Magnetic materials and devices for integrated radio-frequency electronics

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Magnetic Materials and Devices

for

Integrated Radio-Frequency Electronics

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Magnetic Materials and Devices for

Integrated Radio-Frequency Electronics

PROEFSCHRIFT

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

op gezag van de Rector Magnificus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op dinsdag 14 oktober 2008 om 12:30 uur

door

Pedram KHALILI AMIRI

Bachelor of Science in Electrical Engineering, Sharif University of Technology geboren te Tehran, Iran

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Prof. Dr.-Ing. J.N. Burghartz Copromotor:

Dr. B. Rejaei-Salmassi

Samenstelling promotiecommissie: Rector Magnificus, voorzitter

Prof. Dr.-Ing. J.N. Burghartz, Technische Universiteit Delft, promotor Dr. B. Rejaei-Salmassi, Technische Universiteit Delft, copromotor Prof. Dr. R. Dekker, Technische Universiteit Delft

Prof. Dr. G.E.W. Bauer, Technische Universiteit Delft

Prof. Dr. G. Schütz, Max-Planck-Institut für Metallforschung (Germany) Prof. Dr. S. Blügel, Forschungszentrum Jülich (Germany)

Prof. Dr. M. Yamaguchi, Tohoku University (Japan)

Pedram Khalili Amiri,

Magnetic Materials and Devices for Integrated Radio-Frequency Electronics, Ph.D. Thesis Delft University of Technology.

Keywords: radio-frequency integrated circuits, magnetic thin films, passive devices, transmission lines, microstrip, inductors, permeability, ferromagnetic resonance, shape-induced anisotropy, granular materials, reactive sputtering, electrical resistivity, spin waves, magnetostatic waves, nonreciprocity, magnetic multilayers. ISBN: 978-90-8559-418-5

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.

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Chapter 1 Introduction

1.1 A tale of towers and antennas

Communication, the transmission of information over distances in space and time, has been one of humanity’s most distinctive desires and abilities throughout the ages. Important human inventions such as language and script essentially serve the need for us to communicate, both amongst each other and with future generations. Since ancient times, as the story of the tower of Babel tells us, the ability to communicate through a shared language has been thought of as enabling humans to reach for the heavens. While in that story the endeavor famously fails due to the confusion arising from the multitude of different languages, humanity has never ceased to invent new techniques of communication (figure 1.1), ranging from couriers, pigeon post, ship flags, and smoke signals to modern air mail, radio, television, telegraph, telephone, and wireless communication systems.

Presumably, one of the earliest examples of wireless communication over long distances used smoke signals, a technique that incidentally, as known today, was based on electromagnetic (optical) waves. However, the story of modern wireless communications using electromagnetic wave propagation, as it is usually told, starts with the theoretical discoveries of Maxwell in 1873, and the subsequent experiments by Hertz, Marconi, and others. Maxwell’s contribution to the then-existent equations of electricity and magnetism was a perhaps aesthetically inspired observation that, since changing magnetic fields – as Faraday had shown earlier – could produce electric fields, the reverse had also to be true; namely, that changing electric fields

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should produce magnetic fields as well. As a result, he could fix an obviously incomplete continuity equation for current, as his equations allowed for currents to flow in circuits that were not complete loops. His equations also predicted the existence of electromagnetic waves, an assertion that Hertz showed to be correct experimentally fourteen years later, in 1887 [1, 2].

Figure 1.1: Examples of communication methods: (a) the watchtowers of the Great Wall of China were used to transmit smoke signals, (b) a postage stamp, (c) a telegraph key, and (d) a mobile phone.

The discoveries of Maxwell sparked a multitude of technological advances, revolutionizing the way people live and interact up to the present day. They are a prime example of the fact that often the simplest, most fundamental contributions to science can be also the most fruitful in terms of applications. “From a long view of the history of mankind”, as Feynman would later say, Maxwell’s discovery will be remembered as “the most significant event of the nineteenth century”, while another event of the same decade, the American civil war, “will pale into provincial insignificance” [1].

Inspired by the discoveries of Hertz, it was Marconi who demonstrated the first transatlantic wireless communication, another fourteen years later, in 1901 [2, 3]. (Interestingly, Tesla had shown wireless transmission to be possible a few years

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before Marconi’s experiment. Being primarily concerned with energy distribution, however, it seems that he did not immediately realize the potential of his invention for information transfer [2].) While one-way wireless transmission of radio (and later television) signals quickly developed and expanded during the following decades, two-way wireless communication did not enter daily life for a long time. It took several more developments, amongst which the invention of the transistor and of the integrated circuit (IC), to make small, affordable, and reliable mobile communication systems a reality [4]. The cell phone in our pockets is just one result of those efforts.

1.2 Radio-frequency integrated circuits

Most of us know from personal experience that the size, weight, and cost of mobile phones have been shrinking continually ever since they were first introduced. While two-way wireless communication was initially confined to military applications, the introduction of integrated circuits made it possible to jam more and more components of a communication handset onto one semiconductor chip, thereby lowering the fabrication costs needed to realize a desired system. Integration, by its very nature, proved to be space-saving and increased the reliability, bringing cell phones into the domain of everyday use, and allowing for developments such as wireless local area networks (WLAN) and navigation using the global positioning system (GPS) [2, 4]. Furthermore, scaling – the shrinking of on-chip components in integrated circuits – allowed one to make more and more components on one chip, increasing both the speed (thus operation frequency) and the functionalities of the circuits. The latter point about functionality is in particular interesting, since it allows the system (or in fact, its user) to save space in other, more indirect ways. To appreciate that, one merely has to consider the camera, phonebook, calculator, and other tools which are all included in a modern “phone”; and imagine what space and effort would have been needed to carry around all those things in former days. The combination of integration and scaling has thus brought about the proliferation of mobile communication as we know it today.

While scaling has been mostly motivated and defined by the enormous momentum of the digital market, analog and radio-frequency (RF) functions have been following in the same footsteps (though often with some delay), thereby being realized with smaller and smaller transistors. It has become more and more attractive to avoid the cost and effort of developing dedicated technologies for RF, and instead to use standard complementary metal-oxide-silicon (CMOS) technology for these applications as well [5, 6]. There have been, however, difficulties associated with this approach. One arises from the fact that new generations of

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CMOS technology are primarily characterized, modeled, and optimized for digital (e.g. logic) applications, which entail fewer tradeoffs than the typical analog or RF design. As a result, additional characterization and modeling of a new CMOS technology is often needed before it can be used for RF as well [6], while choosing alternatives such as Bipolar/CMOS (BiCMOS) entails its own integration and optimization challenges.

A second, more fundamental challenge is in the integration of passive components (e.g. inductors and capacitors) on the silicon chip for RF applications. Devices such as inductors, capacitors, and transmission lines are needed for impedance matching networks, filters, resonators, and power dividers and are thus indispensable components of RF circuits. Integration of these devices on the silicon chip is advantageous in terms of size, weight, total unit cost, and reliability. However, it is difficult to integrate such passive components into a technology primarily developed for active CMOS devices. While RF engineers have long been committed to the advantages of passive device integration, there are still considerable difficulties in realizing passives on silicon which firstly have sufficiently good characteristics in comparison to their off-chip counterparts, and secondly do not take up too much chip real estate [5, 7].

The operation of lumped passive devices such as capacitors and inductors is essentially based on the storage of electrical and magnetic energy, which is why these devices by nature take up a relatively large volume (or area, when it comes to planar IC technology). On the other hand, when a distributed transmission line is to be used on the chip, often the length of the line has to be comparable to the wavelength of the electromagnetic waves at the frequency of interest. For a quarter-wavelength impedance transformer made on silicon, this means that the length of the line would have to be more than one centimeter at a frequency of two gigahertz, which is comparable to the chip size! Thus, unlike the active components, RF passives made on silicon chips cannot be simply scaled down to save space. In fact, in a famous article by Gordon Moore frequently referred to in connection with the scaling of transistors, a less-frequently cited passage identifies the lack of large-value passives as “the greatest fundamental limitation” to integrated analog electronics [8].

As a result, an enormous portion of the area in a typical RF integrated circuit is occupied by passive components which, even so, exhibit a relatively poor quality. The quality factor of components such as inductors and microstrip transmission lines made on silicon chips is substantially lower than that of their discrete counterparts, while it is difficult to achieve reasonable values of inductance or characteristic impedance [9]. The excessive area consumption not only raises the unit cost, but also degrades the performance because of crosstalk and losses due to field penetration into the silicon substrate.

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A second difficulty with a number of RF passive components is that they require magnetic materials for their operation. These include, in particular, nonreciprocal devices such as isolators and circulators, which have been important components of microwave technology for decades [10]. Traditionally, these devices have been made by using magnetic ferrite cores. Ferrite materials have the attractive property of being dielectrics, therefore not allowing for the flow of parasitic currents which could otherwise contribute to energy loss (heating of the magnetic material). However, the magnetic properties of ferrite materials depend on their specific crystalline structure, the realization of which requires high-temperature processing [11]. This makes ferrites difficult to integrate within the mainstream silicon technology, since the high-temperature step would affect other parts of the integrated circuit. As a result, nonreciprocal components are currently realized as discrete (off-chip) components, therefore not benefiting from the advantages of integration.

The aim of this work is to address the above-mentioned challenges associated with RF passives in silicon technology by exploiting magnetic materials.

1.3 Why magnetic materials?

Off-chip RF passives have traditionally been realized with magnetic cores. In the realm of integrated electronics where the silicon-incompatible ferrites cannot be used, the lack of a low-cost substitute with a reasonable performance has so far impeded the use of magnetic materials. The motivation of the work described in this thesis has been to fill in that gap. The range of investigations has been (inevitably because of the subject, and fortunately for the author) quite diverse.

Figure 1.2 offers a glimpse into the main directions of this research; namely, to use magnetic materials in order to

• Improve the performance of those RF passive devices that are already integrated on silicon (albeit without magnetic cores), and

• Investigate the on-chip realization of RF functions (such as nonreciprocal effects) which are currently only available in discrete form.

To do so, obviously one needs magnetic materials that can be deposited on silicon in compatibility with established process technology. The investigation of material requirements for the above-mentioned devices, as well as the development (if necessary) of new materials with improved properties comprise the third direction of this work.

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Figure 1.2: How magnetic materials can enhance RF integrated circuit technology. (Bottom left) Integrated solenoid inductor and microstrip transmission line with magnetic core. Both devices have nonmagnetic counterparts already integrated on silicon. (Bottom right) Integrated nonreciprocal coupled transmission line structure based on spin waves in a magnetic film.

The following subsections offer a glimpse into the potential application areas of magnetic materials in RF technology, their challenges, and their promises. This is followed by a review of the main properties of magnetic materials relevant to this work.

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1.3.1 Improving conventional integrated passives

A high permeability is perhaps the first property that comes to mind when thinking about ferromagnetic materials. This property is also at the heart of the motivation to use magnetic materials in integrated circuit passives.

Common air-core integrated spiral inductors occupy large chip areas and their quality factors – the measure of how much energy is stored in the device, as opposed to dissipated – are typically rather low [9]. Essentially, both of these problems can be traced back to the fact that the nonmagnetic media (e.g. air or silicon dioxide) surrounding the metal lines in these structures are rather poor when it comes to storing magnetic energy. Since the energy stored in a medium increases with its permeability, the incorporation of a magnetic material with high permeability into these devices would thus allow one to make them smaller and to increase their quality at the same time. The same argument holds for RF transmission lines, where the high permeability reduces the propagation velocity and wavelength for a given frequency, thereby reducing the size of these lines, making them more amenable to integration [12]. As a result, the international technology roadmap for semiconductors (ITRS) has identified magnetic films as a potential solution for RF passive integration in the 0.8–10 GHz frequency range in its 2007 edition [13].

Air-core inductors on silicon are commonly shaped as spirals. This geometry is fairly easy to fabricate and allows for reasonably high (compared to other integrated structures, that is) inductance per unit area values. At the same time, however, it allows for significant field penetration into the silicon substrate, leading to high loss and crosstalk. While approaches such as the use of high-resistivity silicon or partial removal of the substrate beneath the RF passives have been proposed, showing an increase of the quality factor of the devices, they come at the expense of increased cost and higher process complexity.

In the case of RF spiral inductors, moderate inductance and quality factor improvements have been achieved by using a magnetic film underneath the spiral coil, as well as by two magnetic films encapsulating it in a so-called sandwich structure [14, 15]. However, it is important to notice that due to the anisotropic nature of the permeability of the magnetic films, a significant inductance enhancement can only be expected if the ac field created by the current-carrying conductors is parallel to the hard axis of the magnetic film. Since such a field configuration is difficult to realize when using a planar spiral, an alternative approach proposed in recent years has been to return to solenoid structures similar to those used for off-chip inductors (figure 1.3) [16]. Even though on-chip magnetic solenoids allow for a much better exploitation of the magnetic film’s high permeability, and have in fact been shown to yield a significant (up to twenty-fold)

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enhancement of inductance over nonmagnetic solenoids, their quality as compared to conventional air-core spirals on silicon is not yet impressive. Moreover, what is gained in terms of permeability increase is often lost because of the energy dissipation (i.e. quality factor decrease) due to parasitic currents in the (typically conductive) silicon-compatible magnetic core. Since the parasitic current loss increases with the magnetic film’s thickness, this undesirable conductivity is especially problematic in the case of integrated inductors, where a thick magnetic film is usually needed in order to bring about a significant inductance enhancement. In addition, a solenoidal coil is more prone to ohmic loss in the metal, when compared to the spiral coil structure, due to the numerous vias needed between the two metal layers. Although research on integrated ferromagnetic inductors is still ongoing, in this work the emphasis will be on the application of magnetic materials to other RF passive devices.

Figure 1.3: Schematic top views of planar solenoid (left) and spiral (right) integrated inductors. The dashed lines represent the edges of the rectangular-patterned magnetic films. While a spiral is advantageous if no magnetic film is used, the alignment of the RF magnetic field Hac with the hard axis is much easier achieved in

the solenoid structure.

An integrated microstrip transmission line with a magnetic thin film core is shown in figure 1.4. The easy axis of the magnetic film is parallel to the signal line, thereby ensuring that the AC field generated by the current in the conductive metal is aligned with the hard axis, thus sensing a high permeability. Similar to the case of an inductor, the high permeability of the magnetic film increases the inductance per unit length of the transmission line, thereby also increasing its characteristic impedance and quality factor. This is a fortunate result, since the realization of a high characteristic impedance (e.g. the standard 50 ohm usually needed by the circuit designer) in an on-chip microstrip line proves to be a difficult task. The

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reason is that the latter necessitates either the narrowing of the signal line, thus increasing the associated resistive losses in the device, or the moving of the microstrip ground plane to the wafer’s backside, thereby introducing losses due to the silicon wafer itself. As shown in Chapter 2, the tradeoff between characteristic impedance and loss can thus be relieved by the incorporation of a high-permeability ferromagnetic core, allowing for the reduction of overall attenuation in the integrated transmission line while maintaining constant characteristic impedance [12].

While the conductive loss in the magnetic film – as in the case of the inductor – limits the overall acceptable magnetic film thickness, another limitation of this device arises from the fact that the permeability of the magnetic film does not remain constantly high as one goes up in frequency. The frequency range of operation for the microstrip is thus limited by the so-called ferromagnetic resonance (FMR) frequency. One way to increase the FMR frequency is by patterning the magnetic film into narrow rectangular stripes, thereby making it more anisotropic [17]. This shape-induced anisotropy (or more specifically, its nonuniformity over the width of the patterned stripe) is the subject of an experimental study presented in Chapter 3 of this thesis.

Figure 1.4: Schematic representation and top-view microphotograph of an integrated microstrip line with a patterned magnetic core.

As shown by the examples above, the issue of the conductivity of commonly investigated silicon-compatible magnetic films appears when looking at the performance of RF passives based on such films. One possible solution to this problem is to investigate materials in which nanometer-sized magnetic grains (i.e. islands) are separated by nonmagnetic insulating walls. The idea in this case is

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simply that the insulating walls would prohibit the flow of currents between the individual magnetic grains, thereby increasing the overall resistivity of the film [18-20]. An investigation of such a film structure is presented in Chapter 4 of this thesis, where a range of granular films are presented along with devices based on them.

1.3.2 Implementing new integrated functions

Nonreciprocal RF and microwave components such as isolators, circulators, nonreciprocal phase-shifters, and gyrators, have so far only been realized as off-chip components using dielectric ferrites [10, 21]. As ferrites are not well compatible with silicon technology, the implementation of such devices in RF integrated circuits requires the study of nonreciprocal effects in silicon-compatible magnetic films.

The problem here, as in the case of the reciprocal devices discussed in the previous section, is mostly the high conductivity of the magnetic films, which tends to overshadow the nonreciprocal effects that one intends to observe. Nevertheless, as reported in Chapter 5 of this work, it is possible to realize significant nonreciprocity even in conventional metallic magnetic films. To do so, their thickness is chosen to be within a certain range, ensuring that there is enough magnetic material to give rise to the desired nonreciprocal effect while still being thin enough to suppress conductive losses. The proposed device essentially consists of two transmission lines that are coupled by means of spin waves propagating on a magnetic film placed underneath the lines [22]. These spin waves, which constitute the basic excitations of magnetization in the magnetic film, are often also referred to as magnetostatic waves, with the choice of which term to use in a specific setting being somewhat loosely defined (and scarcely followed) in terms of wavelength [23] (see section 1.4 and appendix A). They have found application in many ferrite-based microwave devices in the past, reciprocal and nonreciprocal alike, examples being filters, resonators, and phase-shifters [24]. Throughout this work, both terms will be used interchangeably, although technically we will only be concerned with the long-wavelength case traditionally referred to as magnetostatic waves.

One approach to avoid the limitation on magnetic film thickness posed by the film conductivity is to use multilayered films, where magnetic layers are separated by dielectrics, allowing for a large overall film thickness while keeping individual layers thin enough to avoid high energy dissipation. A general analysis of magnetostatic wave propagation in such a configuration is given in Chapter 6. It can serve as a basis for extending the ideas of the other chapters to layered films, as well as for the design of new magnetostatic wave-based integrated passives [25].

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1.4 Ferromagnetic materials at high frequencies

In this section we will briefly review some of the properties of magnetic materials which are relevant to this thesis. While a comprehensive and rigorous introduction to magnetism is beyond the scope of this work, the intention here is to aid the reader by introducing those concepts frequently referred to throughout the thesis.

When seeking a classification based on magnetic properties, substances at first glance can be described as either diamagnetic or paramagnetic. The latter group is characterized by the presence of elementary magnetic moments, which can be aligned under an applied magnetic field to yield a strong magnetization in a particular direction. A number of paramagnetic substances, however, have the interesting property that the ordering of their magnetic moments happens spontaneously if their temperature is kept below a certain value, which is called Curie temperature. Since in many cases the latter is high enough to allow for magnetic ordering at room temperature, one does not usually observe such materials in the paramagnetic state, instead referring to them as ferromagnetic, anti-ferromagnetic, or ferrimagnetic, depending on the type of arrangement of the magnetic moments in their ordered state [1, 23]. The interaction mechanism giving rise to this spontaneous ordering is called exchange interaction, and is of quantum mechanical origin. The magnetic materials used throughout this work belong to the ferromagnetic group, where the elementary moments are aligned in parallel, i.e. they point in the same direction. Ferrimagnets, which are occasionally mentioned, exhibit a more complex magnetic order. However, within the microwave frequency range, they essentially have the same macroscopic behavior as ferromagnetic materials, and can thus be understood by using the same concepts [23].

In most cases, there exists a preferred axis of alignment in a ferromagnet, called the easy axis, along which the magnetic ordering preferably takes place. The existence of an easy axis leads to anisotropic behavior in the magnetic medium, and is commonly represented by a so-called magnetocrystalline (or internal) magnetic anisotropy field, which strives to magnetize the film along its easy axis even if no external field is applied [11, 23].

For the purpose of investigating the application of magnetic materials in high-frequency devices, one has to consider the dynamics of magnetization under an externally applied magnetic field. In a typical device such a field can be created, for example, by a current-carrying conductor placed in the vicinity of the magnetic sample. In general, the time evolution of the magnetization M inside a magnetic material is given by the Landau-Lifshitz-Gilbert (LLG) equation [23]

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eff M M M H M t M t α γ ∂ _{= −} _× ₊ _×∂ ∂ ∂ , (1.1)

where Heff is an effective magnetic field accounting for the internal

magnetocrystalline anisotropy field, the externally applied magnetic field Hext, as

well as the so-called demagnetizing field arising due to the physical confinement of the magnetic sample. The latter is defined by the shape of the magnetic material, which is why it is also referred to as the shape-induced magnetic anisotropy field. It is in general position-dependent (larger near the edges of the magnetic pattern), except for in the case of ellipsoidal bodies, where it is uniform throughout the sample. In the case of rectangular magnetic elements commonly used in on-chip devices, this nonuniformity can in fact be used to advantage, as described in the following chapters. The constant γ is called the gyromagnetic ratio and is given by

2 28 GHz T

γ π ≃ . The parameter α accounts for energy dissipation in the magnetic system, and is called the Gilbert damping constant. Its presence in the above equation means that the precessional motion of the magnetization M under the influence of a DC field (represented by the first term on the right hand side, see figure 1.5) eventually tends to align the magnetization with the effective magnetic field acting on it.

Figure 1.5: Dynamics of magnetization under an applied magnetic field, as described by the LLG equation (1.1).

The nonlinear Landau-Lifshitz-Gilbert equation given above is rarely required for the analysis of RF and microwave magnetic devices at the power levels we are interested in. Thus, considering a small-signal condition and assuming the RF

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excitation to have a time-harmonic form, this equation can be linearized to give a susceptibility tensor χ

describing the response of the magnetization to an external field [10, 23]. One can then write

(

)

0 0 0 0 0 0 1 a a i I i µ µ µ µ χ µ µ µ     = + = _− _     , (1.2) in which I

is a unit tensor, and we have m =χ hɶext

, where m and h represent ɶext

small-signal time-harmonic quantities. Note, that the ferromagnetic material exhibits only a small permeability µ₀ along its easy axis (which is the z-axis in this case), and that its permeability tensor µ

is non-symmetric (gyrotropic). The frequency dependence of its components is given by [23]

(

)

2 2 2 H H M H ω ω ω ω µ ω ω + − = − , (1.3) 2 2 M a H ωω µ ω ω = − , (1.4) 0, M M H Ha i ω =γ ω =γ + αω, (1.5)

where M₀ is the saturation magnetization of the magnetic material. The effective magnetic anisotropy field H_a accounts for both internal and shape-induced anisotropies, as well as for any external DC magnetic field applied to the sample.

In many RF and microwave devices, magnetic materials in the form of thin films are used, where device operation is based on the generation of RF magnetic fields using current carrying conductors. Such a thin film structure is particularly suitable for devices that are meant to be compatible with planar IC technology. The conducting metal line is typically stretched parallel to the easy axis of the magnetic film, ensuring that the magnetic field generated by the current senses a high permeability, and the in-plane direction perpendicular to the easy axis is then commonly referred to as the hard axis (figure 1.6). The relevant permeability in this case is the so-called effective transverse permeability given by [23, 26, 27]

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(

)

(

)

2 ₂ 2 2 2 H M a H H M ω ω ω µ µ µ µ ω ω ω ω ⊥ + − − = = + − . (1.6)

The frequency dependence of this permeability is plotted in figure 1.6. The frequencies ω_FMR = ω ω_H

(

_H +ω_M

)

and ω_AR =ω_H +ω_M, in between which the real part of µ_⊥ becomes negative, are commonly referred to as the ferromagnetic resonance (FMR) and anti-resonance frequencies, respectively.

Figure 1.6: (Left) Schematic representation of a conducting metal line carrying a current I placed on top of a thin film magnetic element. The easy and hard axes are indicated. (Right) Effective transverse permeability µ_⊥ (solid: real part, dashed: imaginary part) along the hard axis. The broadness of the peak is due to the magnetic loss represented by α.

For a number of RF passive elements based on magnetic materials, analyzing the device operation requires an understanding of the propagation characteristics of electromagnetic waves in ferromagnetic films. The LLG equation (1.1) and its linearized form (the susceptibility tensor) given in (1.2) essentially describe the interaction of these waves with the elementary magnetic moments (electron spins) of the magnetic material. For this reason, the solutions of Maxwell’s equations in magnetic media are commonly referred to as “spin waves”. Some of the general properties of these waves are reviewed in appendix A. Having a small phase and group velocity (i.e. being slow waves), they are also frequently referred to as “magnetostatic waves” [23, 28].

An instructive way of thinking about spin waves is to view them as a nonuniform collective precession of the spins in a magnetic material [28, 29]. This is illustrated in figure 1.7, which shows a snapshot of the individual spins in the magnetic medium, each following a precessional motion with the angle changing

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along the array. Thus, unlike the uniform precession shown in figure 1.5 (where the moments are in phase and add up to a single magnetization), the neighboring spins in this case have a phase delay defined by the propagation wavelength λ (or equivalently, the wave number k=2 /π λ). The uniform precession shown in figure 1.5 thus follows as a special case with k =0.

Figure 1.7: Spin waves viewed as a collective precession of the magnetic moments in a ferromagnetic material. For a given time, the spins are shown in perspective (top) and from above (bottom), illustrating one wavelength.

For small values of λ, the misalignment of the neighboring magnetic moments due to their phase delay becomes significant. As a result, the exchange interaction (which is responsible for the magnetic ordering and tends to align the moments) becomes an important factor defining the propagation characteristics. Spin waves in this limit are therefore often referred to as exchange spin waves, as opposed to non-exchange spin waves, i.e. those having wavelengths large enough to ignore this effect. Throughout this work we will only be dealing with the latter.

1.5 Outline of this thesis

An overview of the ideas addressed in this work is given in figure 1.2, and can be summarized as follows:

• Chapter 2 presents an experimental demonstration of the advantages of incorporating ferromagnetic thin films into integrated microstrip transmission lines. Using sputtered Ni-Fe and Co-Ta-Zr films as the magnetic material, it is demonstrated that the quality factor and inductance

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of the microstrip lines increase, while also their attenuation and propagation wavelength are reduced.

• Chapter 3 deals with the shape-induced anisotropy field in patterned magnetic stripes. Patterning of the magnetic film is a simple method to increase its ferromagnetic resonance frequency and thus the upper frequency limit of device operation by taking advantage of the demagnetizing fields in the stripe. The shape-induced anisotropy field, however, is known to be nonuniform over the width of the stripe (larger near its edges). In this chapter, we use integrated transmission lines with different widths made on identical magnetic patterns to probe this nonuniform field and extract its distribution.

• Chapter 4 presents a series of high-resistivity granular Co-Al-O magnetic films deposited by reactive sputtering. While a very high resistivity is achieved by optimizing the deposition conditions, it is shown that the reduction in conductive loss due to the increased resistivity is accompanied by a high magnetic relaxation loss in the granular film.

• Chapter 5 presents a demonstration of nonreciprocal surface spin wave propagation in conductive Ni-Fe films. Transmission and reception of the spin waves is performed by microstrip antennas built on top of the magnetic film. The observed nonreciprocal effect can serve as a basis for integrated nonreciprocal microwave devices on silicon.

• Chapter 6 presents a theoretical analysis of magnetostatic wave propagation in layered media consisting of magnetic films separated by dielectric spacers. It can be applied to expand the work on devices presented in the previous chapters, as well as to the design of new integrated passives based on magnetostatic waves.

• Chapter 7 provides a summary of the main conclusions and presents a number of recommendations for future work in this area.

• Appendix A presents an overview of the main characteristics of spin waves in magnetic films.

• Appendices B and D provide details of calculations which have not been presented in the main text for brevity reasons, while appendix C describes details of the transmission line parameter extraction procedures.

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• Finally, appendix E presents the flowchart for the fabrication of devices used in this work.

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[13] “International Technology Roadmap for Semiconductors (ITRS)”, Semiconductor Industry Association, San Jose, California, 2007. (Available online at http://www.itrs.net/.)

[14] M. Yamaguchi, M. Baba, K.-I. Arai, “Sandwich-type ferromagnetic RF integrated inductor”, IEEE Trans. Microwave Theory Tech., Vol. 49, No. 12, pp. 2331-2335, 2001.

[15] A.M. Crawford, D. Gardner, S.X. Wang, “High-frequency microinductors with amorphous magnetic ground planes”, IEEE Trans. Magn., Vol. 38, No. 5, pp. 3168-3170, 2002.

[16] Y. Zhuang, M. Vroubel, B. Rejaei, J.N. Burghartz, “Integrated RF inductors with micro-patterned NiFe core”, Solid-State Electron., Vol. 51, No. 3, pp. 405-413, 2007.

[17] P.K. Amiri, B. Rejaei, M. Vroubel, Y. Zhuang, J.N. Burghartz, “Experimental determination of the nonuniform shape-induced anisotropy field in thin Ni-Fe films”, IEEE Trans. Magn., Vol. 43, No. 5, pp. 1880-1883, 2007.

[18] L. Li, A.M. Crawford, S.X. Wang, A.F. Marshall, M. Mao, T. Schneider, R. Bubber, “Soft magnetic granular material Co–Fe–Hf–O for micromagnetic device applications”, J. Appl. Phys., Vol. 97, pp. 10F907/1-3, 2005.

[19] Y. Zhuang, M. Vroubel, B. Rejaei, J.N. Burghartz, K. Attenborough, “Magnetic properties of electroplated nano/microgranular NiFe thin films for RF application”, J. Appl. Phys., Vol. 97, No. 10, pp. 10N305/1-3, 2005.

[20] P.K. Amiri, Y. Zhuang, H. Schellevis, B. Rejaei, M. Vroubel, Y. Ma, J.N. Burghartz, “High-resistivity nanogranular Co-Al-O films for high-frequency applications”, J. Appl. Phys., Vol. 101, No. 9, pp. 09M508/1-3, 2007.

[21] G.P. Rodrigue, “A generation of microwave ferrite devices”, Proc. IEEE, Vol. 76, No. 2, pp. 121-137, 1988.

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[22] P.K. Amiri, B. Rejaei, M. Vroubel, Y. Zhuang, “Nonreciprocal spin wave spectroscopy of thin Ni-Fe stripes”, Appl. Phys. Lett., Vol. 91, No. 6, pp. 062502/1-3, 2007.

[23] A.G. Gurevich, G.A. Melkov, “Magnetization oscillations and waves”, CRC Press, New York, 1996.

[24] W.S. Ishak, “Magnetostatic wave technology: a review”, Proc. IEEE, Vol. 76, No. 2, pp. 171-187, 1988.

[25] P.K. Amiri, B. Rejaei, “Magnetostatic waves in layered materials and devices”, J. Appl. Phys., Vol. 100, No. 10, pp. 103909/1-9, 2006.

[26] A. Sukstanskii, V. Korenivski, A. Gromov, “Impedance of a ferromagnetic sandwich strip”, J. Appl. Phys., Vol. 89, No. 1, pp. 775-782, 2001.

[27] B. Rejaei, M. Vroubel, “Impedance of a planar solenoid with a thin magnetic core”, J. Appl. Phys., Vol. 101, No. 7, pp. 074904/1-6, 2007.

[28] D.D. Stancil, “Theory of magnetostatic waves”, Springer-Verlag, New York, 1993.

[29] A.H. Morrish, “The Physical Principles of Magnetism”, Wiley-IEEE press, New York, 2001.

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Chapter 2 Microstrip Transmission Lines with

Ferromagnetic Thin Films

2.1 Introduction

Radio Frequency (RF) interconnects in standard silicon technology suffer from high loss and crosstalk arising due to the penetration of the electromagnetic field into the silicon substrate underneath [1-8]. Proposed solutions include the use of micromachining techniques as well as engineering the conductivity of the silicon [3-8] to achieve improved characteristics. These approaches, however, often require sophisticated processing and/or get in conflict with further requirements on the substrate conductivity dictated by the active device regions in monolithic RF systems. Moreover, in cases where distributed RF devices, such as transmission lines, are to be integrated on-chip (applications such as phase shifters, impedance transformers, filters, etc.), losses in the conductive silicon substrate can result in a higher attenuation constant. Field penetration in the silicon substrate is particularly problematic, due to their geometry, in coplanar waveguides and two-sided microstrip lines with a signal line at the front and a ground plane at the backside of the wafer. The latter also necessitate the use of through-wafer vias, as well as rather wide signal lines to achieve the commonly desired values of characteristic impedance (e.g. 50 Ω), resulting in excessive area consumption.

A solution applicable to the problems associated with both interconnects and on-chip distributed transmission lines is to realize them by using front-side

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microstrips. The advantage in this case is the shielding of the electromagnetic field provided by the metallic ground layer which is now in between the substrate and the signal line, thus reducing both crosstalk and substrate loss (see figure 2.1). However, the suppression of the parasitic substrate effects comes at the expense of significant increase of the conductor loss. This is caused by the small dielectric separation (d) between the microstrip and the ground, requiring a narrow signal line. This can be seen by considering the line inductance L, capacitance C, and resistance R (per unit length) which, while neglecting the fringe effects nearby the lateral edges of the microstrip, are given by

2 , , d w L C R w d w µ ε σδ = = = . (2.1)

Here, µ and ε denote the permeability and permittivity, respectively, of the dielectric layer separating the signal line from the ground plane; w is the microstrip width, σ is the metal conductivity, and δ = 2 /ωµ σ₀ is the skin depth in the conductors. Since d does not exceed a few microns in conventional IC processes, the attenuation due to conductor loss [9]

1 2 c R C L d ε α σδ µ ≈ = (2.2)

becomes very large. Note that the calculation presented for R (and thus αc) already

assumes conductors with a thickness exceeding the skin depth δ . The use of thinner metal layers would, therefore, lead to further increase of the attenuation. Moreover, the small value of d also results in a low characteristic impedance for the line, which is approximately given by

0 ( )

Z ≈ L C = d w µ ε . (2.3)

This is a crucial disadvantage for the implementation of resonant tanks, impedance matching networks and couplers used in RF circuits, which require a wide range of characteristic impedances (30-300 Ω).

In this chapter, it is experimentally demonstrated how these problems can be relieved by the incorporation of a thin ferromagnetic film into the transmission line structure. The increase in inductance, brought about by the high-permeability magnetic core, results in a reduction of conductor loss of the transmission line, as

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well as an increase in the characteristic impedance. Experiments carried out on microstrip lines equipped with thin Ni-Fe and Co-Ta-Zr films show significant increase in inductance and quality factor, as well as reduction of attenuation compared to conventional devices without a magnetic film.

2.2 Device fabrication and characterization

A schematic of the microstrip lines is shown in figure 2.1. Devices were fabricated with aluminum ground and signal layers with thickness of 2 µm and 3 µm, respectively. Isolation layers were 1 µm-thick plasma-enhanced chemical-vapor-deposited (PECVD) SiO2. The microstrip structures were built on standard silicon

wafers covered with 2 µm thermal oxide. Signal line widths ranged from 20 µm to 50 µm. The complete process flow is given in appendix E. These devices can be fully embedded into the multi-level interconnect stack of standard integrated circuit processes, though adding extra process steps for magnetic material deposition (sputtering in this work), patterning, and the corresponding isolation layer deposition.

Figure 2.1: Top view microphotograph (left) and schematic cross section (right) of the microstrip structure. The magnetic film (in our case, Ni-Fe or Co-Ta-Zr) was 100 µm wide and magnetized along the microstrip length. Ground and signal layers were 2 µm and 3 µm thick, respectively, and isolation layers consisted of 1 µm PECVD oxide. Magnetic core thickness ranged from 50 nm to 200 nm in devices based on Ni-Fe films, and was 1 µm in the Co-Ta-Zr transmission lines.

Two types of ferromagnetic materials were investigated in our experiments: (i) Ni-Fe films with a saturation magnetization of ~1.1 T, resistivity of ~16 µΩ-cm, and thickness ranging from 50 nm to 200 nm, and (ii) Co-Ta-Zr layers with a saturation magnetization of ~1.3 T, resistivity of ~100 µΩ-cm, and a thickness of 1 µm. The

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magnetic films were deposited by sputtering of Ni78-Fe22 and Co91.5-Ta4.5-Zr4

targets, and exhibited coercivities of ~3 Oe and ~0.3 Oe, respectively. In the case of the Co-Ta-Zr layers, an internal magnetic anisotropy field of ~20 Oe was induced by applying an external field during sputter deposition, as evident from B-H loop measurements shown in figure 2.2a.

Figure 2.2: (a) B-H loop measurements along the hard and easy axes of the (unpatterned) Co-Ta-Zr ferromagnetic film, indicating an internal magnetic anisotropy field of ~20 Oe. (b) Initial-magnetization B-H measurements along the hard axis (stripe width) of 4 mm-long rectangular Ni-Fe elements, demonstrating the increase of shape-induced anisotropy with decreasing stripe width.

The ferromagnetic films were patterned into long (1 to 4 mm) but narrow stripes of 100 µm width, by using ion milling and diluted HNO3 wet etching for Co-Ta-Zr

and Ni-Fe films, respectively. As a result, demagnetizing fields arising from the lateral confinement of the magnetic stripe lead to a shape-induced magnetic anisotropy field [10-12]. This anisotropy is larger for narrower magnetic patterns, as

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evident from figure 2.2b, which shows B-H measurements along the stripe width for rectangular Ni-Fe elements. Shape is the major source of anisotropy in these Ni-Fe films, since no magnetic field was used during their deposition to induce an internal anisotropy. It is worth mentioning that the shape-induced anisotropy field is nonuniform over the stripe width. Its value sharply increases towards the edges of the magnetic pattern, where the demagnetizing fields are larger [12-14] (see next chapter). For this reason, one can expect devices with identical magnetic films to exhibit higher ferromagnetic resonance frequencies if their signal lines are placed near the edges of the magnetic core rather than on top of its center region. Both types of devices were fabricated in our experiment in order to facilitate a comparison, as described in the next section.

Scattering parameter measurements on the microstrip lines were performed on a line-reflect-match (LRM) calibrated HP-8510 network analyzer in connection with a Cascade Microtech probe station. A ground-signal-ground (GSG) two-port configuration was used for the measurements, and no external magnetic field was applied to the devices. The scattering parameters were then converted to impedance parameters, from which the inductance, resistance, and capacitance per unit length were extracted (see appendix C).

2.3 Experimental results and discussion

2.3.1 Microstrip transmission lines with Ni-Fe films

Figure 2.3 compares the inductance per unit length (L) and quality factor (Q) of microstrips without Ni-Fe and with a 200 nm Ni-Fe film. The quality factor of the line is defined as Q=β/2α, where α and β are the real and imaginary parts of the complex propagation constant γ , respectively. They can be found from

(

)

j j C R j L

γ α= + β = ω + ω , (2.4)

where C and R are the capacitance and series resistance per unit length of the transmission line, respectively. (We have neglected the shunt conductance per unit length G, which is negligible for the dielectric layer used). The increase in L due to the high-permeability magnetic layer (~6 times at 1 GHz) results in a corresponding increase in Q (~5 times at 650 MHz and ~3 times at 1 GHz). The fact that Q does not increase by the same factor as L is related to additional magnetic and eddy current losses in the conductive Ni-Fe layer. These lead to an increase in R (e.g. by a factor of ~2 at 1 GHz), as can be seen in figure 2.4. In particular, the sharp increase

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in R due to ferromagnetic resonance, together with the associated drop in L, is responsible for the rapid drop of the quality factor at frequencies beyond 1 GHz.

Figure 2.3: Inductance per unit length (top) and quality factor (bottom) of microstrips without (dashed) and with (solid) a 200 nm-thick ferromagnetic Ni-Fe core. The signal line width is 20 µm.

It is worth noting that the integration of the magnetic film, as depicted in figure 2.4, also results in an increase of the transmission line’s capacitance per unit length C. The reason can be explained as follows. The capacitance can be approximated by

0 SL

C =εw d in the case of a microstrip without magnetic core, with ε being the permittivity of the dielectric oxide, w representing the signal line width, and _SL d

being the signal-to-ground separation. When the magnetic film is inserted, however, the capacitance is given by C_FM =C C₁ ₂

(

C₁+C₂

)

, where C₁=2εw_SL d is the signal-to-ferromagnet capacitance, and C₂ =2εw_FM d is the ferromagnet-to-ground capacitance with w_FM representing the magnetic core width. Since w_FM >w_SL in our

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devices, we have C₂ >C₁=2C₀, and thus C_FM >C₀. As expected, the capacitance increase is smaller for wider signal lines (where w is closer to _SL w_FM), e.g. reducing from ~50% for 20 µm-wide lines (as shown in figure 2.4) to ~30% for a 50 µm-wide signal line.

Figure 2.4: Resistance (top) and capacitance (bottom) per unit length of microstrips without (dashed) and with (solid) a 200 nm-thick ferromagnetic Ni-Fe core. The signal line width is 20 µm.

Figure 2.5 shows the increase in characteristic impedance of the devices, given by

(

)

0

Z = R+ j Lω j Cω , when the magnetic film thickness is increased, for devices with a signal line width of 20 µm. The incorporation of a magnetic film thus relieves the limitation on Z set by the small separation (d in (2.3)) between the signal line ₀ and the ground layer. As can be seen from equation (2.2), the increase in µ due to the high-permeability magnetic film also results in a reduction of the metal loss and the associated attenuation. This is shown in figure 2.6, which compares two devices with similar characteristic impedances (~22 Ω), one without and one with a 200 nm Ni-Fe core. It is seen from figure 2.6 that for the device with magnetic core the overall attenuation α is reduced from 1.6 dB/cm to 0.7 dB/cm at 500 MHz. Incorporation of the magnetic film, due to its high permeability, also results in a

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shortening of the propagation wavelength, which is shown to be ~65% at 1 GHz in figure 2.7. Combined with the lower attenuation, this can be beneficial in the further miniaturization of on-chip microwave devices, and in particular distributed elements such as phase shifters and impedance transformers.

Figure 2.5: Characteristic impedance (real part) of microstrip lines with a 20 µm-wide signal line with no magnetic core (dotted), 50 nm Ni-Fe core (dash-dotted), 100 nm Ni-Fe core (dashed), and 200 nm Ni-Fe core (solid).

Figure 2.6: Attenuation reduction as a result of incorporating a 200 nm-thick ferromagnetic Ni-Fe core into the microstrip transmission line. The dashed line represents a control device without magnetic core. The magnetic film is only advantageous up to ~0.9 GHz, beyond which ferromagnetic resonance losses increase the microstrip attenuation dramatically.

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Figure 2.7: Wavelength reduction ratio for a device with a 200 nm-thick Ni-Fe core, when compared to a similar device without magnetic core.

2.3.2 Microstrip transmission lines with Co-Ta-Zr films

Although clearly demonstrating the advantages of microstrips with ferromagnetic cores, the devices based on our Ni-Fe films suffer from a number of limitations. Firstly, the magnetic Ni-Fe layers are metallic, and thus conductive. To suppress the flow of eddy currents in these films (and the associated degradation of device performance) one has to use only very thin Ni-Fe layers. Increasing the Ni-Fe film thickness from 200 nm to 500 nm, for example, already results in a reduction of Q by a factor of ~2 due to the high conductivity of the magnetic film, rendering thicker Ni-Fe films essentially useless. The limited thickness of the ferromagnetic material, however, limits the performance enhancement (e.g. inductance and characteristic impedance increase) of the device.

A second issue is that the advantages associated with these Ni-Fe films are strongly limited by ferromagnetic resonance (FMR), persisting only up to ~2 GHz and ~3 GHz for quality factor and inductance increase, respectively (figure 2.3). The ferromagnetic resonance frequency can be increased in a number of ways: Finer patterning of the magnetic film can be used to enhance the shape anisotropy [10-12], thereby shifting FMR to higher frequencies. While using a thicker magnetic film would also increase the shape-induced anisotropy field, this is only a viable option for high-resistivity films where the flow of eddy currents is suppressed [15-20]. Other approaches include the use of an external magnetic field during device operation (which is, however, not practical for on-chip applications), as well as the use of materials with a higher saturation magnetization and internal magnetic anisotropy field [21]. For any given width of the magnetic core, however, an

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interesting approach to increase the FMR frequency is to exploit the nonuniform profile of the shape-induced anisotropy [12-14] by placing the signal line close to the magnetic film’s edges, as described below.

The inductance and quality factor of microstrip lines with and without an amorphous Co-Ta-Zr ferromagnetic film (with a resistivity ~6 times higher than Ni-Fe) are given in figure 2.8. The signal line is 50 µm-wide in this case and is located near the center of the magnetic stripe, as depicted in figure 2.1. The microstrips show an increase of inductance by a factor of ~11 at 4 GHz. Moreover, L remains constant up to ~4.5 GHz, and is higher than the inductance of the control lines up to ~6 GHz. The Q factor increases by a factor of ~6 at 0.7 GHz and remains higher than that of the control lines up to ~3 GHz.

Figure 2.8: Inductance per unit length (top) and quality factor (bottom) of microstrips without (dashed) and with (solid) a 1 µm-thick ferromagnetic Co-Ta-Zr core. The signal line width is 50 µm.

Note, that the fairly high FMR frequency in this device is mostly a result of the shape-induced magnetic anisotropy field, as the 20 Oe internal anisotropy (seen in

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figure 2.2a) is too small to lead to such a high resonance frequency. The high resistivity (large skin depth) of the Co-Ta-Zr material thus allows for the incorporation of a relatively thick (1 µm) magnetic film without inducing excessive conductive loss, thus maintaining a reasonable enhancement of Q factor of the device. Indirectly, it also improves the high-frequency behavior, as the shape-induced anisotropy field increases with the thickness of the magnetic film [10, 11].

Figure 2.9: Increasing the FMR frequency using the higher shape-induced anisotropy field near the magnetic stripe edges. For identical 1 thick, 100 µm-wide Co-Ta-Zr cores, microstrips with a 20 µm-µm-wide signal line placed at the edge of the magnetic stripe (solid) exhibit a much better high-frequency performance than devices with the signal line at the center of the stripe (dash-dotted). The dashed curve represents control lines without a magnetic core. Note, that the higher anisotropy field near the magnetic film edges comes at the price of a smaller effective permeability, reducing the inductance enhancement at low frequencies.

We next consider the effect of the signal line position on the FMR frequency. In order to more effectively probe the high demagnetizing field near the stripe edges, a

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narrower signal line is used in this case. Figure 2.9 depicts the inductance and quality factors of microstrip lines with 20 µm-wide signal lines, comparing devices with and without a Co-Ta-Zr magnetic core. Both cases of signal lines placed at the center and at the edge of the magnetic core are shown in this figure.

Looking at the centered line, it can be seen that the inductance enhancement in this device (a factor of ~8.5 at 4 GHz in figure 2.9) is slightly smaller than for the 50 µm-wide signal line shown in figure 2.8. This is likely a result of the increased influence of the narrow conducting line’s lateral edges, leading to a poor alignment of the RF magnetic field with the hard axis of the magnetic core. Similar to the previous case, the inductance L remains higher than that of the control lines up to ~6 GHz. Consistent with the expectation of a higher overall anisotropy field, the microstrip with a 20 µm-wide signal line placed at the edge of the magnetic stripe exhibits an improved frequency behavior, and the inductance enhancement in this case is maintained up to ~10 GHz. The higher anisotropy, however, also leads to a lower value for the magnetic permeability, translating into a smaller increase of inductance than in the device with a centered signal line. Nevertheless, inductance enhancement by a factor of ~6 is still realized at 4 GHz in this case. A similar pattern is seen in the quality factor, which remains higher than the control line values up to ~4 GHz for the signal line placed at the core edge, as compared to ~3 GHz for the centered line. Exploiting the nonuniform distribution of the shape-induced anisotropy is thus a possible option for optimizing the high-frequency performance of magnetic RF passives.

2.4 Conclusions

In summary, the advantages of incorporating ferromagnetic thin films into planar on-chip transmission lines have been demonstrated in this chapter using front-side microstrips with Ni-Fe and Co-Ta-Zr cores. Increases in the characteristic impedance, inductance, and quality factor, and decreases in attenuation and propagation wavelength have been shown to be feasible. Device characteristics of the Co-Ta-Zr lines were dramatically improved with respect to both non-magnetic control devices and transmission lines with Ni-Fe films. The high resistivity of Co-Ta-Zr allows for the incorporation of a relatively thick magnetic film without inducing excessive conductive loss. This results in an order-of-magnitude increase in inductance, while simultaneously maintaining a reasonable enhancement of the quality factor and improving the high-frequency behavior of the line by realizing a large shape-induced anisotropy.

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References

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[2] J.-K. Wee, Y.-J. Park, H.-S. Min, D.-H. Cho, M.-H. Seung, H.-S. Park, “Modeling the Substrate Effect in Interconnect Line Characteristics of High-Speed VLSI Circuits”, IEEE Trans. Microwave Theory Tech., Vol. 46, No. 10, pp. 1436-1443, 1998.

[3] G.E. Ponchak, A. Margomenos, L.P.B. Katehi, “Loss CPW on Low-Resistivity Si Substrates with a Micromachined Polyimide Interface Layer for RFIC Interconnects”, IEEE Trans. Microwave Theory Tech., Vol. 49, No. 5, pp. 866-870, 2001.

[4] J. Ankarcrona, L. Vestling, K.-H. Eklund, J. Olsson, “Low Resistivity SOI for Substrate Crosstalk Reduction”, IEEE Trans. Electron Devices, Vol. 52, No. 8, pp. 1920-1922, 2005.

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[7] K.J. Herrick, J.-G. Yook, L.P.B. Katehi, “Microtechnology in the Development of Three-Dimensional Circuits”, IEEE Trans. Microwave Theory Tech., Vol. 46, No. 11, pp. 1832-1844, 1998.

[8] A.M. Niknejad, R.G. Meyer, “Analysis of Eddy-Current Losses Over Conductive Substrates with Applications to Monolithic Inductors and Transformers”, IEEE Trans. Microwave Theory Tech., Vol. 49, No. 1, pp. 166-176, 2001.

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[10] G. Perrin, J. C. Peuzin, O. Acher, “Control of the resonance frequency of soft ferromagnetic amorphous thin films by strip patterning”, J. Appl. Phys., Vol. 81, No. 8, pp. 5166-5168, 1997.

[11] M. Vroubel, Y. Zhuang, B. Rejaei, J.N. Burghartz, A.M. Crawford, S.X. Wang, “Calculation of Shape Anisotropy for Micropatterned Thin Fe–Ni Films for On-Chip RF Applications”, IEEE Trans. Magnetics, Vol. 40, No. 4, pp. 2835-2837, 2004.

[12] P.K. Amiri, B. Rejaei, M. Vroubel, Y. Zhuang, J.N. Burghartz, “Experimental determination of the nonuniform shape-induced anisotropy field in thin Ni-Fe films”, IEEE Trans. Magnetics, Vol. 43, No. 5, pp. 1880-1883, 2007.

[13] R. I. Joseph, E. Schlömann , “Demagnetizing Field in Nonellipsoidal Bodies”, J. Appl. Phys., Vol. 36, No. 5, pp. 1579-1593, 1965.

[14] X. H. Huang, M. Pardavi-Horvath, “Local Demagnetizing Tensor Calculation for Arbitrary Non-ellipsoidal Bodies”, IEEE Trans. Magn., Vol. 32, No. 5, pp. 4180-4182, 1996.

[15] Y. Zhuang, M. Vroubel, B. Rejaei, J.N. Burghartz, K. Attenborough, “Magnetic properties of electroplated nano/microgranular NiFe thin films for rf application”, J. Appl. Phys., Vol. 97, pp. 10N305-1-3, 2005.

[16] P.K. Amiri, Y. Zhuang, H. Schellevis, B. Rejaei, M. Vroubel, Y. Ma, J.N. Burghartz, “High-resistivity nanogranular Co-Al-O films for high-frequency applications”, J. Appl. Phys., Vol. 101, No. 9, pp. 09M508/1-3, 2007.

[17] M. Munakata, M. Namikawa, M. Motoyama, M. Yagi, Y. Shimada, M. Yamaguchi, K.-I. Arai, “Magnetic properties and frequency characteristics of (CoFeB)x-(SiO1.9)1-x and CoFeB films for RF application”, Trans. Magn. Soc.

Japan, Vol. 2, No. 5, pp. 388-393, 2002.

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[19] L. Li, A.M. Crawford, S.X. Wang, A.F. Marshall, M. Mao, T. Schneider, R. Bubber “Soft magnetic granular material Co–Fe–Hf–O for micromagnetic device applications”, J. Appl. Phys., Vol. 97, pp. 10F907-1-3, 2005.

[20] D.S. Gardner, G. Schrom, P. Hazucha, F. Paillet, T. Karnik, S. Borkar, “Integrated On-Chip Inductors With Magnetic Films”, IEEE Trans. Magnetics, Vol. 43, No. 6, pp. 2615-2617, 2007.

[21] Y. Lamy, B. Viala, “Combination of ultimate magnetization and ultrahigh uniaxial anisotropy in CoFe exchange-coupled multilayers”, J. Appl. Phys., Vol. 97, pp. 10F910-1-3, 2005.

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Magnetic materials and devices for integrated radio-frequency electronics

Magnetic Materials and Devices

for

Integrated Radio-Frequency Electronics

Magnetic Materials and Devices for

Integrated Radio-Frequency Electronics

PROEFSCHRIFT

Pedram KHALILI AMIRI

Contents

Chapter 1

Introduction

1.1 A tale of towers and antennas

1.2 Radio-frequency integrated circuits

1.3 Why magnetic materials?

1.3.1

Improving conventional integrated passives

1.3.2

Implementing new integrated functions

1.4 Ferromagnetic materials at high frequencies

(

)

(

)

(

)

(

)

(

)

1.5 Outline of this thesis

References

Chapter 2

Microstrip Transmission Lines with

Ferromagnetic Thin Films

2.1 Introduction

2.2 Device fabrication and characterization

2.3 Experimental results and discussion

2.3.1

Microstrip transmission lines with Ni-Fe films

(

)

(

)

(

)

2.3.2

Microstrip transmission lines with Co-Ta-Zr films

2.4 Conclusions

References