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: lixiuhan@bjtu.edu.cn

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

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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

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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

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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

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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

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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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