Reaction path analysis for thin-film deposition processesfocapo-cpc.org/pdf/Adomaitis.pdfReaction...
Transcript of Reaction path analysis for thin-film deposition processesfocapo-cpc.org/pdf/Adomaitis.pdfReaction...
1/50
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
2/50
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
3/50
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
3/50
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
4/50
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
4/50
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
5/50
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...
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
6/50
...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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
7/50
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
9/50
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
10/50
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)
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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)
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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?
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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?
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
15/50
Elements of an ALD reaction process
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”
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
15/50
Elements of an ALD reaction process
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”
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
15/50
Elements of an ALD reaction process
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
15/50
Elements of an ALD reaction process
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
15/50
Elements of an ALD reaction process
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
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
25/50
SR graph rules for extracting invariants
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
26/50
SR graph rules for extracting invariants
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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)
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
38/50
Precursor doses generated by short (ms) precursor pulses
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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 sur- face 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 stretch- ing 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 vibra- tions and an increase in the broad infrared ab- sorbance 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 ab- sorbance 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 fea- ture. This behavior is consistent with a slight accu- mulation 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 ab- sorbance in the AlO-H stretching region. The unre- active AlOH species may be attributed to the forma- tion 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.
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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′
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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′
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu
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
FOCAPO-CPC 2017 Ray Adomaitis - thinfilm.umd.edu