We present time-resolved microscopy of motion and shape transformation of liquid indium (In) sessile droplets on InAs(001) surface. For temperatures up to 800 K, the droplets spontaneously move across the crystal undergoing stick-slip motion that is strongly affected by atomic steps and coalescence events. Above a critical temperature of around 800 K, the droplets stop moving and further increase in temperature causes them to change shape progressively from spherical to rectangular. The process of shape transformation is coherent, reversible and associated with temperature dependent wetting of the surface as well as crystalline anisotropy dependent arsenic solvation and evaporation rates. The etched rectangular substrate depressions formed under the droplets, giving them a rectangular shape, reveal unusual rheology with deeper regions at the corners. Our high spatial resolution measurements link the macroscopic behavior of the metallic droplets with the microscopic topography features and can be used for the metallic liquid droplet nano-manipulation.

Wetting of a solid by a liquid is of great importance in a wide range of fields and applications spanning biology,1 medicine,2 and industrial processes such as coating,3 printing, and forming electronic interconnects. The vast majority of research has been limited to non-metallic droplets on solid substrates, which are usually non-reactive and to a good approximation obey the Young's equation, which relates the contact angle to the surface tension at the vapor-liquid-solid triple point.4 Much less explored and understood is the wetting of metallic liquid droplets, in general a very complex process, involving the interaction between disparate components, which may evolve through mutually induced chemical and physical interfacial processes.5 

Low temperature melting point elements such as indium (In) and gallium (Ga) are well suited for studying the properties of metallic wetting because they maintain the liquid state over a wide temperature range. The liquid properties of In, Ga, and their alloys have been already harnessed in devices such as stretchable/flexible electronic circuits, where their rheology and chemical activity have strong impact on device performance.6,7 The suppressed interband electronic transitions and inherently smooth surfaces make liquid In and Ga also interesting as low-loss plasmonic materials with optical responses extending into the UV region.8,9

Such applications of liquid metals bring instantly to attention the importance of synthesis, in particular, the possibility of self-assembly and agile control of position and geometry. In this paper, we study the mechanisms governing the kinematics and geometry of liquid In droplets. With real-time in-situ measurements by Low Energy Electron Microscopy (LEEM) and Photoemission Electron Microscopy (PEEM),10,11 we study how liquid In droplets move and change in shape on the nanometer scale.

We found that the droplets' kinematics and shapes are strongly affected by the crystallographic surface anisotropy and atomic step orientation. Furthermore, we demonstrate how temperature can reversibly control transformation of the droplets between the spherical and rectangular shapes.

The formation of In droplets is achieved through heating the InAs(001) wafer above the congruent evaporation temperature, TC, which preferentially evaporates As2, leaving behind excess In. We observe the nucleation of In droplets on sublimating InAs(001) at around 700 K, which is close to the previously reported TC = 715 K.12 The In segregates on the surface in liquid droplets, as has been reported for InAs(111),13,14 InP(001)15,16 and InP(111).16 To minimize the number of defects and prepare an atomically flat surface, we apply the following procedure: InAs(001) samples are soaked in NH4S solution for 30 min at 320 K,17 then rinsed under flowing de-ionized water, dried, and inserted into the UHV system. Subsequently, they are processed in the LEEM/PEEM chamber (SPECS)18 by ion bombardment (Ar+, 700 eV) and gradual annealing (over 24 h in total) up to 730 K. The temperature of the sample is monitored with a pyrometer. This protocol prepares a well-ordered In-rich surface with the surface reconstruction composed of both (4 × 2) and c(8 × 2) phases, as confirmed by Low Energy Electron Diffraction (LEED). The c(8 × 2) and (4 × 2) reconstructions are a consequence of evaporation of As, which leaves excess of In during the annealing process.19,20 The surface exhibits atomically flat terraces with widths of around 300 nm (Figure 1(a)). At the same time, the excess In segregates in liquid droplets on the surface, with a typical diameter of hundreds of nanometers and the density of around 1 per 50 μm2. With further annealing of the InAs(001) substrate up to around 800 K, the terraces broaden, the density and size of the In droplets increase, and the droplets begin to move.

FIG. 1.

(a) LEEM image of the InAs(001) surface with c(8 × 2)/(4 × 2) reconstruction at RT showing the atomic step contrast. (b) PEEM image of InAs(001) with In droplets acquired at 800 K. The average over 36 s image allows tracking of the In droplet motion. (c) Acceleration of the droplet deduced from the data in (b) as a function of time/position shows the non-linearity of movement. (d)–(f) LEEM snapshots of an In droplet movement in the vicinity of step bunches at 800 K. Red circle marks the reference point on the InAs(001) substrate. The crystallographic orientation shown in (a) is the same for all images.

FIG. 1.

(a) LEEM image of the InAs(001) surface with c(8 × 2)/(4 × 2) reconstruction at RT showing the atomic step contrast. (b) PEEM image of InAs(001) with In droplets acquired at 800 K. The average over 36 s image allows tracking of the In droplet motion. (c) Acceleration of the droplet deduced from the data in (b) as a function of time/position shows the non-linearity of movement. (d)–(f) LEEM snapshots of an In droplet movement in the vicinity of step bunches at 800 K. Red circle marks the reference point on the InAs(001) substrate. The crystallographic orientation shown in (a) is the same for all images.

Close modal

By recording LEEM movies of individual droplet's movement, we can follow the velocity distributions with respect to the crystallographic directions and the atomic steps. Optimizing the LEEM contrast in the range 5–7 eV incident electron energy enables imaging both the droplet shape and size, as well as the underlying surface topography; the focus is adjusted on the latter to image single atomic step contrast. By a combination of LEEM and PEEM, we can image single droplets and follow the dynamics of several droplets in a larger field of view.

A PEEM image showing an In droplet movement is shown in Figure 1(b). The PEEM images are generated with 4.9 eV photon excitation from an Hg lamp, which is sufficiently energetic to exceed the work functions of InAs and In. In the PEEM mode, liquid In droplets are brighter against the InAs(001) substrate due to differences in their work functions. The image in Figure 1(b) has been averaged over 45 frames for a total exposure of 36 s in order to visualize the motion path of the droplet. The color scales linearly with time, as shown in the inset. Among the three droplets within the field of view, only one of them is moving. The motion consists of three stages: displacement x1, steady state (no motion) and displacement x2 (see the inset for the corresponding time scales). For both displacements, the droplet moves in punctuated accelerations. In Figure 1(c), the acceleration d2x2/dt2 vs. time dependence is plotted. Clearly, the motion has a stick-slip character. Based on the analysis of nearly 40 different droplets recorded by PEEM, we observe that stick-slip motion is common to all moving droplets in the temperature range T = 770–820 K. A change of the motion direction, as from x1 to x2 in Figure 1(b), is a characteristic for ∼50% of the recorded motions. Such two-step motion (in some cases three-step) is usually interrupted by complete or nearly complete stopping, as in the case shown in Figure 1(b) (marked as a steady state on the time/color scale). We observe that on average there is no preferable direction of the movement and thermal gradients as well as gravity can be ruled out as the driving forces. Such spontaneously moving droplets have previously been observed for several III–V semiconductor surfaces such as GaAs,21–24 InAs(111),13 and InP.16 As discussed by Tersoff et al. for Ga droplets,22 the motion of self-running droplets is triggered by local changes in the interfacial energies, which in turn depend on the local chemical potentials. Note that in contrast to the previous studies of In13,16 and Ga21–24 droplets, we use the LEEM mode to image the motion rather than the mirror electron microscopy (MEM) mode because it resolves the atomic scale surface topography.

On the microscopic level, either the atomic steps or the neighboring droplets are nearly constantly affecting the motion of droplets. Because of the high-resolution imaging with LEEM, we can follow precisely the droplet motion and correlate it with the surface topography. For example, representative LEEM images of the In droplet motion in the vicinity of atomic step bunches are shown in Figures 1(d)–1(f). Initially, the droplet moves slowly on an atomically flat terrace with a speed of around 0.03 μm/s. As it moves across the terrace, it leaves a track corresponding to several atomic layers of the substrate that have been etched by the droplet. Once the droplet arrives at the step bunch edge, it abruptly accelerates and moves down the steps with the velocity of nearly 2 μm/s. Afterwards, droplet changes the direction by 90° and moves along the step edges with constant speed of 0.1 μm/s. The reason for such a rapid acceleration and turn is the different surface energies of the planar regions and the step edges. Note that because As evaporation rate is proportional to the step density,21 it is particularly enhanced in the region of such step bunches where the surface is rich in In; this naturally attracts the incoming droplet through cohesive forces. For the entire movie of the In droplet motion recorded by LEEM, we refer to the video S1 in the supplementary material.

The step bunches form by segregation of steps in some regions as a consequence of planarization of the surface during the prolonged annealing.25,26 They can also be formed at exposed, etched areas of the substrate that are produced by moving droplets, as can be seen in the droplet trail left in the image Figures 1(d) and 1(e). The various kinetics of liquid droplets in the presence of atomic steps seem to depend on the energetics of the particular system. For instance, the Pt-Si liquid droplets27,28 driven by thermal gradients on the Si(001) surface move along steps and step bunches, similar to our findings. This behavior is in contrast with Ga droplets on GaP(111), where the motion is exclusively perpendicular to the surface steps in the upward direction.29 As discussed in Ref. 16, the directionality of the self-running metallic droplets depends on factors such as the surface energy and elemental diffusion and therefore varies for different III–V compounds and their crystalline facets. Note that because at elevated temperatures the orientation of the atomic steps and step bunches is not well defined, on the macroscopic scale, there is no preferable droplet motion direction with respect to the crystallographic directions.

Continuous annealing of the sample results in the eventual formation of larger droplets with a diameter d > 2 μm. The growth occurs by diffusion of In from enriched terraces into existing droplets as well as droplet coalescence. After 2–3 h of annealing at 800 K, when the surface areas of the droplets exceed 3.1 μm2, the sample reaches another equilibrium where the droplet mobility decreases significantly. This can be understood by recalling that adhesion depends on the surface area and, therefore, with increasing size the adhesive forces become too large to displace droplets in response to fluctuations in the surface energy. This is in contrast to the motion of micro-sized Pt-Si droplets on Si(001), which is driven by a thermal gradient with velocity that does not depend on the droplet diameter.30 

With further increase in the surface temperature to above 800 K, the In droplets enter another phase. While still maintaining their positions, the droplets' shape changes from round to rectangular. Moreover, the shape transformation is reversible by controlling the temperature, as shown in Figure 2(a). The droplets respond coherently and adiabatically starting out as round at 600 K and transforming to rectangular shape upon annealing to 950 K (except small ones with d < 2 μm). Once the temperature is reduced, the droplets return to their initial round shape.

FIG. 2.

Effect of temperature on the shape of In droplets as seen by PEEM (a) and LEEM (b). The excitation light for PEEM is incident at 70° from the surface normal; hence, shadows are cast on the underside of the droplets. For movies of the shape transitions recorded by PEEM and LEEM, see videos S2 and S3 in the supplementary material.

FIG. 2.

Effect of temperature on the shape of In droplets as seen by PEEM (a) and LEEM (b). The excitation light for PEEM is incident at 70° from the surface normal; hence, shadows are cast on the underside of the droplets. For movies of the shape transitions recorded by PEEM and LEEM, see videos S2 and S3 in the supplementary material.

Close modal

To examine in detail the shape transformation, we image a single droplet with LEEM mode at higher spatial resolution and within a narrower temperature range. As illustrated in Figure 2(b), decreasing the temperature of the surface from 900 to 850 K modifies the shape of the droplet rounding its corners. Reversing process by heating back to 900 K causes the droplet to return to its initial shape. The shape cycles in Figures 2(a) and 2(b) can be achieved as quickly as a few seconds limited only by the heating and cooling rates. Based on our observations, we conclude that the volume of a droplet remains essentially constant during the shape transformation. By increasing temperature from the melting point, we convert spherical droplets with a large contact angle into rectangular ones with a small contact angle at temperatures above 900 K (or vice versa). Hence, temperature defines the wetting of the substrate by In liquid droplets.

We argue that the major driving force for the shape changes is the competition between the droplet cohesion and adhesion forces. At high temperatures, the evaporation of As2 via dissolution in In droplets is faster than desorption from the terraces or by diffusion of As on terraces to the droplets; hence, In droplets etch pits.31,32 The pits become rectangular because the wetting angle is small, and therefore the droplets can take on the shape that is determined by the limiting anisotropic dissolution rates.33 The edges of rectangular droplets are precisely aligned with the [110] and [-110] crystalline axes of the InAs(001) substrate. The rectangular rather than square shape can be explained by the fact that (111) planes of zinc-blende structures, as InAs, are not chemically equivalent.32 When a depressed region develops, (111) facets can be expected to form at their sides because they are the densest and, therefore, the most energetically favorable low index planes. Consequently, the (111), (-1-11) and orthogonal to them (-111), (1-11) facets will have different etching rates and therefore reflect the in-plane symmetry of the depressed regions (see Figure 3(b) for orientation of (111), (-111) and (001) planes at the etched region).

FIG. 3.

Top view (a), (c) and side view (b), (d) SEM images of In droplets at RT. Fully receded droplet—(a) and (b); partially receded droplet—(c) and (d). The orientation of crystallographic planes at the etched region is shown (b).

FIG. 3.

Top view (a), (c) and side view (b), (d) SEM images of In droplets at RT. Fully receded droplet—(a) and (b); partially receded droplet—(c) and (d). The orientation of crystallographic planes at the etched region is shown (b).

Close modal

To get more insight into rheology of the surface beneath In droplets and the depressed regions that they create, we imaged the samples at room temperature by scanning electron microscopy (SEM) after the thermal processing up to 1000 K. This allows for examination of the underlying substrate topography after droplets have receded from the rectangular to spherical shapes, thereby uncovering the depressed regions where the substrate etching occurred. We present the top (Figures 3(a) and 3(c)) and side views (Figures 3(b) and 3(d)) of four different indium droplets. The etched rectangular regions are evident in all the cases. The small pockmarks on the droplet surface are most likely nanocrystalline InAs particles, which form on drop surfaces as the sample is cooled. The energy dispersive X-ray spectroscopy (EDS) confirms the droplets to be predominantly In.

A closer look at topography (see Figures 3(a) and 3(b)) reveals non-uniformity of the etched regions, with deeper depressions at the corners divided by straight humps. The depression bottoms are atomically flat (001) facets depressed by around 200 nm below the surrounding substrate. To understand such rheology of the substrate, let us first recall the liquid-solid interface profile during isotropic wetting. It is known that for a non-rigid/reactive substrate, a vertical component of liquid surface tension can deform an underlying substrate. The strength and shape of this deformation depends strongly on the contact angle and is different for advancing and receding liquid fronts.34,35 In particular, for a receding droplet, the interfacial energy is minimized through stretching of the liquid surface in the vicinity of the triple junction, which can undercut below the surface of the substrate.34 In our anisotropic wetting system, the droplet transition from rectangular to round requires liquid recession from its corners and consequently leads to enhanced etching at these regions. In addition, both the short diffusion length of As through the In droplet and preferential building up of liquid convection at the corners naturally enhance evaporation of As (and therefore dissolution of the substrate) at these regions. The exact rheology of the substrate should therefore depend on the history of the sample and change as a function of: (i) advancing/receding cycles and (ii) time during which the rectangular/spherical shape is sustained.

While droplets in Figures 3(a) and 3(b) are fully receded, Figures 3(c) and 3(d) illustrate the examples of only partially receded ones, which solidified before taking on the thermodynamically favored shape and thus are frozen into the rectangular regions. This demonstrates a competition between adhesion and cohesion, during the annealing/cooling cycles. Based on the analysis of nearly a hundred droplets, we found that around 70% of them return to the spherical shape, while the rest remain attached at one or more corners of the rectangular pits. Truly rectangular frozen droplets make only a few percent of the total population.

Our findings explain the previously observed appearance of frozen square droplets for In/InP(001)15 and Ga/GaAs(001),31,36 where the shapes were considered to develop as a function of a cluster size.15,31,36 Combined real-time, in-situ, temperature dependent measurements performed here clearly demonstrate that fundamentally, the shape conversion is controlled by the temperature and ability of the surface to reach equilibrium.

In summary, we have examined the thermally induced dynamics of In sessile droplets under the Langmuir evaporation of InAs(001) surface. We demonstrate that upon annealing to the temperatures of around 800 K, spherical In droplets with diameters up to 2 μm move in a stick-slip manner, with velocity vectors directly related to the surface topography. For larger droplets, the balance between adhesion and cohesion can be manipulated by adjusting temperature; this allows the shape and wetting contact angle to be controlled, with the geometry of the droplets determined by their anisotropic dissolution of the substrate. The mechanisms that we unveiled can be extended to other reactive wetting systems, opening the possibility of tailoring the droplets' shape and contact angle through the topography and temperature.

See the supplementary material for movies S1, S2 and S3 recorded by LEEM and PEEM showing indium droplet movements and shape changes.

We acknowledge the technical support of the Nanoscale Fabrication and Characterization Facility (NFCF) at the University of Pittsburgh, the financial support from the NSF Grant Nos. DMR-1311845 and CHE-1414466, and the Chair of Excellence from the Nanoscience Foundation Grenoble, Rhone Alpes COOPERA and ANR OH-Risque TOPONANO.

1.
A. R.
Parker
and
C. R.
Lawrence
,
Nature
414
,
33
34
(
2001
).
2.
D.
Gonzalez-Rodriguez
,
K.
Guevorkian
,
S.
Douezan
, and
F. C.
Brochard-Wyart
,
Science
338
,
910
917
(
2012
).
3.
R.
Wang
,
K.
Hashimoto
,
A.
Fujishima
,
M.
Chikuni
,
E.
Kojima
,
A.
Kitamura
,
M.
Shimohigoshi
, and
T.
Watanabe
,
Nature
388
,
431
432
(
1997
).
4.
P. G.
de Gennes
,
Rev. Mod. Phys.
57
,
827
863
(
1985
).
5.
L.
Yin
,
B. T.
Murray
,
S.
Su
,
Y.
Sun
,
Y.
Efraim
,
H.
Taitelbaum
, and
T. J.
Singler
,
J. Phys.: Condens. Matter
21
,
464130
(
2009
).
6.
J. W.
Boley
,
E. L.
White
,
G. T.-C.
Chiu
, and
R. K.
Kramer
,
Adv. Funct. Mater.
24
,
3501
3507
(
2014
).
7.
A.
Hirsch
,
H. O.
Michaud
,
A. P.
Gerratt
,
S.
de Mulatier
, and
S. P.
Lacour
,
Adv. Mater.
28
,
4507
4512
(
2016
).
8.
M. G.
Blaber
,
C. J.
Engel
,
S. R. C.
Vivekchand
,
S. M.
Lubin
,
T. W.
Odom
, and
G. C.
Schatz
,
Nano Lett.
12
,
5275
5280
(
2012
).
9.
J. M.
McMahon
,
G. C.
Schatz
, and
S. K.
Gray
,
Phys. Chem. Chem. Phys.
15
,
5415
5423
(
2013
).
10.
E.
Bauer
,
Surface Microscopy with Low Energy Electrons
(
Springer
,
New York
,
2014
).
11.
R. M.
Tromp
and
M. C.
Reuter
,
Ultramicroscopy
50
,
171
178
(
1993
).
12.
J.
Shen
and
C.
Chatillon
,
J. Cryst. Growth
106
,
543
552
(
1990
).
13.
S.
Kanjanachuchai
and
P.
Photongkam
,
Cryst. Growth Des.
15
,
14
19
(
2015
).
14.
B.
Mandl
,
J.
Stangl
,
E.
Hilner
,
A. A.
Zakharov
,
K.
Hillerich
,
A. W.
Dey
,
L.
Samuelson
,
G.
Bauer
,
K.
Deppert
, and
A.
Mikkelsen
,
Nano Lett.
10
,
4443
4449
(
2010
).
15.
T. D.
Lowes
and
M.
Zinke-Allmang
,
Phys. Rev. B
49
,
16678
16683
(
1994
).
16.
S.
Kanjanachuchai
and
C.
Euaruksakul
,
Cryst. Growth Des.
14
,
830
834
(
2014
).
17.
D. Y.
Petrovykh
,
M. J.
Yang
, and
L. J.
Whitman
,
Surf. Sci.
523
,
231
240
(
2003
).
18.
R. M.
Tromp
,
J. B.
Hannon
,
A. W.
Ellis
,
W.
Wan
,
A.
Berghaus
, and
O.
Schaff
,
Ultramicroscopy
110
,
852
861
(
2010
).
19.
O. E.
Tereshchenko
,
E.
Placidi
,
D.
Paget
,
P.
Chiaradia
, and
A.
Balzarotti
,
Surf. Sci.
570
,
237
244
(
2004
).
20.
N.
Olszowska
and
J. J.
Kolodziej
,
Surf. Sci.
644
,
95
101
(
2016
).
21.
J.
Tersoff
,
D. E.
Jesson
, and
W. X.
Tang
,
Phys. Rev. Lett.
105
,
035702
(
2010
).
22.
J.
Tersoff
,
D. E.
Jesson
, and
W. X.
Tang
,
Science
324
,
236
238
(
2009
).
23.
S.
Kanjanachuchai
and
C.
Euaruksakul
,
ACS Appl. Mater. Interfaces
5
,
7709
7713
(
2013
).
24.
W. X.
Tang
,
C. X.
Zheng
,
Z. Y.
Zhou
,
D. E.
Jesson
, and
J.
Tersoff
,
IBM J. Res. Dev.
55
,
10:1
10:7
(
2011
).
25.
D.
Lee
and
J.
Blakely
,
Surf. Sci.
445
,
32
40
(
2000
).
26.
H.-C.
Jeong
and
E. D.
Williams
,
Surf. Sci. Rep.
34
,
171
294
(
1999
).
27.
P.
Sutter
,
P. A.
Bennett
,
J. I.
Flege
, and
E.
Sutter
,
Phys. Rev. Lett.
99
,
125504
(
2007
).
28.
P. A.
Bennett
,
J.
Chobanian
,
J. I.
Flege
,
E.
Sutter
, and
P.
Sutter
,
Phys. Rev. B
76
,
125410
(
2007
).
29.
E.
Hilner
,
A. A.
Zakharov
,
K.
Schulte
,
P.
Kratzer
,
J. N.
Andersen
,
E.
Lundgren
, and
A.
Mikkelsen
,
Nano Lett.
9
,
2710
2714
(
2009
).
30.
W. C.
Yang
,
H.
Ade
, and
R. J.
Nemanich
,
Phys. Rev. B
69
,
045421
(
2004
).
31.
T. D.
Lowes
and
M.
Zinke-Allmang
,
J. Appl. Phys.
73
,
4937
4941
(
1993
).
32.
W. Y.
Lum
and
A. R.
Clawson
,
J. Appl. Phys.
50
,
5296
5301
(
1979
).
33.
G. M.
Rosenblatt
,
Acc. Chem. Res.
9
,
169
175
(
1976
).
34.
E.
Saiz
,
A. P.
Tomsia
, and
R. M.
Cannon
,
Acta Mater.
46
,
2349
2361
(
1998
).
35.
E.
Saiz
,
A. P.
Tomsia
, and
R. M.
Cannon
,
Scr. Mater.
44
,
159
164
(
2001
).
36.
K.
Shorlin
and
M.
Zinke-Allmang
,
Surf. Sci.
601
,
2438
2444
(
2007
).

Supplementary Material