Thermally actuated high frequency dimple MEMS

Resonators

Amir Rahafrooz, Arash Hajjam and Siavash Pourkamali

Department of Electrical and Computer Engineering

University of Denver

Denver, CO, USA 80208

Email: spourkam@du.edu

Abstract—This study demonstrates the possibility of

thermally actuating high-frequency micromechanical resonators.

A single-mask fabrication process was used to fabricate high

frequency single crystal silicon resonators on SOI substrates. The

resonators were operated in a one-port configuration with parts

of the resonator structure performing both thermal actuation and

piezo-resistive sensing. Quality factors as high as 90,000 and

resonance frequencies as high as 5.4MHz have been

demonstrated. Previously thermal actuation was not thought of

as a reliable and justified method of actuating thermal

resonators; however, in this paper it is shown theoretically and

experimentally that thermal actuation is a more suitable

approach for higher frequency resonators with dimensions in the

lower microns and nanometer range

Keywords—thermal actuation, MEMS resonator,

piezoresistive, quality factor

I. INTRODUCTION

Over the past decade a lot of interest has been paid to Micro-electro-mechanical resonators and they have been attracting a lot of attention as the potential emerging technology for integrated electronic filters and frequency references as well as ultra-high resolution sensors [1]. Piezoelectric or electrostatic transduction mechanisms, each having their advantages and disadvantages are typically used for high frequency electromechanical resonators; Piezoelectric driving mechanisms require either piezoelectric substrates or the deposition of piezoelectric thin films [2]. Electrostatic excitation [3,4] is not suitable because it requires submicrometer air gaps which results in unwanted squeezed film damping and might be clogged in an environmental sensing application. In contrast to this, electrothermal excitation is shown to be effective and simple to implement while requiring only heating resistance [5,6]. Thermal actuation is a well known mechanism used in different microscale devices. Thermal actuators have great properties such as large actuation force, low operating voltage and simplicity of fabrication, however, there are downsides towards these type of fabricated devices, the most notable being their relatively large power consumption and high body temperature which limits their application in some cases. Furthermore, thermal actuators are usually known and referred to as slow actuators suitable for DC or very low-frequency applications. This is mainly due to the required time for the temperature of the heating element of a thermal actuator to reach the desired level and generate the expected force.

Thermally actuated micromechanical resonators with frequencies up to ~800kHz have been previously demonstrated [7]. In this paper we demonstrate thermal actuation of resonators with much higher frequencies in the MHz range and show theoretically and experimentally that as opposed to the general assumption, thermal actuation could in fact be very suitable for higher frequency applications.

II. DESCRIPTION AND JUSTIFICATION

Figure 1 shows the schematic view of a dimple resonator used in this work.. Thermal actuation of such resonator occurs by passing a combination of a DC and an AC current between the two pads on the two sides of the structure resulting in a fluctuating ohmic loss in the structure. Due to their higher resistance, most of the heat is generated in the thin pillars in the middle of the structure. The AC force generated in the pillars as the result of the fluctuating heating power and therefore fluctuating temperature in the pillars, can actuate the resonator in its in-plane extensional resonance mode as shown in Figure1. At the same time as the resonator vibrates, the alternating tensile and compressive stress in the pillars results in fluctuations in their electrical resistance (due to the piezoresistive effect). Since the resonator is biased with a constant DC voltage, this results in fluctuations in the DC current passing through the resonator that represents the vibration amplitude (output signal) of the resonator.

Figure 1. Top view schematic diagram of a thermally actuated Dimple

resonator showing the current flow and the qualitative distribution of AC

temperature fluctuation amplitude (red being the maximum and blue

minimum).

Superiority of Thermal Actuation at Nanoscale: Thermal phenomena at macro-scale have time constants in the few seconds to few minutes range. Thermal actuation is generally considered a slow mechanism (with response times in the milliseconds range) in conventional MEMS with dimensions in the tens to hundreds of microns. However, it can be shown that the time constant for solid phase thermal actuation is inversely proportional to the square of the thermal element dimensions. Similar to electrical systems, in a time variant thermal system, thermal time constant can be defined as the product of the thermal resistance and thermal capacitance of the element

(TTT

CR .=τ ). Similar to electrical resistance, thermal

resistance is proportional to the length and inversely proportional to the cross-sectional area of the path between the element and the thermal ground (locations with negligible temperature fluctuations, e.g. resonator wirebonding pads). Therefore, if all dimensions of a structure are shrunk down by a factor of X, the thermal resistance increases by a factor of X. On the other hand, thermal capacity is proportional to the mass

of the element and shrinks proportionally to X3

. Hence, the

thermal time constant reduces by a factor of X2

. Considering the fact that, for mechanical resonators resonance frequency is inversely proportional to the scale. For example thermal resistance increases by a factor of X in this case which leads to the response time of the thermal actuators shrinking faster than the raise in the resonator frequency. Therefore, it can be concluded that thermal actuation becomes a more suitable mechanism for operation of electromechanical resonators as their dimensions are shrunk down to lower micron and into the nanoscale.

III. FABRICATION

A single mask was used to fabricate the resonators on the SOI substrate. Figure 2 shows the fabrication process which begins with an SOI wafer with a 200nm thermally grown silicon dioxide deposited on its surface. At the next step the silicon dioxide is patterned to form the resonator structures, and then both RIE (reactive ion etching) and DRIE (deep reactive ion etching) are applied to etch the silicon on two different SOIs.

In the RIE machine, the SF6 gas can be used to etch the silicon isotropically; so in order to make the process close to anisotropic etching, we applied the Bosch process [8] using the RIE. The way this was done was using a set of values already found for SF6 pressure, RF power and etching process time of the machine respectively. Then, by replacing the gas by O2, a thin oxide was deposited in order to protect the sidewalls from excessive etching. Later the gas was switched back to SF6 again and this loop was continuously repeated until the desired etch depth was obtained. Although vertical sidewalls could not be achieved, however an optimal set of parameters that led us into having sidewalls of the highest possible slope were obtained. Some dimple resonators with different dimensions have been fabricated on a 100 N-type SOI wafer with the device layer thickness of 10 µm and the buffered oxide thickness (BOX) of 3 µm respectively.

However the RIE machine was not the only method used to etch silicon. The silicon was also etched using the DRIE

machine which can provide vertical silicon etched sidewalls. In this case, we used a 100 P-type SOI wafer with a device layer thickness of 15µm and a buffered oxide thickness (BOX) of 5µm respectively.

Figure 2. Process flow used for fabrication of the resonators.

Figure 3. SEM view of a fabricated thermal dimple resonator (Table1-Res.1)

using RIE. It’s fabricated on a 100 N-type SOI wafer with a device layer

thickness of 10 µm and a buffered oxide thickness (BOX) of 3 µm repectively.

After etching the silicon, the structures were released by applying HF. Fabricated dimple resonators are shown in figures 3, 4 and 5. The resonators in figures 3 and 5 have been etched using the RIE, while the DRIE was used to fabricate the resonator in figure 4. The other main difference between these three dimple resonators is them having different masses attached to them. The resonator shown in figure 3 has two small bulk cubic masses attached to both its ends while figures 4 and 5 show a gradual increase in the size of the masses respectively. Therefore this leads to figure 5 having the largest set of masses at both ends. As it can be seen, holes have been implemented inside each of masses in order to makes it possible for the whole structure to be rapidly released without over-releasing the testing pads. As shown in figure 6, all three resonators have the same length (L= 640µm) and width(W=80 µm), however the width of the cubic mass which is located at

both ends of the resonators are l=140, 200 and 300 µm for figures 3,4 and 5 respectively.

Figure 4. SEM view of a fabricated thermal dimple resonator (Table1-Res.2)

using the DRIE which shows vertical sidewalls. It’s fabricated on a 100 P-type

SOI wafer with a device layer thickness of 15µm and a buffered oxide

thickness (BOX) of 5µm respectively.

Figure 5. SEM view of a fabricated thermal dimple resonator (Table1-Res.3)

using the RIE. It’s fabricated on a 100 N-type SOI wafer with a device layer

thickness of 10 µm and a buffered oxide thickness (BOX) of 3 µm repectively.

IV. MEASUREMENT RESULTS

The fabricated resonators were tested in a one-port configuration with the thin pillars of the structures acting simultaneously as both thermal actuators and piezo-resistive sensors (figure 6). The main problem with this configuration is that the output signal is added on top of the input signal requiring extra calibration and data processing steps to filter out the resonance response of the devices. Figure 7 shows the measured frequency responses for a 5.4MHz (figure 3), 1.67MHz (figure 4) and 1.5MHz (figure 5) dimple resonators respectively. As expected, together with the increase in the DC bias current the output signal level increases while the resonator frequency decreases due to the higher static temperature and softening of the structural material, Quality

factors as high as 90,000 were measured for the 1.67MHz resonator.

Figure 6. Schematic diagram of the electrical connections to the resonator

for one-port operation

-100

-90

-80

-70

-60

5.404 5.4063 5.4086 5.4109MHz

dB

Q=7700

Rm=170KΩ

I=28mA

Q=21600

Rm=525KΩ

I=21mA

-105

-95

-85

-75

-65

-55

1.67 1.6718 1.6736 1.6754 1.6772MHZ

dB

Q=6700

Rm=80KΩ

I=64mA

Q=8400

Rm=160KΩ

I=51mA

Q=11100

Rm=240KΩ

I=44mA

Q=90000

Rm=400KΩ

I=40mA

-105

-95

-85

-75

-65

-55

1.5025 1.50407 1.50564 1.50721MHz

dB

Q=7500

Rm=100KΩ

I=22mA

Q=10500

Rm=260KΩ

I=15mA

Figure 7. Measured frequency responses for two thermally actuated dimple

resonators with different actuator dimensions. Each graph shows the response

of one resonator with two or more different bias currents.

All the results are summarized in Table 1. As it can be seen, by decreasing the DC bias voltage, both the resonance frequency and the quality factors increase while the output signal level decreases. Another interesting point is that the quality factor of the 1.67MHz resonator has reached 90,000 which is higher than the other two resonators. That can mainly occur as a result of having vertical sidewalls which dissipates less energy during in-plane resonance movement. Although this resonator has wider and shorter supports in comparison with the other two dimple resonators, however it seems that the effect of having vertical sidewalls is dominant in determining the quality factor. It is also clearly shown that by increasing the amount of mass connected to each resonator; a decrease in frequency from 5.4MHz to 1.5MHz was obtained.

TABLE I. SUMMARY OF THE MEASUREMENT RESULTS OBTAINED FROM

THREE DIFFERENT DIMPLE RESONATORS; RES.1, RES.2 AND RES.3 ARE THE

RESONATORS WHICH ARE SHOWN IN FIGURES 3,4 AND 5 RESPECTIVELY.

Resonator

type

DC

Voltage

(V)

Current

(mA)

Frequency

(MHz)

Peak

level

(dB)

Quality

factor

Rm

(KΩ)

Res. 1

l=140µm 10.5 28 5.4072 -64.5 7700 170

Res. 1

l=140µm 8 21 5.4079 -74.4 21600 525

Res. 2

l=200µm 19 64 1.67 -58.4 6700 80

Res. 2

l=200µm 16 51 1.6746 -64.1 8400 160

Res. 2

l=200µm 14 44 1.675 -67.5 11100 240

Res. 2

l=200µm 12.7 40 1.6754 -72.0 90000 400

Res. 3

l=300µm 8.2 22 1.5049 -59.8 7500 100

Res. 3

l=300µm 5.4 15 1.5062 -68.4 10500 260

V. CONCLUSIONS AND FUTURE WORK

This study demonstrated theoretically and experimentally that thermal actuation is not only a viable approach for

actuation of micro and nanoscale high frequency electromechanical resonators, but also becomes a preferred approach as the resonator dimensions are shrunk down to reach higher operating frequencies.

Future work will include demonstration of stronger electrothermo-mechanical coupling (lower equivalent impedance) and high-Q operation of smaller scale resonators with orders of magnitude higher frequencies and lower power consumption. We are also hoping to be able to use these resonators as mass sensors with integrated piezoresistive impact sensing mechanisms.

ACKNOWLEDGMENT

This work was supported by National Science Foundation (NSF) under grants #0839951 and #0800961.

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