (Kowarik et al., 2009a) and makes it possible to

follow structural changes and strain with a resolution below 0.01 Å

–1

with

a time resolution of < 30 s.

Specular re ectivity measurements, for which q changes only along the

surface normal, is useful to resolve changes along the surface normal, which

usually coincides with the direction of growth. experiments are typically

performed at the Bragg condition to monitor the phase content, or at half the

Bragg q vector which corresponds to the out-of-phase anti-Bragg condition.

Both the Bragg re ection of a thin  lm and the re ectivity at the anti-Bragg

point are usually weak enough that the kinematic approximation can be

employed (the approximation breaks down close to the total re ection edge

or at a strong Bragg re ection). Adapted to X-ray scattering which does not

exclusively scatter at the surface but penetrates into the substrate, eq. 5.6

can be rewritten using the form factor of the adlayer f(q):

ected

ubs

()

It()It

(

Aq (Aq

ubs

Aq (Aq

ubs

Aq (Aq

(

)·

ef +ef

(

ef (ef

)·

ef +ef

(

ef (ef

nnn

(

)·

te)·te

(

i·n·

q·

(

q·

[5.7]

Note that the substrate scattering amplitude and phase is  xed in time, and for

the purpose of the time-dependent growth studies (i.e., θ

(t) and the temporal

change of the resulting scattering intensity) it is not important that A

substrate

may actually have to be calculated using dynamical theory.

ThinFilm-Zexian-05.indd 95 7/1/11 9:40:44 AM

