reaction path analysis for thin-film deposition processesfocapo-cpc.org/pdf/adomaitis.pdfreaction...

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Reaction path analysis forthin-film deposition processes

Raymond A. Adomaitis

Chemical Engineering and ISRUniversity of Maryland, USA

9 January 2017

Collaborators/Students: Vivek Dwivedi (NASA GSFC)Hossein Salami, KP Ramakrishnan

Support: National Science Foundation, NASA

FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu

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Thin-film processing

Bottom: Applied Materials

Dynamic, multiscale,nonlinear process

Interplay between transportand reaction processescrucial to understandingthese systems

A traditional but hardreaction engineering problem

An unconventional designproblem

Numerous interesting PSEchallenges


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Process control/monitoring

Badgwell, T.A., Breedijk, T., Bushman, S.G., Butler, S.W., Chatterjee, S.,Edgar, T.F., Toprac, A.J., Trachtenberg, I. (1995) Modeling and control ofmicroelectronics materials processing. Computers Chem. Engng, 19, 1-41.

Armaou, A., Christofides, P.D. (1999) Plasma enhanced chemical vapordeposition: Modeling and control. Chem. Engng Sci., 54, 3305-3314.

Qin, S.J., Cherry, G., Good, R., Wang, J., Harrison, C.A. (2006) Semiconductormanufacturing process control and monitoring: A fab-wide framework. J. Proc.Control, 16, 179-191.

Xiong, R., Grover, M.A. (2009) A modified moving horizon estimator for in situsensing of a CVD process. IEEE Trans.Control Sys, Tech., 17, 1228-1235.

Detailed modeling

Moffat, H.K., Jensen, K.F. (1988) Three-dimensional flow effects insilicon CVD in horizontal reactors. J. Electrochem. Soc., 135, 459-471.

Badgwell, T.A., Edgar, T.F., Trachtenberg, I. (1992) Modeling andscale-up of multiwafer LPCVD reactors. AIChE J., 38, 926-938.

Ingle, N.K., Theodoropoulos, C., Mountziaris, T.J., Wexler, R.M., Smith,F.T.J. (1996) Reaction kinetics and transport phenomena underlying theLP-MOCVD of GaAs. J. Crystal Growth, 167, 543-556.


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Multiscale studies

Maroudas, D., Shankar, S. (1996) Electronic materials process modeling. J.Comp.-Aided Mat. Design, 3, 36-48.

Lam, R., Vlachos, D.G. (2001) Multiscale model for epitaxial growth of films:Growth mode transition. Phys. Rev. B, 64, 035401.

Braatz, R.D., Alkire, R.C., Seebauer, E., Rusli, E., Gunawan, R., Drews, T.O.,Li, X., He, Y. (2006) Perspectives on the design and control of multiscalesystems. J. Proc. Control, 16, 193-204.

Model reduction (POD, etc.)

Aling, H., Banerjee, S., Bangia, A.K., Cole, V., Ebert, J., Emami-Naeini,A., Jensen, K.F., Kevrekidis, I.G., Shvartsman, S. (1997) Nonlinear modelreduction for simulation and control of rapid thermal processing. Proc.ACC, 4, 2233-2238.

Theodoropoulou, A., Adomaitis, R.A., Zafiriou, E. (1998) Modelreduction for optimization of rapid thermal chemical vapor depositionsystems. IEEE Trans. Semicond. Manuf., 11, 85-98.

Banks, H.T., Beeler, S.C., Kepler, G.M., Tran, H.T. (2002) Reducedorder modeling and control of thin film growth in an HPCVD reactor.SIAM J. Appl. Math., 62, 1251-1280.


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Nano-scale and low dimensional devices...

PERSPECTIVEdoi:10.1038/nature12385

Van der Waals heterostructuresA. K. Geim1,2 & I. V. Grigorieva1

Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leadingtopics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomicplanes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. Thefirst, already remarkably complex, such heterostructures (often referred to as ‘van der Waals’) have recently beenfabricated and investigated, revealing unusual properties and new phenomena. Here we review this emergingresearch area and identify possible future directions. With steady improvement in fabrication techniques and usinggraphene’s springboard, van der Waals heterostructures should develop into a large field of their own.

G raphene research has evolved into a vast field with approxi-mately ten thousand papers now being published every yearon a wide range of graphene-related topics. Each topic is covered

by many reviews. It is probably fair to say that research on ‘simplegraphene’ has already passed its zenith. Indeed, the focus has shiftedfrom studying graphene itself to the use of the material in applications1

and as a versatile platform for investigation of various phenomena.Nonetheless, the fundamental science of graphene remains far frombeing exhausted (especially in terms of many-body physics) and, asthe quality of graphene devices continues to improve2–5, more break-throughs are expected, although at a slower pace.

Because most of the ‘low-hanging graphene fruits’ have already beenharvested, researchers have now started paying more attention to othertwo-dimensional (2D) atomic crystals6 such as isolated monolayers andfew-layer crystals of hexagonal boron nitride (hBN), molybdenumdisulphide (MoS2), other dichalcogenides and layered oxides. Duringthe first five years of the graphene boom, there appeared only a few

experimental papers on 2D crystals other than graphene, whereas thelast two years have already seen many reviews (for example, refs 7–11).This research promises to reach the same intensity as that on graphene,especially if the electronic quality of 2D crystals such as MoS2 (refs 12, 13)can be improved by a factor of ten to a hundred.

In parallel with the efforts on graphene-like materials, anotherresearch field has recently emerged and has been gaining strength overthe past two years. It deals with heterostructures and devices made bystacking different 2D crystals on top of each other. The basic principle issimple: take, for example, a monolayer, put it on top of another mono-layer or few-layer crystal, add another 2D crystal and so on. The resultingstack represents an artificial material assembled in a chosen sequence—asin building with Lego—with blocks defined with one-atomic-plane pre-cision (Fig. 1). Strong covalent bonds provide in-plane stability of 2Dcrystals, whereas relatively weak, van-der-Waals-like forces are sufficientto keep the stack together. The possibility of making multilayer vander Waals heterostructures has been demonstrated experimentally only

1School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. 2Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK.

Graphene

hBN

MoS2

WSe2

Fluorographene

Figure 1 | Building van der Waalsheterostructures. If one considers2D crystals to be analogous to Legoblocks (right panel), the constructionof a huge variety of layered structuresbecomes possible. Conceptually, thisatomic-scale Lego resemblesmolecular beam epitaxy but employsdifferent ‘construction’ rules and adistinct set of materials.

2 5 J U L Y 2 0 1 3 | V O L 4 9 9 | N A T U R E | 4 1 9

Macmillan Publishers Limited. All rights reserved©2013Geim, Grigorieva, Van der Waals heterostructures Nature (2013) 419

Nanoscale devicesassembled from2D materials

with tunableproperties

held together byvan der Waalsforces

applicable tonanoscaleelectronics,sensors,optoelectronics,PV, more...


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...and their fabrication methods

MR45CH01-Terrones ARI 20 May 2015 11:24

Chemical/mechanicalexfoliation

Soft chalcogenizationM(s) + X2(g) MX2

X2(g)/H2X(g)

Substrate Substrate

Metal film MX2

PowderBr2

Natural bulkcrystals

Crystal

Mo(CO)6 + H2SMoCl5 + H2SMoCl5 + S(g)

W(CO)6 + (CH3)2SeWCl5 + H2Se

W(CO)6 + H2S

MoS

2W

Se2

Hea

ting

elem

ents

WS 2

Hot Cold

Chemical vapordeposition

Powdervaporization

Chemical vaportransport

Bulk crystal formation

Metaltransformation

Transition metaldichalcogenide

(MX2)

• Molecular beam epitaxy• Electrochemical synthesis• Pulsed laser deposition• Spray pyrolysis

• Molecular beam epitaxy• Electrochemical synthesis• Pulsed laser deposition• Spray pyrolysis

Solid-state reactionsM(s) + X2(s) MX2

Substrate SubstrateMetal film

X(S/Se/Te) MX2Heat

M(s) + 2X(s) + transport agent(s) MX2 + TA(g)(Br2 or I2)

Metal-organicprecursors

Typical carrier:H2/N2/Ar

MX2

Substrate

T = 200–1,100°CP = 1–760 Torr

T = 600–950°CP = 1–760 Torr

Other

MoO3 + H2SMoCl5 + SMoO3 + S

WO3+ SeWSe2

WO3+ SWO3+ H2S

MoS

2W

Se2

WS 2

Furnace

X powder

X(g)

M-based powder

Ar/N2

Substrate

Figure 3Summary of primary growth techniques for the formation of monolayers of transition metal dichalcogenides. These methods includechemical vapor deposition, powder vaporization, metal transformation, chemical vapor transport, chemical exfoliation, pulsed laserdeposition, molecular beam epitaxy, spray pyrolysis, and electrochemical synthesis.

(33). The first single-layer MoS2 (circa 1986) (4) was achieved via chemical exfoliation using Liintercalation to separate MoS2 sheets in solution. In contrast, the mechanically exfoliated flakesused today (6, 34, 35) often come from bulk crystals that are synthesized via chemical vaportransport (36). Chemical vapor transport (Figure 3) has been used to synthesize a wide range ofTMDs (TaS2, TaSe2, MoTe2, WTe2, etc.) (37–39) under near equilibrium conditions throughthe use of a transport agent [often bromine (Br2) or iodine (I2)] to transport the metal (M) andchalcogen (X) constituents across a thermal gradient under vacuum (36). This process typicallyrequires days or weeks to complete and results in bulk crystallites along the walls of the synthesisvessel. Similarly, direct vapor transport utilizes a thermal gradient to vaporize stoichiometricquantities of TMD parent materials (M and X) and to recrystallize them at the cold end of thefurnace without a transport agent. This route has been quite successful for the synthesis of a widevariety of bulk TMD crystals (MoS2, WS2, MoSe2, WSe2, TaSe2, etc.), with bulk crystals reaching>10 × 10 mm (37, 40, 41).

Although bulk crystals of TMDs provide a route for achieving ultrahigh-quality, crystallineflakes of materials for scientific investigations, they are not considered suitable for large-areaTMD electronics. Adequate techniques include, for example, pulsed laser deposition (42), spraypyrolysis (43), sputter deposition (44, 45), spin deposition and dip coating (46), and atomic layerdeposition (47); however, most techniques focus on vaporization of a metal (M = Mo, W, Nb, Ta,etc.) and/or chalcogen (X = S, Se, Te) precursor material followed by subsequent reaction on a

www.annualreviews.org • Beyond Graphene 5

Ann

u. R

ev. M

ater

. Res

. 201

5.45

:1-2

7. D

ownl

oade

d fro

m w

ww

.ann

ualre

view

s.org

Acc

ess p

rovi

ded

by U

nive

rsity

of M

aryl

and

- Col

lege

Par

k on

01/

03/1

7. F

or p

erso

nal u

se o

nly.

Das, S. et al., Beyond graphene: 2D materials, vdW solids Annu. Rev. Mater. Sci. (2015) 1


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GaAs nanowire solar cell

solar cell yields an apparent efficiency of 40%. To understand theextreme photon collection boost in free-standing single GaAs nano-wires, we used a finite-difference time-domain (FDTD) method tomodel a 2.5-mm-long nanowire embedded in SU-8 as a functionof its diameter and of the wavelength of the plane-wave radiation pro-pagating along the nanowire axis30–32. Figure 2a shows the wavelengthand diameter dependence of the absorption rate of such a nanowire.Note that the absorption is zero for wavelengths larger than 900 nmwhere the absorption coefficient of GaAs goes to zero. Two dominantbranches for low and high diameters are observed, corresponding toresonances similar to the Mie resonances observed in nanowireslying on a substrate25. Light absorption in the standing nanowire isenhanced by a factor of between 10 and 70 with respect to the equiv-alent thin film. Another way to express this enhancement in

absorption is through the concept of an absorption cross-section.The absorption cross-section is defined as Aabs¼ ah, where a is thephysical cross-section of the nanowire and h is the absorption effi-ciency. It is largely accepted that the absorption cross-section innanoscale materials is larger than their physical size. In systemssuch as quantum dots, the absorption cross-section can exceed thephysical size by a factor of up to 8 (ref. 33). We calculated the absorp-tion cross-section of the nanowires as a function of the nanowirediameter and incident wavelength (Fig. 2b). The absorption cross-section is, in all cases, larger than the physical cross-section of thenanowire. It is interesting to note that the absorption of photonsfrom an area larger than the nanowire itself is equivalent to a built-in light concentration C. Light concentration has an additionalbenefit in that it increases the open-circuit voltage with a termkT ln C, thereby increasing the efficiency34–36. The largest absorptioncross-section in Fig. 2b is 1.13× 106 nm2 for a nanowire diameterof 380 nm (a¼ 9.38 × 104 nm2), corresponding to an overall built-in light concentration of "12.

Measurements of the external quantum efficiency (EQE) nor-malized by the physical area for both lying and standing nanowiredevices are shown in Fig. 3a (see Supplementary Section S1 for

1,100a

b

1,000 14

×1027

Absorption rate

12

10

8

6

4

1.0

0.8

Absorption cross-section area (µm

2)

0.6

0.4

0.2

0.0

2

0

AM

1.5G absorption rate (J −1 s −1)

900

800

700

Wav

elen

gth

(nm

)600

100 200 300 400Diameter (nm)

500

300

400

0.005 0.020Geometric cross-section area (µm2)

0.050 0.100 0.1501,100

1,000

900

800

700

Wav

elen

gth

(nm

)

600

100 200 300 400Diameter (nm)

500

300

400

Cross-section

Figure 2 | Optical simulations of a single nanowire solar cell.a,b, Simulations of light absorption in a 2.5 mm standing GaAs nanowire thatis fully embedded in SU-8 (n¼ 1.67) on a silicon substrate: the absorptionrate of solar AM 1.5G radiation (a) and simulated absorption cross-section(b) exhibit two main resonant branches, similar to Mie resonances observedin nanowires lying on a substrate. The periodic modulation with wavelengthis a result of Fabry–Perot interference in the polymer layer and not anartefact of the simulation.

a

ITO

SU-8

Si - p-doped - SiO2 on top

n-type,Si doped

p-type,Be doped

Undoped

cb

0.5 µm

0.5 µm

5 µm

d

Dark

Current (pA)300

200

100

−0.3 −0.2 −0.1 0.0 0.0 0.1 0.2 0.3 0.5

−100

−200

−300

AM 1.5

Voltage (V)

ISC = 256 pA (180 mA cm−2)VOC = 0.43 VFF = 0.52

00.4

Figure 1 | Electrical characterization of a single nanowire solar cell (device 1).a, Schematic of the vertical single-nanowire radial p–i–n device connected to ap-type doped silicon wafer by epitaxial growth. b, Left: doping structure of thenanowire. The p-type doped core is in contact with the doped silicon substrateand the n-type doped shell is in contact with the ITO. Right: Scanning electronmicroscope (SEM) image of a nanowire solar cell before adding the topcontact, with a 308 angle from the vertical. c, SEM images of the device seenfrom the top electrode. The nanowire is "2.5mm high and has a diameter of"425 nm. d, Current–voltage characteristics of the device in the dark andunder AM 1.5G illumination, showing the figure-of-merit characteristics.

ARTICLES NATURE PHOTONICS DOI: 10.1038/NPHOTON.2013.32

NATURE PHOTONICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephotonics2

0.5 µm

solar cell yields an apparent efficiency of 40%. To understand theextreme photon collection boost in free-standing single GaAs nano-wires, we used a finite-difference time-domain (FDTD) method tomodel a 2.5-mm-long nanowire embedded in SU-8 as a functionof its diameter and of the wavelength of the plane-wave radiation pro-pagating along the nanowire axis30–32. Figure 2a shows the wavelengthand diameter dependence of the absorption rate of such a nanowire.Note that the absorption is zero for wavelengths larger than 900 nmwhere the absorption coefficient of GaAs goes to zero. Two dominantbranches for low and high diameters are observed, corresponding toresonances similar to the Mie resonances observed in nanowireslying on a substrate25. Light absorption in the standing nanowire isenhanced by a factor of between 10 and 70 with respect to the equiv-alent thin film. Another way to express this enhancement in

absorption is through the concept of an absorption cross-section.The absorption cross-section is defined as Aabs¼ ah, where a is thephysical cross-section of the nanowire and h is the absorption effi-ciency. It is largely accepted that the absorption cross-section innanoscale materials is larger than their physical size. In systemssuch as quantum dots, the absorption cross-section can exceed thephysical size by a factor of up to 8 (ref. 33). We calculated the absorp-tion cross-section of the nanowires as a function of the nanowirediameter and incident wavelength (Fig. 2b). The absorption cross-section is, in all cases, larger than the physical cross-section of thenanowire. It is interesting to note that the absorption of photonsfrom an area larger than the nanowire itself is equivalent to a built-in light concentration C. Light concentration has an additionalbenefit in that it increases the open-circuit voltage with a termkT ln C, thereby increasing the efficiency34–36. The largest absorptioncross-section in Fig. 2b is 1.13× 106 nm2 for a nanowire diameterof 380 nm (a¼ 9.38 × 104 nm2), corresponding to an overall built-in light concentration of "12.

Measurements of the external quantum efficiency (EQE) nor-malized by the physical area for both lying and standing nanowiredevices are shown in Fig. 3a (see Supplementary Section S1 for

1,100a

b

1,000 14

×1027

Absorption rate

12

10

8

6

4

1.0

0.8

Absorption cross-section area (µm

2)

0.6

0.4

0.2

0.0

2

0

AM

1.5G absorption rate (J −1 s −1)

900

800

700

Wav

elen

gth

(nm

)

600

100 200 300 400Diameter (nm)

500

300

400

0.005 0.020Geometric cross-section area (µm2)

0.050 0.100 0.1501,100

1,000

900

800

700

Wav

elen

gth

(nm

)

600

100 200 300 400Diameter (nm)

500

300

400

Cross-section

Figure 2 | Optical simulations of a single nanowire solar cell.a,b, Simulations of light absorption in a 2.5 mm standing GaAs nanowire thatis fully embedded in SU-8 (n¼ 1.67) on a silicon substrate: the absorptionrate of solar AM 1.5G radiation (a) and simulated absorption cross-section(b) exhibit two main resonant branches, similar to Mie resonances observedin nanowires lying on a substrate. The periodic modulation with wavelengthis a result of Fabry–Perot interference in the polymer layer and not anartefact of the simulation.

a

ITO

SU-8

Si - p-doped - SiO2 on top

n-type,Si doped

p-type,Be doped

Undoped

cb

0.5 µm

0.5 µm

5 µm

d

Dark

Current (pA)300

200

100

−0.3 −0.2 −0.1 0.0 0.0 0.1 0.2 0.3 0.5

−100

−200

−300

AM 1.5

Voltage (V)

ISC = 256 pA (180 mA cm−2)VOC = 0.43 VFF = 0.52

00.4

Figure 1 | Electrical characterization of a single nanowire solar cell (device 1).a, Schematic of the vertical single-nanowire radial p–i–n device connected to ap-type doped silicon wafer by epitaxial growth. b, Left: doping structure of thenanowire. The p-type doped core is in contact with the doped silicon substrateand the n-type doped shell is in contact with the ITO. Right: Scanning electronmicroscope (SEM) image of a nanowire solar cell before adding the topcontact, with a 308 angle from the vertical. c, SEM images of the device seenfrom the top electrode. The nanowire is "2.5mm high and has a diameter of"425 nm. d, Current–voltage characteristics of the device in the dark andunder AM 1.5G illumination, showing the figure-of-merit characteristics.

ARTICLES NATURE PHOTONICS DOI: 10.1038/NPHOTON.2013.32

NATURE PHOTONICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephotonics2

© 2013 Macmillan Publishers Limited. All rights reserved.

Krogstrup, et al., Nature Photonics (2013)I < 0

+

-

Rsh

Rs

V = voltage drop

Iph n-type

p-type

Idiode

Ish

Need > 1012 nanowire PV cells


8/50

Energy engineering design across multiple scales

Nanoscale benefits ofelectrochemical energystorage (G. Rubloff):

1 Improved iontransport

τ ∼ L2

D

2 More effective useof ion storagematerial

Q: How do we scale to applications?

storage cell

exposed

integrated high

power electrical

storage system

packaged (electrolyte inside)

storage & control

chips on substrate(flexible or board)storage chip

storage chips

control chip

utility, 3m3, 100MW

village, 450cm3, 15kW


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Relation to Advanced (chemical) Manufacturing

The United States has launched the Manufacturing USA(formerly known as NNMI or National Network forManufacturing Innovation) program

It establishes a network of manufacturing institutes, each witha specialized technology focus.The program goal is to promote innovation, collaboration, andeducation.

To support this nationwide initiative, AIChE has undertakenan in-depth study to identify the opportunities and challengesto the manufacture of chemical-based products.


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Institutes for Advanced Manufacturing

Established

America Makes, the National Additive ManufacturingInnovation Institute (Youngstown, OH)

Digital Manufacturing and Design Innovation Institute(Chicago, IL)

Lightweight Innovations for Tomorrow (Detroit, MI)

Power America (Raleigh, NC)

Institute for Advanced Composites Manufacturing Innovation(Knoxville, TN)

American Institute for Manufacturing Integrated Photonics(Rochester, NY)

Next Flex, the Flexible Hybrid Electronics ManufacturingInnovation Institute (San Jose, CA)

Advanced Functional Fabrics of America (Cambridge, MA)

Smart Manufacturing Innovation Institute (Los Angeles, CA)


11/50

AIChEformstheRAPIDManufacturingIns9tute

•  RAPIDhasappliedforthesupportfromtheU.S.DepartmentofEnergyfor“ModularChemicalProcessIntensifica9onIns9tuteforCleanEnergyManufacturing”

•  ThisIns9tute,whenannounced,wouldbethetenthins9tuteformedaspartoftheU.S.ManufacturingUSAini9a9ve

•  RAPID’sfocuswillbeontheapplica9onofprocessintensifica9ontomanufacturingprocessesasameansofloweringcosts,improvingenergy-andresource-efficiency,andincreasingoverallproduc9vity.

RapidAdvancementinProcessIntensifica4onDeployment(RAPID)

AIChE forms the RAPID Manufacturing Institute

RAPID has applied for the support from the U.S. Departmentof Energy for Modular Chemical Process IntensificationInstitute for Clean Energy Manufacturing

This Institute, just announced, is the tenth institute formedas part of the U.S. Manufacturing USA initiative

RAPID’s focus will be on the application of processintensification to manufacturing processes as a means oflowering costs, improving energy- and resource-efficiency, andincreasing overall productivity.


12/50

Advanced Manufacturing - AIChE PAIC view

Overlap

Shares deep integration of ChE transport and reactionprocesses with Process Intensification, together with itsmodularization goals

Shares precursor/energy use and emissions control goals ofSustainability initiatives

Shares advanced sensor/actuator, simulation, and processflexibility objectives of Smart Manufacturing

Complement

Highlights the need to develop the unique process analysis andconcurrent product/process design methods currently lacking foremerging chemical product markets


13/50

Atomic layer deposition

Cyclic operation: A . . . purge . . . B . . . purge . . . A . . . purge . . .

O O O O O O O O

M M

M M

M

Precursor A Purge Precursor B Purge

M M M M M M M M M M M M M M M M M O O O O O O O O O

M

O

O

O

O M M M M M M M M M O O O O O O O O O

O O O O O O O O O O O O O O O O O O

55 nm Al2O3 (top)100 nm ZnO (middle)Si substrate (bottom)

2 ML3(g) + 3 H2O(g) → M2O3(b) + 6 HL(g)ML2(g) + H2O(g) → MO(b) + 2 HL(g)


14/50

Motivation

ALD surface process kinetics modeling issues:

1 Fragmented reaction mechanismstudies

2 Competing reaction paths to aproduct species; multiple timescales

3 Mechanistic origins of self-limitingand steady cyclic-growth processes?

This talk

Can we assess whether we have an “proper” ALD reaction networkbefore investing time in determining reaction rates?


15/50

Elements of an ALD reaction process

ML2(g) + H2O(g) → MO(b) + 2HL(g)

Reactions

Rates

Atoms

Species

Phases

Moles

Balances

reaction net rate

ML2(g) + 2S + HO HML2 + O(b) f0HML2 HML‡2 (1/ε)g0

HML‡2 → HL(g) + S + ML f1

H2O(g) + ML H2OL + M(b) f2H2OL H2OL‡ (1/ε)g1

H2OL‡ → HL(g) + S + HO f3

Rates

From experiments, quantum chemical + CTST


15/50


ML2(g) + H2O(g) → MO(b) + 2HL(g)

Reactions

Rates

Atoms

Species

Phases

Moles

Balances

A = {M,O, L,H}

S = {ML2(g),H2O(g),HL(g),

S,HO,HML2,HML‡2,ML,H2OL,H2OL‡,

M(b),O(b)}

⇒ in terms of the “atoms”


15/50


ML2(g) + H2O(g) → MO(b) + 2HL(g)

Reactions

Rates

Atoms

Species

Phases

Moles

Balances

P = {φ0 (gas), φ1 (growth surface), φ2 (film)}

m =[ML2, HO, HML‡2, . . .

]TdML2

dt= −φ1f0

dHO

dt= −φ1f0 + φ1f3

dHML‡2dt

=1

εg0 − φ1f1

...FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu

16/50

Reaction factorization

Molar balance on each of the twelve species, isothermal batchsystem:

dm

dt=

1

εQg + Pf

subject to specified initial condition m(0) = mo .

A singularly perturbed system in nonstandard form (Daoutidis, 2015)

Prior to ε→ 0

Following Rodrigues, Srinivasan, Billeter, and Bonvin (2015), wewish to find transformation T that decouples gi , fj


17/50

Reaction factorization to obtain SPS in standard form

dT n

dt=

1

εT[

Qtng×ng

Qb

]g + T

[Pt

ng×nf

Pb

]f

≈ I

g/εf0

note ≈

Our decoupled batch system in terms of Rodrigues, et al. (2015)

xrg =1

εQt−1Qtg + Qt

−1Ptf

xrf =1

ε0g + [Rt

−1 0][Pb −QbQt−1Pt]f

xiv =1

ε0g + 0f


18/50

Computing elements of TA Gauss-Jordan factorization procedure decouples the gi[

Qt−1 0

−QbQt−1 I

]dm

dt=

[Qt−1 0

−QbQt−1 I

](1

εQg + Pf

)=

1

ε

[I0

]g +

[Qt−1Pt

Pb −QbQt−1Pt

]f

to find the DAE system for ε→ 0

0 = g[−QbQt

−1 I] dm

dt=[

Pb −QbQt−1Pt

]f =

[Rt

Rb

]f

thus,

[Rt−1 0

−RbRt−1 I

] [Pb −QbQt

−1Pt

]f =

[Inf×nf

0(ns−ng−nf )×nf

]f


19/50

Computing elements of T , cont

RecalldT n

dt≈ I

g/εf0

rank(Qt) < ng?

=⇒ invalid set of equilibrium relationships (gi cannot bedecoupled)

rank(Rt) < nf ?

=⇒ OK, but redundant reaction paths (fj cannot be decoupled)=⇒ factor using forward elimination, integer arithmetic


20/50

Reaction invariants: xiv =1

ε0g + 0f

Variant/invariants, representative studies, mainly in PSE

Asbjørnsen, O.A., Fjeld, M. (1970) Response modes of continuous stirredtank reactors. Chem. Engng Sci., 25, 1627-1636.

Othmer, H.G. (1981) A graph-theoretic analysis of chemical reactionnetworks. I. Invariants.

Chilakapati, A., Ginn, T., Szecsody, J. (1988) An analysis of complexreaction networks in groundwater modeling, Water Resources Res., 34,1767-1780.

Dochain D, Couenne F, Jallut C. (2009) Enthalpy based modelling anddesign of asymptotic observers for chemical reactors. Int. J. Control, 82,1389-1403.

Rodrigues, D., Srinivasan, S., Billeter, J. Bonvin, D. (2015) Variant andinvariant states for chemical reaction systems. C&CE, 73, 23-33.

Zhao, Z. Wassick, J.M., Ferrio, J., Ydstie, B.E. (2016) Reaction variantsand invariants based observer and controller design for CSTRs. Proc.DYCOPS 2016, 1091-1096.


21/50

Archetype ALD process - invariant analysis

12 molar balances:dm

dt=

1

εP

[g0

g1

]+ Q

f0f1f2f3

can be reduced to 2 eq relationships and 4 independent dynamicmodes =⇒ good

Reaction invariants =⇒ hard to interpret

−HML2 − HML‡2 − S + HO = w0

ML2 + O = w1

2ML2 − S + HL = w2

2HML2 + 2HML‡2 + H2OL + H2OL‡ + S + ML = w3

HML2 + HML‡2 + H2OL + H2OL‡ −ML2 + S + H2O = w4

−HML2 − HML‡2 − H2OL− H2OL‡ + ML2 − S + M = w5


22/50

Graphs in RN analysis and energy applications

Craciun, G., Fienberg, M. (2006) Multiple equilibria in complex chemicalRN: The Species-Reaction graph. SIAM J. Appl. Math. 66, 1321-1338.

Heo, S., Rangarajan, S., Daoutidis, P., Jogwar, S.S. (2014) Graphreduction of complex energy-integrated networks: Process systemsapplications. AIChE J. 60, 995-1012.

1

1

-2

1

-1

-1

1

-1

-1

1

A

f0

B

D

g1

g0

A+

M

f1

S

A

f0

B

D

g1

g0

A+

M

f1

S

A

f0

B

D

g1

g0

A+

M

f1

S

gas phase

surface

surface

bulk film

2 M g0 D

M + S f0 A

A g1 A‡

A‡ f1→ B + S

Q: Relationship between SR graph and variants/invariants?FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu

23/50

Species-Reaction (SR) graph rules for extracting invariants

Key concept: An invariant is a path through an SR graph

Case 1: Terminal species → Terminal species, linear graph

νR0 νP0 νR1 νP1

D +|νR0||νP0|

[A +|νR1||νP1|

B

]= invariant

2D + A + B = w0


24/50

SR graph rules for extracting invariants

Case 2: Cycles - conserved quantities

-1

-1

1

2

2

-4

A

f0

C B

f1

f2

A

f0

C B

f1

f2

A

f0

C B

f1

f2-1

2

-11

2

-4

f0 f1

C B

f2

A1A0

f0 f1

C B

f2

A1A0

f0 f1

C B

f2

A1A0

4A(0) + 2B + C + 4A(1) = w0

A(0) + A(1) = A

Cycles can be equivalent to linear graphs


25/50


Case 3: Species branches - conserved quantities

e.g., ligand substitution e.g., thermal decomposition

w0 =A(0) + B(0) + C

+ A(1) + B(1) + D

=A + B + C + D

Function as logical ANDs


26/50


Case 4: Reaction branches: AB + H2 → AH + BH

Thru a) H2 + AH = constreaction b) H2 + BH = const

c) AB + AH = constd) AB + BH = b + c - a

Thru e) H2 - AB = a - ccomplex f) BH - AH = b - a


27/50

Reaction branches, continued

Linearly H2 + AH = constindependent H2 + BH = const

AB + AH = const

Meaningful 2H2 + AH + BH = w0

AB + AH = w1

AB + BH = w2

Atomic balance array A:

H2 AB AH BH

A 0 1 1 0 (w1)B 0 1 0 1 (w2)H 2 0 1 1 (w0)

nullity = no. columns - rank(A) = 1

kernel = [−1,−1, 1, 1]T

Think logical OR


28/50

Archetype ALD process

Let us return to

reaction net fwd rate

ML2(g) + 2S + HO HML2 + O(b) f0HML2 HML‡2 (1/ε)g0

HML‡2 → HL(g) + S + ML f1

H2O(g) + ML H2OL + M(b) f2H2OL H2OL‡ (1/ε)g1

H2OL‡ → HL(g) + S + HO f3

e.g., Zn(C2H5)2(g) + H2O(g) → ZnO(b) + 2C2H6(g)


29/50

Archetype ALD process - SR graph

1

1

-1

-11

-11

-2 -1

1

1

1

-1

1

-1

-1

1

1

-1

11

f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2


30/50

Invariant 0: M conservation

1

1

-1

-11

-11

-2 -11

1

1

-1

1

-1

-1

1

1

-1

1

1

f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2

ML2(g) + HML2 + HML‡2 + ML + M(b) = w0


31/50

Invariant 1: O conservation

1

1

-1

-11

-11

-2 -11

1

1

-1

1

-1

-1

1

1

-1

1

1

f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2

H2O(g) + H2OL + H2OL‡ + HO + O(b) = w1


32/50

Invariant 2: H conservation

1

1

-1

-11

-11

-2 -1

1

1

1

-1

1

-1

-1

1

1

-1

1

1

f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2

H2O(g) + H2OL + H2OL‡ + HL(0)(g) + HO + HML2 + HML‡2 +

H2O(g) + H2OL + H2OL‡ + HL(1)(g) = w2


33/50

Invariant 3: L conservation

1

1

-1

-11

-11

-2 -1

1

1

1

-1

1

-1

-1

1

1

-1

1

1

f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3 g1

g0 ML

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2

ML2(g) + HML2 + HML‡2 + HL(0)(g) + ML + H2OL + H2OL‡ +

ML2(g) + HML2 + HML‡2 + HL(1)(g) = w3


34/50

Invariant 4: Surface-phase reactive site conservation

1

-1

-11 1

-2 -1

11

1

-1

-111

-1

f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2

HO(0) + HML2 + HML‡2 + ML + H2OL + H2OL‡ + HO(1) = w4


35/50

Invariant 5: Ligand steric hindrance

1

-1

-11 1

-2 -1

11

1

-1

-111

-1

f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2

S (0) + HML2 + HML‡2 + ML + H2OL + H2OL‡ +

S (1) + HML2 + HML‡2 = w5


36/50

Summary: archetype ALD process

Metal, oxygen, ligand, and H conservation invariants -spanning all three phases

Two reaction surface properties originating in ALD’sself-limiting nature - each half-reaction breaks these cycles

1

-1

-11 1

-2 -1

1

1

1

-1

-11

1

-1

f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2

1

-1

-11 1

-2 -1

1

1

1

-1

-11

1

-1

f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2


36/50

Summary: archetype ALD process

Metal, oxygen, ligand, and H conservation invariants -spanning all three phases

Two reaction surface properties originating in ALD’sself-limiting nature - each half-reaction breaks these cycles

1

-1

-11 1

-2 -1

1

1

1-1

-11

1

-1

f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2

1

-1

-11 1

-2 -1

1

1

1

-1

-11

1

-1

f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2f0

f1

f2

f3 g1

g0 MLHML2+

S

H2OL+

HO H2OL

HML2


37/50

ALD archetype RN - open system (CSTR)

-1

-21

-1

1

-1

-1

1

1 -1

-1 1

1 -1

1

-1

1

1

1

-1

-1

1

-1

1

f0

f1

f2

f3

f4 f5

g1

g0 ML

f6

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3

f4 f5

g1

g0 ML

f6

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2f0

f1

f2

f3

f4 f5

g1

g0 ML

f6

M

S

O

HML2+

ML2 H2O

H2OL+

HO

HL

H2OL

HML2

Gas-phaseinlet/outlet flows:

f4 = MLdose2 δ(t − tA)− ω(t)ML2

f5 = H2Odoseδ(t − tB)− ω(t)H2O

f6 = −ω(t)HL


38/50

Precursor doses generated by short (ms) precursor pulses


39/50

Invariants

S + 2HML2 + 2HML‡2 + ML + H2OL + H2OL‡ = w0 L area cons

HO + HML2 + HML‡2 + ML + H2OL + H2OL‡ = w1 rxn site cons

M(b) + ML + HML‡2 + HML2 − O(b) = w3 meaning??

Cycle invariants =⇒ film stoichiometry

∫ tcycle

0[M(b) + ML + · · · − O(b)] dt =⇒ M(b)− O(b) = w3

Final practical note

Use invariants to remove critical complexes (e.g., HML‡2) fromvariants


40/50

Alumina ALD

2 Al(CH3)2 + 3 H2O → Al2O3 + 6 CH4

≈ 300 TMA/water alumina ALD citations in Miikkulainen,Leskela, Ritala, and Puurunen, J. Appl. Phys. (2013)

“Traditional” view ofreaction mechanism:

Dillon, Ott, Way, George

(1995) Surf. Sci., 322, 230-242

4.C. Dillon et al. /Surface Science 322 (1995) 230-242 238

A.)

B.) + 3CQ (9)

3H20

Fig. 15. Possible mechanisms for the surface chemistry of Al,O, controlled deposition using TMA and H,O in a binary reaction sequence.

infrared spectrum. These spectral results reveal that the TMA reaction with a hydroxylated alumina surface does not go to completion at 300 K.

The third spectrum in Fig. 2 reveals the changes in the infrared spectrum following a 2 Torr, 5 min TMA exposure at 500 K. The broad AlO-H stretching vibration virtually disappears and a significant increase is observed in the C-H, stretching region. These results indicate that the TMA reaction with hydroxylated alumina at the higher temperature of 500 K removes all the AlOH surface species as illustrated in Fig. 15a.

Fig. 3 displays the changes in the infrared spectra of a porous alumina membrane versus sequential 0.3 Torr, 1 min H,O and TMA exposures at 500 K. The initial spectrum in Fig. 3 is of an alumina membrane with a saturation hydroxyl coverage. The second spectrum was recorded following a 0.3 Torr, 1 min TMA exposure at 500 K. The third spectrum in Fig. 3 reveals that a subsequent 0.3 Torr, 1 min H,O exposure at 500 K results in the disappearance of the infrared absorbance of the C-H, stretching vibrations and an increase in the broad infrared absorbance of the AlO-H stretching vibrations. This H,O exposure is sufficient for a complete reaction between H,O and the surface AlCH, species as portrayed in Fig. 15b.

The spectral results in Fig. 3 are consistent with

Al,O, growth on the alumina surface according to the ABAB . . . binary reaction sequence:

(A) AlOH + Al(CH,),

+ Al-0-Al(CH,), + CH,,

(B) Al-0-Al(CH,), + 2 H,O

+ Al-O-Al(OH)z + 2 CH,.

The spectra indicate that both reactions are complete and self-limiting. The repetitive application of the AB reaction cycles should therefore lead to the controlled deposition of Al,O,. Although the above reaction scheme indicates that TMA reacts with one hydroxyl group, TMA molecules may react with more than one AlOH surface species as discussed in Section 4.4.

After the second TMA exposure, a slight absorbance in the AlO-H stretching region is observed in the last infrared spectrum in Fig. 3. An additional 2 Torr, 5 min TMA exposure at 500 K did not result in the disappearance of this AlO-H absorption feature. This behavior is consistent with a slight accumulation of unreactive hydroxyls on the alumina surface. These results are consistent with previous studies of the reaction of TMA with silica surfaces [45]. Subsequent H,O and TMA exposures in an ABAB... binary reaction sequence resulted in a gradual increase in AlOH species that were not consumed by additional TMA exposure.

Annealing the alumina to 1000 K for 10 min resulted in the disappearance of detectable absorbance in the AlO-H stretching region. The unreactive AlOH species may be attributed to the formation of an amorphous Al,O, film with AlOH sites inaccessible to the TMA molecules. Annealing the sample to 1000 K results in dehydroxylation through the reaction AlOH + AlOH + Al-O-Al + H,O [41] as observed in Figs. 10 and 11. The prevention of excess hydroxyl accumulation may be achieved by annealing the alumina to 1000 K following a set of 10 TMA/H,O binary reaction cycles.

4.3. Reaction rate kinetics

The relative reaction rate kinetics for the (A> and (B) binary reactions are revealed in Figs. 4-7. Figs.


41/50

TMA adsorption on HO surfaces (Elliott and Greer, 2004)

Al

Me

Me

Me

CH4

↓ ↑

OHf0 OH

AlMe3g1

O

H

Me

Al

Me

Mef2→ O

Al

Me Me

Me3Al′ + HO′ Me3AlHO Me3AlHO‡ Me2Al′ + MeH+ 3S + Al + Al′ + S

OH + O

Al

Me Me

g3

HO

Al

MeMe

Og4

O

H Al

MeMe

Of5→ O

Al

Me

O + CH4

HO′ + Me2Al′ Me2AlHO Me2AlHO‡ MeAl′ + MeH+ S + Al′


42/50

Densification, water adsorption (Hass et al., 1998)

CH4

↑

OH + O

Al

Me

Og6

O

Al

Me

OOH

g7

O

Al

Me

OO

Hf8→ O

Al

OO

HO′ + MeAl′ MeAlHO MeAlHO‡ Al′ + S + MeH

H2O↓

Al

O

Alf9 Al

OH2 O

Alg10

Al

OH

H

O

Alf11

→ 2 OH

2Al′ + H2O′ H2O + O H2O‡2 2HO′


43/50

TMA adsorption, surface O sites (Elliott and Greer, 2004)

Al

Me

Me

Me↓

Al

O

Alf12

Al

O

Al

AlMe3

g13

Al

O

Al

Me

Al

Me Me

Me3Al′ + 2 Al′ + 3S Me3AlO + Al Me2Al′ + MeAl

O

Al

Me Me

+ O

Al

OO

g14

O

Al

Me Me

O

Al

OO

f15

→ 2 Al

Me

Me2Al′ + Al′ Me2Al2O‡ 2MeAl


44/50

Water adsorption on Me sites (Delabie et al., 2012)

H2O↓

2 Al

Mef16

Al

Me OH2

+ Al

Meg17

Al

Me O

H

H Me

Al

2 MeAl + H2O′ MeAlH2O + O + MeAl Me2Al2H2O‡

Al

Me O

H

H Me

Alf18

→ Al

Me O

H

Al + MeH

Me2Al2H2O‡ MeAlHO + MeH + S

=⇒ Recall MeAlHO intermediate in the previous reaction cycle


45/50

Al2(CH3)6 + 3H2O→ Al2O3 + 6CH4

Me3Al′(g)+HO′+3S Me3AlHO+O

Me3AlHO Me3AlHO‡

Me3AlHO‡ → Me2Al′+Al′+Al+S+MeH(g)Me2Al′+HO′ Me2AlHO

Me2AlHO Me2AlHO‡

Me2AlHO‡ → MeAl′+Al′+S+MeH(g)MeAl′+HO′ MeAlHO

MeAlHO MeAlHO‡

MeAlHO‡ → Al′+S+MeH(g)

H2O′(g)+2Al′ H2O+O

H2O H2O‡2

H2O‡2 → 2HO′

Me3Al′(g)+2Al′+3S Me3AlO+AlMe3AlO Me2Al′+MeAl

Me2Al′+Al′ Me2Al2O‡

Me2Al2O‡ → 2MeAl

H2O′(g)+2MeAl MeAlH2O+MeAl+O

MeAlH2O+MeAl Me2Al2H2O‡

Me2Al2H2O‡ → MeAlHO+S+MeH(g)

Remmers, Travis, Adomaitis, Chem. Engng Sci. (2015)

Elementary surface processesinclude:

Adsorption anddesorption

Ligand exchange

Densification

(Limited) surfacediffusion

19 reactions, 23 species


45/50

Al2(CH3)6 + 3H2O→ Al2O3 + 6CH4

Me3Al′(g)+HO′+3S Me3AlHO+O

Me3AlHO Me3AlHO‡

Me3AlHO‡ → Me2Al′+Al′+Al+S+MeH(g)Me2Al′+HO′ Me2AlHO

Me2AlHO Me2AlHO‡

Me2AlHO‡ → MeAl′+Al′+S+MeH(g)MeAl′+HO′ MeAlHO

MeAlHO MeAlHO‡

MeAlHO‡ → Al′+S+MeH(g)

H2O′(g)+2Al′ H2O+O

H2O H2O‡2

H2O‡2 → 2HO′

Me3Al′(g)+2Al′+3S Me3AlO+AlMe3AlO Me2Al′+MeAl

Me2Al′+Al′ Me2Al2O‡

Me2Al2O‡ → 2MeAl

H2O′(g)+2MeAl MeAlH2O+MeAl+O

MeAlH2O+MeAl Me2Al2H2O‡

Me2Al2H2O‡ → MeAlHO+S+MeH(g)

Remmers, Travis, Adomaitis, Chem. Engng Sci. (2015)

Reduction process:

9 NAEs

8 reaction variants

6 reaction invariants

Further dynamic reduction to4 modes is possible


46/50

Physical interpretation of the conserved modes

In terms of major species (Adomaitis, JVST A, 2016):

MeH + 3Me3Al′ + MeAl + 2Me2AlHO = w0 (1)

Me3Al′ + Al = w1 (2)

MeAl + 2Me2AlHO + S = w2 (3)

O + H2O′ = w3 (4)

MeAl + Me2AlHO + HO ′ + Al ′ = w4 (5)

MeH + 2H2O′ + Me2AlHO + HO ′ = w5 (6)

(1) conservation of Me groups(2) Al incorporation conservation(3) surface site conservation: self-limiting ALD(4) conserved O(5) rxn site conservation: stable rxn surface(6) H-transfer reaction H conservation


47/50

ALD deposition kinetics - CTST

A(g) + O′r0 AO

K1 AO‡r2→ M′ + X(g) + O

18/44

ALD deposition kinetics - CTST

A(g) + O0 E0⌦ AOE1⌦ AO‡ I2! M0 + X(g) + O

AO‡ : O

H

Me

Al

Me

Me

Ray Adomaitis - 8 May 2015 30 years of ISR

Reaction energetics,transition-stateconfigurations fromquantum chemicalcomputations (DFT)

Eq constants,rates, partitionfunctions fromstatisticalmechanics

r0 =kBT

h

[PAK0[O ′]

kBT− [AO]

] Z2DGA ZO′

ZAO [O ′]e∆E0,0/kBT

[AO‡][AO]

= K1 =l1ZAO‡

ZAOe−∆E0,1/kBT r2 =

kBT

h[AO‡]

Travis and Adomaitis, 2014


48/50

Limit-cycle solution

T = 450 KPA = 2 PaPB = 2 Pa

1.5× 104 L

gpc = 1.23 A

A . . . purge . . . B . . . purge

48 50 52 54 56 58 60time, s

0

2

4

6

8

10

12

surf

ace

conc,

nm

-2

MeAl

Me2 Al

SMe2 AlHO

HO

Al


49/50

Dynamic optimization

Maximize ALD tool throughput

Objective function:

maxτA,τB

gpc(τA, τB , ...)

τcycle

Note units: A/time

0.2 0.4 0.6 0.8 1.0Vbc/Vrxr %

0.1

0.2

0.3

0.4

0.5

0.6

B s

ec

CVD conditions

base-case design

0.180

0.195

0.210

0.225

0.240

0.255

0.270

0.285

0.300

react

or

thro

ughput

/s


50/50

Concluding remarks

How to coherently integrate reaction path segments from a rangeof sources into a “proper” ALD/CVD reaction network....

...and to distill that to its lowest dynamical dimension to be usefulfor high-throughput thin-film process design and optimization.

Our definition of a “proper” RN:

1 Correct separation of time scales, e.g.,pseudo-equilibrium from finite-rate

2 Atomic and surface feature invariants

3 Self-limiting behavior during half-reactions

4 Correct film stoichiometry

5 Potential for measuring reaction rates

6 May be beneficial in biological andheterogeneous catalysis applications


reaction path analysis for thin-film deposition processesfocapo-cpc.org/pdf/adomaitis.pdfreaction...

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