Designing Bulk Acoustic Wave Resonators for Parametric Ampliﬁcation of Spin Waves

AN ABSTRACT OF THE THESIS OF

Pratim Chowdhury for the degree of Master of Science in Electrical and Computer Engineering presented on November 12, 2013.

Title: Designing Bulk Acoustic Wave Resonators for Parametric Ampliﬁcation of Spin Waves

Abstract approved: Pallavi Dhagat

Spintronics is an emerging field of research dealing with devices that can potentially exploit the additional degree of freedom provided by the electron spin along with or instead of the con ventional electronic charge. One of the most promising aspects of spintronics is the potential use of magnetostatic spin waves as information carriers in logic devices, where information is encoded in the electron spin. A major obstacle in making this a practically viable alternative to conventional electronics is the very large intrinsic spin wave damping in most known magnetic materials. In this work, we propose a new technique of parametrically amplifying spin waves by means of acoustic resonators. An equivalent electrical model of an acoustic resonator was de veloped to efficiently design the acoustic resonators for the desired frequency ranges. Backward volume magnetostatic spin waves were measured in Yttrium Iron Garnet films at frequencies of 1.7 GHz or higher, requiring acoustic resonators to be designed for at least 3.4 GHz or higher for parametric amplification. Acoustic resonators with resonance frequency of 4 GHz were fab ricated. ©c Copyright by Pratim Chowdhury November 12, 2013 All Rights Reserved Designing Bulk Acoustic Wave Resonators for Parametric Amplification of Spin Waves

Pratim Chowdhury

A THESIS

submitted to

Oregon State University

in partial fulﬁllment of the requirements for the degree of

Master of Science

Presented November 12, 2013 Commencement June 2014 Master of Science thesis of Pratim Chowdhury presented on November 12, 2013.

APPROVED:

Major Professor, representing Electrical and Computer Engineering

Director of the School of Electrical Engineering and Computer Science

Dean of the Graduate School

I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request.

Pratim Chowdhury, Author ACKNOWLEDGEMENTS

I would like to express my gratitude and utmost respect for my major advisor, Prof. Pallavi Dhagat. It has been a wonderful experience being her student and I would like to thank her for the unwavering support that I have received from her throughout the past two years. It is with great delight and excitement that I look forward to continuing my research under her beyond this Masters degree. I would also like to thank Prof. Albrecht Jander, whose continued encouragement and innovative ideas have contributed majorly to the progress in this project. I would like to thank my fellow magnetics lab members Ben Buford, Weiyang Li and Han Song - who have been responsible for sharing a good number of ideas for taking this work forward. They are truly few of the best lab mates one can ever ask for, and working with them continues to be a tremendous source of joy and inspiration for me as a researcher. And ﬁnally, I would like to thank my family and friends, without whose support, none of this would ever have been possible in the ﬁrst place. TABLE OF CONTENTS Page

1 Introduction 1 1.1 Motivation ...... 1 1.2 Parametric Ampliﬁcation ...... 2 1.2.1 Parametric Ampliﬁcation of Spin Waves by Acoustic Energy . . . . . 4 1.3 Bulk Acoustic Wave resonator ...... 6 1.3.1 High Overtone Bulk Acoustic Wave Resonator ...... 7 1.4 Thesis Organisation ...... 7

2 Literature Review 9 2.1 Equations of motion of acoustics ...... 9 2.1.1 Tensor Notation ...... 11 2.2 Piezoelectricity ...... 12 2.2.1 Piezoelectricity in one dimension ...... 14 2.2.2 Piezoelectric Materials ...... 16 2.3 Zinc Oxide Thin Film Deposition Techniques ...... 17 2.3.1 Sputtering ...... 18

3 Modeling and Fabrication of Acoustic Resonators 20 3.1 Transmission Line Model of a Non-piezoelectric slab ...... 20 3.2 Equivalent Electrical Model of a Piezoelectric Slab ...... 22 3.3 Comparison between measurement and simulation of BAW resonators ...... 26 3.4 Choice of materials for acoustic stack of Bulk Acoustic Wave resonator . . . . . 27 3.4.1 Piezoelectric ...... 27 3.4.2 Electrodes ...... 27 3.5 Fabrication of BAW Resonators ...... 31 3.5.1 Bottom Electrode ...... 32 3.5.2 Piezoelectric layer ...... 33 3.5.3 Top Electrode ...... 33 3.6 Effect of Oxygen Partial Pressure on Properties of Zinc Oxide Films ...... 33

4 Experimental Results and Discussion 36 4.1 Spin Wave Measurements ...... 36 4.2 Simulation and Measurement of Bulk Acoustic Wave Resonators ...... 37 TABLE OF CONTENTS (Continued) Page

4.3 Measurement of Vibration Amplitude of HBAR ...... 46 4.4 Simulation of HBARs using Aluminium Nitride as the Piezoelectric ...... 49

5 Conclusion and Future Work 51

Bibliography 51 LIST OF FIGURES Figure Page

1.1 A child riding a swing periodically standing at the midpoint and squatting at the end points. This periodic motion results in parametric ampliﬁcation of the swing amplitude...... 3

1.2 Device proposed to achieve parametric ampliﬁcation of spin waves by acoustic energy. It has a BAW resonator on one side, and a thin YIG ﬁlm on the other side of a Gadolinium Gallium Garnet (GGG) substrate...... 4

1.3 Amplitude of the propagating spin wave can be ampliﬁed in the region under neath the BAW resonator ...... 5

1.4 Bulk Acoustic Wave resonator ...... 6

1.5 Resonance condition of a Bulk Acoustic Wave resonator ...... 7

1.6 Standing wave pattern through the acoustic stack of a High Overtone Bulk Acous tic Wave resonator ...... 8

2.1 A ﬁnite slab of any material subjected to two unequal forces acting on its two opposite faces ...... 9

2.2 The molecule is electrically neutral when no stress is applied, as shown on the left. Under stress, a small effective dipole is created as shown on the right. . . . 13

2.3 All the dipole moments inside the material get mutually cancelled. Surface charges are generated as shown, and hence a voltage appears across the material. 13

3.1 Propagation of acoustic waves through a ﬁnite slab bounded by two dissimilar materials ...... 20

3.2 Equivalent circuit of a ﬁnite non-piezoelectric slab ...... 22

3.3 Equivalent circuit of a ﬁnite piezoelectric slab ...... 24

3.4 Equivalent electrical model of acoustic transducer showing the value of elec tromechanical transformer turns ratio ...... 25

3.5 Complete equivalent model of an acoustic resonator ...... 25

3.6 Comparison of measured and simulated results of BAW resonators fabricated on glass substrates...... 26 LIST OF FIGURES (Continued) Figure Page

3.7 Stress ﬁeld comparison between BAW resonators using high and low impedance electrode materials. The high impedance material conﬁnes a greater amount of stress in the piezoelectric layer ...... 28

3.8 Resonator A and resonator B are identical except for one uses aluminium and the other uses gold electrodes respectively...... 28

3.9 ADS simulations for resonators A and B showing variation of device impedance with frequency...... 29

3.10 ADS simulations for resonators A and B with zinc oxide thickness of resonator B adjusted to have the resonance frequency as resonator A...... 30

3.11 Process ﬂow diagram for BAW resonator fabrication...... 31

3.12 3D structure of the fabricated BAW resonator ...... 32

3.13 XRD patterns of zinc oxide thin ﬁlms deposited at different argon to oxygen ratios 34

3.14 Resistivity of sputtered zinc oxide ﬁlms as a function of oxygen content in the chamber ...... 35

3.15 Determination of optimal oxygen concentration in the sputter chamber to achieve highest resistivity and best c-axis orientation of the zinc oxide ﬁlm ...... 35

4.1 Spin waves measured in YIG ﬁlm at different applied magnetic ﬁeld ...... 36

4.2 Simulation of HBAR having acoustic resonance at 4 GHz ...... 37

4.3 HBAR measurement set up ...... 38

4.4 (a) and (b) show the simulation and (c) and (d) the measurement of the HBAR fabricated on 0.5 mm GGG substrate with a thin YIG layer on both sides. (e) shows the fabricated HBAR under consideration...... 39

4.5 Measurement setup of wirebonded device ...... 40

4.6 Electrical response of HBAR wirebonded to 50 ohm transmission line - no acous tic resonance could be observed around 4 GHz...... 40

4.7 Electrical response of wirebonded HBAR at lower frequencies ...... 41 LIST OF FIGURES (Continued) Figure Page

4.8 Equivalent electrical model of HBAR with bond wire included ...... 41

4.9 Simulation showing effect of wire bond impedance on acoustic response at higher frequencies ...... 42

4.10 Comparison of electrical response of HBAR connected by a (a) single bond wire and (b) two bond wires in parallel ...... 42

4.11 Increase in maximum frequency of acoustic resonance with increase in number of parallel bond wires: (a) two bonds (b) three bonds (c) four bonds (d) ﬁve bonds 43

4.12 Plot showing increase in maximum frequency up to which acoustic resonance could be observed with increase in number of parallel bond wires ...... 44

4.13 Wirebonded HBAR with compensating capacitor connected in series . . . . . 45

4.14 Simulation results showing improved performance of the fabricated HBAR with an appropriately chosen series capacitor used to compensate for the bond wire inductance at the transducer resonance frequency ...... 45

4.15 Heterodyne interferometer setup ...... 46

4.16 (a) experimental set-up for measuring vibration amplitude of HBAR (b) effect of matching network on HBAR response ...... 48

4.17 Resultant interference pattern from interferometer ...... 49

4.18 Comparison of HBARs using aluminium nitride and zinc oxide as piezoelectric 50 LIST OF TABLES Table Page

2.1 Comparison of important acoustic properties among common piezoelectric ma terials ...... 17

3.1 Resonator parameters as extracted from simulations shown in Fig 3.8 ...... 29

3.2 Resonator parameters as extracted from simulations shown in Fig 3.9 ...... 31 Chapter 1: Introduction

Spin waves have been studied for a number of years in a variety of magnetic materials and nanos tructures. Spin waves typically exist in the microwave frequency range and they are a promising prospect for the development of microwave information processing devices. However, a major obstacle in the study of spin waves in the majority of known materials is the very large intrinsic spin wave damping. A combination of short magnon lifetimes and slow magnon speeds typically limit observable spin wave propagation distances to only few tens of micrometers [1],[2]. Research in this ﬁeld got a big boost in the 1960s, mainly due to the discovery of a new material, Yittrium Iron Garnet (YIG), which has a uniquely low magnetic damping which allows spin wave propagation to be observed over centimeter distances [3]. That period saw the devel opment of many innovative YIG-based analog signal processing devices, but most of them could not survive the competition from the newer semiconductor devices.

1.1 Motivation

Recent interest in the study of spin waves has been sparked from the intriguing possibility of using spin waves for logic devices [4]. Spin waves can be used as information carriers in logic devices, with the information being represented by the electron spin, as opposed to the electron charge in conventional present day electronics [5]. This can potentially open the door to over coming one of the major limitations of conventional electronics - that of power consumption . In modern day electronics, with the device sizes growing smaller and smaller, another ma jor issue is the interconnect problem. The increasing number of devices per unit area leads to great difficulties in interconnection wiring [6]. Impedance mismatch between devices and wires is another serious issue. Inductively coupled circuits can be used for information processing, whereby information can be transmitted between circuits using a magnetic flux, without trans mitting current via wires. The change in magnetic flux through a surface generates an inductive voltage proportional to the rate of change of the magnetic flux - as given by Eind = −dΦ/dt. Magnetic materials can be used to direct the magnetic flux among the circuits and the change in 2 magnetization in those materials gives rise to the inductive voltage signal. Propagation of spin wave through the magnetic material is a very energy efficient way of changing the magnetiza tion through the material. Thus spin waves can also potentially be used in establishing wireless interconnection among small scale electronic circuits. [7] Despite these potential advantages, practical use of spin waves continues to face one major obstacle - the amplitude of the propagating spin waves exponentially decays due to the magnon phonon, magnon-magnon and other scattering processes - even in a material with as uniquely low magnetic damping as Yttrium Iron Garnet. It therefore naturally follows that viable amplification mechanisms for spin waves are of crucial importance in order to make further progress in this field. There are few well known mechanisms that can be used for spin wave amplification. For example, passing electric current in a conducting ferromagnet along the direction of spin wave propagation can lead to spin wave amplification [8]. A spin wave can also be amplified by an alternating magnetic field, whereby a microstrip structure can be used to generate an ac magnetic field operating at twice the frequency of the propagating spin wave signal. This technique is called the parametric parallel microwave pumping, as demonstrated in [9]. In this work, we propose of new technique of spin wave amplification - parametric pumping of spin waves using bulk acoustic waves.

1.2 Parametric Ampliﬁcation

A parametric process is one in which the temporally periodic variation of a system parameter drives or sometimes brings about some other coupled temporally periodic process. In case of an oscillator, if the system parameter varies at roughly twice the frequency of the oscillator, the system can absorb energy - resulting in a gradual ampliﬁcation of the system amplitude. This is called a parametric oscillator where energy is pumped into the oscillator not by a force varying with time, but by periodic variation of one of the system parameters. This phenomenon can be best demonstrated by the example of a child riding a swing. It is a fairly well known phenomenon that a child riding a swing can cause the swing’s oscillations to increase in amplitude by merely standing and squatting periodically. We consider the system as described in Fig 1.1 where the swing can be thought of as an oscillating rod of length ’l’ - with the child as a point mass sitting up and down at the end of the rod. We consider the case where the child stands up and squats at exactly the midpoint and the 3

Figure 1.1: A child riding a swing periodically standing at the midpoint and squatting at the end points. This periodic motion results in parametric ampliﬁcation of the swing amplitude. two extreme points respectively. Let the displacement of the child in each case be given by Δx. When standing up at the midpoint, the child does work against two opposing forces

Work done against force of gravity given by ΔWg = mg.Δx and mv2 Work done against centrifugal force given by ΔWc = l Δx (v the maximum velocity of the swing)

This results in potential energy being stored in the system given by ΔWg + ΔWc. Similarly, when the child squats down at the extreme point, where the swing velocity is zero - a part of the potential energy is given up in favor of the gravitational force - roughly equal to mg.Δx mv2 Thus it can be easily seen that in each cycle of the swing, energy equal to 2 l Δx is being stored in the system. This leads to an increase in the maximum velocity of the swing each cycle, which in turn causes the amplitude of the swing to increase gradually. This is a classical example of a parametric oscillator in which the child’s motion causes the moment of inertia of the system to vary at twice the frequency of the swing, resulting in gradual ampliﬁcation of the swing’s amplitude. 4

1.2.1 Parametric Ampliﬁcation of Spin Waves by Acoustic Energy

Ampliﬁcation in the amplitude of propagating spin wave through a ferromagnetic material can potentially be achieved by periodically varying the direction of the easy axis of the ferromagnet, as has been demonstrated by numerical simulations in [10].

Figure 1.2: Device proposed to achieve parametric ampliﬁcation of spin waves by acoustic en ergy. It has a BAW resonator on one side, and a thin YIG ﬁlm on the other side of a Gadolinium Gallium Garnet (GGG) substrate.

The underlying principle behind this phenomenon is the magnetoelastic interactions between a piezoelectric and a magnetostrictive material. A magnetostrictive material is one which under goes changes in its shape or physical dimensions under an applied field. The inverse magne tostrictive effect, also known as the Villari effect is also observed in those materials, whereby the magnetization of the material can be altered by the application of a mechanical stress or strain. In a structure consisting of a piezoelectric and a magnetostrictive thin film, an electric field ap plied to the piezoelectric produces stress, which on coupling into the magnetostrictive film, can cause the easy axis to rotate. Parametric amplification can potentially be achieved if the rotation of the easy axis can be done at twice the frequency of the propagating spin wave. It has already been demonstrated by numerical modeling that rotating the direction of the easy axis can lead to amplification of spin wave amplitude. 5

We hereby propose the set up as illustrated in Fig 1.2 to achieve parametric ampliﬁcation of spin waves by acoustic energy.

Figure 1.3: Amplitude of the propagating spin wave can be ampliﬁed in the region underneath the BAW resonator

It consists of a Bulk Acoustic Wave (BAW) resonator on one surface of a GGG substrate, which has very low acoustic losses, with the YIG film on the other surface. At first, a dc mag netic field is applied along the length of the YIG film, in order to line up all the electron spins in the direction of the applied field. Microstrip antennae are used to excite spin waves in the YIG film. An ac electric voltage is applied across the top and bottom electrodes of the acoustic resonator, causing the piezoelectric thin film to produce vertically propagating acoustic waves, which induces strain in the YIG film. Now besides having the lowest known spin wave damping, YIG also has the desirable property of being a magnetostrictive material [11]. Thus, the strain in duced by the vertically propagating acoustic waves causes the easy axis of the YIG film to rotate 6 at the frequency of the acoustic waves. Parametric amplification can be achieved if the acoustic resonant frequency of the BAW resonator can be made twice the frequency of the propagating spin wave. Fig 1.3 demonstrates how this set up can be used to achieve spin wave amplification. In this setup, the substrate is Gadolinium Gallium Garnet, or GGG which serves a twofold role. Firstly, best quality YIG thin films have always been grown by high temperature liquid phase epitaxy on GGG substrates [12], [13]. The lattice constants of YIG and GGG are very closely matched, allowing for high quality, defect free unstressed YIG films. Secondly, GGG is known to have extremely low acoustic attenuation [14]. This allows the bulk acoustic waves generated by the acoustic resonator to propagate through the substrate and couple into the YIG film. This entire structure is called a High Overtone Bulk Acoustic Wave Resonator or HBAR [15].

1.3 Bulk Acoustic Wave resonator

Figure 1.4: Bulk Acoustic Wave resonator

A Bulk Acoustic Wave resonator or BAW resonator as it is called consists of a piezoelectric thin film sandwiched between two thin metal electrodes as shown in Fig. 1.4. This structure is also called an acoustic transducer. When an ac excitation is applied across the piezoelectric film, it induces stress/strain in the film, which generates an acoustic wave propagating vertically through the structure. Resonance 7 condition is achieved when the thickness of the acoustic transducer equals half a wavelength of the propagating wave, as shown in Fig. 1.5.

Figure 1.5: Resonance condition of a Bulk Acoustic Wave resonator

1.3.1 High Overtone Bulk Acoustic Wave Resonator

An HBAR is a structure in which a low loss non piezoelectric crystal cavity is attached to an acoustic stack comprising of a piezoelectric thin ﬁlm sandwiched between two metal electrodes. When an ac electric voltage is applied across the piezoelectric thin ﬁlm, bulk acoustic waves are generated. This leads to the formation of standing waves in the low loss substrate, essentially resulting in an acoustic Fabry Perot interferometer [16]. This is demonstrated in Fig 1.6. The structure essentially consists of two coupled cavities - the function of the transducer is to couple a small amount of energy into the high Q cavity, without introducing appreciable acoustic losses. The low loss acoustic cavity is very large in comparison to the wavelength of the bulk acoustic waves (equal to twice the thickness of the transducer). As a result, the device operates at a very high harmonic of its fundamental, and hence the name.

1.4 Thesis Organisation

In chapter 2, we review the basic equations of motion of acoustics and also discuss the origin and equations of piezoelectricity. We discuss some of the most commonly used piezoelectric materials and compare some of the important acoustic properties of those materials. Sputtering 8

Figure 1.6: Standing wave pattern through the acoustic stack of a High Overtone Bulk Acoustic Wave resonator is one of the most commonly used techniques to deposit thin films of piezoelectric materials for acoustic resonators. We give a brief overview of the various sputtering techniques that are typically used. In chapter 3, we develop equivalent electrical models for both piezoelectric and non piezo electric thin films. From these models, we arrive at the complete equivalent electrical model of a BAW resonator, the well known one dimensional Mason’s model. A comparison between different simulation results is done to determine the most suitable materials for fabricating the acoustic resonator. Finally we give a description of the fabrication procedure used to fabricate the BAW resonators for our experiments. Chapter 4 contains the experimental results. First, it shows the backward volume magnetostatic spin waves measured in Yttrium Iron Garnet films. We then present the simulation and experimental results for the fabricated Bulk Acoustic Wave resonators. 9

Chapter 2: Literature Review

2.1 Equations of motion of acoustics

We begin by presenting a brief review of some of the basic mechanical equations of motion in one dimension. The four fundamental parameters constituting the mechanical equations of motion are stress = T strain = S particle displacement = u particle velocity = v

Figure 2.1: A ﬁnite slab of any material subjected to two unequal forces acting on its two oppo site faces

Consider a slab as described in Fig 2.1, having a cross section dA = dx.dy with its two 10

opposing faces subjected to two unequal stresses T1 and T2 (T2 > T1). Then, from Newton’s law, we get ∂T ∂2u = ρ (2.1) ∂z ∂t2 where ρ is the density in Kg/m3 . Particle velocity is given by ∂u v = (2.2) ∂t As indicated in Fig 2.1, the particle displacement u changes gradually with position. Strain is deﬁned as the spatial rate of change of particle displacement:

∂u S = (2.3) ∂z

Lastly, according to Hooke’s law, there is a linear relationship between stress and strain, as given by T = cS (2.4) where c is called the stiffness constant. Equations 2.1 to 2.4 together comprise the mechanical equations of motion in one dimension. Differentiating Eqn. 2.3 with respect to time t and substituting from Eqns. 2.2 and 2.4, we get

∂v 1 ∂T = (2.5) ∂z c ∂t

Again, differentiating Eqn. 2.5 with respect to t and Eqn. 2.1 with respect to z we get

∂2v 1 ∂2T = (2.6) ∂t∂z c ∂t2

1 ∂2T ∂2v = (2.7) ρ ∂z2 ∂z∂t From Eqns. 2.6 and 2.7, we get 1 ∂2T 1 ∂2T = (2.8) ρ ∂z2 c ∂t2 This is the fundamental one dimensional wave equation, the solution of which is a propagating 11 function having phase velocity c v = (2.9) a ρ This is the phase velocity of an acoustic wave propagating through a solid. Another very important property of an acoustic system is the characteristic acoustic impedance of the medium(Zc), which is deﬁned as

T Z = − (2.10) c v

(the negative sign is to make the impedance positive, as the stress and particle velocity are oppo sitely directed in an acoustic system) Substituting from the previous equations, we ﬁnally arrive at the relation

Zc = ρva (2.11)

Both the characteristic acoustic impedance and the phase velocity are important material prop erties governing the propagation of acoustic waves through the medium.

2.1.1 Tensor Notation

In reality, a much more complicated three dimensional analysis is required to accurately model the propagation of acoustic waves in materials under stress. This is mainly due to the fact that when stress is applied to a material in a particular direction, it not only causes strains in the same direction, but also in the perpendicular directions. For instance, a stress applied in the x direction couples to strains in the y and z directions. Moreover, these couplings are not necessarily the same in different directions. This leads to Hooke’s law in three dimensions:

T = c : S (2.12) where T, c and S are now matrices. The complete matrix form of the equation may be written as 12

⎡⎤⎡ ⎡⎤ ⎤ T1 c11 c12 c13 c14 c15 c16 S1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ T2 ⎥ ⎢c21 c22 c23 c24 c25 c26 ⎥ ⎢ S2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ T ⎥ ⎢c c c c c c ⎥ ⎢ S ⎥ ⎢ 3 ⎥ ⎢ 31 32 33 34 35 36 ⎥ ⎢ 3 ⎥ ⎢ ⎥ = ⎢ ⎥ × ⎢ ⎥ (2.13) ⎢ T4 ⎥ ⎢c41 c42 c43 c44 c45 c46 ⎥ ⎢ S4 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ T ⎥ ⎢c c c c c c ⎥ ⎢ S ⎥ ⎣ 5 ⎦ ⎣ 51 52 53 54 55 56 ⎦ ⎣ 5 ⎦ T6 c61 c62 c63 c64 c65 c66 S6 All the terms in the upper left quadrant of the stiffness matrix represent coupling between longi tudinal stress and longitudinal strain. Amongst these terms, the diagonal elements (c11, c22, c33) couple stresses and strains in the same direction, while the off-diagonal terms couple stresses and strains in the orthogonal directions. The elements in the lower right quadrant represent cou pling between shear stresses and shear strains. The elements of the lower left and the upper right quadrants respectively represent the couplings between shear stresses and longitudinal strains and longitudinal stresses and shear strains.

2.2 Piezoelectricity

Piezoelectricity, which means ”pressing” electricity forms a bridge between electrical and me chanical phenomena. In 1880, French physicists Jacques and Pierre Curie discovered that ex ternal force applied to certain crystals generated a surface charge on those crystals, which was roughly proportional to the applied mechanical stress [17]. Piezoelectricity is a reversible pro cess leading to direct and inverse piezoelectric effects as brieﬂy discussed below:

• Direct piezoelectric effect - The internal generation of electrical polarization in a material due to applied mechanical stress

• Inverse piezoelectric effect - The internal generation of stress (and strain) in a material under the application of an electric ﬁeld

The underlying phenomenon behind piezoelectricity is the change in polarization P of a material when subjected to a mechanical stress. This can be better explained by a very simple model of piezoelectricity as demonstrated in Fig. 2.2. It considers the case of a single molecule of an ionic crystal. When no mechanical stress is applied, all the anions and cations are so distributed with respect to a point of symmetry that it results in the overall charge neutrality of the molecule. When a mechanical stress is applied, it 13

Figure 2.2: The molecule is electrically neutral when no stress is applied, as shown on the left. Under stress, a small effective dipole is created as shown on the right. causes a deformation of the lattice which breaks down the symmetric distribution of the anions and the cations about the center. It is this shifting of the anions and the cations that leads to the appearance of a net electric dipole in the previously neutral molecule as shown. A slightly more elaborate model of piezoelectricity is demonstrated in Fig. 2.3.

Figure 2.3: All the dipole moments inside the material get mutually cancelled. Surface charges are generated as shown, and hence a voltage appears across the material.

All the individual dipoles inside the material get mutually cancelled. The net result of the change in polarization P of the crystal manifests itself as the appearance of surface charges upon the crystal faces. This in turn leads to an effective electric ﬁeld across the crystal. 14

2.2.1 Piezoelectricity in one dimension

When a potential difference is applied across a material, there results an electric field across the material. This causes the bound charges in the material to slightly separate, thereby creating a local electric dipole moment. The polarization of the material P , defined as the number of dipoles per unit volume is proportional to the electric field E

P = E0κE (2.14) where E0 is the permittivity of free space, and κ is the electric susceptibility. The electric displacement ﬁeld D is related to the electric ﬁeld according to

D = EE (2.15) where E, the permittivity of the material, is given by E(= E0(1 + κ)). Now as already discussed, piezoelectricity is essentially a combination of the electrical behavior of a material and the stress-strain coupling of a material, as given by Hooke’s law. (Eqn. 2.4) Thus Eqns. 2.4 and 2.15 can be combined together to arrive at the so-called coupled equations as given by D = ET E + dT (2.16)

S = dE + sE T (2.17) where d is the piezoelectric strain coefficient, s is the elastic compliance coefficient (= 1/stiffness constant) The first term of Eqn 2.16 and second term of Eqn 2.17 are the normal piezoelectrically ”un coupled” relations, which are true in all materials. The second term of Eqn. 2.16 represents the piezoelectric effect, while the first term of Eqn. 2.17 represents the inverse piezoelectric effect. The superscripts T and E denote that the permittivity and the elastic compliance needs to be measured under conditions of constant stress and constant electric field respectively. The impor tance of this can be easily understood as follows. If an electric field is applied, it produces both an electric displacement and a strain. This strain is coupled to stress, which in turn changes the very relationship between D and E. It is to eliminate this twofold coupling that the permittivity of a piezoelectric material should be measured at constant (usually zero) stress. Similar argu ment applies as to why the elastic compliance of a piezoelectric material should be measured 15

under constant electric ﬁeld. Eqn. 2.17 may be transformed into a more useful form from the point of view of acoustic wave calculations, in which strain is the independent variable. It may be written as

T = cE S − eE (2.18)

where cE is the stiffness constant measured at constant electric field, while e is the piezoelectric stress coefficient. Due to the piezoelectric effect, the propagation velocity of acoustic waves in a piezoelectric medium is higher than that in a non - piezoelectric one. This effect arises from the fact that the stiffness coefficient in the piezoelectric material is modified with respect to the non - piezoelec tric case. This is called the stiffening of the stiffness coefficient, and is done by incorporating the piezoelectric coefficient and the permittivity. The modified stiffness coefficient of a piezoelectric material is expressed as e2 c' = cE + (2.19) ES Plugging this into Eqn. 2.9, we get the stiffened phase velocity as given by � cE + e2 v ' = bS (2.20) a ρ

From Eqns 2.9 and 2.20, the effect of piezoelectricity on acoustic wave propagation becomes evident by formulating the relationship between the stiffened and unstiffened phase velocities as

' 2 1/2 va = va(1 + K ) (2.21)

2 e2 where K = cE bS is called the piezoelectric coupling constant. The electromechanical coupling coefﬁcient is also deﬁned as K2 k2 = (2.22) t K2 + 1

These two coupling terms K and kt are arguably the two most important ﬁgures of merit for piezoelectric materials, depending on whether they are being used in the thickness excitation mode (acoustic waves propagating parallel to the resonator plate normal) or lateral excitation mode (acoustic waves propagating perpendicular to the resonator plate normal) in the acoustic resonator. Physically, the coupling coefﬁcient gives a measure of the ratio of the mechanical 16

(electrical) energy stored to the electrical (mechanical) energy applied.

2.2.2 Piezoelectric Materials

Since the discovery of the piezoelectric effect in quartz by the Curie brothers, many other mate rials with piezoelectric properties have been discovered and synthesized. Quartz is still widely used as a piezoelectric material for a variety of applications mainly due to its unique advantage of having an almost linear response even under conditions of extremely high stress or electric field. However, it is not a viable option to be used as a thin film in acoustic resonators, as there are no known methods of depositing crystalline quartz as a thin film. Piezoelectric ceramics such as lithium niobate (LiNbO3) and barium titanate (BaTiO3) are two other well known materials but they are not suitable for application in acoustic resonators due to difficulties related deposit ing thin films of these materials. A key aspect of BAW resonator technology is the development of novel piezoelectric materials having high electromechanical coupling coefficient, low elec tromechanical losses, high thermal stability and low fabrication cost. Currently, the three most popular materials for BAW applications are zinc oxide (ZnO), aluminium nitride (AlN) and lead zirconium titanate (PZT). Aluminium nitride at present is arguably the most commonly used piezoelectric in BAW resonators. It is possible to grow fairly high quality aluminium nitride thin films on electrodes such as aluminium and gold which are typically used in BAW applications. BAW resonators with AlN as the piezoelectric typically present coupling values of around 6.8% - 7%. One advantage of using aluminium nitride as the piezoelectric in BAW resonators is its very high acoustic velocity, which allows one to achieve high frequency acoustic resonances while still maintaining a fairly thick piezoelectric layer. An important criteria for growing high quality piezoelectric films is for the thin film to have a high degree of c-axis orientation. Increasing thickness of the growing film facilitates higher degree of c-axis orientation. Thus using AlN as the piezoelectric can result in stronger acoustic responses at higher frequencies. Zinc oxide has an electromechanical coupling coefficient higher than that of aluminium ni tride - typically around 9%. It is also possible to grow fairly high quality piezoelectric zinc oxide films on most of the commonly used BAW electrode materials. However the process becomes more and more challenging as the resonant frequency of the BAW resonator goes up beyond 2.5 GHz. Acoustic losses in zinc oxide also become more and more significant, with the increase in frequency. 17

Table 2.1: Comparison of important acoustic properties among common piezoelectric materials

2 Material Longitudinal acoustic velocity Coupling coefﬁcient (kt ) Intrinsic losses AlN 10800 - 11200 m/s 6.5 - 7 % very low ZnO 6350 m/s 8.5 - 9 % low PZT 4000 - 6000 m/s 17 - 19 % high

Lead zirconium titanate (PZT) has a remarkably high electromechanical coupling coefficient, with values as high as 19.8% having been reported. However it also has very high intrinsic losses at higher frequencies. Another major draw back of PZT is its very low acoustic velocity, which requires very thin films for most BAW applications. This makes the control of acoustic behavior very difficult. Fabricating PZT thin films is also more challenging than zinc oxide or aluminium nitride. Sputtering good quality PZT thin films is very difficult, as it requires accurate control of the stoichiometry of lead, zirconium and titanium. However recently good quality PZT films have been fabricated using the sol gel process [18]. Table 2.1 gives a comparison of some of the important parameters of these three materials [19].

2.3 Zinc Oxide Thin Film Deposition Techniques

Owing to its good coupling coefficient, and relatively low acoustic losses, zinc oxide is an attrac tive material for use in BAW application. There are many different techniques that are in vogue for depositing zinc oxide thin films such as sol - gel process, chemical vapor deposition (CVD), molecular beam epitaxy and physical vapor deposition (PVD). Each of these techniques has its own advantages and limitations in terms of the quality of the film grown, as well as process cost and complexity. Amongst these, the PVD and CVD techniques are more commonly used for depositing zinc oxide thin films. A fundamental difference between these two techniques is that in the former, the material to be deposited already exists in the solid form, while in the latter, the material does not exist beforehand and is synthesized by the reaction and/or decomposition on the substrate of one or more of the volatile precursors used. Among the different PVD techniques, sputtering is most commonly used for depositing zinc ox ide films as it allows one to grow good quality films with uniform thickness on a wide variety of substrates. 18

2.3.1 Sputtering

Sputtering is a widely used technique in semiconductor and MEMS technology to deposit thin films on substrates [20]. The term sputtering is used to describe the mechanism by which atoms are ejected from the surface of a material when that surface is struck by sufficiently energetic particles, mostly ions. In sputtering, the target material can be an element, alloy or a compound - and it can also be conductive or insulating. This is one of the reasons why sputtering is such a widely used technique. In this process, gaseous plasma discharges are used to bombard surface materials off of a target which is made of the material to be deposited. Atoms from the target are then displaced and carried to the substrate by means of a potential difference maintained between the target and substrate, the target being the cathode and the substrate being the anode. The plasma typically consists of partially ionized argon gas, which provides the energetic ions discharged onto the target. There are many different types of sputter deposition techniques such as 1) dc sputtering, 2) rf sputtering 3) magnetron sputtering 4) reactive sputtering. One major drawback of dc sputtering is that it cannot be used to sputter insulators, since the plasma cannot be maintained with a dc voltage if the electrodes are covered with insulating layers. This is due to the following sequence of events. The positive ions, on bombarding the cathode, get neutralized by extracting an electron from the cathode surface. If the cathode is a conductor, then those electrons can be replaced by electrical conduction so as to maintain the negative potential on the cathode surface required to sustain the plasma. However, in case of an insulator, the electrons which are extracted from the cathode surface by the impinging positive ions cannot be replenished by conduction from the insulator interior. As a result, the cathode surface begins to accumulate a positive charge, which over time, causes the potential difference between the cathode and the anode to fall below the level required to sustain the plasma. One solution to this drawback can be provided by replenishment of the lost electrons to the insu lator surface. This can be achieved by applying an ac voltage to the electrodes. This technique is known as rf sputtering. Let us consider the target electrode - when the rf voltage is first applied, during the negative portion of the cycle, positive ions strike the surface, leaving behind a positive charge as electrons are removed. However, during the positive cycle, the target electrode attracts and collects electrons. Since the electrons are much lighter than the positive ions, they can be accelerated much more quickly towards the target electrode than the positive ions. This results in a net negative charge building up on the target electrode during the first few cycles. However, as this negative charge builds up, it repels some of the incoming electrons during the positive part 19 of the cycle, while strongly attracts the positive ions during the negative part. This eventually results in a steady state condition, where the positive charge accumulated on the target surface during the negative part of the cycle is exactly replenished by the impinging electrons during the positive part. Thus the net charge buildup on the target surface during each complete cycle of the waveform is zero, which allows the plasma to be maintained. In both dc and rf sputtering, the electron trajectories are defined by only the electric field between the cathode and the anode. The efficiency of ionization between the electrons and the gas atoms is quite small. Thus as the electrons are accelerated towards the anode, they need to encounter a relatively large number of gas atoms along the trajectory to produce the sufficient number of electron-ion pairs needed to sustain the glow discharge. This requires the chamber pressure to be fairly high, about 20 mTorr - 100 mTorr to sustain any reasonable ion current. Such high gas pressures result in very poor transport of the sputtered atoms away from the cathode surface, resulting in very slow deposition rates. This drawback can be overcome by using magnets to confine the electrons near the target, in what is called magnetron sputtering. By placing a bar or horseshoe magnet behind the target, the resulting magnetic field forces the electrons into a spiral motion until they collide with an Argon atom. The trajectory of the electron thus elongated, the probability of ionizing a gas atom during its travel from the cathode to the anode is much enhanced. This in turn allows magnetron sputter systems to sustain the plasma at much reduced pressures (as small as 1 mTorr) compared to ordinary dc and rf sputter systems. Thus, the sputtered ions from the target can arrive at the wafer surface without undergoing too many collisions with the sputter gas atoms, leading to a dramatic increase in the sputter rate. 20

Chapter 3: Modeling and Fabrication of Acoustic Resonators

In this chapter, we discuss an equivalent electrical model of a BAW resonator, which can allow us to predict the device response as a function of the different materials used to fabricate the BAW resonator, as well as the thickness of each layer. Such a model allows one to have some idea about the required thicknesses of the different materials of the acoustic stack (the entire struc ture through which the acoustic wave propagates) to achieve a certain desired acoustic resonant frequency.

3.1 Transmission Line Model of a Non-piezoelectric slab

We begin by considering a ﬁnite slab bounded on two sides by the planes z = z1 and z = z2 as shown in Fig. 3.1. The acoustic waves travelling through the slab will get reﬂected at each boundary. This results in two waves travelling through the slab - one to the left and the other to the right.

Figure 3.1: Propagation of acoustic waves through a ﬁnite slab bounded by two dissimilar mate rials

The particle displacement at any point in the slab can then be expressed as

u = ae−jkz + bejkz (suppressing the time variation) (3.1) 21 where k is the wave number, a and b are constants. The ﬁrst term is the wave travelling to the right, while the second term is the wave travelling to the left. It is the interaction between these two waves that gives rise to the resonance condition, which in turn greatly inﬂuences the electrical characteristics of acoustic devices. It should be noted here that the acoustic analogue of voltage is force, while that of current is particle velocity.

Let v1 and v2 be the particle velocities at the left (z = z1) and right (z = z2) boundaries respectively. Then the constants a and b of Eqn. 3.1 may be evaluated as

v ejkz2 − v ejkz1 jωa = 1 2 (3.2) 2jsin(kd)

v e−jkz2 − v e−jkz1 jωb = 2 1 (3.3) 2jsin(kd) where d is the width of the slab. In Eqn. 2.10, the characteristic acoustic impedance was deﬁned as the ratio of stress to particle velocity. Since in this one dimensional analysis, force and not stress is being used as the analogue of voltage, we deﬁne a new impedance parameter, Z, of the medium given by Z = AZc. In other words, the new impedance term is simply the characteristic acoustic impedance scaled by the area A. From Eqns 2.9 and 2.11, the characteristic acoustic impedance may be expressed as

ck Ack Z = or Z = (3.4) c ω ω

We know that in a non-piezoelectric medium,

∂u F = Ac ∂z = jkcA(ae−jkz − bejkz) = Z(jωae−jkz − jωbejkz) (3.5)

Let the forces on the slab at the right and left boundaries be F1 and F2. Then substituting the expressions for jωa and jωb from Eqns. 3.2 and 3.3 into Eqn 3.5, we can derive the following two expressions for F1 and F2

Z kd F = (v − v ) + jZtan v (3.6) 1 jsin(kd) 1 2 2 1 22

Z kd F = (v − v ) − jZtan v (3.7) 2 jsin(kd) 1 2 2 2 Keeping in mind that the force and particle velocity respectively are the acoustic analogues for voltage and current, from Eqns. 3.6 and 3.7, an equivalent circuit of a ﬁnite thickness non- piezoelectric slab can be developed as shown in Fig 3.2

Figure 3.2: Equivalent circuit of a ﬁnite non-piezoelectric slab

3.2 Equivalent Electrical Model of a Piezoelectric Slab

The equation of current through a dielectric may be expressed in terms of the electric displace ment ﬁeld D as I = jωDA (3.8)

If the dielectric material is piezoelectric, then the electric field through the material may be expressed as D e ∂u E = − (3.9) ES ES ∂z where the first term is the external electric field, while the second term is internally generated by the acoustic wave. We consider the same finite slab as shown if Fig. 3.1, but now it is of a piezoelectric material. The voltage V across the slab can be calculated by integrating the electric 23

ﬁeld across the slab from z1 to z2 which gives

d I h V = + (v − v ) (substituting for D from Eqn. 3.8) (3.10) ES jωA jω 1 2

e where h = bS . On solving Eqn. 3.10 for I, we ﬁnally arrive at

I = jωC0V + hC0(v1 − v2) (3.11)

bS A where C0 = d is the static capacitance across the slab. Thus, the current in the piezoelectric is composed of two terms : 1. The ﬁrst term representing the displacement current through the static capacitance 2. The second term representing the current resulting from the conversion of mechanical energy to electrical energy. The force on the slab (at the left boundary) is now modiﬁed to

E F1 = c SA − eEA (3.12) where the ﬁrst term is identical to that in the non piezoelectric slab, while the second term is the piezoelectric contribution. This results in Eqn. 3.6 to be modiﬁed to give the following expression for the force on the left surface of the piezoelectric slab :

Z kd h F = (v − v ) + jZtan v + I (3.13) 1 jsin(kd) 1 2 2 1 jω

Here the last term is the force component due to conversion of electrical energy to mechanical energy. Eqn. 3.11 and 3.13 demonstrate the electromechanical energy conversion that takes place in a piezoelectric slab, which can be represented in an equivalent circuit as a transformer. Thus the equivalent circuit of the piezoelectric slab may be represented as in Fig. 3.3. An acoustic current

(v1 − v2) which is analogous to the particle velocity in the slab exists on the right side of the transformer, while a real electrical current and real electrical elements are present on the left side. h It is clear from Eqns. 3.6 and 3.13 that Vcd = jω I. Now, the acoustic current on the right side of the transformer is v1 − v2 and we know from Eqn. 3.11, that the acoustic contribution to the electrical current ﬂowing on the left of the transformer 24

Figure 3.3: Equivalent circuit of a ﬁnite piezoelectric slab

is hC0(v1 − v2). This leads to the conclusion that the turns ratio of the transformer is simply hC0. Thus the voltage Vab, which is the real voltage on the electrical side of the transformer may be expressed as V = I . From the KVL on the electrical side of the transformer, ab jωC0

VZe = V − Vab (3.14) I − I I = 1 − (3.15) jωC0 jωC0 I = − 1 (3.16) jωC0

From Eqn. 3.16, it is clear that Z = − 1 . So it behaves like a capacitor in so far as the e jωC0 inversely proportional relationship with frequency, but its magnitude is negative. Thus Ze is essentially a negative capacitor −C0. The equivalent circuit of the piezoelectric slab may now be redrawn as shown in Fig. 3.4. The equivalent circuit for the entire stack of the acoustic resonator can now be pieced to gether by cascading the equivalent circuit blocks of a piezoelectric and non piezoelectric block. This is the well known one dimensional Mason’s model of an acoustic resonator [21], [22] as demonstrated in Fig 3.5. The two free surfaces of the acoustic stack, the top surface of the top electrode and the bottom surface of the YIG ﬁlm are not subjected to any stress. Since stress in the acoustic domain corresponds to voltage in the electrical domain, these two surfaces are represented in the equivalent electrical model as ”acoustic shorts”. 25

Figure 3.4: Equivalent electrical model of acoustic transducer showing the value of electrome chanical transformer turns ratio

Figure 3.5: Complete equivalent model of an acoustic resonator 26

3.3 Comparison between measurement and simulation of BAW resonators

BAW resonators with different piezoelectric layer thicknesses were fabricated on glass substrates and the equivalent electrical model of identical structures was simulated using Agilent’s Ad vanced Design System (ADS) 2011.05 software. Figure 3.6 shows the comparison between the measured and simulated results.

Figure 3.6: Comparison of measured and simulated results of BAW resonators fabricated on glass substrates.

The two BAW resonators as shown in the figure consist of 1 micron and 900 nm thick Zno layers respectively sandwiched between 150 nm thick aluminium electrodes. The reflection coefficients or S11 of the devices were measured, which gives a measure of the ratio of reflected power to incident power. The two BAW resonators having ZnO thicknesses of 1 micron and 900 nm had resonant frequencies at 2.7 GHz and 3.4 GHz respectively as indicated by the dips in the S11. The figure also demonstrates the good agreement between the measured results and simulations using the equivalent electrical model. It can also be seen from Fig. 3.6 that the resonance frequency of the BAW resonators goes up with the decrease in thickness of the piezoelectric layer. This is because resonance is achieved when the thickness of the transducer is equal to half a wavelength of the acoustic wave. Thus, 27 smaller the thickness, smaller is the wavelength at resonance, hence higher is the resonance frequency.

3.4 Choice of materials for acoustic stack of Bulk Acoustic Wave res onator

3.4.1 Piezoelectric

Zinc oxide was chosen as the piezoelectric material since it has the highest known coupling coef ficient (excluding ferroelectrics, which suffer from a decrease in coupling coefficient with time). Intrinsic acoustic losses in zinc oxide are also quite low. In order to get excellent piezoelectric response, zinc oxide thin films need to be optimized so as to achieve

• high piezoelectric coupling coefﬁcient, which requires growth of highly c-axis oriented zinc oxide ﬁlms

• high electrical resistivity, which requires growth of stoichiometric zinc oxide thin ﬁlms

3.4.2 Electrodes

The performance of an acoustic resonator is greatly influenced by the electrode configuration as discussed in [23]. The electrodes impact the effective coupling coefficient as well as the resonant frequency of the transducer. For typical electrode thicknesses used in BAW resonators, an electrode having a high acoustic impedance can achieve higher coupling values than one having a lower acoustic impedance. This becomes evident from the comparison shown in Fig. 3.7. In the figure, the comparison of stress field distribution between two resonators having iden tical layer thicknesses, but using different electrode materials is shown. It can be seen that for the resonator using the higher impedance electrode material, the integral of the stress in the piezoelectric layer is more than the one having the low impedance electrode material. Thus, the coupling coefficient, which is proportional to the integral of the stress in the piezoelectric layer is higher for a high impedance electrode material. Two of the most commonly used electrode materials for BAW resonators are aluminium and gold. The acoustic impedance of gold is 62.5 MRayl, while that of aluminium is 17.2 MRayl. We 28

Figure 3.7: Stress ﬁeld comparison between BAW resonators using high and low impedance electrode materials. The high impedance material conﬁnes a greater amount of stress in the piezoelectric layer consider two acoustic resonators as shown in Fig. 3.8, both having identical layer thicknesses, but one using aluminium, and the other using gold as the electrode material.

Figure 3.8: Resonator A and resonator B are identical except for one uses aluminium and the other uses gold electrodes respectively.

These two resonators can now be simulated using ADS, in order to extract the effective coupling coefﬁcient of each. For any given resonator, the effective coupling coefﬁcient is given 29

Table 3.1: Resonator parameters as extracted from simulations shown in Fig 3.8

2 Resonator fS fp keff (%) A (Al) 3561.46 MHz 3700.15 MHz 8.89 B (Au) 1951.37 MHz 2027.95 MHz 8.96 by 2 2 π fs fp − fs k eff = ( )( ) (3.17) 4 fp fp where fs and fp are the resonance and antiresonance frequencies respectively. Fig. 3.9 shows the simulation results for resonators A and B.

Figure 3.9: ADS simulations for resonators A and B showing variation of device impedance with frequency.

Table 3.1 summarizes the important resonator parameters as extracted from the simulations shown in Fig. 3.9. It can be clearly seen that the resonator having the electrode with higher acoustic impedance, 30 gold, indeed has an improved effective coupling coefﬁcient than the one having electrode with lower acoustic impedance, aluminium. However, one important thing that should be noted is that in resonator B, the resonance frequency has been lowered signiﬁcantly in comparison to resonator A. This is due to the fact that the acoustic velocity is gold is much lower than that in aluminium. So a gold electrode lowers the resonance frequency of the resonator much more than an aluminium electrode of the same thickness. In order to get the resonance frequency

Figure 3.10: ADS simulations for resonators A and B with zinc oxide thickness of resonator B adjusted to have the resonance frequency as resonator A. of resonator B up to be the same as that of resonator A, the thickness of the zinc oxide layer in resonator B would need to be reduced considerably, from 700 nm to 200 nm. Fig. 3.10 shows the simulation results for resonators A and B*, with the zinc oxide thickness of resonator B adjusted so as to have the same resonance frequency as resonator A. Table 3.2 summarizes all the important resonator parameters as extracted from the simula tions shown in Fig. 3.10. Thus it is seen that when both resonators are designed for the same resonance frequency, the one with aluminium electrodes has the higher effective coupling coefﬁcient. This, coupled with the fact that aluminium has relatively low intrinsic losses made aluminium the preferred choice for electrode material in this work. 31

Table 3.2: Resonator parameters as extracted from simulations shown in Fig 3.9

2 Resonator fS fp keff (%) A (ZnO = 700 nm) 3561.46 MHz 3700.15 MHz 8.89 B* (ZnO = 200 nm) 3561.46 MHz 3667.3 MHz 7.54

3.5 Fabrication of BAW Resonators

Figure 3.11 details the procedure in which the BAW resonators were fabricated in this work.

Figure 3.11: Process ﬂow diagram for BAW resonator fabrication.

Figure 3.12 shows a three dimensional illustration of the fabricated BAW resonator. 32

Figure 3.12: 3D structure of the fabricated BAW resonator

3.5.1 Bottom Electrode

The processing begins with a GGG substrate with a 7 micron thin YIG film on its bottom side. The substrate is first thoroughly cleaned using acetone, isopropyl alchohol and deionized water and then dried well by putting on a hot plate at 100 ◦C for ten minutes. After drying the substrate, the positive photoresist S1818 was spun on the substrate to get uniform coverage. It was then patterned using an MJB3 Karl Suss Photo Aligner and then developed using the MF 351 devel oper. A 150 nm thick bottom aluminium electrode was then deposited in an AJA Orion sputter system using dc magnetron sputtering. A 99.999 % pure 3 inch diameter aluminium target was used for the deposition. Deposition was carried out at a power of 400 W and an argon flow rate of 20 sccm. The chamber pressure was adjusted to be at 6 mTorr. The electrode thickness was verified using an Alpha-Step 500 Profilometer. After the deposition, the bottom aluminium electrode was patterned into a 700 micron diameter disc using the lift off technique. After lift off, the substrate was thoroughly rinsed with acetone to strip off any remaining photoresist. 33

3.5.2 Piezoelectric layer

After patterning the bottom electrode, the zinc oxide ﬁlm was deposited next. This was also done in the AJA Orion Sputter system using rf magnetron sputtering. During deposition, the substrate stage was heated up to 300 ◦C in order to achieve better crystalline orientation of the zinc oxide ﬁlm - following process reported in [24] and [25]. Deposition was carried out at an rf power of

100 watts and an Ar:O2 flow rate of 15 sccm:5 sccm was maintained. The chamber pressure was maintained at 5.6 mTorr. After the deposition of the film, the photoresist was again spun on the substrate and patterned and developed in the same manner as described above. The zinc oxide film was then patterned to a 1 mm diameter disc by etching, using a 1 part by 900 dilute HCl solution. On completion of etching, the substrate was rinsed with deionized water to remove any remaining etchant and the photoresist stripped off by rinsing with acetone.

3.5.3 Top Electrode

After patterning of the zinc oxide layer, the top aluminium electrode was deposited and patterned in exactly the same way as the bottom electrode.

3.6 Effect of Oxygen Partial Pressure on Properties of Zinc Oxide Films

As mentioned in 3.3.1, to design good BAW resonators using zinc oxide, it is crucial to optimize the zinc oxide film for a high degree of c-axis orientation as well as high electrical resistivity. During sputtering of zinc oxide, oxygen concentration in the chamber greatly affects both these properties of the film. Figure 3.13 shows x-ray diffraction (XRD) patterns of zinc oxide thin films deposited at different argon to oxygen ratios in the sputter chamber. The solitary peak observed at 34.3 degree is due to the ZnO (002) plane. The absence of any crystalline zinc or other zinc oxide peaks in all the films allows us to take the intensity of the (002) peak as a direct indication of the c-axis orientation of the zinc oxide films. This is in apparent contradiction to the results from [26], which reports an increase in c-axis orientation of zinc oxide films with increase in oxygen concentration. It has however been proposed in [27] that there are in fact two counter active influences on the c-axis orientation of the growing zinc oxide film - on one hand, increase in oxygen content in the sputtering gas mixture indeed tends 34

Figure 3.13: XRD patterns of zinc oxide thin films deposited at different argon to oxygen ratios to improve the c - axis orientation of the zinc oxide film, while on the other hand, bombardment of high energy particles like neutral oxygen atoms amorphizes the film and tends to degrade its c-axis orientation. At a pressure of 5.6 mTorr at which these films were deposited, the latter effect is more dominant. Thus, it is the resputtering of the growing film caused by the neutral oxygen atoms that causes the c-axis orientation of the films to degrade with increasing oxygen content in the sputter chamber. The dc resistance across the piezoelectric layer of the BAW resonators was measured by applying a voltage across the electrodes of the BAW resonators and measuring the current flowing through the piezoelectric layer. Figure 3.14 shows the variation in electrical resistivity of the zinc oxide films as a function of the oxygen content in the chamber. It was observed that the film resistivity increased with increase in oxygen content. Similar results have been reported in [28]. Thus it was observed that on one hand, the increase in oxygen content in the sputter chamber increases the resistivity of the zinc oxide film, while on the other hand, it also degrades the c-axis orientation of the film. Thus, in order to grow zinc oxide films that can maximize the performance of the BAW resonator, an optimum oxygen content in the chamber is required. Figure 3.15 helps determine the optimal oxygen content in the sputter chamber that gives the highest resistivity and the best c-axis orientation of the zinc oxide film. From the figure, it can be observed that the optimal oxygen concentration in the chamber is about 25%. It is for this reason that during fabrication of the BAW resonators, an argon to oxygen ratio of 3:1 was maintained in the sputter chamber. 35

Figure 3.14: Resistivity of sputtered zinc oxide ﬁlms as a function of oxygen content in the chamber

Figure 3.15: Determination of optimal oxygen concentration in the sputter chamber to achieve highest resistivity and best c-axis orientation of the zinc oxide ﬁlm 36

Chapter 4: Experimental Results and Discussion

4.1 Spin Wave Measurements

As has already been discussed, in order to achieve parametric ampliﬁcation of spin waves, the acoustic resonator needs to have a resonance frequency twice that of the frequency of the spin wave. Fig. 4.1 shows the spin wave measurements in the YIG ﬁlm at different applied magnetic

ﬁelds. The transmission coefﬁcient or S21 between the excitation and detection antennae was measured, with peaks in the S21 indicating propagation of a spin wave signal between the two antennae.

Figure 4.1: Spin waves measured in YIG ﬁlm at different applied magnetic ﬁeld

It was observed from the measurements that spin waves could be excited down to about 1.8 GHz, at an applied field of 21 mT. A key aspect that needs to be considered here is that the resonance frequency of the BAW res onators should be kept as low as feasible. This is because the higher the resonance frequency, lower is the thickness of the zinc oxide layer - and with decrease in the zinc oxide layer thick ness, it becomes more and more difficult to achieve high film piezoelectricity and good effective coupling coefficient. From these considerations, a target was set for achieving 4 GHz resonance frequency BAW resonators. 37

4.2 Simulation and Measurement of Bulk Acoustic Wave Resonators

Before beginning fabrication of the BAW resonators, ADS simulations were carried out to deter mine the thicknesses of the different layers in the acoustic stack required to achieve a resonance frequency of 4 GHz. Fig. 4.2 shows the simulation for an acoustic transducer on a GGG sub strate driven by a 50 ohm impedance. For 150 nm thick aluminium electrodes, a zinc oxide thickness of 800 nm was required to achieve the resonance at 4 GHz.

Figure 4.2: Simulation of HBAR having acoustic resonance at 4 GHz

The figure shows a typical response of an HBAR, where the smooth band-like response as shown in Fig. 4.2(a) is due to the resonances in the low loss GGG substrate spaced very close together. They can be distinguished clearly when zoomed in over much smaller frequency ranges, as shown in figures (b), (c), (d) and (e). At the lower frequencies, the substrate acous tic resonances are quite sharp, while they gradually become weaker and weaker with increase in frequency due to increase in acoustic losses in the substrate with frequency. The substrate resonances get amplified again within the transducer resonance around 4 GHz, while at higher frequencies, they almost completely disappear. An HBAR having 150 nm aluminium electrodes and 800 nm zinc oxide layer was then 38

Figure 4.3: HBAR measurement set up fabricated on a 0.5 mm thick GGG substrate with a 7 micron thick YIG layer on both sides. The device was then measured using a Cascade Microtech air coplanar probe and Agilent E5071C vector network analyzer, as shown in Fig. 4.3. Figure 4.4 shows the comparison between measured and simulated results of the fabricated HBAR, with Fig. 4.4(a) and (b) showing simulated result and Fig. 4.4(c) and (d) showing measured results. As shown in Fig. 4.4(a) and (c), the broad transducer resonance occurs at around 4.1 GHz, while the substrate resonances can be observed on zooming in, as shown in Fig 4.4(b) and (d). One interesting thing to note here are the additional resonances occurring within the envelope of the transducer resonance, at spacings of roughly 0.25 GHz. These are the resonances occurring within the YIG layer sandwiched between the transducer and the GGG substrate. The frequency difference between consecutive substrate resonances was observed to be about 6.4 MHz. Again, the frequency difference between any two consecutive substrate resonances is given by

v Δf = (4.1) 2t where v is the longitudinal acoustic velocity in GGG and t is the thickness of the GGG substrate. From Eqn. 4.1, for a 0.5 mm thick GGG substrate, the longitudinal acoustic velocity in GGG was calculated to be about 6400 m/sec, which is fairly consistent with previously reported values in [29],[30]. This is a definite proof that the dips in the reflection coefficient are due to acoustic resonances occurring in the HBAR. 39

Figure 4.4: (a) and (b) show the simulation and (c) and (d) the measurement of the HBAR fabricated on 0.5 mm GGG substrate with a thin YIG layer on both sides. (e) shows the fabricated HBAR under consideration.

An acoustic transducer having identical layer thicknesses as the one in Fig. 4.4(e)was next fabricated on a GGG substrate having a 7 micron thick YIG layer only on its opposite surface. The device was then wirebonded to a 50 ohm microstrip transmission line and driven by the network analyzer as shown in Fig. 4.5. Ideally, the transducer resonance was expected to be observed at around 4.1 GHz, as seen in Fig. 4.4(c). However, no acoustic resonances around that point were observed for this device, as seen in Fig. 4.6. Figure 4.7 shows the electrical response of the device at a much lower frequency range of 0.5 - 1.5 GHz. It can be seen that up to about 1 GHz, very strong acoustic resonances could be observed. Then the resonances gradually become weaker, and disappear beyond 1.2 GHz. 40

Figure 4.5: Measurement setup of wirebonded device

Figure 4.6: Electrical response of HBAR wirebonded to 50 ohm transmission line - no acoustic resonance could be observed around 4 GHz.

This could be due to the fact that the impedance of the bond wires introduces a mismatch with the 50 ohm transmission line. As a result, a lot of unwanted reﬂections occur. At relatively lower frequencies, the bond wires do not add a signiﬁcant impedance to cause a large enough mismatch, as a result of which, acoustic resonances could still be observed up to around 1.2 GHz. However, with the increase in frequency, the bond wire impedance goes up and the mismatch becomes more severe, attenuating the acoustic resonances. Very similar behavior can also be seen in the simulation results as shown in Fig. 4.9. First, only the HBAR as fabricated was simulated. A strong acoustic transducer resonance at around 41

Figure 4.7: Electrical response of wirebonded HBAR at lower frequencies

Figure 4.8: Equivalent electrical model of HBAR with bond wire included

4.1 GHz, as expected, is observed. Then bond wires of similar length to the ones actually used for connecting the device, were included in the model, as shown in Fig. 4.8. It was observed that the bond wires indeed cause a dramatic attenuation of the acoustic resonances at higher frequencies. 42

Figure 4.9: Simulation showing effect of wire bond impedance on acoustic response at higher frequencies

Figure 4.10: Comparison of electrical response of HBAR connected by a (a) single bond wire and (b) two bond wires in parallel 43

One possible solution to this problem could be achieved by trying to reduce the inductance of the bond wires, so as to lower their impedance at higher frequencies. This can be achieved by using multiple bond wires in parallel instead of a single one.

Figure 4.11: Increase in maximum frequency of acoustic resonance with increase in number of parallel bond wires: (a) two bonds (b) three bonds (c) four bonds (d) ﬁve bonds

Figure 4.10 clearly demonstrates the effects of lowering the bond wire inductance in this 44 manner, whereby the device connected by two bond wires in parallel is seen to have acoustic resonances till much higher frequencies than the one connected with a single wire bond. With each additional bond wire in parallel, the inductance could be reduced more allowing acoustic resonances to be observed at higher frequencies. An experiment was done where the number of parallel bond wires used to connect the HBAR was gradually increased and the maxi mum frequency up to which acoustic resonances could be observed was recorded on the network analyzer. These results are shown in Fig. 4.11. It can clearly be seen that with each additional bond wire, the maximum frequency of acous tic resonance could be pushed higher. However with increase in the number of bonds, the per centage of increase also gradually decreases, as demonstrated by data in Fig. 4.12. From this, it can be concluded that this was not a feasible technique for pushing the resonant frequency to the desired 4 GHz point.

Figure 4.12: Plot showing increase in maximum frequency up to which acoustic resonance could be observed with increase in number of parallel bond wires

Another technique of compensating for the impedance of the bond wires is to have capacitors connected in series with each bond wire before connecting to the active part. The capacitor value can be appropriately chosen so as to precisely compensate for the wirebond inductance at the designed transducer resonance frequency. However, careful consideration needs to be given to the choice of type of capacitor to be used so as to ensure lumped element behavior at such high frequencies. As a rule of thumb, in 45

Figure 4.13: Wirebonded HBAR with compensating capacitor connected in series order to be considered a lumped element, all dimensions of the structure to be used should be less than a tenth of the wavelength at the desired frequency of operation. The wavelength at 4 GHz is around 7 cm - thus any capacitor to be used should have its largest dimension less than 7 mm, in order to behave as a lumped element. Surface mount capacitors of appropriate values are ideal for this purpose. Also, the best possible compensation for the wire bond inductance can be achieved by placing the capacitors as close to the bond wire as practically possible.

Figure 4.14: Simulation results showing improved performance of the fabricated HBAR with an appropriately chosen series capacitor used to compensate for the bond wire inductance at the transducer resonance frequency 46

Figure 4.13 shows the wirebonded HBAR with the compensating capacitor connected in series. Simulation results showing the effect of the compensating series capacitor as described above are shown in Fig. 4.14. Bond wires of about 3 mm in length were used for connecting the HBAR to the transmission. A rough estimate of bond wire inductance is about 3 nH/mm. Thus, for simulation of the structure shown in Fig. 4.13, 3 nH inductors were used to represent the bond wires. A capacitor of 0.5 pF was then added in series to the bond wire as then the LC resonance of the capacitor and bond wire would coincide with the transducer resonance frequency of 4.1 GHz. Thus it can be seen that the series capacitor compensation technique can be used to overcome the impedance mismatch caused. However, in order to achieve efﬁcient matching with this technique, an accurate estimation of the bond wire inductance is necessary in order to choose the appropriate capacitor values.

4.3 Measurement of Vibration Amplitude of HBAR

A heterodyne interferometer setup as demonstrated in [31] was used in order to get a quantitative idea of the amplitude of acoustic vibrations in the HBAR. The optical setup of the interferometer is shown in Fig. 4.15.

Figure 4.15: Heterodyne interferometer setup

As shown in the figure, a single mode HeNe laser produces a linearly polarized and colli mated beam which is then split into two separate beams by an acousto-optical modulator. One 47 of the two beams passes on straight through the modulator, and is focused with a microscope objective to a diffraction-limited spot on the surface of the HBAR, while the second beam is deflected and frequency shifted with respect to the first one, and serves as the reference beam of the interferometer. After being reflected from the HBAR surface, the first beam recombines with the second one and the two are then propagated to a power detector. The resultant intensity of the two beams is then observed on a spectrum analyzer, from which the vibration amplitude of the HBAR can be estimated as explained.

Let the two beams have intensities I1 and I2, and let the acousto-optical modulator shift them in frequency by an amount ωmod. Let λ be the wavelength of the HeNe laser, and A be the amplitude of vibration of the HBAR. Then, according to [32], if the amplitude of vibration A be much smaller than the wavelength, then the resultant intensity of the interference of the two beams is expressed as

Ires(t) = 2 I1I2cos(ωmodt + ϕ0)+ 2π 2 I I A {sin[(ω − ω )t + ϕ − φ]+ 1 2 λ mod HBAR 0

sin[(ωmod + ωHBAR)t + ϕ0 + φ]} (4.2) where ϕ is a slow time varying term representing the optical phase variation between the two beams of the interferometer, while φ represents the phase of the HBAR. Figure 4.16 (a) shows the experimental set-up for measurement of vibration amplitude of the HBAR. The system is driven by an Agilent E5071C Vector Network Analyzer (VNA), while an OPHIR RF 5094-F rf power amplifier is used to ramp up the driving power to 3 watts. A Maury Microwave 8045-N manual matching network is then used to match the HBAR efficiently at a particular substrate resonance frequency, as shown in Fig. 4.16 (b). The substrate resonance at 715 MHz was chosen for this experiment as shown in the figure and the entire system was driven by the VNA at that frequency. The observed interference pattern from the interferometer is as shown in Fig. 4.17. From Eqn. 4.2, it can be seen that the amplitude of vibration of the HBAR can be calculated from the ratio of the amplitudes of the signal peaks at frequencies ωmod and ωmod + ωHBAR according to the relation A 2π 1 = A (4.3) A2 λ 48

Figure 4.16: (a) experimental set-up for measuring vibration amplitude of HBAR (b) effect of matching network on HBAR response

where A1 and A2 are the amplitudes of the signal peaks at frequencies ωmod and ωmod +ωHBAR respectively, A is the amplitude of vibration of the HBAR, and λ is the wavelength of the laser.

As can be seen from Fig. 4.17, A1 is equal to -72 dBm, while A2 is equal to -121 dBm. The wavelength of the HeNe laser is 632.8 nm. By plugging in all these values into Eqn. 4.3, the amplitude of vibration of the HBAR was calculated to be about 10 picometers. This tiny HBAR vibration amplitude as calculated suggests different techniques should be adopted in order to achieve a stronger acoustic response. One potential way of achieving that is to design HBARs having aluminium nitride as the piezoelectric. 49

Figure 4.17: Resultant interference pattern from interferometer

4.4 Simulation of HBARs using Aluminium Nitride as the Piezoelectric

Along with zinc oxide, aluminium nitride is the other most commonly used material for BAW applications. The acoustic velocity of aluminium nitride is 11200 m/s, which is much higher than that in zinc oxide, around 5600 m/s. Thus, to achieve the same resonance frequency, acoustic resonators using aluminium nitride can have a much thicker piezoelectric layer than those using zinc oxide, as shown in Fig. 4.18. Two key requirements for growing high quality piezoelectric thin films are a) high degree of c-axis orientation and b) high resistivity of the thin film. As has already been discussed, it is possible to achieve higher degree of c-axis orientation in a thicker film. Moreover, resistivity of aluminium nitride is higher than that of zinc oxide [33],[34]. These above points, together with the simulation result shown in Fig. 4.18 suggest that HBARs using aluminium nitride as the piezoelectric can potentially have a stronger acoustic response than those using zinc oxide. 50

Figure 4.18: Comparison of HBARs using aluminium nitride and zinc oxide as piezoelectric 51

Chapter 5: Conclusion and Future Work

In this work, a new technique for amplification of magnetostatic spin waves has been proposed, that is parametric amplification of the spin waves using acoustic energy. This amplification technique can potentially allow spin waves to be used as information carriers in logic devices thereby overcoming one of the major limitations of conventional present day electronics, that of power consumption. Spin waves were measured in Yttrium Iron Garnet films down to about 1.7 GHz. Simu lations of an equivalent electrical model of a BAW resonator were carried out in Agilent ADS software to determine the materials and thicknesses required for the different layers of the acous tic stack of the resonator to achieve a resonance frequency of 4 GHz (approximately twice the spin wave frequency). 4 GHz high overtone bulk acoustic wave resonators were then fabricated on GGG/YIG substrates using zinc oxide as the piezoelectric layer and aluminium electrodes. The attenuating effect of the inductance of interconnecting bond wires on the acoustic re sponse of the HBAR was observed and a mechanism for compensating the bond wire parasitics is proposed based on simulation results. In the future, experiments need to be done to verify the proposed technique for compensation of wire bond inductance using surface mount capacitors in series. Also, HBARs with potentially superior performance at these high frequencies can be fabricated using aluminium nitride as the piezoelectric layer. A much higher acoustic velocity, higher electrical resistivity and lower intrinsic acoustic losses of aluminium nitride in comparison to zinc oxide can allow HBARs using aluminium nitride as the piezoelectric to have a stronger acoustic response than those using zinc oxide. Finally, the ultimate goal is to experimentally demonstrate the parametric amplification of spin waves by the designed HBARs. Acoustic transducers fabricated on GGG substrates having Yttrium Iron Garnet films can be positioned inside a magnetic field. Spin waves can be excited in the YIG film at frequency f, while a signal driving the transducer at a frequency 2f can be turned on and off to observe the change in spin wave amplitude. 52

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