Fully integrated MEMS TGA device for inspection of nano-masses

Fully Integrated

MEMS TGA Device

for

Inspection

of

Nano-masses

Fully integrated MEMS

TGA device for inspection

of nano-masses

Fully integrated MEMS TGA device for

inspection of nano-masses

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op woensdag 2 mei 2012 om 12:30 uur

door

Elina IERVOLINO

Dottore Magistrale in Ingegneria Elettronica, van Universita’ degli Studi di Napoli Federico II, Italia

Prof. dr. P. M. Sarro

Samenstelling promotiecommissie: Rector Magnificus, voorzitter

Prof. dr. P. M. Sarro, Technische Universiteit Delft, promotor Prof. dr. O. Paul, University of Freiburg, Germany

Prof. dr. C. Schick, University of Rostock, Germany

Prof. em. V.B.F. Mathot, Katholieke Universiteit Leuven, Belgium Prof. dr. P.J. French, Technische Universiteit Delft

Prof. dr. M.J. Vellekoop, Universit¨at Bremen, Bremen Dr. ir. A.W. van Herwaarden, Xensor Integration Reservelid:

Prof. dr. Prof. dr. C.I.M. Beenakker, Technische Universiteit Delft

Elina Iervolino,

Fully integrated MEMS TGA device for inspection of nano-masses, Ph.D. Thesis Delft University of Technology,

with summary in Dutch.

Keywords: Thermal analysis, resonator. ISBN 978-94-6203-031-2

Copyright c 2012 by Elina Iervolino

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written permission of the copyright owner.

Contents

List of Symbols v

1 Introduction 1

1.1 Thermal analysis of nanogram samples . . . 1

1.2 MEMS for Thermal analysis . . . 3

1.3 Typical Applications of MEMS Calorimeters and TGA . . . . 3

1.4 MEMS Calorimeter . . . 5

1.4.1 MEMS Differential scanning calorimeter . . . 7

1.4.2 MEMS calorimeter for liquid samples . . . 8

1.4.2.1 The device . . . 10

1.4.2.2 Sensor Characteristics . . . 11

1.5 MEMS TGA . . . 12

1.6 Review of MEMS TGA . . . 13

1.7 Research objective . . . 14

1.8 Structure of the thesis . . . 14

2 Cantilever resonators 17 2.1 Introduction . . . 17

2.2 Cantilever beam resonance frequency . . . 18

2.3 Temperature dependence of cantilevers resonance frequency . 19 2.4 Temperature distribution on a cantilever beam . . . 22

2.5 Temperature dependence of MEMS TGA resonance frequency 24 2.6 Temperature distribution along cantilever paddles . . . 28

2.6.1 Simulation . . . 28

2.6.2 Measurements . . . 30

2.7 Resonance frequency measurements . . . 31

2.7.1 Device . . . 32

2.7.2 Measurements . . . 32

2.8 Conclusions . . . 35

i

3 MEMS ThermoGravimetric Analysis device 37 3.1 Introduction . . . 37 3.2 Design requirements . . . 39 3.3 Sensing cantilever . . . 41 3.3.1 Uniform heating . . . 41 3.3.2 Local heating . . . 42

3.4 Cantilever actuation principles . . . 44

3.5 Thermal actuation . . . 44

3.5.1 Bimorph actuator . . . 45

3.6 Piezoresistors . . . 51

3.7 Resonance frequency and cross talk . . . 53

3.8 Sample mass dependence of the resonance frequency . . . 54

3.9 Device Layout . . . 57 3.10 Fabrication . . . 58 3.11 Conclusion . . . 60 4 Temperature calibration 61 4.1 Introduction . . . 61 4.2 Device description . . . 62

4.3 Device electrical characterization . . . 64

4.3.1 Main heater . . . 64

4.3.2 Device time constant . . . 67

4.3.3 Temperature measurements . . . 68

4.4 Isothermal calibration . . . 69

4.4.1 Measurement setup . . . 69

4.4.2 Extraction method . . . 71

4.5 Calibration accuracy determination . . . 73

4.6 Conclusions . . . 77

5 Calibration of MEMS TGA 79 5.1 Introduction . . . 79

5.2 Temperature calibration . . . 80

5.3 Mass calibration . . . 81

5.3.1 Calibration with Molybdenum spots . . . 82

5.3.1.1 Specimen choice . . . 82

5.3.1.2 Measurement set-up and calibration results . 82 5.3.1.3 Molybdenum specimen thermal analysis . . . 85

5.4 Resonance frequency calibration . . . 87

CONTENTS

iii

6 Thermogravimetric measurements 89 6.1 Introduction . . . 89 6.2 Measurement setup . . . 90 6.3 Thermogravimetric measurements . . . 92 6.3.1 Polyamide 6 . . . 92 6.3.2 Paraffin . . . 94

6.3.3 Copper sulfate pentahydrate . . . 95

6.4 Conclusions . . . 96

7 Conclusions and Recommendations 99 7.1 Conclusions . . . 99

7.1.1 Cantilever resonators . . . 99

7.1.2 MEMS ThermoGravimetric Analysis device . . . 100

7.1.3 Temperature calibration . . . 100

7.1.4 Calibration of MEMS TGA . . . 101

7.1.5 Thermogravimetric measurements . . . 101 7.2 Recommendations . . . 101 Bibliography 105 Summary 115 Samenvatting 117 List of publications 119 Acknowledgments 123 Biography 125

List of Symbols

α Coefficient of Thermal Expansion [1/K] . . . 19

Co Thermal conductivity [W/mK] . . . 24

Cog Thermal conductivity air[W/mK] . . . 24

∆f Resonance frequency shift [Hz] . . . 27

∆T Temperature variation respect to ambient temperature [K] . . . . 19

∆m ∆f Mass change sensitivity [pg/Hz] . . . .27

E Young’s modulus [Pa] . . . .18

EP Maximum potential energy [J] . . . 22

EK Maximum kinetic energy [J] . . . 22

η Correction factor [-] . . . 24

f Frequency [Hz] . . . 19

f_∞ Cantilever resonance frequency @ ambient temperature [Hz] . . 25

I Cantilever moment of inertia [m4_{] . . . 18}

Kpad Cantilever paddle spring constant [N/m] . . . 41

k Cantilever spring constant [N/m] . . . 19

L Cantilever length [m] . . . 18

Lh Heater length [m] . . . 23

Lm Minimum cantilever length [m] . . . 26

mC Cantilever mass [kg] . . . 19

mef f Cantilever effective mass [kg] . . . 19

mpadef fCantilever paddle effective mass [kg] . . . 42

ρ Mass density [kg/m3_{] . . . 18}

S Cantilever cross-sectional area [m2_{] . . . 18}

s Gap between cantilever beam and substrate [m] . . . .24

T Temperature [K] . . . 19

T CE1 First order temperature coefficient of Young’s modulus [1/K] . 20 Th Heater temperature [K] . . . 24

T_∞ Ambient temperature [K] . . . 22

t Cantilever thickness [m] . . . 19

w Cantilever width [m] . . . 22

v

wh heater width [m] . . . 23

wm Minimum cantilever width [m] . . . 26

Chapter 1

Introduction

1.1

Thermal analysis of nanogram samples

Thermal analysis (TA) is the science of studying the properties of materials as they change with temperature and time. TA techniques are used in a wide range of disciplines, from pharmacy, chemistry, biochemistry to poly-mer science and material science. In practice, TA techniques are applied in any field where changes in sample behavior are observed under controlled heating or controlled cooling conditions [1]. TA techniques provide funda-mental information on the material properties of the system under test.

Depending on the measured material property it is possible to distin-guish several TA techniques of which the most widely used are listed below: • Differential thermal analysis (DTA): temperature difference between

a sample and a reference.

• Heat flux calorimetry (HFC): temperature difference across the ther-mal conductance between the experimental chamber and the outer shell.

• Thermomechanical analysis (TMA): change of a dimension or a me-chanical property of a sample.

• Thermo-optical analysis(TOA): temperature dependence of the opti-cal properties of a sample.

• Differential scanning calorimetry (DSC): difference in the amount of heat required to increase the temperature of a sample and a reference. • Thermogravimetric analysis (TGA): changes in mass of a sample.

Detailed definitions of TA techniques can be found in [2]. In this thesis the attention is given to the last two aforementioned methods: DSC and TGA.

Instruments for TGA and DCS are commercially available [3,4] and used in both industry and scientific research. In Fig. 1.1 a TGA instrument of Netzsch is shown as example of standard TGA. The sample mass resolution of such instrument is reported to be 0.1 µg [3]. This mass resolution could represent a limiting factor in many application fields where smaller masses have to be analyzed. In chemistry, for instance, to study the decomposition point of explosives, or, in forensic investigation. For safety reasons, in the first case, or for the scarcity of sample materials, in the second case, samples in the nanogram range have often to be analyzed.

sample

Figure 1.1: TG 209 F3 Tarsus of Netzsch. A 3D profile of the TG 209 F3 Tarsus is shown on the right side of the picture. The picture is downloaded from the Netzsch website: www.netzsch-thermal-analysis.com.

The shift of the measurable sample mass from the µg range to the ng range opens also to new possibilities for the thermal characterizations of materials.

In fact, TA of nanogram samples can find its application in the charac-terization of nanocomposite materials. The analysis of nanogram amounts of sample could also allow to perform measurements with fast temperature scan rates, i.e. > 103 _{K/s, thus giving the possibility to perform Fast DSC}

1.2 MEMS for Thermal analysis

3

temperature scan rate of 750 K/min [5], High Performance DSC (HPerDSC) instruments offer temperature scan rate up to 2000 K/min [6].

Investigation of metastable states would profit from fast scanning rates, as well as time-dependent transitions. Fast scan rates are very important for studying the phase transitions of polymers [7–10]. With these fast scan rates, polymers can be analyzed under the same conditions that occur for example during injection moulding, that is the most common method of part manufacturing.

There is therefore the need for new instruments which are capable of performing TGA of nanogram samples.

1.2

MEMS for Thermal analysis

Micro Electro-Mechanical Systems (MEMS) technology gives an opportu-nity to shift the operational range of TA instruments towards lower sample masses and therefore, towards higher scan rates. The high sensitivity and short response times of the MEMS devices make them suitable for TGA or calorimeter measurements.

MEMS cantilevers have been successfully used for TGA measurements [11]. MEMS devices with a close or tethers membrane have been demon-strated for calorimeter measurements [12, 13].

Fig. 1.2 shows a device used to analyze the crystallization behavior of fast crystallizing polymers such as isotactic polypropylene (iPP) [14]. The analysis in [14] was performed with heating and cooling rates up to several thousand Kelvin per second, which can not be reached with standard calorimeter instruments. [3].

Although examples of MEMS devices for calorimeter measurements can be found in literature [12, 13, 15], the use of MEMS technology applied to thermal analysis poses many challenges to the design as well as the calibra-tion of the devices.

1.3

Typical Applications of MEMS

Calorime-ters and TGA

TA can add the needed insight to learn more about material properties. Calorimetry is mainly used for the analysis of physical reactions and very well suited to study chemical reactions. In particular, it is possible to ana-lyze materials by exposing them to a temperature sweep, either in an inert atmosphere (nitrogen or helium) or in an oxidizing atmosphere. Then, all

Figure 1.2: Thin-film chip calorimeter based on the thermal con-ductivity gauge TCG 3880 [www.xensor.nl].

effects such as glass transition, crystallization, melting, evaporation, decom-position, and even oxidation can be detected. It is also possible to determine the heat of exothermic and endothermic reactions. For this, a DSC is used. When mass samples smaller then a milligram have to be analyzed, MEMS calorimeters can be used. MEMS calorimeters have became widely used to study thermal properties of sub-microgram samples as function of temper-ature. They are powerful tools as the small addenda of the calorimetric cell enable to study small amounts of material [16, 17]. Ultra-fast-scanning calorimeters are commercially available and extensive characterizations are reported in literature [18–20]. Scan rates as fast as 1 kK/sec prevent re-crystallization of the sample during the scan [7–10].The study of living cells (with their heat production of about 1-100 pW [21]) and the efficiency of enzymatic conversions can be studied using a MEMS liquid calorimeter. A MEMS liquid calorimeter can also be used for the measurement of thermal conductivity and diffusivity of liquid samples [22–24].

Mass changes due to oxidation and evaporation are detected by ther-mogravimetry (TG). MEMS TGA are used for the analysis of picogram amounts of samples. They also enable TGA of thin films deposited directly on the device [25].

In the following sections details are given on MEMS for calorimetry and TGA.

1.4 MEMS Calorimeter

5

1.4

MEMS Calorimeter

A calorimeter is a device which measures the heat generated or absorbed in chemical reactions or physical changes in a sample as well as heat capacity of samples. In practice, a calorimeter measures the heat exchange between the sample under test and the calorimeter itself. Often other quantities are being measured as well, such as temperature and amount of present substance.

In silicon (Si) technology a MEMS calorimeter usually consists of: • a heater to uniformly heat the sample under test.

• a temperature sensor to measure the temperature of the sample under test.

• a membrane to thermally isolate the sample area from the surround-ings. p-Si Frame SiN Heater Thermopile Al

Figure 1.3: Schematic of a MEMS calorimeter: on a thin-film membrane the heater and the hot junctions of the thermopile (temperature sensor) are located. The cold junctions of the ther-mopile are on the Si frame that acts as heat sink and also gives mechanical stability to the device. [Picture loaded from the web-site www.xensor.nl]

In Fig. 1.3 the main elements of the MEMS calorimeter are schematically depicted: the hot spot that delimits the sample area where the experiment is performed; the temperature sensor that measures the temperature; and the thin membrane that thermally isolates the sample area from the sur-rounding. The Si frame gives mechanical stability to the calorimeter and acts as heat sink.

With MEMS calorimeters it is possible to scale down the sample to nanogram amounts of material [16, 17] and increase the temperature scan

Figure 1.4: Flash DSC 1 of Mettler-Toledo. The instrument core is the MEMS device UFS 1 [Picture loaded from the website www.mt.com]. A description of the MEMS device can be found in Chapter 4

rate to 106 _{K/s. Different designs of calorimeter chips have been proposed}

with the intent to come to a device capable of fast temperature scan rates [19, 26, 27]. The main drawback of the MEMS calorimeters was the absence of a commercial available apparatus and software for the signal analysis. The problem has been overcome with the recent introduction on the market of the Flash DSC 1 of Mettler-Toledo, see Fig. 1.4.

In the following subsections a MEMS DSC device and a MEMS calorime-ter for liquid sample are presented as examples of MEMS calorimecalorime-ters. The MEMS DSC shows the potentialities of a MEMS calorimeter for the anal-ysis of solid samples while the MEMS calorimeter for liquid sample allows to study the thermal properties of microliter amounts of liquid.

1.4 MEMS Calorimeter

7

1.4.1

MEMS Differential scanning calorimeter

The differential scanning calorimeter (DSC) is one of the most used calorime-ters for routine characterization of metals or polymers. In the DSC the experimental chamber is not kept at one temperature, but it is swept over a temperature range. To compensate for common-mode errors, scanning calorimeters are often built with twin experimental sites in order to be able to perform differential measurements. One site is for the sample under test; the other site serves as reference, which is either left empty or contains ma-terial resembling the sample under test as much as possible, except for the phenomena to be measured. MEMS DSC have been fabricated to obtain fast scan rates with a small amount of sample material [20, 26, 28, 29]. In general they consist of a heater and a thermometer on a thin dielectric film.

Most reported MEMS calorimeters are single cell types.

A twin MEMS calorimeter has been developed to enable differential measurements on the same device [30]. This has the advantage that sample and reference cell can be considered to be at the same ambient temperature, and it also saves space. A detailed description of the device and its tem-perature calibration can be found in Chapter 4. Only a brief description of the device is included here.

The device is made of two identical cells, the reference and sample cell, respectively. Both cells consist of a membrane that is 1.6×1.6 mm2 _large

and about 2 µm thick. A picture of the device mounted on the ceramic package is reported in Fig. 1.5

Figure 1.5: _{Differential scanning calorimeter chip 5 mm × 3.3} mm × 0.3 mm mounted on a ceramic package 24 mm × 24 mm × 0.6 mm.

The membranes of the two cells are separated by a thick Si frame of 300 µm that acts as heat sink. Two heaters are integrated in the center of the membrane. The main heater, with a resistance of about 5 kΩ, is used for the general temperature scan program. The other heater, of about 4 kΩ, is active only in power compensation mode and has to compensate for temperature differences between the reference and the sample cell. The two heaters, covered by an aluminum (Al) layer, make up a circular area with a diameter of 0.5 mm, where the sample can be loaded. The Al layer is used to get temperature uniformity in the sample area. The temperature of the heated area is measured with an integrated thermopile. This MEMS calorimeter has been designed for the Flash DSC 1 of Mettler-Toledo. In Fig. 1.4 the Flash DSC 1 is shown.

1.4.2

MEMS calorimeter for liquid samples

The interest in measuring the thermal properties of microliter liquid sam-ples has become increasing relevant with the development of microfluidics and lab-on-a-chip applications [31, 32]. In literature various methods are described for measuring thermal properties of liquids. Optical techniques are based on, for example, photo-pyroelectric effects [33] or on interferom-etry [34]. These methods require an electromagnetic coupling between the optical actuation and the thermal property of the sample. Also MEMS calorimeters have been commonly used to measure thermal conductivity, thermal diffusivity and specific heat of liquid samples [35]. The thermal conductivity is the property of a material that indicates its ability to con-duct heat. The thermal diffusivity is a measure of how fast the heat is transferred through the material. The specific heat is defined as the amount of energy that has to be transferred to or from one unit of mass (kilogram) or amount of substance (mole) to change the system temperature by one degree. Most of the MEMS calorimeters are limited to the measurement of one of the three aforementioned thermal properties.

The performance and the reliability of these thermal sensors are of-ten limited by the poor thermal isolation of the liquid cells. In particular, calorimeters with a glass micro-fluidic chamber [24, 36–38] are not suitable for thermal diffusivity measurements. The proximity of the heater to the thermopile is a limiting factor in such calorimeters as the effective thermal diffusivity of the membrane-sample system is dominated by the thermal diffusivity of the membrane. In [39] a CMOS sensor is proposed for mea-suring the thermal diffusivity of liquid samples dropped directly onto the device. Another external factor that can influence the measurements of the thermal properties of the sample under test is the frequency of the applied

1.4 MEMS Calorimeter

9

Figure 1.6: Photograph of the two chips which form the device XI-318-9. The transparent membranes are 3.8 mm × 0.8 mm (top chip, dashed rectangle) and 2 mm × 0.8 mm (bottom chip)

signal. The 3-ω method is commonly considered for the measurements of the frequency dependent complex heat capacity. Another method, temper-ature wave analysis (TWA), is used to obtain the thermal diffusivity of solid sample by measuring phase and amplitude of a thermal wave transmitted through the sample itself [40]. In this technique an oscillating heat flow P= P0cos(ωt) is applied to one side of the plate-like sample and the

oscillat-ing temperature T= T0cos(ωt +φ) is detected on the other side. A recent

work [41] used the same principle shown in [40] to measure the complex heat capacity C(ω) with a two-channel calorimeter. In [22] a fluidic MEMS calorimeter is proposed. The device is made up of two calorimeter chips glued on top of each other forming a close chamber for the liquid to be analyzed. The design allows the simultaneous measurement of both ther-mal conductivity and therther-mal diffusivity of microliter liquid samples, see Fig. 1.6. Moreover, working with a closed chamber calorimeter allows the accurate characterization of volatile liquids. The MEMS liquid calorime-ter [42] has been also used to measure the thermal properties of amino acid and proteins in aqueous solution. A detail description of the device and its working principle is given here.

1.4.2.1

The device

The device consists of two stacked calorimeter chips. Both MEMS calorime-ter chips have a heacalorime-ter and a thermopile on top of a freestanding 2 µm thick silicon nitride (SiN) membrane. The heater is made from p-type polycrys-talline silicon (poly-Si) and is located in the center of the membrane. The thermopile consists of 36 p-polySi/n-polySi thermocouples. The hot junc-tions of the thermocouples are located on the freestanding membrane at 20 µm distance from the heater whereas the cold junctions are located on the frame of the Si chip. The large thermal mass and the good thermal conductance of the Si frame keep the cold junctions at room temperature while the membrane, that has a low thermal conductance, allows the hot junctions to follow the rise in temperature of the heater.

(a) (b) Top device Bottom device Al block Teflon tubes

Figure 1.7: (a) Schematic view of the device XI-318-9. It is shown: the two stacked chips (XI-318 XI-319); the Al block; the Teflon tubes. Not to scale. (b) Bottom side of the Al block.

The liquid sample is isolated between these membranes, which are 300 µm apart. The general idea is to create a liquid volume that is mainly contained between the thin SiN membranes. In this way, a good thermal isolation towards the ambient is obtained. The device is also glued on top of an aluminum (Al) block with a large thermal mass to reduce the thermal drift. An enlarged view of the device is presented in Fig. 1.7a where the two chips glued on top of each other, the Al block and the two Teflon tubes are visible. The Al block has openings aligned to the inlet and outlet of the chip. The liquid sample is injected into the device via a syringe through a Teflon tube that is screwed into the aluminum block inlet and exit from the device through the other Teflon tube. In Fig. 1.7b we show the other side of the measurement setup. We can see the two holes used to mount the Teflon tubes. They correspond to the inlet and outlet of the chip. A third hole in between the two Teflon tubes has been made to avoid a hermetical

1.4 MEMS Calorimeter

11

seal of the cavity underneath the membrane of the bottom chip. The chip is not visible in Fig. 1.7b as it is glued on the other side of the Al block. In order to perform the measurements, the device is inserted inside a Clima Temperatur Systeme (CTS oven T -65/50) and a lock-in amplifier (SR830) is used to apply the signal to the heater and to read the output signal.

Table 1.1: Comparison of liquid calorimeter chips.

Parameter

[36]

[38, 43]

[24, 37]

XI-318-9 [22]

Transfer

[V/W]

1.0

0.75

0.94

11

Volume

[µl]

30

2

0.1

1

Thermal

resistance

[K/W]

10

25

200

1000

Output

resistance

[kΩ]

50

8

200

50

Time

con-stant [s]

0.7

5

0.1

0.5

Noise

[µV]

2.5

3

0.1

2.5

NEP

[µW]

2.5

3

0.1

0.2

1.4.2.2

Sensor Characteristics

The relative Seebeck coefficient αscof the p-polySi/n-polySi thermocouple

is about 300 µV/K at 293 K so, the nominal sensitivity of the thermopile is about 11 mV/K. The transfer of the thermopile was measured varying the power dissipated in the heater. When the device is filled with non-flowing water the transfer is about 11 V/W. With flowing water the transfer value decreases. For 10 µl/min flow the decrease is 2,5 % and at 500 µl/min the transfer is nearly halved. The thermal resistance can be calculated from the values of the measured transfer and the nominal thermopile sensitivity. The calculated thermal resistance is, therefore, 1 kK/W. The time constant is measured by applying heat pulses to the heater and measuring the response

of the thermopile. A value of 0.5 s is found when the device is filled with non-flowing water.

In Table 1.1 we compared a few liquid calorimeter chips with the chip XI-318-9. The transfer [V/W] of this chip is much higher than previously reported chips, while the volume is generally lower. For use with exper-iments where the signal is generated by a volumetric reaction, the power produced in a much smaller volume is proportionally lower. This, however, is to some degree compensated by a much higher transfer, so that the sen-sitivity of the device for volumetric reactions, such as enzyme conversions, is comparable. Much less chemicals are though needed, which can be an advantage when the chemicals are expensive or scarce. The smaller volume also has advantages in refreshing time.

It is important to compare the capability of the devices in reducing the noise. A noise of 2.5 V it is measured in non-flowing water. It is interesting to note that the noise is about the same for all the devices except for the chip presented by Zhang [24, 37].

He measured with glucose at a flow rate of 15 nl/s. The noise was ten times lower, but the Noise Equivalent Power (NEP), defined as the ratio between the noise voltage and the device transfer, is comparable with what we calculated. This is because of the low transfer he measured.

1.5

MEMS TGA

TGA is commonly employed in research but also in the industrial environ-ment to determine degradation temperatures, absorbed moisture content or level of inorganic and organic components in materials. TGA is largely used to study the decomposition points of explosives, and to estimate the high temperature oxidation and corrosion kinetics of materials.

If ThermoGravimetric (TG) measurements have to be performed with a MEMS, then it should schematically consists of:

• a heater to uniformly heat the sample under test.

• a temperature sensor to measure the temperature of the sample under test.

• a membrane to thermally isolate the sample area from the surround-ing.

• the decoupling of the sample mass and temperature dependence of the resonance frequency of the device.

• the device needs an actuator to bring the resonator into vibration and a sensing element for the readout of the device resonance frequency.

1.6 Review of MEMS TGA

13

The working principle of a MEMS TGA device is based on measuring shifts in the resonance frequency of the MEMS resonator, while the sample is heated up, and the sample temperature is recorded. Among the MEMS TGA reported in literature no one is fully integrated but they still rely on an external heater [44] or external piezoelectric actuators [45]. To provide thermal analysis of nanogram samples the MEMS community is facing the challenge to find fully integrated devices for thermogravimetric measure-ments that fulfill the aforementioned requiremeasure-ments.

1.6

Review of MEMS TGA

Several solution for MEMS TGA have been proposed in literature [11,44,45], all based on a cantilever-type microbalance.

In [44] thermogravimetry was demonstrated with the use of two Si can-tilevers clamped on a heater. One cantilever is used as sensor and another as reference. The cantilevers are self oscillating and their resonance frequen-cies are measured with an optical system. The differential measurement minimize the influence on the resonance frequency of noise sources, such as temperature variation and pressure change in the measurement system. Furthermore the optical read out has the advantage that it does not inter-fere with the vibration [46]. The main disadvantage of this solution is that the system can not be integrated.

In the solution proposed by [11] a commercially available piezoresistive cantilever has been employed for thermogravimetry by using the integrated Si piezoresistor as heater, temperature sensor and strain gauge. An ex-ternal piezoelectric actuator is used to activate the device. Whereas the device reaches temperatures as high as 800 K, the decrease of the piezore-sistive coefficient of the strain gauge limits the useful temperature range. The proposed solution makes the determination of the sample temperature problematic since the temperature read out is an average of the overall de-vice temperature. Also in this case the choice of a Si dede-vice makes the resonance frequency of the device strongly temperature dependent.

A cantilever hot-plate with independent mass sensing has been pre-sented in [45]. The microcantilever hot plate has an integrated heater and integrated temperature-compensated strain-sensing piezoresistors. Also in this case Si is chosen as the material for the cantilever. The activation of the cantilever is realized with an external piezoelectric actuator.

Despite the presence in literature of different solutions for MEMS TGA all of them have to deal with a strong temperature dependence of the reso-nance frequency. Furthermore, none of them is fully integrated.

1.7

Research objective

The aim of the work presented in this thesis is the design, fabrication and calibration of a fully integrated TGA device in MEMS technology for in-spection of nano-masses.

The primary goal is the design and fabrication of a fully integrated MEMS TGA with low temperature sensitivity of the resonance frequency. The device consists of a cantilever paddle with integrated thermal actuators and mass detector. In order to achieve low temperature sensitivity of the resonance frequency, a Low Pressure Chemical Vapor Deposition (LPCVD) SixNy (with x/y ≈ 1) cantilever paddle is designed and fabricated as

sens-ing element. The choice of SiN (thermal conductivity Co = 3.2 [K/W]) as a structural layer improves the thermal isolation between the heated sam-ple area and the part of the device where most of the mechanical energy is stored, thus overcoming the weaknesses of solutions where Si, (thermal conductivity Co = 150 [K/W]) is used for the sensing cantilever [45].

For the actuation of the device, integrated thermal actuators, but sep-arate from the sensing cantilever paddle, are chosen. During actuation the heat does not easily transfer to the sensing cantilever, thus the thermal cross-talk is reduced compared to solutions where the thermal actuators are on the sensing cantilever [47].

The secondary goal of the research presented in this thesis is the demon-stration of a method for the temperature calibration of the MEMS calorime-ter UFS1 developed for the new commercially available differential scan-ning calorimeter (DSC),the Flash DSC1 of Mettler-Toledo. The calibration method allows to use devices with uncalibrated heater resistance in the tem-perature range from 208 K to 723 K with a typical maximum error of ± 5 K. The calibration method consists of two steps: 1) Isothermal calibration of the main heater resistance and calibration of the thermopile sensitivity; 2) Calibration accuracy determination with primary standards of which the phase transitions are often fixed or defined International Temperature Scale 1990 (ITS-90) points.

1.8

Structure of the thesis

In this thesis, a MEMS device for TGA measurements based on a cantilever structure and a calibration method for MEMS calorimeters are presented.

In Chapter 2 the issue of the temperature dependence of the resonance frequency of cantilevers is addressed. First a theoretical study, supported by simulations, is carried out to determine the temperature dependence of the resonance frequency of cantilever beams with non-uniform temperature

1.8 Structure of the thesis

15

distribution along their length. The resonance frequency shift of a locally heated cantilever beam is calculated when a temperature gradient is present along its length. As confirmation of the theoretical results, measurements of the frequency shift for a SiN cantilever paddle are shown.

The design requirements for the TGA sensing cantilever and thermal actuators are listed in Chapter 3. The concept of bimorph thermal actu-ators is presented together with the heat transfer model for the actuator. A bimorph thermal actuator separated from the sensing cantilever, which reduces the problem of temperature increase on the sensing cantilever, is proposed. The chapter ends with the fabrication process of the TGA de-vice. From this study it can be concluded that the TGA device requires a SiN cantilever paddle as sensing cantilever and two bimorph actuators sep-arated from the sensing cantilever and connected to it through SiN tethers. In Chapter 4 a method for the temperature calibration of MEMS calorime-ter is presented. This method combines electrical calibration and calibration with primary standards. The proposed method allows to use devices with uncalibrated heater resistance in the temperature range from 208 to 723 K with a typical maximum error of ± 5 K.

Chapter 5 contains the calibration results of the MEMS TGA. The methods for mass, temperature and frequency calibration are presented. The performance of the MEMS TGA in terms of mass sensitivity is inves-tigated.

Chapter 6 contains the TGA experimental results. Three different sam-ples: PA6, paraffin and CuSO4·5H2O are used to show the performance of

the MEMS TGA.

The conclusions and recommendations for further research are presented in Chapter 7. A new design for higher heater temperatures of the MEMS TGA is proposed. The new proposed design minimizes the displacement difference between the different points on the proof mass.

Chapter 2

Cantilever resonators

2.1

Introduction

As already mentioned in Chapter 1 the MEMS TGA device presented in this thesis schematically consists of a cantilever paddle with integrated thermal actuators.

To perform a TGA measurement the resonance frequency of the can-tilever paddle has to be measured while the sample to analyze is heated by the integrated heater, located on the paddle of the cantilever. Because of the heater temperature increase the cantilever paddle is subject to a tem-perature gradient along its length. The cantilever paddle properties that are temperature dependent can be influenced by the temperature gradient on the cantilever.

Since the resonance frequency of an unloaded cantilever paddle, or more in general of a cantilever, is determined by its elastic modulus, density and geometry that are temperature dependent properties, the temperature gradient on the cantilever can influence the resonance frequency.

The dependence of the resonance frequency of cantilever beams and other resonators with the ambient temperature is reported in literature and techniques are proposed to minimize this dependence [48–52].

Dependence of the resonance frequency of cantilever beam with the average temperature along the cantilever has also been shown in literature. The variation of the resonance frequency of Si cantilevers with the average temperature on the cantilever is reported in [53].

Theoretical studies and measurements have also been performed on Si cantilevers subjected to a linear temperature distribution along their length [54].

In practice, for cantilever beams locally heated at their tip, for instance with an integrated heater or with a laser, the temperature distribution along the length of the cantilevers is non-linear [55]. For this reason it is of interest to understand how the temperature dependence of the resonance frequency relates to the non-linear temperature profiles on the cantilever.

In the first part of the chapter the theoretical evidence of the depen-dence of the resonance frequency of cantilever beams on temperature is pointed out. The resonance frequency is then calculated for locally heated cantilever beams. The analysis continues with the calculations of the tem-perature profile along the beam. To simulate different temtem-perature profiles, three cantilevers with equal dimensions but made of different materials: Si, LPCVD SiN and silicon dioxide (SiO2) respectively, have been considered

for the analysis. To validate the theoretical results, Finite element (F.E.) simulations have been performed. From F.E. simulations it appears that SiN is the better choice for the fabrication of the MEMS TGA device. The device made in SiN is therefore selected for further analysis.

The temperature distribution along the SiN MEMS TGA is measured and the results compared with the theoretical analysis and with the sim-ulations. The last part of the chapter contains measurements of the tem-perature dependence of the resonance frequency performed on a SiN device made for TGA.

2.2

Cantilever beam resonance frequency

The resonance frequency of an initially flat rectangular thin cantilever beam can be derived by solving the following homogeneous undamped equation [56]: EI∂ 4_{y(x, τ )} ∂x4 = −ρS ∂2_{y(x, τ )} ∂τ2 (2.1)

where E is Young’s modulus of elasticity, I is the moment of inertia of the cantilever, y is the transverse displacement of the beam, ρ is the mass density, and S is the cross-sectional area of the cantilever.

To solve this fourth order differential equation four conditions are needed. The boundary conditions for a cantilever beam of length L clamped at x = 0 and free at x = L are here considered. The deflection and the slope are zero at x = 0 and the bending moment and the shear force are zero at x = L: y(0) = 0, y′_{(0) = 0 for the clamped end and y}′′_{(L) = 0, y}′′′_{(L) = 0 for the}

free end.

With these boundary conditions the resulting mode shapes yn(x) of a

2.3 Temperature dependence of cantilevers resonance

frequency

19

yn(x) = cosh( βnx L ) − cos( βnx L ) − Cn[sinh( βnx L ) − sin( βnx L )] (2.2) where βn and Cn are integration constant determined by the boundary

conditions. For the first mode βn=1.875 and Cn = 0.734.

The natural frequency is calculated as: f = 1 2π s k mef f (2.3) where k is the spring constant and mef f is the effective mass of the

can-tilever beam. For a cancan-tilever beam having a rectangular cross section, it becomes:

mef f= 0.24mC (2.4)

where mC is the mass of the cantilever.

2.3

Temperature dependence of cantilevers

res-onance frequency

The temperature dependence of the natural frequency of a non-damped cantilever beam with a rectangular cross section can be calculated from Equation (2.3): f (T ) = 1 2π s E(T )t(T )2 0.96L(T )4_{ρ(T )} (2.5)

where the temperature dependence of the parameters t and L, thickness and length of the cantilever, respectively, has been explicitly highlighted.

Considering that both t and L, subjected to thermal expansion, are pro-portional to (1 + α∆T ), and being the density propro-portional to (1 + α∆T )−3

the resonance frequency results to be proportional top(1 + α∆T ), where α is the thermal expansion coefficient of the material. Taking into account also the temperature dependence of Young’s modulus, for cantilever beams with uniform temperature distribution along their length the temperature dependence of the resonance frequency can be calculated as:

ST = df f dT ≈ α 2 + dE 2EdT (2.6)

Table 2.1 lists the theoretical ST for the cantilever materials considered

Table 2.1: Thermal properties of Si, SiO2and SiN. The reported

ST values are calculated using Equation 2.6.

material

α

Co

E

TCE

1

S

T

[ppm/K]

[W/mK]

[GPa]

[ppm/K]

[ppm/K]

Si

2.6

150

201

-60*

-28.7

SiO

2

0.5

1.4

75

+195.8*

+98.2

SiN

3.3

_≈2**

200

-48***

-22.4

* [58], **Value measured for 1µm tick SiN [59] ***Value measured

for Si

3

N

4

[60].

Young’s modulus (T CE1) is indicated too. In Table 2.1 the literature values

for Si and SiO2 are reported.

Young’s modulus for the SiN layer is measured. The measurements are realized with the method presented in [61] extending the temperature range up to 373 K. The measurements are performed on a wafer with 1.5 µm thick SiN.

Table 2.2: SiN Young’s modulus measured for temperature rang-ing from 293 K to 373 K.

Temperature

Young’s modulus

[K]

[GPa]

298

_{200 ± 20}

323

_{222 ± 50}

348

_{193 ± 3}

373

_{181 ± 16}

The wafer is placed on an hot plate and Young’s modulus measured in the temperature range from 293 K to 373 K with a step of 25 K. The measurement setup limits the use of higher temperatures.

At each temperature two structures are measured. The measured values are reported in Table 2.2 together with their standard deviation. Looking at the results there is no clear temperature dependence of Young’s modulus for temperatures up to 373 K.

Similar results are obtained in [60] for Si3N4-based ceramics in the same

temperature range. No temperature dependence of the Si3N4Youngs

2.3 Temperature dependence of cantilevers resonance

frequency

21

the E occurs for temperature from 423 K up to ≈ 1300 K giving a T CE ≈ -48 [ppm/K]. A steep decrease occurs above that temperature. This steep decrease corresponds to the decrease of the material strength [60].

For the theoretical calculations performed in this thesis the value of the T CE measured in [60] for Si3N4is used as reference value for the SiN layer.

Looking at the values reported in Table 2.1 it can be seen that the largest contribution to ST is the second term in Equation (2.6) that is the

variation of the E with the temperature. The highest ST is shown by the

cantilever beam made of SiO2.

For cantilever beams with non-uniform temperature distribution along their length, Equation (2.5) can not be used since the material properties as well as the sizes of the cantilever are functions of the temperature, and therefore of the coordinate along the cantilever length (x). To make the the calculation reading easy, the coefficient E(x) will still be called Young’s modulus.

To calculate the temperature dependence of the resonance frequency, the resonance frequency has to be recalculated since Young’s modulus is now function of the coordinate x. Neglecting the temperature dependence of the cantilever beam dimensions, that is neglecting the change of the beam dimensions due to thermal expansion [62], Equation (2.1) can be rewritten as follows: ∂2_EI ∂x2 ∂2_y ∂x2 = −ρS ∂2_y ∂τ2 (2.7)

By taking the deflection of the beam while vibrating in the form of:

y = Y ejωτ _(2.8)

where Y determines the mode of vibration, Equation (2.7) becomes: ∂2_EI

∂x2

∂2_Y

∂x2 = ρSω

2_{Y (2.9)}

that is a differential equation with non-constant coefficients. For a linear distribution of the temperature along the cantilever beam Equation (2.9) has been solved in [54] expressing the coefficients in polynomial variation form, from which the fundamental solutions based on a power series can be obtained. A simpler approach is given by the method of Ritz-Raileigh used here to calculate an approximate value of the resonance frequency [56].

This method requires to calculate the maximum potential and maximum kinetic energy. The maximum potential and maximum kinetic energy are:

EP = 1 2 Z l 0 EI d 2_Y dx2  dx (2.10)

EK = ω2 2ρ Z l 0 SY2dx (2.11)

By equating the potential and kinetic energies, the angular frequency is obtained: ω2=I ρ R0 LE( d2_Y dx2)2dx R0 LSY2dx (2.12) The exact solution of the frequency will be the one for which the left side of Equation 2.12 is minimized. To obtain instead the approximated solution, the shape of the deflection curve Y has to be taken in the form of a series. The series is chosen to match the conditions at the ends. It is wise to use a deformed shape that is analytically similar to the expected solution. The chosen function is:

G(x) = (x2+ 6L2_{− 4Lx)/24} (2.13) multiplied by the series x2_{, x}4_{, ... . The approximated value of the resonance}

frequency for a cantilever beam with E=E(x):

f (T (x)) = 0.01 v u u t RL 0 E0(1 − T CE1(T − T∞))wt3 d 2_G(x)2 dx2 dx RL 0 SG(x)2dx (2.14) where w is the width of the cantilever and T∞ is the ambient temperature.

The shift of the resonance frequency due to temperature variation along the cantilever beam has to be calculated for each specific temperature distri-bution along the cantilever beam. Therefore it is necessary to calculate first the temperature distribution along the cantilever beam and then calculate the frequency using Equation 2.14.

2.4

Temperature distribution on a cantilever

beam

In this section the temperature distribution along three cantilever beams having the same dimensions and showing the same temperature difference ∆T at their ends but made of different materials is calculated. Then, with the support of F.E. simulations the thermal drift of the resonance frequency is shown for the three cantilever beams analyzed.

A cantilever beam with the following dimensions is considered: L = 280 µm and w = 60 µm, and t = 1 µm, where L, w and t are the length, the width and the thickness of the cantilever beam, respectively. The cantilever

2.4 Temperature distribution on a cantilever beam

23

Figure 2.1: Schematic of a cantilever beam with an integrated heater at its tip (Drawn not to scale).

is heated by an integrated heater. The length and width of the heater are Lh = 40 µm and wh = 60 µm , respectively. The heater temperature is

assumed to be uniform and equal to T (Lh), therefore the heat equation is

calculated only for Lh<x <L. A schematic of the cantilever beam is given in

Fig. 2.1. 300 350 400 450 500 40 90 140 190 240 290

Distance from cantilever free end [µm]

T e m p e ra tu re [ K] Si SiN SiO2

Figure 2.2: Calculated temperature distribution along the can-tilever length. Three different temperature profiles are found for the cantilevers made of Si, SiN and SiO2 respectively.

In order to calculate the temperature distribution in the cantilever beam the following assumptions are made: the ambient temperature is uniform and constant; the frame of the cantilever beam is at ambient temperature; the system is in a steady state condition, which means that the temperature is constant over time; the temperature in the cantilever beam is uniform in the y-direction. Furthermore it has been assumed that the heater temper-ature is uniform over the integrated heater. Under these assumptions the

heat equation is: d2_{(T − T} ∞) dx2 + ǫ(T − T∞) = 0 (2.15) with ǫ = ηCog Cobst (2.16) where ǫ represents the heat lost through the surrounding gas (air), T_∞ is the ambient temperature, Cog and Cob are the thermal conductivity of the

gas (air) at ambient pressure and the beam respectively . The term t in Equation (2.15) is the thickness of the cantilever beam and s represents the gap between the cantilever beam and the substrate. The parameter η is the correction factor that accounts for the fringing of the heat flux through the gap (typically close to one) [63]. The general solution of Equation (2.15) is:

T − T∞= C1e √ ǫx_{+ C} 2e− √ ǫx _(2.17)

with C1and C2constants determined applying the following boundary

con-ditions:

• T (Lh) = Th

• T (L) = T∞

It has been assumed that the temperature Th is known. The

tempera-ture distribution along the length of cantilever beams made of Si, SiN and SiO2 respectively have been calculated in order to simulate three different

temperature profiles. Fig. 2.2 shows the temperature trends for the three considered cases with T∞ = 300 K and Th = 500 K . The Si cantilever

beam shows an almost linear profile of the temperature. If the average is performed on the calculated temperatures, the Si cantilever shows the high-est value of average temperature. The smallhigh-est one is shown by the SiO2

cantilever beam that, compared to Si and SiN, is the material with a lower thermal conductivity.

Once the temperature distribution along the cantilever length has been calculated, it is possible to determine the resonance frequency per each temperature distribution along the cantilever length using Equation 2.14. The calculations are shown in the next section.

2.5

Temperature dependence of MEMS TGA

resonance frequency

To perform a thermogravimetric measurement with a MEMS TGA based on a cantilever beam, the resonance frequency of the device loaded with

2.5 Temperature dependence of MEMS TGA resonance

frequency

25

the sample to be analyzed is measured at different sample temperatures. Knowing the relation between the cantilever resonance frequency and the sample mass, it is possible to determine the thermogravimetric curve.

The TGA measurements relying on the property of the cantilever res-onance frequency to be sample mass dependent. The temperature depen-dence of the resonance frequency do not have to be forgotten during the measurements.

Minimization of the temperature dependence of the cantilever resonance frequency is possible during the design of the MEMS TGA.

To keep the fabrication process simple and suitable for mass produc-tion the possible structural material is chosen between: Si, SiO2 and SiN,

as these layers are generally available in most conventional IC fabrication processes. A theoretical analysis is performed in order to choose the mate-rial that minimizes the temperature dependence of the cantilever resonance frequency. The results are shown in Fig. 2.3 and explained in more details later in this section.

About the cantilever dimensions, together with the need to minimize the temperature dependence of its resonance frequency, some considerations about its final use and its sensitivity need to be done.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 SiO2 Si SiN Material (f -f∞ )/ f ∞ [ % ] L=100 μm

Figure 2.3: Fractional resonance frequency change at T = Th =

950 K respect to its value at ambient temperature (f_∞) as function of the cantilever structural material. The calculations are made for cantilevers beam 100 µm long.

The minimum possible size of the cantilever is dictated by the required final applications of the device. The device has indeed to be used by an operator that has to manually load nanogram amounts of sample on the

integrated heater of the MEMS TGA. For this reason the heater dimensions have been chosen to be Lh = 40 µm and wh = 120 µm that is about the

size of 1 ng of a 2 µm thick layer of polyamide 6 (PA-6), standard material for TGA instruments calibration. The minimum length of the cantilever is therefore chosen to be Lm = 100 µm, a bit bigger than the double of

the heater length. This makes it easy to place the heater and the sensing elements on the cantilever. The minimum cantilever width is instead wm=

wh= 120 µm.

Using Equation 2.14 and the results obtained in section 2.4, the reso-nance frequency shift of cantilevers made of Si, SiO2 and SiN, respectively,

and with a length Lm, width wm and 1 µm thick, are calculated. In the

calculations, the heater temperature Th is chosen to be equal to the

maxi-mum temperature required by the specifications for the design of the MEMS TGA, that is 950 K, see Chapter 3. The ST used in the calculations are the

ones reported in Table 2.1. The theoretical results obtained using Equation 2.14 are reported in Fig. 2.3.

The SiN shows the smallest frequency variation compared to the other two solutions and it appears to be the best choice for a TGA device. Mul-tilayers, like the combination of Si and SiO2, are also used in literature to

reduce the ambient temperature dependence of the cantilever beams reso-nance frequency [64], but they are not considered in this work.

0 0.5 1.0 1.5 50 100 150 200 250 300 350 400 450 500 Cantilever length [µm] (f -f∞ )/ f ∞ [ % ] SiO2 Si SiN

Figure 2.4: Fractional resonance frequency change at T = Th =

950 K respect to its value at ambient temperature (f_∞) as function of the cantilever length for SiO2, Si and SiN cantilevers. The

cantilevers are considered to have a width w = 120 µm and a thickness t = 1 µm.

2.5 Temperature dependence of MEMS TGA resonance

frequency

27

The temperature dependence of the resonance frequency for a SiN tilever has been further investigated for different lengths of the SiN can-tilever. Fig. 2.4 shows the temperature dependence of the cantilever reso-nance frequency on the cantilever beam length, calculated using Equation 2.14.

Let’s associate a mass mf to the resonance frequency shift due to the

temperature gradient on the cantilever length. The mass mf can be

calcu-lated once the mass change sensitivity is known.

By assuming that the spring constant is not affected by an added sample mass, and differentiating Equation 2.3 with respect to the mass m, the minimum detectable sample mass ∆m is derived as follows:

    ∆m mC     = 2∆f f_∞ → ∆m ∆f = 2 mC f_∞ (2.18) where ∆m

∆f is the mass change sensitivity of the cantilever, mC is the

cantilever mass calculated from the material density and cantilever geome-tries, ∆f here indicates the minimum detectable frequency shift, and f_∞is the cantilever frequency calculated at ambient temperature, when no tem-perature variation is present along the cantilever length.

Table 2.3: The theoretical resonant frequency and mass change sensitivity for SiN cantilevers with different length but with the same width w = 120 µm and thickness t = 1 µm. The mass mf associated with the resonance frequency shift due to the

tem-perature dependence of the cantilever resonance frequency is also shown. Considered heater temperature Th= 950 K.

L [µm]

f

0

[Hz]

∆m_∆f

[pg/Hz]

m

f

[pg]

100

122341

0,6

227

150

54374

1,9

156

200

30585

4,5

94

250

19574

8,7

54

300

13593

15,1

31

500

4894

69,9

5

In Table 2.3 the values of detectable mass change per frequency are given for different cantilever length. It is obvious from the table that the mass change sensitivity is increased by miniaturizing the cantilever.

By multiplying the mass change sensitivity with the resonance frequency shift, due to a temperature variation across the cantilever length of ∆Tmax

= 950 - 300 = 650 K, it is possible to determine the mass mf that would

correspond to the resonance frequency shift. Or, in other words it is possible to determine the mass change resolution of the MEMS TGA for ∆Tmax.

A compromise between the mass change sensitivity and the temperature dependence of the resonance frequency has to be made.

Let’s assume that a sample mass change resolution in the order of 300 pg is needed for the MEMS TGA, and let’s assume a frequency resolution of 1 Hz. For a 300 µm-long cantilever the mass mf represents about the 10

% of the total mass change.

The mass mf for the fabricated MEMS TGA device is expected to be

higher than the calculated value. In fact, the MEMS TGA device is a mul-tilayer structure with an integrated heater, temperature sensor and sensing element, and the temperature dependence of the resonance frequency will be different from the one reported in Table 2.1. In fact, the temperature de-pendence of the resonance frequency is -150 ppm/K (instead of -48 ppm/K), for a Si3N4 cantilever beam covered by 160 nm of Au [48] .

2.6

Temperature distribution along cantilever

paddles

2.6.1

Simulation

In this section the temperature distribution on the cantilever paddle is sim-ulated for different temperature profiles along its length. Simulations are performed with COMSOL using the model: AC/DC; heat transfer by con-duction and structural mechanics.

A picture of the simulated device is shown in Fig. 2.5.

The simulated device is a cantilever paddle with an integrated heated located on the paddle. To simulate different temperature profile three can-tilever paddles made of Si, SiN and SiO2respectively, are considered. The

goal of the simulations is to validate the theoretical calculations made for cantilever beam in section 2.4.

Fig. 2.6 shows the simulated temperature distribution for Si, SiN and SiO2cantilever paddle. The heater temperature is not uniform on the heater

area, as assumed in the theoretical analysis. This does not affect the theo-retical results obtained for the resonance frequency shift of the considered cantilever paddles. Indeed the same theoretical resonance frequency shift as for constant heater temperature is obtained if the experimental data of the heater temperature reported in section 2.6.2 are fitted with a 5th order polynomial and used in the calculations.

2.6 Temperature distribution along cantilever paddles

29

Figure 2.5: COMSOL simulation for the temperature distribu-tion on a SiN cantilever paddle.

300 350 400 450 500 550 0 50 100 150 200 250 300

Distance from cantilever free end [µm]

T e m p e ra tu re [ K] Si SiN SiO2

Figure 2.6: Simulated temperature distribution along cantilever paddles made of Si, SiN and SiO2 respectively. Simulations are

performed with COMSOL using the model:’AC/DC; heat transfer by conduction and structural mechanics’.

Respect to the simulations, the lower temperature obtained for the cal-culated temperature distribution of a SiN cantilever paddle (see Fig. 2.7) can be mainly attributed to the use of a constant thermal conductivity of the air.

The simulations confirm the theoretical results that the cantilever pad-dle made in Si shows the highest average temperature compared to the other two cantilevers.

In the next paragraph the simulated and theoretical values are compared with the measurement results obtained for a SiN cantilever paddle.

2.6.2

Measurements

The temperature distribution along a SiN cantilever fabricated for TGA is measured [65] with an infrared camera. The ambient temperature is kept constant while the temperature of the integrated heater increases. Fig. 2.7 shows a thermal map obtained for the TG device when the heater is biased at 8 V.

The infrared thermo-camera was equipped with a focal plane array (FPA) of 320×256 InSb sensors sensitive in the 3-5 µm wavelength range.

2.7 Resonance frequency measurements

31

453 K 473 K 493 K 513 K 533 K 553 K 573 K CUT

Figure 2.7: Measurement made with an infrared thermo-camera equipped with a focal plane array (FPA) of 320 256 InSb sensors sensitive in the 3-5 µm wavelength range.

The spatial resolution is about 6 µm while noise equivalent temperature difference (NETD) is estimated to be 0.5 K.

Fig. 2.8 depicts the measured temperature along the ideal cut visible in Fig. 2.7.

The measured temperatures along the length of the cantilever together with the calculated temperature profile for a SiN cantilever are shown. In the curve showing the measured temperature, the temperature increase near the fixed end of the cantilever is due to the thermal cross talk of the thermal actuators biased at 1.5 V. The simulated temperature profile along the length of a cantilever paddle is also included in Fig. 2.8.

2.7

Resonance frequency measurements

The measurements of the dependence of the resonance frequency on the temperature of the integrated heater are performed on a SiN cantilever. A detailed description of the device together with a 3D-drawing can be found in Chapter 3. Here only a brief description of the device is presented, followed by the experimental results.

300 350 400 450 500 550 0 50 100 150 200 250 300

Distance from cantilever free end [µm]

T e m p e ra tu re [ K ] Measured Calculated F.E. simulation

Figure 2.8: Measured, simulated and calculated temperature dis-tribution along the cantilever paddle when 8 V and 1.5 V are ap-plied to the heater and the actuators, respectively. The measure-ments are carried out with an infrared camera [62].

2.7.1

Device

The sensor consists of a 283 µm long LPCVD SixNy (with x/y ≈ 1)

can-tilever paddle, which is the sensing cancan-tilever, and two membranes arranged symmetrically on both sides of the cantilever paddle, see Chapter 3 Fig. 3.1. A piezoresistor, located near the clamped side of the cantilever paddle, is used as strain sensor. A compensation resistor is located outside the can-tilever paddle and is designed to be identical to the strain sensor. A heater is present at the cantilever free end. The LPCVD poly-silicon (polySi) heater on the paddle covers the sample area of 128 µm x 38 µm. The heater temperature can be measured by the p-polySi/n-polySi thermocouple with an estimated sensitivity at room temperature of about 0.5 mV/K. The two membranes form the thermal actuators. The thermal actuators are based on a bimorph structure of SiN and Au layers heated up by n-polySi resistor heaters.

2.7.2

Measurements

First, the resonance frequency of the devices was measured without tip heat-ing. A schematic drawing of the measurement setup is shown in Chapter 6, Fig. 6.1. The devices were mounted on a dedicated holder and a lock-in amplifier (SR830) was used to excite the device and to read out the

out-2.7 Resonance frequency measurements

33

-160 -140 -120 -100 -80 -60 -40 -20 0 20 40 0 370 470 570 670 770 870 970 Temperature [K] Device 1 Device 2 Device 3 Device 4 Δ f [H z ]

Figure 2.9: Measured resonance frequency variation as function of the heater temperature for four devices belonging to the same wafer.

put of the Wheatstone bridge. The measurements were remote controlled with a LabView program. The resonance frequency was then measured applying increasing voltages on the heater resistor. In Fig. 2.9 the reso-nance frequency variation as function of the heater temperature is shown for four different devices. The non-linear response could be explained by the different thermal expansion coefficients of the materials that make up the cantilever paddle [48].

With a close look to the graph it is possible to see that it can be divided into two reproducible distinct areas: below and above 590 K.

In the temperature range from 290 K to 590 K no change of the res-onance frequency is measured, within the measurements error, for all four devices.

Above 590 K, i.e. for heater temperatures going from 590 K to 920 K, Fig. 2.9 reports a temperature dependence of the resonance frequency. In Fig. 2.9 it can be seen that the resonance frequency variation shows a step function like behavior. The presence of the steps in the measured resonance frequency variation could be caused by the step increase of the heater temperature. Indeed a step function voltage is applied to bias the heater. 14680 14700 14720 14740 14760 14780 14800 14820 14840 14860 290 390 490 590 690 790 890 Temperature [K] F re q u e n c y [ H z ] Meas 10 Meas 9 Meas 8 Meas 7 Meas 6 Meas 5 Meas 4 Meas 3 Meas 2 Meas 1

Figure 2.10: Ten repeated measurements of the resonance fre-quency of a TGA device as function of the heater temperature. Assuming a linear dependence of the resonance frequency with the heater temperature [58,62,66] committing a maximum approximation error of 18 Hz, a first order temperature coefficient of the resonance frequency

2.8 Conclusions

35

of about 20 ppm/K is calculated in the temperature range from 590 K to 920 K. The good repeatability of the measurements is shown in Fig. 2.9. The ten measurements are shown to overlap to each other below 590 K. Above this temperature and below 850 K a maximum deviation of 40 Hz is measured. The deviation between the measurements increases to 60 Hz for temperatures above 850 K. Using the mass sensitivity calculated in Chapter 5, a deviation of 60 Hz would corresponds to a mass deviation of 0.35 ng.

Using the mass sensitivity calculated in Chapter 5 a frequency shift of 100 Hz corresponds to a mass resolution of ±0.28 ng at ambient tempera-ture.

2.8

Conclusions

In this chapter the temperature dependence of the resonance frequency for a locally heated cantilever beam has been investigated. The resonance fre-quency for cantilever with uniform and non-linear temperature distribution along the cantilever length has been calculated. For the case of uniform temperature distribution along the cantilever beam the calculated resonance frequency is differentiated with respect the temperature and the tempera-ture dependence of the resonance frequency ST is calculated. ST is shown to

be mainly dependent on the variation of E with the temperature, as already found by other research groups. Cantilever beams made of SiO2are showing

the highest temperature dependence of the resonance frequency compared with cantilever beams made of SiN or Si. Different is the case for non-linear temperature distribution along the cantilever length.

If a non-linear temperature profile is present along the cantilever beam the temperature dependence of the resonance frequency has to be calculated at each temperature profile. For this reason the temperature profiles along the cantilever length have been theoretically calculated and simulated con-sidering three cantilevers with equal dimensions but made of Si, SiN and SiO2, respectively. The temperature dependence of the cantilever resonance

frequency can be then calculated and the results indicates that cantilever beams made of SiN or SiO2 have a smaller temperature dependence of the

resonance frequency compared to cantilever made of Si. The theoretical results are applied to find the size and the structural material for a MEMS TGA that minimize the temperature dependence of the resonance frequency. Measurements of the temperature distribution along a SiN cantilever paddle are also shown to validate the theoretical results. In addition it was found that the resonance frequency of a cantilever pad with a total length of 280 µm is constant with the heater temperature in the temperature range from 290 K to 590 K. The device exhibits a temperature dependence of the

resonance frequency of about 20 ppm/K, for heater temperature from 590 K to 920 K.

The results obtained on the resonance frequency temperature depen-dence of cantilever beams together with the design requirements are used for the design of the MEMS TGA, shown in the next chapter. After a short introduction of the state of the art MEMS TGA, the fabricated MEMS TGA is presented in detail. The sensing cantilever and the thermal actu-ators layout is analyzed. F.E. simulations are performed in order to find a good match between the activation of the sensing cantilever and a low thermal cross talk. The fabrication process for the fully integrated MEMS TGA is also shown.

Chapter 3

MEMS

ThermoGravimetric

Analysis device

3.1

Introduction

TGA instruments measure the amount and rate of change in the mass of a material as a function of temperature or time in a controlled atmosphere. As discussed in the introduction, often TGA has to be performed on sam-ples with mass smaller than a microgram. Miniaturization of the measuring device to improve sensitivity and response time is therefore essential. The high performance of MEMS, in particular the high sensitivity and short ther-mal response times of cantilever-based techniques, makes them suitable for TGA devices for sample masses in the nanogram range. Cantilever devices have been successfully used as mass sensors reaching resolution of attogram (10-18_{g) [67] and recently zeptogram (10}-21_{g) resolution was attained with a}

nanomechanical resonator [68]. The sensing principle of resonator mass sen-sors is based on measuring the shift in resonance frequency of the resonator upon loading samples on the sensor. Moreover cantilever devices allow to perform TGA of thin-film materials directly deposited on the device [25].

In general a MEMS TGA device can be described as composed by: (1) a resonator; (2) an actuator (3) a resonance frequency sensing element (4) a temperature sensor and (5) a heater. Different solutions have been proposed in the literature in order to perform TGA measurements. These TGA devices are based on a cantilever actuated with an external actuator