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TECHNICAL PAPER
Continuously tunable terahertz metamaterial employinga thermal actuator
Xiuhan Li • Tianyang Yang •
Wangqiang Zhu • Xiaoguang Li
Received: 21 September 2012 / Accepted: 6 December 2012 / Published online: 19 December 2012
� Springer-Verlag Berlin Heidelberg 2012
Abstract In order to increase the flexibility of the reso-
nance frequency, a widely and continuously tunable tera-
hertz metamaterial structure that employs a thermal actuator
for tuning the resonance frequency of a two-cut split-ring
resonator is proposed in this paper. The tunable metama-
terial device model is designed and simulated based on the
MetalMUMPs process. The use of V-shaped thermal actu-
ators enables continuous tuning of the resonance frequency
over a large range from 1.374 to 1.574 THz. The trans-
mission curves have a sharp dip in every resonance fre-
quency, which indicates an excellent performance of strong
resonance. The geometrical parameters of the V-shaped
thermal actuator are optimized by COMSOL Multiphysics
4.2 in order to obtain enough displacement under minimum
driven current. The relationship between driven current and
slabs’ displacement is also characterized. The reliability of
the metamaterial structure array actuated by the thermal
actuator is also calculated and discussed.
1 Introduction
In recent years, Terahertz (1 THz = 1012 Hz) frequency
regime has become an optimistic candidate for numerous
sensing (Debus and Bolivar 2007), imaging (Kawase et al.
2003), medical diagnosis (Knobloch et al. 2002), and ultra
broad band communication (Piesiewicz et al. 2007) etc.
However, many materials inherently do not respond to THz
radiation, and the tools that are necessary to construct
devices operating within this range do not exist (Chen et al.
2006). Metamaterials are fascinating new manmade mate-
rials that can be engineered to have very large or very small
(even negative) effective permeability due to the magnetic
resonance excited by external electromagnetic (EM)
waves. Their structure is basically composed of subwave-
length metallic resonators where the electromagnetic
response originates from oscillating electrons in highly
conducting metals, such as gold or copper, allowing for a
designed specific resonant response of the electrical per-
mittivity (e) or magnetic permeability (l) (Fang et al. 2005;
Siegel 2002; Kersting et al. 2002; Shelby et al. 2001). This
is especially important for the technologically relevant THz
frequency regime which is difficult to be reached due to
lack of functional sources and detectors.
The SRR unit cell (Pendry et al. 1999) developed by
Pendry is the decisive component on the property of
metamaterial. Usually, the metamaterial only resonate at a
specific frequency due to the fixed simple unit cell structure
(Chen et al. 2007), which limits the application area
of metamaterials. The resonance frequency of unit cells
can be tuned by modifying the geometrical parameters
(Withayachumnankul and Abbott 2009) or hanging the
relative permittivity and/or the thickness of the substrate of
the resonator (Nemec et al. 2009; Singh et al. 2011).
Since the critical dimension of unit cell for THz is tens
of microns or smaller, where micro-electromechanical
Systems (MEMS) technologies show extreme power and
flexibility in terms of fabrication (Tao 2010). There have
been some efforts to make frequency-tunable metamateri-
als by utilizing MEMS actuation method, such as magnetic
(Ozbey and Aktas 2011), thermal (Tao et al. 2009), bi-
material (Alves et al. 2012), electrostatic (Bouyge et al.
T. Yang is co-first author with X. Li.
X. Li (&) � T. Yang � W. Zhu � X. Li
School of Electronics and Information Engineering,
Beijing Jiaotong University, Haidian District,
Beijing 100044, China
e-mail: [email protected]
123
Microsyst Technol (2013) 19:1145–1151
DOI 10.1007/s00542-012-1713-8
2011). The reconfigurability of metamaterial is realized in
different degrees for the response of THz radiation (Ozbey
and Aktas 2011; Tao et al. 2009). In order to achieve the
tunability of resonance frequency for metamaterial, there
are two keypoints: one is the range of the tunable fre-
quency; the other is to build strong resonance to improve
the response characteristics. THz metamaterials with the
above mentioned superiorities will show better perfor-
mance in high resolution imaging, flexibility for spectrum
detection, adaptive sensing and reconfigurable frequency-
selecting for ultra wide band THz communication.
A continuously tunable terahertz metamaterial employ-
ing thermal actuators is proposed in this paper. A two-cut
split-ring resonator (SRR) structure is introduced in Sect. 2
which can be fabricated easily by MEMS technologies. The
transmission spectrum of the metamaterial is discussed in
Sect. 3. A V-shaped thermal actuator is proposed and
optimized in Sect. 4, and the reliability of the metamaterial
structure is also discussed in this section. Finally the THz
metamaterial actuated by V-shaped thermal actuators
realizes a large tunable frequency range and exhibits a
transmission minimum \0.1 through the whole frequency
range, which is presented in Sect. 5.
2 Tunable metamaterial device model based
on the MetalMUMPs process
The device model of the continuously tunable metamaterial
based on the MetalMUMPs process (Cowen et al. 2012)
and the two-cut SRR unit cell are shown in Fig. 1. Two
metal slabs are added on the two sides of the split ring. The
slabs are released from the silicon substrate and connected
with the thermal actuator, which are moveable toward the
cuts. Theoretical and experimental investigations have
shown that the resonance of the two-cut SRR structures is
due to the series inductor and capacitor that effectively
exist in the structure (Zhang and Zhu 2011). The current
induced in the two-cut SRR experiences an inductive effect
as it flows around the ring and a capacitive effect across the
gaps between the slabs and the split ring. Hence the reso-
nance frequency of the two-cut SRR can be adjusted by
changing the gaps between the slabs and the split ring to
adjust the capacitive effect. The thickness of every layer is
defined by the MetalMUMPs design rules.
The cross section of the two-cut SRR and thermal
actuator based on the MetalMUMPs process is given in
Fig. 2. Electroplated nickel is used as the structural mate-
rial of the metamaterial and thermal actuator. Gold is used
to coat the surface and sidewalls of the two-cut SRR and
slabs. Silicon nitride is used as an isolation layer and
support beams. A 25 lm trench in the high-resistivity sil-
icon substrate is etched under the arrayed two-cut SRR and
slabs to reduce the influence of the substrate.
3 Spectral characteristic of the two-cut SRR periodic
structure
In this section, the spectral characteristic of the two-cut
SRR is simulated. The simulations are performed using the
commercial simulator CST Microwave Studio, which is a
3D full-wave solver that employs the finite integration
technique. As shown in Fig. 1, the period of unit cell (u) is
300 lm 9 300 lm. The dimension of one two-cut SRR
(L) unit cell is 150 lm 9 150 lm. The length of slabs
(s) is 70 lm. The cut (b) is 50 lm. The gap between the
slab and the split ring (g) is 8 lm. The width of the metal
wire (w) is 10 lm. The incident light is normal to the
surface of the metamaterial. The direction of electric field
is parallel to the slabs.
Figure 3 shows that a transmittance dip exists at
1.574 THz. This dip can be attributed to a resonance of the
two-cut SRRs: the electric field is concentrated in the gaps
between the slabs and split ring at the resonance frequencyFig. 1 Schematic of the tunable metamaterials and the two-cut SRR
unit cell
Fig. 2 Cross section of the two-cut SRR and thermal actuator
fabricated with the MetalMUMPs process
1146 Microsyst Technol (2013) 19:1145–1151
123
as shown in Fig. 4a. Figure 4b shows the map of electric
field at off-resonance frequency of 1.3 THz. At off-reso-
nance frequencies, the electric field appears between the
side lines of the two-cut SRR. Figure 5a displays the vector
plot of the current density at 1.574 THz, the same as the
direction of the E-field. Figure 5b is the map of the
intensity of current density at 1.574 THz. It indicates that
the induced current is concentrated on both slabs and the
direction of the induced current is the same as the direction
of the incident electric field.
Electroplated nickel is used as the primary structural
material of the arrayed two-cut SRRs and slabs, while the
high resistivity of nickel results in a bad transmission
characteristic of the metamaterial. Based on skin effect
(Wheeler et al. 1942), gold is used to coat the surface and
Fig. 3 Transmission spectrum of the metamaterials
Fig. 4 a Map of electric field of the two-cut split-ring resonator
(SRR) at resonance frequency (f = 1.574 THz). b Map of electric
field of the two-cut SRR at off-resonance frequency (f = 1.3 THz)
Fig. 5 a Map of the direction of current density in the two-cut SRR at
resonance frequency (f = 1.574 THz). b Map of intensity of current
density in the two-cut SRR at resonance frequency (f = 1.574 THz)
Microsyst Technol (2013) 19:1145–1151 1147
123
the sidewalls of the two-cut SRR and the slabs as shown in
Fig. 2, and the transmission characteristic of the metama-
terial is improved obviously as shown in Fig. 6.
4 Mechanical analysis of the continuous moving
thermal actuated structures
The moveable slabs shown in Fig. 1 can be actuated by
several methods such as electrostatic actuation (Girbau
et al. 2006) and thermal actuation (Girbau et al. 2007),
which are realized by the MetalMUMPs process. As the
thermal actuator is a kind of actuation with high reliability
and the applied DC driven voltage is much lower than the
electrostatic actuator, the V-shaped electro-thermal actua-
tor is adopted to drive the slabs and realize the tunability of
resonance frequency according to Fig. 1. The mechanical
characteristic of the thermal actuator and the reliability of
the metamaterial structure array are calculated and opti-
mized by the commercial software COMSOL Multiphysics
4.2 in this section.
4.1 Design of thermal actuated structures
DC voltage is applied on both ends of the V-shaped actuator.
As current passes through the beams, they heat and expand.
Because of the shallow angle of the beams, the center cusp
experiences an amplified displacement in the direction of the
offset as shown in Fig. 7. The V-shaped actuator has proven
to be robust and suitable for the MetalMUMPS process As
shown in Figs. 1 and 2, the slabs are connected with the center
shuttle of the V-shaped actuator through a thin silicon–nitride
cantilever beam. When the center shuttle of the V-shaped
actuator experiences a displacement, the slabs move towards
to the cuts of the two-cut SRR.
In general, the displacement of the center shuttle of a
V-shaped actuator increases with the increased leg length and
decreased leg offset angle u. The displacement is insensitive
to the cross-sectional area of the legs and is not affected by the
number of parallel legs, (Baker et al. 2004) so one buckle-
beam V-shaped actuator is adopted in order to reduce the
power consume. When the DC voltage is applied to the ends
of the V-shaped actuator increases, the temperature of the
beams and the displacement of the center shuttle of the
V-shaped actuator increase. In this paper, the displacement of
the center shuttle is designed to be 8 lm, which is the same as
the gap between the slab and the split ring.
Table 1 provides the optimized parameters of the three
designs, where L, w, t, and u are the actuator length, width,
thickness, and shallow angle of the beams respectively.
As shown in Fig. 8, larger leg length (L) results in
bigger displacement and smaller actuation power under the
same DC voltage. However, larger leg length occupies
larger area on the wafer and will result in longer silicon–
nitride support beam. In consideration of both actuation
power and chip area, the design 2 is adopted. The maxi-
mum temperature at the V-shaped actuator is also taken
into account. According to Fig. 8a, for design 2 approxi-
mate 0.1 VDC voltage is needed to drive the slabs to
generate a displacement of 8 lm. Figure 9 indicates that
the maximum temperature of 478 K is achieved when a
displacement of 8 lm is generated, which is moderate.
4.2 Reliability of the metamaterial structure array
As shown in Fig. 1, slabs are connected in series through a
thin silicon–nitride cantilever beam which is hung by two
Fig. 6 Comparison of the two-cut SRRs with coated gold and
without coated gold
Fig. 7 Schematic of the V-shaped thermal actuator
Table 1 Geometric dimensions of the V-shaped thermal actuator
Parameter Design 1 Design 2 Design 3
L (lm) 800 400 600
w (lm) 10 10 10
t (lm) 20 20 20
u 1.15� 1.53� 2.29�
1148 Microsyst Technol (2013) 19:1145–1151
123
V-shaped actuators on both ends. Driving plenty of slabs
together can decrease chip area and actuation power
effectively. Hence, the reliability of the silicon–nitride
cantilever beams is analyzed.
The thin silicon–nitride cantilever is a two ends fixed
beam and the force loaded on the beam is generated by the
gravity of the electroplated nickel slabs. Simulated by
COMSOL Multiphysics 4.2, the maximum stress of the
beam appears on the two fixed ends and the value is
1.34 9 106 N/m2 which is much less than the fracture
strength of silicon–nitride beam (6.4 GPa) (MetalMUMPs
Material Properties) Fig. 10 shows the deformation of sil-
icon–nitride beam with different beam length. Through
1 * 2 THz frequency range, a 3,000 lm silicon–nitride
beam which is 10 times of the wavelength is sufficient to
characterize the performance of the two-cut SRR array.
As shown in Fig. 10, the deformation of a 3,000 lm
Fig. 8 a Slab displacement as a function of the applied DC voltage
for different actuators’ beam length. b The actuation power as a
function of the applied DC voltage under different actuators’ beam
length
Fig. 9 Change of maximum temperature of the V-shaped actuator as
a function of applied DC voltage
Fig. 10 Change of deformation of the silicon–nitride beam as a
function of the length of beam
Fig. 11 Change of resonant frequency as a function of displacement
of slab
Microsyst Technol (2013) 19:1145–1151 1149
123
silicon–nitride beam is less than 2 lm. When the defor-
mation of silicon–nitride beam is set to be 2 lm, the dif-
ference of the resonance frequency between silicon–nitride
beam with and without deformation is given in Fig. 11. It is
clear that the deformation has no effect on both the reso-
nance frequency and the tunable frequency range.
5 Continuously tunable spectral characteristics
and discussions
The working principle of the two-cut SRR can be modeled
via a series RLC resonant circuit (Baena et al. 2005). The
resonance frequency can be adjusted by changing the
capacitance which can be adjusted by changing the gap
between the slab and the cut. The more the effective
capacitance of the two-cut SRR changes, the larger the
resonance frequency moves. The variation of effective
capacitance of the two-cut SRR with constant displacement
of the slab can be adjusted by optimizing the length of the
slab and the cut according to Fig. 1. A large tunable fre-
quency range can be achieved by increasing the displace-
ment of the slab or by optimizing the length of the slab and
the cut. The displacement of the slab is limited by the
thermal actuator which is discussed in Sect. 4.
As the length of the slab (s) and the cut (b) have great
effect on the band width of the tunable metamaterials, s and
b are optimized to obtain larger tunable frequency range.
Firstly, the tunable frequency ranges vs different s and b
are calculated and compared in Fig. 12a under the fixing
displacement of slab (g = 8 lm). It is indicated that the
largest frequency range is achieved when the length of the
slab and the cut(s = b = 60 lm)are equal in Fig. 12b.
Figure 13 is the tunable spectrum characteristics when s
is equal to b under different gaps. The transmission at every
resonance frequency is \0.1, which indicates an excellent
performance of strong resonance. Figure 11 shows the
change of resonance frequency as a function of the dis-
placement of slab. It can be seen that the highest resonance
frequency is achieved when the displacement is zero cor-
responding to a gap of 8 lm between the slab and the split
ring. The lowest resonance frequency is achieved when the
displacement is 8 lm and the slabs are contacted with the
split ring. The resonance frequency decreases linearly with
increased displacement of the slab from 0 to 7 lm. There is
a rapid change of resonance frequency as the displacement
of slab increase from 7 to 8 lm. The tunable frequency
range covers the frequencies from 1.371 to 1.574 THz.
6 Conclusions
A continuously tunable two-cut SRR THz metamaterial is
designed and simulated, which can be fabricated by the
MetalMUMPs process. To better understand the physical
Fig. 12 Fix g = 8 lm, u = 300 lm, L = 150 lm and w = 10 lm.
a Change of tunable frequency range as a function of the gap of cut
(b) with different lengths of slab. b Change of tunable frequency
range as a function of the gap of cut (b) when the length of slab
(s) equals to the gap of cut
Fig. 13 Tunable characteristics of the two-cut SRR with different
gaps (g) between slab and cut
1150 Microsyst Technol (2013) 19:1145–1151
123
mechanism of the two-cut SRR metamaterial, electric field
and surface current density are plotted. An optimization of
the dimensions of the two-cut SRR has been proposed and
a large tunable frequency range from 1.374 to 1.574 THz is
achieved. The V-shaped thermal actuator is employed to
drive the slabs of the two-cut SRR. Three designs of the
V-shaped thermal actuator have been investigated and
discussed. The reliability of the silicon–nitride beam of the
two-cut SRR structure has been evaluated. All the details
about the realization of the continuously tunable THz
metamaterial have been presented, which promotes a future
application of the tunable THz metamaterial.
Acknowledgments The authors acknowledge support from the
Fundamental Research Funds for the Central Universities
(2011JBZ002).
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