Electrostatically driven collapsible Au thin films assembled using transferprinting for thermal switching

Hohyun Keum, Myunghoon Seong, Sanjiv Sinha,a) and Seok Kima)

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign,1206 West Green Street, Urbana, Illinois 61801, USA

(Received 19 March 2012; accepted 7 May 2012; published online 22 May 2012)

We report deterministic assembly of 100 nm thick suspended gold films using transfer printing that

are mechanically collapsible. We demonstrate the latter using electrostatic force to establish and

break physical contact between the film and a silicon dioxide substrate in a reversible and

repeatable manner. Modeling the thermal conductance at the interface between the suspended

film and the substrate, we show that the fabricated structure behaves as a thermal switch. The

on-state corresponds to the collapsed film and the off-state to the fully suspended film. The on- to

off-state ratio for thermal conductance exceeds 106 in theory. VC 2012 American Institute ofPhysics. [http://dx.doi.org/10.1063/1.4720397]

Sub-micrometer thick suspended films find widespread

use in micro/nano-scale transduction due to their large surface-

area-to-volume ratio and ease of reversible deformation. On

account of these characteristics, they are indispensable in sens-

ing, actuation, and switching in micro/nano-devices.1–9 While

a few devices can be fabricated using wafer-level direct bond-

ing,4 most suspended films in such devices are fabricated by

film deposition followed by etching of the sacrificial layers.

Such fabrication is known to generate “fabrication stiction”

problems, where thin films are pinned to substrates during

aqueous rinse and dry cycles.10 A wide variety of processing,

surface treatments, and physical schemes have been suggested

for anti-stiction. However, existing approaches are limited by

dimension and materials selection, process complexity, high

pressure safety issues, or by the difficulty in scaling to dimen-

sions larger than wafer size.

Here, we report deterministic assembly of a suspended

gold (Au) film on supporting structures using transfer print-

ing, inherently without any fabrication stiction. Determinis-

tic assembly (<few micrometer lateral resolution) using

transfer printing enables not only homogeneous but also het-

erogeneous materials integration on large area substrates.

Research over the last few years has demonstrated capabil-

ities of this technique in fabricating unusual electronic devi-

ces for photovoltaics,11 lighting,12 chemical and biological

sensing,13 and energy harvesting.14 One of the outstanding

challenges of transfer printing is the deterministic assembly

of nanometer scale thick suspended films due to the highly

floppy and fragile nature of the thin film as well as a severely

reduced contact area between the printed thin films and

receiving supporting structures. In this letter, we present

deterministic assembly of 100� 100 lm square laterally,

100 nm thick Au films suspended over 800 nm air gap using

an advanced form of transfer printing which was recently

reported elsewhere.15,16 We demonstrate that the assembled

thin film can be reversibly and repeatedly collapsed to estab-

lish contact with the substrate using electrostatic forces. We

propose that this reversibility can be used in fabricating an

electrically activated thermal switch and theoretically inves-

tigate such behavior.

We have recently reported measurements of the

interfacial thermal conductance between transfer printed

gold films and different substrates.16 The interfacial thermal

conductance at room temperature ranges between 10 and

40 MW/m2K. This is directly comparable to interfaces

formed by sputtered Au films that exhibit thermal conduct-

ance of �65 MW/m2K. The relatively high thermal conduct-

ance for transfer-printed films motivates their use in thermal

applications where heat conduction can be electrically

manipulated by forming and breaking physical contact

between a transfer-printed suspended film and a substrate.

We describe the design and the fabrication of this structure

below, and then use contact mechanics and interfacial ther-

mal transport modeling to predict the performance of the

thermal switch based on the fabricated structure.

A 100� 100 lm square and 100 nm thick Au film was

assembled on an 800 nm thick supporting Au layer deposited

on a 150 nm thick SiO2 layer, both of which were formed on

a highly doped Si wafer. The Au layer was patterned to

make an open area of 50� 50 lm square and a 10 lm wide

channel. The open area was covered by the Au film as shown

in Fig 1(a). In such configuration, the Au film is suspended

on an 800 nm air gap and can be mechanically collapsed on

the SiO2 layer by electrostatic force when a bias voltage is

applied between the Si wafer and the Au layer. The dimen-

sions of the Au film, the Au layer, the SiO2 layer, and the air

gap were chosen by studying the mechanical collapse of sus-

pended films under uniform electrostatic attraction. To deter-

mine the force for the unit area required to collapse the Au

film, we assumed that all sides of the thin film are simply

supported on the edge of the 50� 50 lm square opening of

the Au layer. Mechanical deflection (xmax) of the Au film, at

the moment the Au film starts to contact with the SiO2 layer,

by uniformly applied vertical force per unit area (Pmech) is

calculated with xmax ¼ c1PmechL4

Eh3 , where E, h, and L are

Young’s modulus, thickness, and lateral length of the sus-

pended square Au film, respectively, and c1 is a geometric

dependent value of 0.0444.17 Since xmax is the air gap, fixed

at 800 nm, isolating the force required per unit area (Pmech)

a)Authors to whom correspondence should be addressed. Electronic

addresses: sanjiv@illinois.edu and skm@illinois.edu.

0003-6951/2012/100(21)/211904/4/$30.00 VC 2012 American Institute of Physics100, 211904-1

APPLIED PHYSICS LETTERS 100, 211904 (2012)

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yields a constant value. The SiO2 layer and the air gap are

located in series between the Au film and the Si wafer. Thus,

the total capacitance in this combined dielectric layer is

Ctot ¼ CoxideCair

CoxideþCair, where Coxide and Cair are the capacitance of

the SiO2 layer and the air gap on 50� 50 lm area, respec-

tively. Each capacitance can be written in terms of thickness

(d), area (A), and permittivity (e) of the capacitors as follow-

ing, C ¼ eAd . Total potential energy in capacitance is deter-

mined by U ¼ �CV2

2or U ¼ �eAV2

2d . Taking derivatives of this

function with respective to thickness (d) and dividing by

total area yields the function of electrostatic force per unit

area, Pelec ¼ V2eoxidee2airk

2ðeairdoxideþeoxidedairÞ2. Substituting Pelec with Pmech

and solving for V results in required threshold voltage to

induce enough electrostatic force for the mechanical deflec-

tion (xmax) of the Au film. Figure 1(c) is the plot of the

threshold voltage and SiO2 breakdown voltage18 as a func-

tion of the thickness of the SiO2 layer. The figure implies

that increasing thickness of the SiO2 layer increases the

threshold voltage required for collapse. However, the incre-

ment of oxide breakdown voltage is much stiffer, resulting in

a larger window for us to operate before failure of the device.

The breakdown of the 800 nm thick air gap is not a concern

since, experimental breakdown voltages of sub-micron

ranges at around 70–120 V, according to Hourdakis et al.,19

which is a factor of several times higher than breakdown

voltage of the 150 nm thick SiO2 layer.

Au thin films, mechanically collapsible by electrostatic

force, were fabricated with chosen dimensions by transfer

printing of Au films prepared on a donor substrate onto a tar-

get area on a receiver substrate. To fabricate Au films on a do-

nor substrate, we deposited 100 nm gold by sputtering on

1.1 lm thick thermally grown SiO2 as the sacrificial layer on a

Si wafer. After pattering of the 100 lm� 100 lm Au film, the

SiO2 layer was selectively etched to define a square area of

120 lm� 120 lm in a concentric alignment with the patterned

Au film. Photoresist was spun and patterned on them to form

anchors and frame. Final wet etching with HF eliminated the

remained SiO2 layer and the Au film was then suspended on

the donor substrate with supporting photoresist anchors.16 The

fabrication of a receiver substrate started with a RCA (stand-

ard wafer cleaning steps to remove organic and ionic contami-

nants) cleaned highly doped silicon (Si) wafer (Ultrasil;

q¼ 0.001–0.006 Xcm) and deposited a 150 nm thick SiO2

using plasma enhanced chemical vapor deposition (PECVD;

PlasmaTherm). We then sputtered (AJA international, INC)

an 800 nm thick Au layer on the SiO2 layer. The deposited Au

layer was patterned to define an open area of 50� 50 lm

square and a 10 lm wide channel. The channel allows air to

escape when a film suspended on top of the patterned Au layer

is electrostatically collapsed on the SiO2 layer. On top of the

fabricated receiver substrate, a 100� 100 lm square, 100 nm

thick Au film, prepared on the donor substrate, was transfer

printed using a microtip stamp,15,16 allowing the printed film

suspended on the deposited gold layer and over 800 nm air

gap (Fig. 1(a)). Figure 1(b) shows a scanning electron micro-

scope image of the Au film assembled on the substrate.

Figure 2(a) shows an illustrative cross section and optical

microscope images of the assembled Au film when bias volt-

age was on and off, respectively. After printing the Au film on

the receiver substrate, the film remained free standing in the

absence of any voltage across the Au layer and the Si wafer.

When a voltage of 12 V was applied across them in a sweep

mode, the central air gap region of the Au film, defined by the

50� 50 lm square opening of the Au layer, collapsed

mechanically due to the electrostatic force between the Au

film and the Si wafer as microscopic images in Fig. 2(a) ex-

hibit. Moreover, the Au film reversibly restored its original

flat shape immediately after removing the bias voltage. How-

ever, when excessive voltage (approximately 15 V) was

applied, central region of the thin film stuck to the SiO2 layer.

To test reversibility, we applied bias voltage within a reasona-

ble range (<13 V) and observed the thin film return to its orig-

inal suspended state for more than 30 times without any

observable hysteresis in both mechanical and/or electrical

behavior. During applying bias voltage, the capacitance

change due to collapsing of the Au film, was measured to

demonstrate its deformation in a quantitative way. As the

input voltage increases, the capacitance raises and reaches a

non-specific certain saturation value, which indicates that the

Au film was fully collapsed, thus the total capacitance does

not change significantly before a breakdown occurs in the

SiO2 layer. The capacitance difference between bias voltage

on and off states is about 0.35 pF, which is reasonably lower

than the theoretical maximum difference (Cox � Ctot; 0.55 pF).

Collected microscopic images and measured capacitance

change obviously demonstrate that the assembled suspended

Au film is reversibly collapsible via electrostatic force depend-

ing on the bias voltage in a completely controllable fashion.

FIG. 1. (a) Schematic illustration of transfer printing procedure to assemble

a suspended gold (Au) film on a prepared substrate. (b) Scanning electron

microscope image of the assembled Au film on the substrate in the absence

of voltage bias. (c) Plot of calculated threshold voltage to deflect the

assembled Au film and breakdown voltage of a silicon dioxide (SiO2) layer

under the film as a function of the thickness of the SiO2 layer.

211904-2 Keum et al. Appl. Phys. Lett. 100, 211904 (2012)

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An application of interest for the fabricated structure is a

thermal switch that provides tunable interfacial thermal con-

ductance. In the off-state, an air gap limits heat conduction

between the substrate and the Au film. For the geometry con-

sidered here, the thermal conductance per unit area (heat

transfer coefficient) is the ratio of the thermal conductivity

of air to the thickness of the air gap and is �32 kW/m2K. In

the on-state, the Au film establishes physical contact with the

substrate and heat conduction is limited by interfacial pho-

non transport. Thermal transport at the Au/SiO2 interface is

complicated due to the involvement of electrons in addition

to phonons. Here, we first use the diffuse mismatch model

(DMM)20 to evaluate the thermal conductance at the inter-

face between Au and SiO2 due to phonons. The DMM

assumes phonons scatter diffusely at the interface. The trans-

mission probability is independent of the phonon wave vec-

tor and polarization and depends only on the mismatch

between the phonon density of states at the interface.20 Due

to the lower Debye temperature, hd , of Au (165 K)21 com-

pared to that of SiO2 (492 K),22 phonons with frequencies

higher than the cut-off frequency of Au, xAud ¼ kbh

Aud =�h, can-

not be transmitted across the interface if elastic scattering is

considered.23 At room temperature (295 K), the predicted ther-

mal conductance due to phonon transport is 89.4 MW/m2K,

assuming both materials behave as isotropic Debye solids.20

This is slightly higher than the measured thermal conduct-

ance of 65 MW/m2K for sputtered Au on SiO216. Assuming

perfect contact, the discrepancy can be partially attributed to

the extra resistance posed in the metal by electron-phonon

coupling.24 The conductance, hep, can be assumed to be of

the form hep ¼ wT�1=2, where w ¼ 4:09 �109 using the

measured value.

In order to proceed with the estimation of the interfacial

thermal conductance in the on-state, we need to evaluate the

actual contact area depending on the applied force. Here, we

use a static model for contacting rough surfaces presented by

Kogut and Etsion (KE model),25 which combines elastic26

and plastic deformations27 and the improved Lennard-Jones

potential adhesion model originally developed by Derjaguin

et al. (DMT model),28 and extends them to include highly

plastic deformation.29 Briefly, the KE model predicts the

contact and the adhesion forces due to asperities in different

deformation regimes, which are determined by the degree of

the transition from elastic to plastic deformation based on Fi-

nite element analysis results.29 In addition to the adhesion

forces considered in the KE model, we include the capillary

force due to the water molecules in atmosphere. We assume

that the surface is completely covered with a monolayer of

water. We note that we have assumed the suspended film to

have a similar surface morphology as the SiO2 substrate.

However, the Au film can undergo higher plastic deformation

than the model predictions due to ductility.25 Furthermore,

capillary forces may vary substantially based on humidity

and condensation at the interface. These considerations limit

the quantitative accuracy of the model at present. Despite

these limitations, the model provides insight into the possible

range of thermal conductance in idealized structures.

Figure 3 shows the change in expected thermal conduct-

ance as a function of external electrostatic load applied. The

inclusion of capillary forces yields higher thermal conduct-

ance by increasing the area of contact. The on-state thermal

conductance exceeds 20 GW/m2K. Based on the previous

calculation of conductance through the air gap, we find the

on-state to off-state conductance ratio to be on the order of

106, suggesting the feasibility of such a structure as a thermal

switch. This will be investigated experimentally in future

research. We note that we have neglected convection and

radiation in considerations of thermal transport and provide

justification for this. We do not consider convective transport

FIG. 2. (a) Schematic illustrations and corresponding optical microscope

images of the assembled Au film when bias voltage turns on and off. (scale

bar: 50 lm) (b) Plot of a measured total capacitance of the assemble Au film

area and the contact pad of the substrate with respect to bias voltage.

FIG. 3. Variation in interfacial thermal conductance between Au and SiO2

as a function of external force applied on a 50 lm� 50 lm nominal area.

211904-3 Keum et al. Appl. Phys. Lett. 100, 211904 (2012)

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since the sub-micrometer air gap is much smaller than the

scale needed for convection cells. Further, we are interested

in applications close to room temperature such as in electron-

ics cooling where radiative effects do not dominate.

In summary, nanometer scale thick gold films (�100 nm)

over air gap (�800 nm) were deterministically assembled

using large area scalable transfer printing technique instead of

sacrificial layer or wafer bonding based approaches. Since the

suspended films were constructed without any wet process,

potential capillary force based stiction or any additional com-

plex process for anti-stiction were eliminated. It was demon-

strated that the assembled gold thin film was mechanically

collapsible via input voltage bias and its collapsing behavior

was very reversible and repeatable. We hypothesize that the

fabricated structure can be used as a thermal switch. Our mod-

eling predicts that the on-state to off-state thermal conduct-

ance in such a switch exceeds 106. Future experimental work

will focus on thermal characterization of the structure to

verify the potential for thermal switching.

The authors thank Dr. Sung Hoon Jin and Professor

John A. Rogers in the University of Illinois at Urbana-

Champaign for discussions. This work was supported in part

by the NSF, NSEC: Center for Nano-Chemical-Electrical-

Mechanical Manufacturing Systems and in part by the U.S.

Navy through Grant No. N66001-11-1-4154.

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211904-4 Keum et al. Appl. Phys. Lett. 100, 211904 (2012)

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