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

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76 Thin ﬁlm growth

the concentration prole of catalytic elements to cancel out the catalytic

activity in AlN/TiN composite lms.

4.4 Future trends

Compared to during homo-epitaxial growth, roughness evolution during

hetero- or non-epitaxial growth has not been investigated in depth, despite

its practical importance. This is partly because it is difcult to investigate

complex processes, as scientic research tends to study focused processes

under well-designed experimental conditions and theoretically under simplied

conditions, in order to make calculation feasible. While a previous survey

does exist (Kajikawa, 2008), there is much room to explore.

The rst step to model and control such complex processes is to identify

the essential processes that contribute to the roughness evolution. There are

three types of model: mechanistic, phenomenological, and empirical.

A detailed mechanistic model considering all elementary processes is

feasible, because the nature of the industry is rapidly changing and a detailed

study of physical mechanisms is often impractical (Edgar et al., 2000).

Models must be developed rapidly if they are to be used in developing the

process, and often this is accomplished using phenomenological empirical

models.

The phenomenological model, as focused on in this chapter, is an efcient

and effective one because we can model the process quickly and control

it based on a fundamental understanding. Non-dimensional indicators like

the scaling exponent of nucleation theory can help us to identify essential

processes to be included in the model (Kajikawa et al., 2004a).

The nal model is empirical. Empirical models are built directly from

experimental data to t the trends in experimental measurements (Edgar, 2004).

Data from designed experiments are often used to construct empirical models.

a recent trend in this direction is to use in-situ monitoring and combinatorial

chemistry for efcient control of the process. Such models work well when

experimental data are readily available and the underlying detailed mechanisms

are not well understood. For example, scanning tunneling microscopy (Flewitt

et al., 1999), X-ray reectivity (Kellerman et al., 1997), single wavelength

ellipsometry (Hu et al., 1996), spectroscopic ellipsometry (Fujiwara et al.,

2001; Volintiru et al., 2008), optical reectometry (Deatcher et al., 2003;

Kajikawa et al., 2004c) and UV spectrophotometer (Lee et al., 2010) are

used for in-situ monitoring of deposition processes during CVD. another

recent trend is the increasing attention paid to combinatorial chemistry even

in vapor deposition processes (Koinuma and Takeuchi, 2004; Noda et al.,

2004). The challenge in engineering is to develop an effective and efcient

methodology for practical use, both theoretically and experimentally.

ThinFilm-Zexian-04.indd 76 7/1/11 9:40:21 AM

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77Analysing surface roughness evolution in thin ﬁlms

4.5 References

Amar J G, Family F (1996) ‘Kinetics of submonolayer and multilayer epitaxial growth’,

Thin Solid Films, 272, 208–222.

Amar J G, Family F, Lam P M (1994) ‘Dynamic scaling of the island-size distribution

and percolation in a model of submonolayer molecular-beam epitaxy’, Phys Rev B,

50, 8781–8797.

Amar J G, Family F, Hughes D C (1998) ‘Submonolayer epitaxial growth with long-

range (Levy) diffusion’, Phys Rev E, 61, 7130–7136.

Bales G S, Zangwill A (1997) ‘Self-consistent rate theory of submonolayer homoepitaxy

with attachment/detachment kinetics’, Phys Rev B, 55, R1973–R1976.

Bales G S, Redeld A C, Zangwill A (1989) ‘Growth dynamics of chemical vapor-

deposition’, Phys Rev Lett, 62, 776–779.

Bales G S, Bruinsma R, Eklund E A, Karunasiri R P U, Rudnick J, Zangwill A (1990)

‘Growth and erosion of thin solid lms’, Science, 249, 264–268.

Barrat S, Pigeat P, Bauer-Grosse E (1996) ‘Three-dimensional simulation of CVD diamond

lm growth’, Diam Relat Mater, 5, 276–280.

Bartelt M C, Evans J W (1994) ‘Nucleation and growth in metal-on-metal homoepitaxy –

rate-equations, simulations and experiments’, J Vac Sci Technol A, 12, 1800–1808.

Bouyer E, Henne R H, Müller M, Schiller G (2001) ‘Si

bers synthesized by thermal

plasma CVD’, Chem Vap Deposition, 7, 139–142.

Burton W K, Cabrera N, Frank F C (1951) ‘The growth of crystals and the equilibrium

structure of their surfaces’, Philos Trans Roy Soc London, A243, 299–358.

Cale T S, Raupp G B (1990) ‘Free molecular-transport and deposition in cylindrical

features’, J Vac Sci Technol B, 8, 649–655.

Carrey J, Maurice J L (2001) ‘Transition from droplet growth to percolation: Monte

Carlo simulations and an analytical model’, Phys Rev B, 63, 245408.

Carrey J, Maurice J L (2002) ‘Scaling laws near percolation during three-dimensional

cluster growth: a Monte Carlo study’, Phys Rev B, 65, 205401.

Chambliss D D, Johnson K E (1994) ‘Nucleation with a critical cluster-size of zero –

submonolayer fe inclusions in Cu(100)’, Phys Rev B, 50, 5012–5015.

Chin J, Gantzel P K, Hudson R G (1977) ‘Structure of chemical vapor-deposited silicon-

carbide’, Thin Solid Films, 40, 57–72.

Combe N, Jensen P (1998) ‘Changing thin-lm growth by modulating the incident ux’,

Phys Rev B, 57, 15553–15560.

Cooke M J, Harris G (1989) ‘Monte-Carlo simulation of thin-lm deposition in a

rectangular groove’, J Vac Sci Technol A, 7, 3217–3221.

Deatcher C J, Liu C, Pereira S, Lada M, Cullis A G, Sun Y J, Brandt O, Watson I M

(2003) ‘In situ optical reectometry applied to growth of indium gallium nitride

epilayers and multi-quantum well structures’, Semicond Sci Technol, 18, 212–218.

Deltour P, Barrat J L, Jensen P (1997) ‘Fast diffusion of a Lennard–Jones cluster on a

crystalline surface’, Phys Rev Lett, 78, 4597–4600.

Dobbs H T, Vvedensky D D, Zangwill A, Johansson J, Carlsson N, Seifert W (1997)

‘Mean-eld theory of quantum dot formation’, Phys Rev Lett, 79, 897–900.

Drotar J T, Zhao Y P, Lu T M, Wang G C (2001) ‘Surface roughening in low-pressure

chemical vapor deposition’, Phys Rev B, 64, 125411.

Edgar T F (2004) ‘Process operations: when does controllability equal protability?’,

Computer Chem Engr, 29, 41–49.

Edgar T F, Butler S W, Campbell W J, Pfeiffer C, Bode C, Hwang S B, Balakrishnan

ThinFilm-Zexian-04.indd 77 7/1/11 9:40:22 AM



78 Thin ﬁlm growth

K S, Hahn J (2000) ‘Automatic control in microelectronics manufacturing: practices,

challenges, and possibilities’, Automatica, 36, 1567–1603.

Ehrlich G, Hudda F G (1966) ‘Atomic view of surface self-diffusion – tungsten on

tungsten’, J Chem Phys, 44, 1039–1049.

Family F, Meakin P (1989) ‘Kinetics of droplet growth-processes – simulations, theory,

and experiments’, Phys Rev A, 40, 3836–3854.

Flewitt A J, Robertson J, Milne W I (1999) ‘Growth mechanism of hydrogenated

amorphous silicon studied by in situ scanning tunneling microscopy’, J Appl Phys,

85, 8032–8039.

Fujiwara H, Kondo M, Matsuda A (2001) ‘Real-time spectroscopic ellipsometry studies

of the nucleation and grain growth processes in microcrystalline silicon thin lms’,

Phys Rev B 63, 115306.

Galdikas A (2002) ‘Thin lm deposition onto the rough surface: phenomenological

investigations’, Thin Solid Films, 418, 112–118.

Goela J S, Taylor R L (1988) ‘Monolithic material fabrication by chemical vapor-

deposition’, J Mater Sci, 23, 4331–4339.

Heyraud J C, Métois J J (1987) ‘Equilibrium shape of an ionic-crystal in equilibrium

with its vapor (NaCl)’, J Cryst Growth, 84, 503–508.

Hu M, Noda S, Komiyama H (2002) ‘A new insight into the growth mode of metals on

TiO

(110)’, Surf Sci, 513, 530–538.

Hu Y Z, Diehl D J, Zhao C Y, Wang C L, Liu Q, Irene E A, Christensen K N, Venable

D, Maher D M (1996) ‘Real time investigation of nucleation and growth of silicon

on silicon dioxide using silane and disilane in a rapid thermal processing system’, J

Vac Sci Technol B, 14, 744–750.

Hwang E S, Lee J (2000) ‘Surfactant-catalyzed chemical vapor deposition of copper thin

lms’, Chem Mater, 12, 2076–2081.

Ikegawa M, Kobayashi J (1989) ‘Deposition prole simulation using the direct simulation

Monte-Carlo method’, J Electrochem Soc, 136, 2982–2986.

Iwamoto C, Shen X Q, Okumura H, Matsuhata H, Ikuhara Y (2003) ‘Termination mechanism

of inversion domains by stacking faults in GaN’, J Appl Phys, 93, 3264–3269.

Jensen P (1999) ‘Growth of nanostructures by cluster deposition: experiments and simple

models’, Rev Mod Phys, 71, 1695–1735.

Jensen P, Niemeyer B (1997) ‘The effect of a modulated ux on the growth of thin

lms’, Surf Sci, 384, L823–L827.

Jensen P, Larralde H, Pimpinelli A (1997) ‘Effect of monomer evaporation on a simple

model of submonolayer growth’, Phys Rev B, 55, 2556–2569.

Jensen P, Larralde H, Meunier M, Pimpinelli A (1998) ‘Growth of three-dimensional

structures by atomic deposition on surfaces containing defects: simulations and theory’,

Surf Sci, 412/413, 458–476.

Jensen P, Combe N, Larralde H, Barrat J L, Misbah C, Pimpinelli A (1999) ‘Kinetics of

shape equilibration for two dimensional islands’, Eur Phys J B, 11, 497–504.

Josell D, Kim S, Wheeler D, Moffat T P, Pyo S G (2003) ‘Interconnect fabrication by

superconformal iodine-catalyzed chemical vapor deposition of copper’, J Electrochem

Soc, 150, C368–C373.

Kajikawa, Y (2006) ‘Texture development of non–epitaxial polycrystalline ZnO lms’,

J Cryst Growth, 289, 387–394.

Kajikawa Y (2008) ‘Roughness evolution during chemical vapor deposition’, Mater

Chem Phys, 112, 311–318.

Kajikawa Y, Noda S (2005) ‘Growth mode during initial stage of chemical vapor

deposition’, Appl Surf Sci, 245, 281–289.

ThinFilm-Zexian-04.indd 78 7/1/11 9:40:22 AM



79Analysing surface roughness evolution in thin ﬁlms

Kajikawa Y, Ono H, Noda S, Komiyama H (2002) ‘Growth of trumpet–like protrusions

during chemical vapor deposition of silicon carbide lms’, Chem Vap Deposition,

8, 52–55.

Kajikawa Y, Noda S, Komiyama H (2003) ‘Comprehensive perspective on the mechanism

of preferred orientation in reactive-sputter-deposited nitrides’, J Vac Sci Technol A,

21, 1943–1954.

Kajikawa Y, Noda S, Komiyama H (2004a) ‘Use of process indices for simplication of

the description of vapor deposition systems’, Mater Sci Eng B, 111, 156–163.

Kajikawa Y, Tsuchiya T, Noda S, Komiyama H (2004b) ‘Incubation time during the

CVD of Si onto SiO

from silane’, Chem Vap Deposition, 10, 128–133.

Kajikawa Y, Tsumura T, Noda S, Komiyama H, Shimogaki Y (2004c) ‘Nucleation of

W during chemical vapor deposition from WF

and SiH

’, Jpn J Apply Phys, 43,

3945–3950.

Kajikawa Y, Noda S, Komiyama H (2004d) ‘A simple index to restrain abnormal

protrusions in lms fabricated using CVD under diffusion-limited conditions’, Chem

Vap Deposition, 10, 221–228.

Kellerman B K, Chason E, Adams D P, Mayer T M, White J M (1997) ‘In-situ X-ray

reectivity investigation of growth and surface morphology evolution during Fe

chemical vapor deposition on Si(001)’, Surf Sci, 375, 331–339.

Kern R, Laye G L, Métois J J (1979) Current Topics in Materials Science, ed. by E.

Kaldis, North Holland, New York.

Kim H (2003) ‘Atomic layer deposition of metal and nitride thin lms: current research

efforts and applications for semiconductor device processing’, J Vac Sci Technol B,

21, 2231–2261.

Koinuma H, Takeuchi I (2004) ‘Combinatorial solid-state chemistry of inorganic materials’,

Nature Mat, 3, 429–438.

Komiyama H (1993) in The Expanding World of Chemical Engineering, eds Garside J,

Furusaki S, Gordon and Breach Science Publishers, New York.

Kondo M, Ohe T, Saito K, Nishimiya T, Matsuda A (1998) ‘Morphological study of

kinetic roughening on amorphous and microcrystalline silicon surface’, J Non-Cryst

Solids, 227–230, 890–895.

Kotrla M, Krug J, Šmilauer P (2000) ‘Submonolayer epitaxy with impurities: kinetic

Monte Carlo simulations and rate–equation analysis’, Phys Rev B, 62, 2889–2898.

Krug J (1997) ‘Origins of scale invariance in growth processes’, Adv Phys, 46, 139–

282.

Krug J (2000) ‘Scaling regimes for second layer nucleation’, Eur Phys J B, 18, 713–

719.

Kuipers L, Palmer R E (1996) ‘Inuence of island mobility on island size distributions

in surface growth’, Phys Rev B, 53, R7646–R7649.

Lantz S L, Bell A E, Ford W K, Danielson D (1994) ‘W-nucleation on tin from WF

and SiH

’, J Vac Sci Technol A, 12, 1032–1038.

Leamy H J, Gilmer G H, Jackson K A (1975) in Surface Physics of Materials, ed. Blakely

J M, Academic Press, New York.

Lee S B, Gupta B C (2000) ‘Inuence of small-cluster mobility on the island formation

in molecular beam epitaxy’, Phys Rev B, 62, 7545–7552.

Lee H B, Kwak D K, Kang S W (2005) ‘Enhancement of iodine adsorption on ruthenium

glue layer for seedless CECVD of Cu’ Electrochem Solid-State Lett, 8, C39–C42.

Lee S R, Ahn K M, Kang S M, Ahn B T (2010) ‘Surface morphology control of epitaxial

silicon lms grown by hot wire chemical vapor deposition using hydrogen dilution,

Sol Ener Mater Sol Cells, 94, 606–611.

ThinFilm-Zexian-04.indd 79 7/1/11 9:40:22 AM



80 Thin ﬁlm growth

Leskelä M, Ritala M (2003) ‘Atomic layer deposition chemistry: recent developments

and future challenges’, Angew Chem Int Ed, 42, 5548–5554.

Liu X D, Funakubo H, Noda S, Komiyama H (2001a) ‘Internal microstructure and

formation mechanism of surface protrusions in Pb-Ti-Nb-O thin lms prepared by

MOCVD’, Chem Vap Deposition, 7, 253–259.

Liu X D, Funakubo H, Noda S, Komiyama H (2001b) ‘Inuence of deposition temperature

on the microstructure of Pb-Ti-Nb-O thin lms by metallorganic chemical vapor

deposition’, J Electrochem Soc, 148, C227–C230.

Liu Y J, Kim H J, Takeuchi T, Egashira Y, Kimura H, Komiyama H (1996) ‘Using

simultaneous deposition and rapid growth to produce nanostructured composite lms

of AlN/TiN’, J Am Ceram Soc, 79, 1335–1342.

Luedtke W D, Landman U (1999) ‘Slip diffusion and Levy ights of an adsorbed gold

nanocluster’, Phys Rev Lett, 82, 3835–3838.

Mahalingam P, Dandy D S (1997) ‘Simulation of morphological instabilities during

diamond chemical vapor deposition’, Diam Relat Mater 6, 1759–1771.

Mahalingam P, Dandy D S (1998) ‘Nonlinear stability analysis of the growth surface

during diamond chemical vapor deposition’, J Appl Phys, 83, 6061–6071.

Markov I (1996) ‘Kinetics of nucleation in surfactant-mediated epitaxy’, Phys Rev B,

53, 4148–4155.

Matsunami H, Kimoto T (1997) ‘Step-controlled epitaxial growth of SiC: high quality

homoepitaxy’, Mater Sci Eng R, 20, 125–166.

Meakin P (1993) ‘The growth of rough surfaces and interfaces’, Phys Rep, 235,

189–289.

Mizushima I, Koike M, Sato S, Miyano K, Tsunashima Y (1999) ‘Mechanism of defect

formation during low-temperature Si epitaxy on clean Si substrate’, Jpn J Appl Phys,

38, 2415–2418.

Mulheran P A, Robbie D A (2001) ‘Island mobility and dynamic scaling during thin lm

deposition’, Phys Rev B, 64.

Mullins W W, Sekerka R F (1963) ‘Morphological stability of a particle growing by

diffusion or heat ow’, J Appl Phys, 34, 323–329.

Mullins W W, Sekerka R F (1964) ‘Stability of planar interface during solidication of

dilute binary alloy’, J Appl Phys, 35, 444–451.

Nichols F A, Mullins W W (1965) ‘Morphological changes of a surface of revolution

due to capillarity-induced surface diffusion’, J Appl Phys, 36, 1826–1835.

Noda S, Kajikawa Y, Komiyama H (2002) ‘Cone structure formation by preferred

growth of random nuclei in chemical vapor deposited epitaxial silicon lms’, Chem

Vap Deposition, 8, 87–89.

Noda S, Kajikawa Y, Komiyama H (2004) ‘Combinatorial masked deposition: simple

method to control deposition ux and its spatial distribution’, Appl Surf Sci, 225,

372–379.

Palmer B J, Gordon R G (1988) ‘Local equilibrium-model of morphological instabilities

in chemical vapor-deposition’, Thin Solid Films, 158, 313–341.

Palmer B J, Gordon R G (1989) ‘Kinetic-model of morphological instabilities in chemical

vapor-deposition’, Thin Solid Films, 177, 141–159.

Paritosh Srolovitz D J, Battaile C C, Li X, Butler J E (1999) ‘Simulation of faceted lm

growth in two–dimensions: microstructure, morphology and texture’, Acta Mater,

47, 2269–2281.

Politi P, Grenet G, Marty A, Poncher A, Villain J (2000) ‘Instabilities in crystal growth

by atomic or molecular beams’, Phys Rep, 324, 271–404.

ThinFilm-Zexian-04.indd 80 7/1/11 9:40:22 AM



81Analysing surface roughness evolution in thin ﬁlms

Puurunen R L (2004) ‘Random deposition as a growth mode in atomic layer deposition’,

Chem Vap Deposition, 10, 159–170.

Ratsch C, Venables J A (2003) ‘Nucleation theory and the early stages of thin lm

growth’, J Vac Sci Technol A, 21, S96–S109.

Ratsch C, Zangwill A, Šmilauer P, Vvdensky D D (1994) ‘Saturation and scaling of

epitaxial island densities’, Phys Rev Lett, 72, 3194–3197.

Ratsch C, Šmilauer P, Zangwill A, Vvdensky D D (1995) ‘Submonolayer epitaxy without

a critical nucleus’, Surf. Sci, 329, L599–L604.

Ravi K V (1992) ‘Morphological instabilities in the low–pressure synthesis of diamond’,

J Mater Res, 7, 384–393.

Robbie K, Brett M J (1997) ‘Sculptured thin lms and glancing angle deposition: growth

mechanics and applications’, J Vac Sci Technol A, 15, 1460–1465.

Robbie K, Brett M J, Lakhtakia A (1996) ‘Chiral sculptured thin lms’, Nature, 384,

616.

Roland C, Guo H (1991) ‘Interface growth with a shadow instability’, Phys Rev Lett,

66, 2104–2107.

Ross C, Herion J, Wagner H (2000) ‘Nucleation and growth analysis of microcrystalline

silicon by scanning probe microscopy: substrate dependence, local structural and

electronic properties of as-grown surfaces’, J Non-Cryst Solids, 266–269, 69–73.

Ruan S, Schuh C A (2010) ‘Kinetic Monte Carlo simulations of nanocrystalline lm

deposition’, J Appl Phys, 107, 073512.

Saito Y, Uwaha M (1994) ‘Fluctuation and instability of steps in a diffusion eld’, Phys

Rev B, 49, 10677–10692.

Salik J (1985) ‘Monte-Carlo study of reversible growth of clusters on a surface’, Phys

Rev B, 32, 1824–1826.

Schwoebel R L, Shipsey E J (1966) ‘Step motion on crystal surfaces’, J Appl Phys, 37,

3682–3686.

Shim K C, Lee H B, Kwon O K, Park H S, Koh W, Kang S W (2002) ‘Bottom-up lling

of submicrometer features in catalyst-enhanced chemical vapor deposition of copper’,

J Electrochem Soc, 149, G109–G113.

Singh V K, Shaqfeh E S G (1993) ‘Effect of surface reemission on the surface-roughness

of lm growth in low-pressure chemical-vapor-deposition’, J Vac Sci Technol A, 11,

557–568.

Stoyanov S, Kaschiev D (1981) Current Topics in Materials Science, ed. by Kaldis E,

North Holland, New York.

Takeyama T, Kajikawa Y, Takahashi N, Nakamura T, Itoh S (2006) ‘Growth mechanism

of a-Bi

rods deposited under atmospheric pressure by halide CVD’, Chem Vap

Deposition, 12, 203–206.

Tanenbaum D M, Laracuente A L, Gallagher A (1997) ‘Surface roughening during

plasma-enhanced chemical-vapor deposition of hydrogenated amorphous silicon on

crystal silicon substrates’, Phys Rev B, 56, 4243–4250.

Tang L H (1993) ‘Island formation in submonolayer epitaxy’, J Phys I, 3, 935–950.

Templier C, Muzard S, Galdikas A, Pranevicius L, Delafond J, Desoyer J C (2000) ‘A

phenomenological study of the initial stages of lm growth’, Surf Coat Technol,

125, 129–133.

Thiart J J, Hlavacek V, Viljoen H J (2000) ‘Chemical vapor deposition and morphology

problems’, Thin Solid Films, 365, 275–293.

Thompson C V, Carel R (1996) ‘Stress and grain growth in thin lms’, J Mech Phys

Solids, 44, 657–673.

ThinFilm-Zexian-04.indd 81 7/1/11 9:40:22 AM



82 Thin ﬁlm growth

Thornton J A (1977) ‘High-rate thick-lm growth’, Ann Rev Mater Sci, 7, 239–260.

Urbonavičius E, Petnyčyte E, Galdikas A (1999) ‘The kinetics of thin lm island growth

at initial stages’, Vacuum, 53, 377–380.

van den Brekel C H J, Bloem J (1977) ‘Characterization of chemical vapor-deposition

processes 2’, Philips Res Rept, 32, 134–146.

van den Brekel C H J, Jansen A K (1978) ‘Morphological stability analysis in chemical

vapor-deposition processes 1’, J Cryst Growth, 43, 364–370.

van der Drift A (1967) ‘Evolutionary selection a principle governing growth orientation

in vapour-deposited layers’, Phillips Res Repts 22, 267–288.

Venables J A, Spiller G D T, Hanbücken M (1984) ‘Nucleation and growth of thin-lms’,

Rep Prog Phys, 47, 399–459.

Viljoen H J, Thiart J J, Hlavacek V (1994) ‘Controlling the morphology of CVD lms’,

AIChE J, 40, 1032–1045.

Villain A, Pimpinelli A, Tang L, Wolf D (1992) ‘Terrace sizes in molecular-beam

epitaxy’, J Phys I, 2, 2107–2121.

Volintiru I, Creatore M, van de Sanden M C M (2008) ‘In situ spectroscopic ellipsometry

growth studies on the Al-doped ZnO lms deposited by remote plasma-enhanced

metalorganic chemical vapor deposition’, J Appl Phys, 103, 033704.

Wagner R S, Ellis W C (1964) ‘Vapor-liquid-solid mechanism of single crystal growth

(new method: growth “catalysis” from impurity; whiskers, epitaxial, and large crystals;

Si; E)’, Appl Phys Lett, 4, 89–90.

Watanabe K, Komiyama H (1990) ‘Micro/macrocavity method applied to the study of

the step coverage formation mechanism of SiO

-lms by LPCVD’, J Electrochem

Soc, 137, 1222–1227.

Werner C, Ulacia J I, Hopfmann C, Flynn P (1992) ‘Equipment simulation of selective

tungsten deposition’, J Electrochem Soc, 129, 566–574.

Wild C, Herres N, Koidl P (1990) ‘Texture formation in polycrystalline diamond lms’,

J Appl Phys, 68, 973–978.

Wild C, Koidl P, Müller-Sebert W, Walcher H, Kohl R, Herres N, Locher R, Samlenski

R, Brenn R (1993) ‘Chemical-vapor-deposition and characterization of smooth (100)-

faceted diamond lms’, Diam Relat Mater, 2, 158–168.

Yao J H, Guo H (1993) ‘Shadowing instability in three dimensions’, Phys Rev E, 47,

1007–1011.

Zhao Y P, Drotar J T, Wang G C, Lu T M (2001) ‘Morphology transition during low-

pressure chemical vapor deposition’, Phys Rev Lett, 87, 136102.

ThinFilm-Zexian-04.indd 82 7/1/11 9:40:22 AM



Modelling thin film deposition processes

based on real-time observation

S. KowariK, Humboldt Universität zu Berlin, Germany and

a. HinderHofer, a. GerlacH and

f. ScHreiBer, Universität Tübingen, Germany

Abstract: we introduce time and length scales of growth processes and

then review experimental techniques for real-time and in-situ studies.

in particular, we discuss optical monitoring techniques, time resolved

microscopy, and real-time scattering techniques (X-ray, He-, and electron

scattering). for scattering experiments we discuss details of the analysis,

in particular anti-Bragg growth oscillations as observed in X-ray- and

He-scattering as well as rHeed. we illustrate real-time observation and

modelling of thin lm deposition with examples from organic molecular

beam deposition.

Key words: time resolved surface science, MBe growth, X-ray scattering,

differential reectance spectroscopy, He-scattering, RHEED, dewetting,

scaling laws.

5.1 Introduction: time resolved surface science

As is evident from the various chapters in this book, thin lm growth has

many different facets to it, and growth is inherently a non-equilibrium and

time-dependent phenomenon. While the investigation of the nal product, i.e.

the grown lm, with its structure and morphology, may allow one to partially

reconstruct the growth process, frequently the real-time observation of the

growing lm is required to fully characterize and understand the growth in

its complexity. This is particularly evident if transient phenomena occur

during the growth. in this chapter, after a brief discussion in Section 5.2 of

some concepts of growth and the associated time scales, we present rst an

overview of various techniques (Section 5.3) for real-time studies including

microscopy, optical spectroscopy, and scattering and indicate their strengths

and weaknesses. Scattering techniques are discussed at some length, since

they are at the center of most of the case studies in Section 5.4.

for the foundations of growth and its theoretical background we refer to

other chapters in this book as well as earlier books and reviews (e.g., Venables,

2000; Venables et al., 1984, Zangwill, 1988; Pimpinelli and Villain, 1998;

Barabási and Stanley, 1995; Michely and Krug, 2004; Krug, 1997). for the

ThinFilm-Zexian-05.indd 83 7/1/11 9:40:40 AM

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84 Thin ﬁlm growth

purpose of coherence, the case studies are mostly based on our own work

on systems from organic molecular beam deposition (oMBd) (witte and

wöll, 2004; Schreiber, 2004; forrest, 1997), but it is important to stress that

the concepts outlined here can be very easily transferred to other, of course

also inorganic, systems. it is clear that within the scope of this chapter the

references cannot be exhaustive, but with those given it should be possible

to trace a more complete list of references on a given subject.

5.2 Basics of growth and relevant length of and

timescales for in-situ observation of ﬁlm

deposition

Growth phenomena are extremely rich and include a number of competing

processes. adsorption and desorption processes are followed by thermalisation

and diffusion on the surface terrace. adatoms can form a new crystal grain,

attach to an existing one, or cross a step-edge onto a different terrace.

depending on the relative probabilities of these different processes, the

growth mode varies between layer-by-layer growth (frank–van-der-Merwe),

layer-by-layer plus island growth (Stranski–Krastanov), or island growth

(Volmer–weber). not only the growth mode but also the morphology of the

thin lm varies greatly as the island size and shape depends on the above

processes, leading for example to fractal morphology for diffusion limited

aggregation.

an important issue in the context of experimental real-time observations of

growth and the modelling of these processes is the issue of time and length

scales. length scales in growth range from 10

–12

–10

–3

m: the (sub-)atomic

length scales determine strain and lattice parameters, diffusion length scales

often range in the mm length scale, and, depending on the growth mode,

macroscopic crystallite sizes are possible. further relevant length scales are

the surface roughness s, in-plane correlation length x and island sizes, which

often change during growth. Time resolved techniques offer the particular

advantage that the dependence of length scales on lm thickness d can be

followed and directly compared to, for example, theoretical scaling models,

which describe the time/thickness dependence by scaling laws using the

roughening exponent b and the dynamic exponent z (Krug, 2004):

s ~ d

–b

x ~ d

–1/z

[5.1]

Similarly, growth processes span many orders of magnitude from ultra-fast to

hour-long timescales. in the following sections we will discuss experimental

techniques with a time resolution from ms to hours, which make it possible

to study some of the most important aspects of growth. To give an overview

ThinFilm-Zexian-05.indd 84 7/1/11 9:40:40 AM

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85Modelling thin ﬁ lm deposition processes

of processes occurring during growth, figure 5.1 shows both ultra-fast and

slow timescales.

atomistic processes that underlie and determine the growth behaviour occur

on ultra-fast timescales in the picosecond range. Thermalisation of the adsorbed

atoms/molecules occurs via transfer of translational and rotational energy

to phonon modes of the substrate and, in the case of molecular adsorbates,

also into internal molecular vibrations. Typical oscillation periods lie in the

range of tens of femtoseconds (an example being the 515 cm

–1

raman line

of silicon) up to picoseconds for large molecules. The frequencies of these

(surface phonon) modes often coincide with the typical attempt frequencies

assumed in Monte carlo simulations for diffusion and hopping processes.

intuitively it seems plausible to make a connection between a vibrational

frequency and the frequency of attempts G

to surmount, for example, a

step-edge barrier E

according to an arrhenius relation for the process rate

k ~ G

–e

/kT

[5.2]

indeed, a timescale of around 1ps (i.e., 1 THz) has typically been measured in

experiments and deduced in density functional theory (Ratsch and Schef er,

1998) but it is important to note that there are also other effects such as motion

of a whole cluster of adatoms/admolecules, where the attempt frequency is

changed due to collective effects.

even though the atomic/molecular movement is ultra-fast and the attempt

frequency very high, the often substantial energy barriers for diffusion slow

down the rates by many orders of magnitude. one mechanism of surface

diffusion is hopping of atoms to the nearest neighbour lattice site, while

collective movements such as dimer and cluster diffusion are often neglected.

for the energy barrier E

for hopping, values of around 100 meV (e.g.,

100 meV for ag on ag(111) (Brune et al., 1995), 20 meV for sexiphenyl

(Hlawacek et al., 2008) and 80 meV for PTcda (fendrich and Krug, 2007))

were reported. of course, these strongly depend on the given system. The

diffusion parameter D then is related to the hopping rate by

–e

[5.3]

with l being the jump length and a depending on the dimensionality and

symmetry of motion (a = 2 for a square lattice). Similarly to surface

diffusion, also the diffusion across a step-edge is hindered by the so-called

ehrlich–Schwöbel barrier E

(ehrlich and Hudda, 1966, Schwoebel and

Shipsey, 1966), which is crucial in determining the growth morphology of

the thin  lm (Markov, 2004, Tro mov and mokerov, 2002). Typical values

of E

are in the range of several 100 meV: 139 meV for ag(111) (Haftel,

2001), 670 meV for sexiphenyl (Hlawacek et al., 2008), and 750 meV for

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