Supplemental Material
on
Ni-Mn-Ga Shape Memory Nanoactuation
M. Kohl,1,a) M. Schmitt,1 A. Backen, 2,b) L. Schultz, 2 B. Krevet1, and S. Fähler,2,3
1
Karlsruhe Institute of Technology, IMT, P.O. Box 3640, 76021 Karlsruhe, Germany
2
IFW Dresden, P.O. Box 270116, 01171 Dresden, Germany
3
Technische Universität Chemnitz, Institute of Physics, 09107 Chemnitz, Germany
1. FABRICATION TECHNOLOGY
A single crystalline MgO (100) substrate is used for DC magnetron sputtering of epitaxial NiMn-Ga films. MgO is, however, a chemically inert material that makes the release from the
substrate almost impossible. In order to fabricate free-standing Ni-Mn-Ga nanostructures,
first an intermediate epitaxial Cr layer is sputtered that is used as a sacrificial layer.[15] It has
been demonstrated that the epitaxial Cr layer allows for deposition of the epitaxial Ni-Mn-Ga
layer. Epitaxial layer growth occurs for substrate temperatures between 300 and 400°C. The
working pressure is 8*10-3 mbar and the sputtering power is 70 W. These sputter conditions
result in thin films with thermal shape memory behavior and pronounced magnetic
properties. Further heat treatment is unnecessary since the deposition temperatures are
sufficient to provide chemical order and epitaxial growth of the Ni-Mn-Ga film.
Prior nanofabrication, the Ni-Mn-Ga / MgO samples are cleaned in an ultrasonic bath using
isopropyl alcohol. For electron beam lithography (EBL), a resist layer of PMMA
(polymethylmethacrylate) of 400 nm thickness is deposited and prebaked at 110 °C for 7 min.
EBL is performed at 100 kV using a Vistec VB6 UHR EWF tool. A 1:3 solution of
a)
Corresponding author: Electronic mail: manfred.kohl@kit.edu
Current address: Institut Néel (CNRS & UJF), 25 Rue des Martyrs, BP166, 38042 Grenoble Cedex
9, France.
b)
1
methylisobutylketone and isopropyl alcohol is used in a spray developer for 75 s to develop
the resist structures. The resist structures are transferred into the Ni-Mn-Ga layer by ion beam
etching (IBE) (Ionfab 300, Oxford Instruments). The beam energy is 200 V and the current
density is determined to be 1.13 mA/cm2. To reduce sidewall depositions of sputtered Ni-MnGa on the resist structures, a two-step procedure is established which changes the angle of
incidence from 30° to 70°.
An ultrasonic bath with acetone is used to strip residual PMMA resist structures and eventual
sidewall depositions. A commercially available Cr etchant is used to remove the Cr sacrificial
layer. A time dependent etch stop is applied to allow for sufficient structure release while
keeping the bigger anchor structures intact. A freeze drying process with cyclohexane is
executed to minimize the stiction effect caused by capillary forces of evaporating liquids.
2. ELECTRICAL RESISTANCE OF THE EPITAXIAL NI-MN-GA THIN FILM
The temperatures of martensitic phase transformation of the epitaxial Ni-Mn-Ga films are
determined by four-wire electrical resistance measurements in a thermostat under vacuum
conditions to prevent film oxidation. The temperature is first increased and subsequently
decreased step-wise, while the electrical resistance is recorded after sufficient waiting time to
allow for quasi-stationary conditions. Figure S1 shows electrical resistance characteristics in
the phase transformation regime upon heating and cooling for an epitaxial Ni-Mn-Ga film of
250 nm thickness. The specimen size is about 10 x 10 mm². The measurements show a broad
transformation regime spanning the range from 90 to about 250 °C. Previous investigations
indicate that the epitaxial Ni-Mn-Ga films undergo a multistep martensitic transition.[16]
2
Fig. S1. Electrical resistance characteristics of a reference Ni-Mn-Ga film specimen. The
different relative resistance changes in the phase transformation regime upon heating and
cooling are indicated by
and
, respectively.
3. VIDEO OF SHAPE RECOVERY
A SEM video of shape recovery of nanoactuator #1 has been recorded. After initial
deformation by a nanomanipulator, the double beam stays quasi-plastically deformed with a
corresponding tip deflection of about 1.4 µm. By electrical heating, an almost complete shape
recovery by more than 90 % occurs.
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Fig. S2. Still image taken from the video showing the shape recovery of nanoactuator #1.
4. COUPLED FINITE ELEMENT SIMULATION
A continuum model is considered for simulation of the electrical and thermal properties of
the Ni-Mn-Ga nanobeam structures without taking into account any material anisotropy or
size-dependent effects. The shape memory effect is described by a phenomenological
Tanaka-type model that has been extended to SMA structures of arbitrary 3D shape.[17]
Thermal coupling to the environment is taken into account by a heat transfer model for heat
conduction and convection. The simulation parameters are listed in Table S1. The electrical
resistivity and phase transformation temperatures are determined from own experiments on
the Ni-Mn-Ga films, see Figure S1. As some of the thermal parameters are determined from
different experiments reported in literature on macroscale specimens, however, interpretation
of the simulation results has to be considered with care.
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Table S1. Simulation parameters
Parameter
Value
Unit
2 * 10-5
Wµm-1K-1
Electrical resistivity (Martensite)
0.9102 + 0.0008993 * T(°C)
Ωµm
Electrical resistivity (Austenite)
0.75053 + 0.0005526 * T(°C)
Ωµm
Thermal expansion coefficientb)
1.5 * 10-5
K-1
Heat transfer coefficientc)
8.0 * 10-12
Wµm-2 K-1
Integral latent heat
4500
Jkg-1
Martensite start temperature Ms
165
°C
Martensite finish temperature Mf
85
°C
Austenite start temperature As
105
°C
Austenite finish temperature Af
180
°C
Environmental temperature
25
°C
Thermal conductivitya)
a)
O. Söderberg, I. Aaltio, Y. Ge, O. Heczko, S.P. Hannula, Materials Science and Engineering
A 481, 80 (2008);
V.A. Chernenko, M. Kohl, M. Ohtsuka, T. Takagi, V.A. L’vov, V.M. Kniazkyi, Materials
Science and Engineering A 438, 944 (2006);
b)
c)
A low heat transfer coefficient has been assumed for the vacuum conditions in the SEM.
The simulation procedure consists of two steps that are iterated several times in order to
obtain self-consistent results. In a first electrical simulation step, the local electrical current
profile and corresponding heating power distribution are simulated based on the
experimentally determined electrical resistance temperature characteristics of the epitaxial
Ni-Mn-Ga films in martensitic and austenitic condition provided in the supplemental
information. In the phase transformation regime, a rule of mixture is assumed for the phase
fraction-dependent contributions of the electrical resistances in austenite and martensite. A
von Neumann boundary is assumed for the electrical potential at the beam onset.
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In a second thermal simulation step, the competing effects of local heat generation given by
the electrical current profile and heat losses due to heat conduction and convection are
considered. Heat conduction is enabled by the link between beam structures and bond pads
used for electrical interconnection to the measurement setup. Convective heat exchange with
the environment can be neglected within the SEM. Furthermore radiative heat losses are
expected to become important only at large temperatures (>1000°C), but are neglected here.
The time dependence of heat transfer is simulated using a Crank Nicolson scheme. Quasistationary conditions are obtained by taking into account sufficient time for heat exchange.
Thus, for each electrical current value, a temperature profile is obtained that is used to
calculate a corresponding thermally averaged value of electrical resistance.
5. REFERENCE NI-MN-GA ACTUATOR WITH LARGE BEAM WIDTH
In order to elucidate possible size-dependent effects resulting from the large surface-tovolume ratio of the Ni-Mn-Ga nanoactuators, we compare the drop of electrical resistance of
the Ni-Mn-Ga nanobeam structures with corresponding results of Ni-Mn-Ga actuators having
a much larger beam width of 1 µm. Figure S3 shows electrical current dependence of beam
deflection and corresponding electrical resistance for a Ni-Mn-Ga double beam actuator
having a beam length, width and thickness of 40 µm, 1 µm and 250 nm, respectively
(reference actuator). In this case, the resistance drop is about 7 %, which in line with the
result of the simulation model and the observed resistance change in the Ni-Mn-Ga film
reference sample taking into account that the temperature profile in the beam structures gives
rise to averaged electrical resistance values.
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FIG. S3. Deflection of beam tip during an electrical heating cycle and corresponding
normalized electrical resistance of a Ni-Mn-Ga double beam actuator (reference actuator)
having a length, width and thickness of each nanobeam of 40 µm, 1 µm and 250 nm,
respectively.
6. EFFECT OF CONTACT RESISTANCES AND LEAKAGE CURRENTS
The electrical resistance of the Ni-Mn-Ga double beam actuators may be estimated in the
framework of a continuum model taking into account their geometrical dimensions and
electrical conductivity. Our measurements on the Ni-Mn-Ga reference actuator with beam
length, width and thickness of 40 µm, 1 µm and 250 nm, respectively, reveal an electrical
resistivity of 0.93 µm at room temperature, which is smaller compared to Ni-Mn-Ga bulk
values reported in the literature.[S1] If we assume this value of electrical resistivity for
estimation of electrical resistance of the Ni-Mn-Ga beam nanoactuators, we obtain in each
case an electrical resistance of about 300  as the effects of different geometries cancel out
each other. This value corresponds well to the experimental result on the reference actuator.
For the Ni-Mn-Ga beam nanoactuator of 200 nm beam width (nanoactuator #1) the observed
electrical resistance is by about 13% higher, which could be explained by fabrication
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tolerances of beam widths in the order of 30 nm. This result also indicates that the
contribution of leakage currents cannot be higher than this uncertainty in electrical resistance,
because any leakage current would result in a decrease of electrical resistance rather than an
increase. For the smallest Ni-Mn-Ga nanoactuator #2, experimental values of electrical
resistance differ by almost 100 % as the fabrication tolerances have a much higher impact. In
this case, a rigorous evaluation of electrical resistance change is no longer possible.
Further estimates on the effect of possible temperature-dependent effects on the electrical
resistance have been made on the basis of an electrical circuit model taking into account the
series resistance of the measurement setup and contact resistances. The series resistance of
the measurement setup between the electrical interconnection tips, including all connection
cables and the nanomanipulators is determined to be below 10 . The contact resistances are
estimated to be less than 20 . A possible temperature-dependent change of contact
resistances of 20  results in a rather small change of the overall electrical resistance of about
0.5% and, thus, can be ruled out as an explanation for the observed change of electrical
resistance drop in the nanoactuators.
[S1] V.K. Srivastava, R. Chatterjeea and R.C. O’Handley, Appl. Phys. Lett. 2006, 89,
222107.
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