The underlying mechanism of thermal induced patterning is investigated using a numerical phase-field model. Research on the subject has been mostly restricted to lubrication approximation, which is only valid for the cases that the initial film thickness is smaller than the characteristic wavelength of induced instabilities. Since the long-wave approximation is no longer valid in the later stages of pattern evolution, we employed the full governing equations of fluid flow and the thermally induced Marangoni effect to track the interface between the polymer film and the air bounding layer. Conducting a systematic study on the impact of influential parameters, we found that an increase in the temperature gradient, thermal conductivity ratio, and initial thickness of the thin film resulted in shorter processing time and faster pattern formation. Additionally, the contact angle between the polymer film and the bounding plates showed a significant effect on the shape of created features. Compared to the reported experimental observation by Dietzel and Troian [“Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient,” J. Appl. Phys. 108, 074308 (2010)], our numerical modeling provided a more accurate prediction of the characteristic wavelength against the linearized model currently used in the literature. The numerical findings in this study provide valuable insight into thermal-induced patterning, which can be a useful guide for future experimental works.

1.
M.
Dietzel
and
S. M.
Troian
, “
Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient
,”
J. Appl. Phys.
108
,
074308
(
2010
).
2.
C. G.
Willson
,
R. R.
Dammel
, and
A.
Reiser
, “
Photoresist materials: A historical perspective
,”
Proc. SPIE
3049
,
28
(
1997
).
3.
I.
Nejati
,
M.
Dietzel
, and
S.
Hardt
, “
Exploiting cellular convection in a thick liquid layer to pattern a thin polymer film
,”
Appl. Phys. Lett.
108
,
051604
(
2016
).
4.
L.
Peng
,
Y.
Deng
,
P.
Yi
, and
X.
Lai
, “
Micro hot embossing of thermoplastic polymers: A review
,”
J. Micromech. Microeng.
24
,
013001
(
2014
).
5.
H.
Sirringhaus
,
T.
Kawase
,
R. H.
Friend
,
T.
Shimoda
,
M.
Inbasekaran
,
W.
Wu
, and
E. P.
Woo
, “
High-resolution inkjet printing of all-polymer transistor circuits
,”
Science
290
,
2123
(
2000
).
6.
T. R.
Hebner
,
C. C.
Wu
,
D.
Marcy
,
M. H.
Lu
, and
J. C.
Sturm
, “
Ink-jet printing of doped polymers for organic light emitting devices
,”
Appl. Phys. Lett.
72
,
519
(
1998
).
7.
J.
Kim
,
H.
Oh
, and
S. S.
Kim
, “
Electrohydrodynamic drop-on-demand patterning in pulsed cone-jet mode at various frequencies
,”
Aerosol Sci.
39
,
819
(
2008
).
8.
S. Y.
Chou
,
L.
Zhuang
, and
L.
Guo
, “
Lithographically induced self-construction of polymer microstructures for resistless patterning
,”
Appl. Phys. Lett.
75
,
1004
(
1999
).
9.
E.
Schäffer
,
S.
Harkema
,
M.
Roerdink
,
R.
Blossey
, and
U.
Steiner
, “
Thermomechanical lithography: Pattern replication using a temperature gradient driven instability
,”
Adv. Mater.
15
,
514
(
2003
).
10.
E.
McLeod
,
Y.
Liu
, and
S. M.
Troian
, “
Experimental verification of the formation mechanism for pillar arrays in nanofilms subject to large thermal gradients
,”
Phys. Rev. Lett.
106
,
175501
(
2011
).
11.
N.
Wu
and
W. B.
Russel
, “
Micro- and nano-patterns created via electrohydrodynamic instabilities
,”
Nano Today
4
,
180
(
2009
).
12.
H.
Nazaripoor
,
C. R.
Koch
, and
M.
Sadrzadeh
, “
Ordered high aspect ratio nanopillar formation based on electrical and thermal reflowing of prepatterned thin films
,”
J. Colloid Interface Sci.
530
,
312
(
2018
).
13.
R.
Mukherjee
and
A.
Sharma
, “
Instability, self-organization and pattern formation in thin soft films
,”
Soft Matter
11
,
8717
(
2015
).
14.
J. P.
Singer
, “
Thermocapillary approaches to the deliberate patterning of polymers
,”
J. Polym. Sci., Part B: Polym. Phys.
55
,
1649
(
2017
).
15.
E.
Albisetti
,
D.
Petti
,
M.
Pancaldi
,
M.
Madami
,
S.
Tacchi
,
J.
Curtis
,
W. P.
King
,
A.
Papp
,
G.
Csaba
,
W.
Porod
,
P.
Vavassori
,
E.
Riedo
, and
R.
Bertacco
, “
Nanopatterning reconfigurable magnetic landscapes via thermally assisted scanning probe lithography
,”
Nat. Nanotechnol.
11
,
545
(
2016
).
16.
H.
Nazaripoor
,
C. R.
Koch
,
M.
Sadrzadeh
, and
S.
Bhattacharjee
, “
Thermo-electrohydrodynamic patterning in nanofilms
,”
Langmuir
32
,
5776
(
2016
).
17.
M.
Dietzel
and
S. M.
Troian
, “
Thermocapillary patterning of nanoscale polymer films
,”
MRS Proc.
1179
,
1179
(
2009
).
18.
H.
Bénard
and
H. B.
Étude
, “
Étude expérimentale des courants de convection dans une nappe liquide.—Régime permanent: tourbillons cellulaires
,”
J. Phys. Theor. Appl.
9
,
513
(
1900
).
19.
J. R. A.
Pearson
, “
On convection cells induced by surface tension
,”
J. Fluid Mech.
4
,
489
(
1958
).
20.
E. L.
Koschmieder
and
M. I.
Biggerstaff
, “
Onset of surface-tension-driven Bénard convection
,”
J. Fluid Mech.
167
,
49
(
1986
).
21.
S. H.
Davis
, “
Thermocapillary instabilities
,”
Annu. Rev. Fluid Mech.
19
,
403
(
1987
).
22.
P.
Colinet
,
J. C.
Legros
, and
M. G.
Velarde
,
Nonlinear Dynamics of Surface-Tension-Driven Instabilities
(
Wiley-VCH
,
2001
).
23.
T.
Gambaryan-Roisman
, “
Modulation of Marangoni convection in liquid films
,”
Adv. Colloid Interface Sci.
222
,
319
(
2015
).
24.
A.
Oron
,
S. H.
Davis
, and
S. G.
Bankoff
, “
Long-scale evolution of thin liquid films
,”
Rev. Mod. Phys.
69
,
931
(
1997
).
25.
A.
Oron
and
P.
Rosenau
, “
On a nonlinear thermocapillary effect in thin liquid layers
,”
J. Fluid Mech.
273
,
361
(
1994
).
26.
S. Y.
Chou
and
L.
Zhuang
, “
Lithographically induced self-assembly of periodic polymer micropillar arrays
,”
J. Vac. Sci. Technol., B
17
,
3197
(
1999
).
27.
E.
Schäffer
,
T.
Thurn-Albrecht
,
T. P.
Russell
, and
U.
Steiner
, “
Electrically induced structure formation and pattern transfer
,”
Nature
403
,
874
(
2000
).
28.
H.
Nazaripoor
,
M. R.
Flynn
,
C. R.
Koch
, and
M.
Sadrzadeh
, “
Thermally induced interfacial instabilities and pattern formation in confined liquid nanofilms
,”
Phys. Rev. E
98
,
043106
(
2018
).
29.
F.
Song
,
D.
Ju
,
F.
Gu
,
Y.
Liu
,
Y.
Ji
,
Y.
Ren
,
X.
He
,
B.
Sha
,
B. Q.
Li
, and
Q.
Yang
, “
Parametric study on electric field-induced micro-/nanopatterns in thin polymer films
,”
Langmuir
34
,
4188
(
2018
).
30.
D.
Kim
and
W.
Lu
, “
Three-dimensional model of electrostatically induced pattern formation in thin polymer films
,”
Phys. Rev. B
73
,
035206
(
2006
).
31.
H.
Tian
,
J.
Shao
,
Y.
Ding
,
X.
Li
, and
H.
Liu
, “
Simulation of polymer rheology in an electrically induced micro- or nano-structuring process based on electrohydrodynamics and conservative level set method
,”
RSC Adv.
4
,
21672
(
2014
).
32.
J. S.
Rowlinson
, “
Translation of J. D. van der Waals’ ‘The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density’
,”
J. Stat. Phys.
20
,
197
(
1979
).
33.
J. W.
Cahn
and
J. E.
Hilliard
, “
Free energy of a nonuniform system. I. Interfacial free energy
,”
J. Chem. Phys.
28
,
258
(
1958
).
34.
J.
Cahn
,
S.
Allen
,
J. W.
Cahn
, and
S. M.
Allen
, “
A microscopic theory for domain wall motion and its experimental verification in Fe-Al alloy domain growth kinetics
,”
J. Phys. Colloq.
38
,
C7-51
(
1977
).
35.
Y.
Lin
,
P.
Skjetne
, and
A.
Carlson
, “
A phase field model for multiphase electro-hydrodynamic flow
,”
Int. J. Multiphase Flow
45
,
1
(
2012
).
36.
D.
Jacqmin
, “
Contact-line dynamics of a diffuse fluid interface
,”
J. Fluid Mech.
402
,
57
(
2000
).
37.
V. V.
Khatavkar
,
P. D.
Anderson
, and
H. E. H.
Meijer
, “
Capillary spreading of a droplet in the partially wetting regime using a diffuse-interface model
,”
J. Fluid Mech.
572
,
367
(
2007
).
38.
V. V.
Khatavkar
,
P. D.
Anderson
,
P. C.
Duineveld
, and
H. E. H.
Meijer
, “
Diffuse-interface modelling of droplet impact
,”
J. Fluid Mech.
581
,
97
(
2007
).
39.
P.
Gao
and
J. J.
Feng
, “
Spreading and breakup of a compound drop on a partially wetting substrate
,”
J. Fluid Mech.
682
,
415
(
2011
).
40.
Q.
Yang
,
B. Q.
Li
, and
Y.
Ding
, “
3D phase field modeling of electrohydrodynamic multiphase flows
,”
Int. J. Multiphase Flow
57
,
1
(
2013
).
41.
G.
Karapetsas
,
N. T.
Chamakos
, and
A. G.
Papathanasiou
, “
Thermocapillary droplet actuation: Effect of solid structure and wettability
,”
Langmuir
33
,
10838
(
2017
).
42.
Q.
Yang
,
B. Q.
Li
,
Z.
Zhao
,
J.
Shao
, and
F.
Xu
, “
Numerical analysis of the Rayleigh–Taylor instability in an electric field
,”
J. Fluid Mech.
792
,
397
(
2016
).
43.
H.
Tian
,
J.
Shao
,
Y.
Ding
,
X.
Li
, and
H.
Hu
, “
Electrohydrodynamic micro-/nanostructuring processes based on prepatterned polymer and prepatterned template
,”
Macromol.
47
,
1433
(
2014
).
44.
E.
Schäffer
,
T.
Thurn-Albrecht
,
T. P.
Russell
, and
U.
Steiner
, “
Electrohydrodynamic instabilities in polymer films
,”
Europhys. Lett.
53
,
518
(
2001
).
45.
Z.
Lin
,
T.
Kerle
,
S. M.
Baker
,
D. A.
Hoagland
,
E.
Schärfer
,
U.
Steiner
, and
T. P.
Russell
, “
Electric field induced instabilities at liquid/liquid interfaces
,”
J. Chem. Phys.
114
,
2377
(
2001
).
46.
K. R.
Fiedler
and
S. M.
Troian
, “
Early time instability in nanofilms exposed to a large transverse thermal gradient: Improved image and thermal analysis
,”
J. Appl. Phys.
120
,
205303
(
2016
).
47.
T.
Young
, “
An essay on the cohesion of fluids
,”
Proc. R. Soc. London
1
,
171
(
1800
).

Supplementary Material

You do not currently have access to this content.