Acoustic resonator

Abstract

A resonator includes a piezoelectric film that creates a longer acoustic path in a central region of the resonator than at an edge of the resonator.

Description

Technical Field

[0001] This application claims priority to U.S. Provisional Application No. 62 / 720,107 filed on August 20, 2018 and U.S. Provisional Application No. 62 / 720,111 filed on August 20, 2018, and the entire contents of these two prior applications are incorporated herein by reference. Background Art

[0002] The present invention relates to resonators and, more particularly, to changing the shape or form of a resonator film. Summary of the invention

[0003] A film bulk acoustic resonator (FBAR or TFBAR) consists of a piezoelectric material sandwiched between two electrodes and acoustically isolated from the surrounding medium. FBAR devices using piezoelectric thin films typically resonate in the frequency range of 100 MHz to 10 GHz. Aluminum nitride (AlN) and zinc oxide (ZnO), with thicknesses ranging from a few microns to tens of microns, are two common piezoelectric materials used in FBARs.

[0004] BROADCOM TM (formerly Avago Technologies) is one of the major manufacturers of FBAR devices. The main application of Avago FBAR is in 4G cellular phones, and they are in extremely high demand. Avago FBAR is present in and Avago’s FBARs are not available in its flagship products and there is not enough manufacturing capacity to meet the entire market demand. Avago is almost entirely focused on producing FBARs for cellular phones—except for other orthogonal markets. Domestic manufacturing capacity limits the availability of Avago’s FBARs.

[0005] Therefore, there is a long felt need for improved FBARs. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The present invention is illustrated by way of example and not limitation in the accompanying figures, in which like references indicate similar elements, and in which:

[0007] Figure 1A One embodiment of a side view of a simplified film bulk acoustic resonator (FBAR) structure is depicted.

[0008] Figure 1B One embodiment of a side view of a simplified solid state mounted resonator (SMR) structure is depicted.

[0009] Figure 2A and Figure 2B A pulse simulation with a square FBAR resonator is shown.

[0010] Figure 2C Plotted is the wave diffraction effect of a repeating aperture mask.

[0011] Figure 3A A simple model of the top-hat electric field is shown.

[0012] Figure 3B Draws Figure 3A Stress plot for a simple model of the top-hat electric field.

[0013] Figure 3C A more accurate stress model based on the Fourier components from low wavenumber cutoff to high wavenumber cutoff (resonator impulse response) is shown.

[0014] Figure 3D The simple sum of squares of the 10 lowest harmonics used to construct the top hat function is plotted.

[0015] Figure 3E The individual harmonics are plotted.

[0016] Figure 3F A square fundamental wave showing the variation in response strength is plotted.

[0017] Figure 3G Only the fundamental component of the top hat function is plotted.

[0018] Figure 4A One embodiment of a ground state resonator is depicted.

[0019] Figure 4B Another embodiment of a ground state resonator is depicted.

[0020] Figure 4C Another embodiment of a ground state resonator is depicted.

[0021] Figure 5A An embodiment of a lens focusing the resonator is depicted.

[0022] Figure 5B Another lens embodiment for focusing the resonator is shown.

[0023] Figure 5C Another embodiment of a focused resonator is depicted.

[0024] Figure 5D One embodiment of the geometry of the acoustic beam waist is depicted.

[0025] Figure 5E One embodiment of a resonator geometry is depicted.

[0026] Fig. 5F One embodiment of thickening is depicted using added material of a bonding layer with mismatched acoustic properties.

[0027] Fig. 6A One embodiment of a focused ground state resonator is depicted.

[0028] Figure 6B One embodiment of an injection pattern in a focused ground state resonator is depicted.

[0029] Figure 6C One embodiment of an injection pattern is depicted where there is injection in the resonator film and the electrodes.

[0030] Fig. 7A One embodiment of a cyclic axicon resonator is depicted.

[0031] Figure 7B is an embodiment of a cyclic axicon pattern.

[0032] Figure 7C and Fig.7D Pulse simulations of a cyclic axicon resonator are shown. DETAILED DESCRIPTION

[0033] The present invention discloses methods for improving acoustic resonator designs by changing the shape or form of the resonator film used. In one embodiment, the improvement in one embodiment can be based on doping the resonator film. In one embodiment, the improvement in another embodiment can be based on depositing additional material on the resonator film to produce convex or concave structures. The improvement in another embodiment can be based on etching or depositing patterns in the resonator film stack. In one embodiment, the deposited pattern or etching produces a structure similar to the diffractive embodiment of the optical axicon lens.

[0034] The following detailed description refers to the accompanying drawings, in which the same reference numerals represent the same elements, and specific embodiments of the present invention are illustrated in a schematic manner. The description of these embodiments is detailed enough to enable those skilled in the art to implement the present invention. It is understood by those skilled in the art that other embodiments may be utilized and logical, mechanical, electrical, functional and other changes may be made without departing from the scope of the present invention. Therefore, the following detailed description is not restrictive, and the scope of the present invention is limited only by the appended claims.

[0035] Glossary

[0036] FBAR: Film Bulk Acoustic Resonator, consisting of a piezoelectric material sandwiched between two electrodes and acoustically isolated from the surrounding medium. FBAR contains a resonator isolated by being suspended over an air gap and a resonator isolated by being positioned over a reflector (SMR). FBAR devices using piezoelectric film typically resonate in the frequency range of 100MHz to 10GHz.

[0037] Q Factor: The quality factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is and characterizes the bandwidth of a resonator relative to its center frequency. A higher Q indicates a lower rate of energy loss relative to the stored resonator energy; the oscillations die out more slowly. A pendulum suspended on a high-quality bearing oscillating in air has a high Q, while a pendulum immersed in oil has a low Q. Resonators with a high quality factor have low damping, so they loop longer. The bandwidth of a resonator can be defined in terms of its Q as: Δf = f0 / Q.

[0038] Acoustic resonator: An acoustic resonator, or bulk acoustic resonator, is a device consisting of a piezoelectric material sandwiched between two electrodes, which is acoustically isolated from the surrounding medium. FBARs are used as radio frequency (RF) filters in cellular phones and other wireless applications. Such filters are made of a network of resonators and are designed to allow only a specific frequency range to be received or transmitted.

[0039] Fourier Transform: The Fourier transform decomposes a signal as a function of time into its constituent frequencies. The equation defining the Fourier transform for any real number θ is:

[0040]

[0041] Here, the independent variable x represents time, and the transformed variable θ represents frequency.

[0042] Top-hat function: A "top-hat" function on the interval from -L to +L can be constructed by summing an infinite series of the following form (ignoring normalization):

[0043]

[0044] Where L is the length of the "top hat" function, and n is the nth harmonic of the series. Note that the "top hat" centered at x=0 consists only of odd harmonics, since it is a symmetric function (so the (2n-1) notation only transforms the exponent n from +1 to odd numbers to infinity). An approximate top hat function can be constructed by summing subsets of the harmonics. Figure 3C The simple sum of squares of the 10 lowest harmonics used to construct the top hat function is plotted. Figure 3D The individual harmonics themselves are plotted. Note that the "top hat" function defined here is truncated to zero for values ​​of x less than -L and greater than +L. In other words, for -L <= x <= +L, it is the above function multiplied by 1, and for |x|>L, it is the above function multiplied by 0.

[0045] Acoustic Lens: An acoustic lens is a structure that imparts relative delay to certain parts of the acoustic wave front. In the case of a "converging" or "convex" lens, the material in the central region of the lens has a lower acoustic velocity or is thicker than the surrounding lens material. Conversely, in the case of a "diverging" or "concave" lens, the material in the central region of the lens has a higher acoustic velocity or is thinner than the surrounding lens material. This effect may be referred to as "acoustic lensing."

[0046] Overview

[0047] FBARs are the enabling technology for 4G cell phones, while SAW filters are the enabling technology for analog cell phones. In most cases, such resonators are suspended over an air gap, but solid mounted resonators (SMRs) can also be used. The purpose of the FBARs in the data communication electronics of a cell phone is to distinguish between adjacent data channels (in frequency space). The more selectively the data channels are distinguished, the more channels can be used in a given cell phone frequency band. One limiting factor in how many data channels can be used is the quality factor or "Q" of the FBARs used as channel filters. The higher the Q, the narrower the channels that can be defined, and the more channels that can fit into a given RF transmission or reception bandwidth. Currently, a typical cell phone has 10 to 20 FBAR devices. These FBARs are used to define data channels.

[0048] There are several immediate benefits to reducing the data channel spacing: users have better data performance because more data channels can be utilized, and manufacturers' FBAR sales are proportional to the number of data channels. Improvements in Q depend on resonator size. Therefore, another benefit of improving the Q of a given resonator is that the size of the resonator can be reduced while maintaining or even improving its Q compared to existing designs. This increases the number of devices that can be fabricated on a single wafer, increasing yields and reducing costs. Therefore, improving the Q of FBAR devices is advantageous.

[0049] The reason an oscillator has a finite Q is (primarily) that in real physical systems there are always energy loss mechanisms. The Q of an oscillator system can be defined by its energy loss rate:

[0050]

[0051] FBAR devices are susceptible to energy losses due to a variety of mechanisms. One of the most important energy loss mechanisms is mechanical coupling to their substrate. Other energy loss mechanisms include resistive losses in the electrodes and mechanical (acoustic) losses in the piezoelectric and other materials in the FBAR "stack". Reducing the effects of the worst of these loss mechanisms will improve Q.

[0052] There are two main ways to reduce energy loss into the substrate: by suspending the FBAR above the pit so that its bottom surface is not in contact with anything, or by building a piezoelectric film on a sound reflector (SMR). For the purposes of this discussion, the term "FBAR" encompasses both types of resonators. In practice, the SMR appears to be inferior to the suspension approach in its ability to isolate the resonator structure, since it has the losses of the sound reflector in addition to the edge losses of a similar suspension design. Additionally, energy losses can be further reduced by forming the piezoelectric film in such a way that the acoustic energy is not directed to the edge of the resonator and from there into the substrate.

[0053] Substrate losses in an FBAR suspended over a gap occur only where the FBAR physically contacts the substrate, typically the perimeter of the FBAR. Typically, this results in the FBAR Q having roughly an area / perimeter relationship (larger devices tend to have higher Q). In the case of an SMR device, the entire resonator film is in mechanical contact with the substrate via a reflector stack, but the purpose of the reflector is to acoustically decouple the bottom surface of the resonator from the substrate. However, even though the edges of the SMR may be mechanically separated from the substrate, the SMR may still have the undesirable behavior of excessive parasitic modes caused by acoustic waves propagating tangentially to its surface. Additionally, in the case of an SMR without edge coupling to the substrate, the parasitic modes may be much larger than those in a similar FBAR.

[0054] Figure 1A One embodiment of a simplified FBAR 100 structure is depicted. In this embodiment, a piezoelectric membrane 110 is suspended above a void or dimple 120. The membrane 110 has conductive electrodes 130 on the top 130A and bottom surfaces 130B to provide electric field coupling to the membrane 110 and define the shape of the resonator profile. The portion of the membrane 110 between the bottom and top electrodes is a region 160 that is under piezoelectric stress.

[0055] Figure 1B Another embodiment of a simplified FBAR structure is depicted in which the piezoelectric film is constructed over the reflector instead of over the pit or void. Such a device is called a solid-mounted resonator (SMR). An SMR or solid-mounted resonator is similar to an FBAR, but it utilizes an acoustic reflector instead of an undercut isolation void. In one embodiment, the reflector is an acoustic Bragg reflector stack. Although the following illustrations use an FBAR structure with a void, existing improvements to the FBAR structure can be used for either structure.

[0056] A simple form of FBAR is constructed as a stack of planar layers of material. The resonator 150 itself consists of a top electrode 130A, a layer of piezoelectric material 140, and a bottom electrode 130B. In one embodiment, the piezoelectric material 140 is aluminum nitride (AlN) or zinc oxide (ZnO).

[0057] The resonator 150 is built with the cavity 120 (or reflector 125, if an SMR) underneath it, and is attached to the silicon substrate 180 only at its edges. In one embodiment, the cavity 120 is made by cutting one or more through holes in the AlN layer using a chemical etching process. Since the resonator 150 is built above the cavity 120, only its edges can be mechanically coupled to the substrate 180. If care is taken to design the resonator material to be low-loss (mechanically very homogeneous and stiff, and the electrodes and interconnects very conductive), the only significant losses will be at the edges of the resonator that are in contact with the substrate.

[0058] How much energy actually reaches the edge depends on how well the waves can bounce back and forth on the surface of the FBAR 100, and on the shape of the resonator. A square is a poor choice for design because of its high degree of symmetry and parallel sides. Waves can reflect back and forth on the surface of a square and accumulate to significant amplitudes via constructive interference. In one embodiment, the FBAR structure utilizes an irregular pentagon or other asymmetric polygon with an unreasonable length ratio. Each side is a different length to reduce reflections.

[0059] Figure 2A and Figure 2B Pulse simulations with a square FBAR resonator are shown. The presence of a pronounced "ribbon" structure is evidence of constructive interference at the surface.

[0060] Figure 2C The wave diffraction effects of a repeating aperture mask are plotted. This shows the evolution of the lateral (parasitic) mode structure. The example shown here is a series of repeating square apertures spaced at twice the (effective) acoustic film thickness. This example simulates an SMR structure, so the bottom surface of the resonator has no aperture mask, while the top surface has an aperture mask (top electrode profile). It is assumed that the wave energy diffracted to the edges of the apertures is lost to the device substrate. The number shown is the nth aperture. Frame 1 contains the initial distribution of the pulse energy, and all subsequent frames contain repeated diffractions from the edges of the device. Modeling standing waves in a resonator as traveling waves in a "stack" of identical resonators facilitates physical insights.

[0061] An analogy that may explain why this type of modeling is used is a long corridor with doorless doorframes set at repeated intervals, such that a person traveling in a straight line along the corridor will pass through each doorframe. There is some positional uncertainty or ambiguity in the positions of people walking through the corridor. The positional uncertainty of travelers makes it impossible for them to pass "cleanly" through a doorframe without being slightly deflected by the doorframe. As travelers travel along the corridor, they accumulate uncertainty in their direction of travel because they repeatedly, albeit (initially) weakly, interact with the doorframes. As their direction of travel becomes less and less straight along the corridor, their interactions with the doorframes become stronger and stronger. Eventually, the travelers' directions of travel become confused, such that collisions with doorframes dominate their motion. Obviously, minimizing interactions with doorframes is important for travelers to walk farther along the corridor.

[0062] In the "corridor analogy", the corridor and door frames are arranged linearly, which are only traversed once by passengers. Although easier to understand, it is equivalent to a similar analogy in which the corridor is replaced by a single segment of the hall door of the "room", and the door frame at each end includes a "reflector" that will cause the passenger traveling to the door frame to reverse the component of his movement along the hall door (similar to "a ball bouncing off the wall"). In this analogy, the passenger will "bounce back and forth" between the reflectors in the door frame in the small "room". However, the passenger will still have a weak position uncertainty, as in the above corridor analogy, which will lead to (initially) a weak interaction with the door frame and accumulate uncertainty in their direction of movement. In the end, the movement of the passenger will become as chaotic as in the corridor, although it is more difficult to understand why because of the presence of the "reflector" and the interference of the passenger's forward and backward movement in the room in the description to the imagination.

[0063] One approach is to model the standing waves in a resonator as traveling waves in a repeated "stack" of identical resonators, much like using a "corridor" description instead of a "room" description. The two approaches are equivalent, although they facilitate different physical insights. Figure 2C The simulation exploits this analogy.

[0064] Another way to reduce the energy lost at the edges of the resonator is to suppress the harmonics introduced by driving the entire resonator surface. In a standard resonator, the driving force across the resonator film is constant from one area to the next (constant stress) because the electric field between two parallel planar electrodes is constant (except at the edges).

[0065] The stress induced in the FBAR film is a function of the applied electric field and the piezoelectric response of the material to the electric field. In the case of an FBAR device, the RF electric field tends to be spatially constant across the bulk of the material between the top and bottom electrodes. One way to represent the mode structure of the waves induced by the electric field is the Fourier analysis of the driving field. In the typical case where the applied RF electric field is constant everywhere between the top and bottom electrodes and zero elsewhere, we can use a top hat function and study the resulting Fourier wave components. The top hat function is zero outside a specified range and has a constant finite value within the specified range. Typically, the function is normalized so that the product of its length and amplitude is unity.

[0066] exist Figure 1A In the FBAR 100 shown, the electric field (and resulting material stress) is constant in the bulk of the material between the electrodes and falls off rapidly to zero outside the electrode region. Figure 3A Figure 1 shows a simple model of the top-hat electric field. Because the response of the piezoelectric film is modeled as linear and proportional to the applied electric field, the stress induced in the material should be constant between the electrodes and drop to zero outside the electrodes, as Figure 3B shown.

[0067] The Fourier components in the (impulse) response should generally not contain wave components with higher frequencies than the resonance driven in the bulk material. Unless the film is driven to a higher order excitation mode than the fundamental, for example by nonlinear effects, the shortest wavelength (high wavenumber cutoff) that the Fourier synthesis should include is approximately twice the acoustic thickness of the FBAR. The longest wavelength (low wavenumber cutoff) that the Fourier synthesis can include is twice the acoustic length (or width) of the FBAR device. Therefore, the waves of a limited range accumulate and represent the response of the material to the driving electric field. This analysis ignores nonlinear effects.

[0068] Figure 3C A more accurate stress model based on Fourier components ranging from low to high wavenumber cutoff is shown. The response is calculated by summing the Fourier components of the top hat function in the range between the low and high wavenumber cutoffs and then squaring the resulting resultant function. In this model, rapid fluctuations in amplitude near the edges of the resonator become apparent.

[0069] The energy transfer to the edge of the FBAR device depends on the number, spatial frequency and amplitude of the harmonics. Reducing the presence of these harmonics will prevent them from constructively interfering and accumulating to transfer significant amounts of energy. Since there is a finite upper limit on the frequencies of the Fourier components that can be used to construct the actual response, there may be significant spatial modulation of the response to a spatially constant but time-varying (electric field) stimulus.

[0070] Having only a few lowest harmonic components available to construct an approximate top-hat function leads to the seemingly undesirable result of having large spatial fluctuations in the response function. However, energy transfer depends on the product of the variation in the intensity of the composite function and the speed at which the variation occurs. Therefore, even large variations in the intensity of the resulting waveform from the ideal top-hat function do not necessarily indicate large energy transfer. If the waveform varies slowly in space, energy transfer to the edge of the device may still be small. Figure 3F The first-order harmonic ( Figure 3G In the limit of approximating the top hat by the fundamental component of the top hat function shown in ), something interesting happens: the rate of change of the response intensity is kept to a minimum, so the energy transfer to the edges of the response field (the edges of the device) is minimized.

[0071] Therefore, making a planar resonator structure have a constant top-hat stress distribution on its surface is not a good way to make a low-loss resonator. In one embodiment, variations of the design that can be used to produce a spatial stress distribution in the resonator similar to the fundamental component of the top-hat function include:

[0072] Ground state resonator

[0073] Focusing resonator

[0074] Focusing the ground state resonator

[0075] ·Circular Axicon Resonator

[0076] Embodiments of Improved FBAR

[0077] Ground state resonator

[0078] This design exploits the fact that the electric field strength within the piezoelectric film is cone-shaped and aligned with the piezoelectric axis of the film if the electrodes do not extend all the way to the edge of the film.

[0079] Figure 4A One embodiment of a ground state resonator 400 is depicted in which a pit 440 beneath the piezoelectric film 410 is quite deep, and a bottom electrode 430 is placed on the bottom of the pit 440. The bottom electrode spans only a portion of the resonator to produce a tapered electric field toward the edge of the resonator and a stronger electric field toward its center. This illustration shows an inhomogeneous electric field.

[0080] Figure 4B An alternative embodiment of a ground state resonator FBAR 450 is depicted, wherein a bottom electrode 480 is located on the bottom of a substrate 470, with an insulating and low loss substrate.

[0081] Figure 4C Depicted is the use of oxide wafers Figure 4BAn embodiment of a ground state resonator of the present invention. The Si device layer 496 is used to support the resonator film. When etching the pits, the etching stops on the oxide substrate 498. The bottom electrode 499 is located on the back side of the oxide substrate 498.

[0082] In the ground state resonator, the size of the bottom electrode 480 is smaller than the membrane 410. This will result in a sizeable fringe of electric fields towards the edges of the resonator. The effect of the fringe fields is to reduce the electromechanical response near the edges of the piezoelectric membrane. By adjusting the response of the membrane to more closely match the (idealized) half-cosine shaped deflection, higher frequency modes tangential to the resonator surface will be reduced. This will reduce energy transfer to the edges of the device and improve the Q factor.

[0083] However, any embodiment that moves the top or bottom electrode away from the piezoelectric material has disadvantages. The most important disadvantage is that the strength of the electric field that drives the piezoelectric material is inversely proportional to the distance between the electrodes.

[0084] Focusing resonator

[0085] The acoustic waves can be focused by shaping the resonator to produce a conical convex region in at least a portion of the resonator. The shaping is to change the acoustic thickness of the resonator so that it forms more of a convex (or concave) lens than a flat parallel sheet structure.

[0086] Figure 5A One embodiment of a focused resonator is depicted. A convex structure 520 is formed on top of the resonator 510. In one embodiment, the convex structure 520 is located above the top electrode. In one embodiment, the top electrode 515 can be located on top of the convex structure 520.

[0087] In another embodiment, the convex structure 530 may be formed by thickening the central portion of the resonator 540, such as Figure 5B As shown. In one embodiment, the convex structure 535 can be formed by additionally depositing material in the central portion of the resonator. In one embodiment, such deposits can be tapered, thereby forming a convex area. In one embodiment, thickening the resonator 540 like a lens allows the resonator 540 to act like a lens and focus the acoustic power away from the edges. In one embodiment, the thickening can be achieved by applying additional piezoelectric material through an aperture mask by sputtering. Alternative methods of forming this shape in the resonator can be used, including etching or depositing additional layers of material.

[0088] In one embodiment, the additional material thickness may be a few atomic layers or less, such as a fractional atomic layer, by using a sparse partial coverage of atoms in the center of the resonator.

[0089] In another embodiment, as an alternative to thickening the center portion of the device, the edges of the device may instead be thinned. In one embodiment, the thinning may be achieved by ion milling or some other etching technique (wet or dry) that allows for appropriate spatial selectivity, such that only the portion of the device that needs to be thinned is etched. Either method of adding material or subtracting material will be equivalent, as the end result is a convex (or concave) lens shape relative to the acoustic thickness of the device. However, depending on the device design it may be advantageous to add or subtract material, and which one to use will depend on the design details and available manufacturing processes.

[0090] Figure 5C Another embodiment of a focused resonator is depicted in which a hardened electrode structure is included in the "material stack" of the device. The hardened electrode structure 555 provides a DC electrostatic bias field to the edge of the device. The component of the applied DC field perpendicular to the plane of the device will preload the piezoelectric material of the resonator 560, causing it to harden and have a slightly higher acoustic velocity (or in the case where a diverging lens is required, the resonator electrodes can have a DC bias applied to them and an additional fringe field added to reduce the total field at the edges). This local hardening will cause areas under stress to have shorter acoustic paths, while areas not under stress have longer acoustic paths near the center of the device, even if the physical thickness of the film is constant. The advantage of this embodiment is that it is electrically adjustable for tunable device behavior. However, it does require a stable bias voltage to adjust the focus.

[0091] Focusing resonators work by creating an acoustic path that is longer in the center region of the resonator than at its edges. This causes the curvature of the wavefront in the resonator to be corrected to reduce the energy that propagates into the substrate at the edges of the resonator by diffraction. In general, for a given wavelength and resonator size, the acoustic path will be elongated by about the same amount, regardless of whether the elongation is accomplished by changing material thickness, stiffness, or other means.

[0092] In one embodiment, the increased thickness is based on considerations of wavefront diffraction. The criterion for suppressing diffraction losses into the substrate is to correct the curvature of the wavefront propagating within the resonator, which is opposite to the curvature caused by diffraction. In this way, the wavefront remains perpendicular to the surface of the resonator and does not propagate energy to the edges of the resonator.

[0093] If the waves within the resonator are considered as traveling waves rather than waves reflected between the resonator boundaries, a procedure similar to the standard procedure can be used to find the divergence of the waist of a Gaussian beam. The curvature of the wavefront is zero at the waist and also approaches zero as z → ±∞. It is equal to 1 / R, where R(z) is the radius of curvature as a function of position along the beam, and is given by

[0094]

[0095] where the waist is w0 and z R is the Rayleigh range. Figure 5D The geometry of the beam waist is shown.

[0096] Therefore, when the beam waist is set to the resonator diameter w0 = d, the Rayleigh range After substitution and setting z = λ / 2 (for a half-wavelength thick resonator), the geometry of R(z) is:

[0097]

[0098] The equation for the curvature of the resonator thickness or half the wavelength from the beam waist is used to calculate the added thickness. That is, the beam waist is located on the bottom surface of the resonator, and the calculation determines the curvature of the wavefront at the top surface. The calculation involves the wavefront very close to the beam waist (very close to the diffraction near field). Once the curvature is calculated, and given the size of the resonator, the distance required to add to the acoustic path length at the center of the resonator can be determined.

[0099] Given the curvature of the wavefront at a given distance from the beam waist, we can use simple geometry to find the added thickness z.

[0100]

[0101] Use the small angle approximation θ = (d / 2) / R

[0102]

[0103] To simplify R(z), we note that the 1 in the brackets is R >>z contributes very little, so by eliminating:

[0104]

[0105] For z = λ / 2,

[0106]

[0107] Using this equation to calculate some examples shows that increased thickness is easily achievable. For f = 2.5 GHz, λ = 4 μm (assuming AlN), and d = 100λ / 2 = 200 μm, Angstroms. f = 600 MHz, λ = 16.7 μm (assuming AlN), and d = 400 μm, Angstrom.

[0108] Thus, an added thickness of a few atoms at the center of the FBAR can significantly improve its Q. The added thickness does not have to be a continuous sheet of AlN (or other material in the electrode material or device stack) molecules. In one embodiment, it can be a sparse molecular density of only a partial monolayer and still contribute to a variation in acoustic thickness, which is an average fraction of the molecular layer thickness. In one embodiment, the added material can consist of an additional bonding layer with acoustic properties, i.e., neither a resonator nor an electrode structure. In one embodiment, such added material can have an acoustic mismatch such that the layer can be physically thicker than represented by the above formula, but still introduce a phase delay similar to the phase delay introduced by a very small thickness change described by the above formula. In one embodiment, the relationship of the thickness of the materials that can be bonded can depend on the acoustic properties of the materials.

[0109] Figure 5E One embodiment of the geometry of the center region of the resonator is depicted, showing the size of the relative thickening of the resonator material. The relative thickening can be achieved by adding additional material in the center region or by thinning the edge regions. In one embodiment, the material added to thicken the center portion of the resonator will have a thickness similar to that of the existing Figure 5A and / or Figure 5B The same form shown in , except that the added thickness will be larger (physically thicker), but the sound waves extending into the added material will have greatly reduced amplitude because the mismatched material will be only minimally coupled acoustically to the resonator structure itself.

[0110] In one embodiment, the resonator can be thinned toward its edges to create a convex shape. In one embodiment, the thinning can be achieved mechanically by etching or milling. In one embodiment, the thinning can be achieved by passively stressing the piezoelectric material using ion implantation as described below or by actively stressing the piezoelectric material using an inhomogeneous electrostatic field as discussed above.

[0111] Any method of inducing a variation in acoustic thickness across a resonator will result in some broadening of the resonant frequency of the device, since the resonant frequency of the device is determined by its acoustic thickness. However, care must be taken to optimize the design. There is an implicit tradeoff between the improvement in Q due to the reduction in energy losses from focusing and the reduction in Q from extending the operating frequency of the resonator over a wider bandwidth. However, a 2.5 GHz resonator with very low mass electrodes will have a film thickness of about d = v / 2f = 2 μm. If the thickness variation is a few atomic layers, say half a nanometer, then the bandwidth is widened by only a few tenths of a thousandth. This appears to provide a Q limit of:

[0112]

[0113] The bandwidth widens due to the thickness variation. Since the best current devices have Q-wells below 10,000, this widening is relatively small compared to the benefit obtained from shaping the resonator.

[0114] A resonator will automatically seek the resonant frequency with the least loss. Therefore, the resonator itself will prefer the low frequency portion of the resonance as this will cause the waves to propagate farthest from the edge of the device. If an impulse response is presented to the resonator, the frequencies with the lowest losses will persist longest and have the greatest gain applied to them by the resonator's feedback amplifier electronics. Therefore, the portion of the resonance corresponding to the resonant frequency range at the center of the device will dominate. However, in one embodiment, this effect can be enhanced by pulling the resonator's drive frequency slightly towards the lower shoulder of its operating band. The FBAR can preferentially drive the portion of the resonance that matches the central, lower frequency portion of the shaped resonator structure. This technique improves the performance of the device by effectively modifying the device's response to be greater at the center than at the edges. This will result in a biased Figure 3E The half cosine response and away from Figure 3A By adjusting the drive frequency, the system mitigates Q losses from resonator bandwidth extension due to changes in device thickness (convexity), and provides additional mitigation of energy losses at the resonator edges by reducing excitation of the resonator edges (via resonant mismatch).

[0115] Focusing the ground-state resonator

[0116] Another way to tune the response of the device piezoelectric material to an applied electric field is to implant ions into the device piezoelectric material near the edge of the resonator. This changes the physical properties of the material. In one embodiment, the implantation is performed after the resonator piezoelectric material is constructed but before the FBAR is created. In another embodiment, the piezoelectric material of the electrode structure rather than the FBAR can be hardened because the acoustic waves within the device travel through the electrodes as well as the piezoelectric material. Local changes in the acoustic path length are somewhat agnostic to the location where the change occurs along the acoustic path. For example, ion implantation can be used for hardening of metals.

[0117] Obviously, hardening of the electrode structure rather than the piezoelectric material will leave the piezoelectric response of the device unchanged from its ordinary uniform response. Hardening without changing the piezoelectric response may have design advantages. Alternatively, if more changes to the piezoelectric material are required than would be the case with acoustic focusing alone, it may be advantageous to "overexpose" the ion implantation in some areas of the piezoelectric material and implant ions in the central portion of the electrode structure to compensate. For example, the ion implantation may be overexposed near the edges of the resonator piezoelectric material, and then additional ions may be implanted in the central portion of the electrode structure. Design flexibility may be allowed by separate ion implantation patterns for the piezoelectric material and the electrode structure.

[0118] In one embodiment, the process deposits a uniform thin film on a uniform substrate and then post-processes the thin film layer. In one embodiment, the concentration of the implanted ions will be approximately zero in the central region of the resonator and then have a number density such that it gradually changes the piezoelectric properties of the material towards the edge of the device, resulting in a downward parabolic piezoelectric response. This allows the use of a simple planar electrode structure that is familiar from FBAR construction and suitable for large-scale manufacturing of devices on a wafer. Of course, the electric field strength as a function of space can be appropriately varied and the material response adjusted.

[0119] The density of the ion implantation gradient increases with radius from the center of the device, which also stiffens the piezoelectric material, causing the local velocity of sound through the material to vary upward. Since the implantation is greater near the edge of the device, the speed of sound is greater near the edge. Increasing the speed of sound is the same as reducing the acoustic thickness of the device material. This effective thinning of the acoustic thickness is used to create a self-focusing effect to further confine the acoustic energy away from the edge of the device.

[0120] Fig. 6A One embodiment of a focused ground state resonator 600 is depicted. The resonator film 610 has a bottom electrode 625 and a top electrode 620. The resonator 610 is located above a pit 630 in a substrate 635. The stippling 615 of the resonator film 610 shows one embodiment of an implantation gradient for the ions. In one embodiment, the penetration depth is about 1-2 μm. For resonators operating below 1-2 GHz, this can be achieved by implanting in the top portion of the film. In one embodiment, the system is flexible in terms of ion concentration - the total number of ions is roughly the same as that required to fully harden the material, but the density is concentrated near the top surface of the film. In one embodiment, the ion density is greatest at the stopping depth of the ions in the material, rather than at the top surface.

[0121] By selectively partially disrupting the electromechanical response of the piezoelectric film of the resonator, its response to the drive field approximates a half-cosine function, even when the film itself has a constant physical thickness and even when the electric field from the electrode structure is uniform. The implanted ions disrupt the crystal structure of the film necessary for piezoelectric behavior, stiffening the structure of the material by placing the ion-implanted portions of the film under compressive stress, and the implanted electric polarization can be increased to further enhance the compressive preload by providing an electric field acting locally on any localized portion of the piezoelectric material that still retains the piezoelectric behavior associated with the unbroken crystal structure.

[0122] The spatial structural degradation of the piezoelectric material's response to an electric field (and its ability to generate an electric field) will cause the device's response to be closer to the ground state, the fundamental mode of resonance. Figure 1A and Figure 1B A very simple theoretical 2D cross-sectional slice (shown in Figure 1, where the dimension "sticking out of the page" has been suppressed) has the "fundamental mode" of resonance being the largest half-cosine function that fits between the edges of the resonator. It has the longest wavelength of any mode. For a planar resonator, the "fundamental mode" would be the lowest order harmonic mode of the 2D structure (similar to a half-cosine, but in more than one dimension). The concomitant reduction in active acoustic modes tangential to the device surface would reduce the energy transmitted out of the resonator structure and improve its Q factor. Active acoustic modes refer to the energy content of the available vibrational modes.

[0123] Note that the simplified structure shown here shows a time slice through the resonator structure, rather than the exact response of the resonator as an actual planar structure. The depiction is a 2D cross-sectional slice through the 3D planar structure. This suppresses the portion of the stress / deflection (response) pattern that "sticks out of the page", leaving only a 2D depiction of the response. However, since the thickness of the resonator is viewed as a slice through the repeating structure (similar to the hallway above), the sound waves pass through in one direction, rather than bouncing back and forth, so it is actually a "time" dimension, not a spatial dimension. The deflection pattern is not a cosine function in just 1D, but is the product of two functions, one "across the page" and one "inside / outside the page".

[0124] The full response of a planar resonator depends on the three-dimensional resonator shape. For example (when viewed from the top), a square resonator will have a cosine function along its width times a cosine function along its height. In the cross section, one of the cosine functions is chosen as representative. A circular resonator structure will have a Bessel mode structure as its resonant mode, not a cosine mode. Therefore, a slice through a square gives an actual solution to the response along the portion of the cross section shown, but a slice through a circular resonator will not have a cosine mode as its response. Instead, the response looks somewhat like a cosine function, being larger in the center and zero at the edges, and it is similar to the lowest order mode of the square, but it is not exactly the same. Therefore, while a side-view cross section of a square resonator is indistinguishable from a side-view cross section of a circular resonator, the modes in the two will be different due to the shape of the material that is suppressed in the figure.

[0125] Spatially structured compressive preloading of the piezoelectric material using ion implantation increases its mechanical stiffness and increases the speed at which sound travels through the material. The increase in local sound speed serves to reduce the local acoustic distance in the material, causing its acoustic shape to be convex lens-like in the ion-implanted regions of the resonator film.

[0126] In one embodiment, spatially structured implantation of ions with complementary charges in the upper and lower volumes of a piezoelectric material can be used to place nearby materials in a locally generated electrostatic field.

[0127] Figure 6B One embodiment of an ion implantation pattern 680 is depicted. If the piezoelectric material subjected to this implanted electrostatic field does not have its electromechanical response completely destroyed by the implantation process, it will be placed under tensile or compressive stress to extend or contract due to the applied (implanted) electrostatic field. The placement of the implanted ions in the upper and / or lower portions of the material will affect whether the generated electrostatic field is oriented along or against the piezoelectrically active axis of the material. The appropriate arrangement of the implanted ions can be used to place the material under compressive piezoelectric action, thereby enhancing the compressive effect of the ion implantation and improving the behavior of the resulting acoustic lens. For example, implanted positive ions that provide a positive charge embedded in the top portion of the AlN film will establish an electric field that points downward through the AlN to the ground plane below. If the AlN film is oriented so that the embedded electric field causes the film to piezoelectrically contract, the film will be slightly stiffer due to the preload than areas not subjected to the embedded electric field. Conversely, implanting ions so that the resulting embedded electric field causes the piezoelectric material to expand will also preload the film by placing it under tensile stress rather than compressive stress. There are differences in the behavior of tensile and compressive preloads that may lead to favorable adjustments in film and device behavior. Figure 6CAnother implantation method is depicted, where ion implantation is applied to the resonator as well as the electrode. The electrode in this illustration is shown thicker to allow for illustration of an exemplary implantation pattern. Note that the portion of the resonator below the electrode also has ion implantation. In one embodiment, this design uses separate ion implants for the resonator and electrode.

[0128] Circular Axicon Resonator

[0129] Fig. 7A One embodiment of a cyclic axicon resonator is depicted. One embodiment of a "cyclic axicon resonator" resonator 700 design consists of an etched pattern of rings 730 on the top electrode 720 of the device. Etching the top electrode 720 causes the resulting "ripple" structure to have the sharpest, most vertical sidewalls, which has the sharpest contrast steps in the resulting acoustic structure. This may be desirable in cases where sharp steps in thickness give a favorable diffraction pattern. Other ways of producing the ring pattern may be used, such as material deposition, cutting, ion implantation to harden and change the hardness of the piezoelectric material or to change the hardness of the electrode structure, or other methods. These methods can give a more gradual change in the acoustic depth of the axicon ring, resulting in a different diffraction behavior that has different advantages compared to the diffraction behavior produced by an axicon mask with sharp depth steps.

[0130] The etch depth of the circular "corrugations" 730 is tens of nanometers for resonators with multi-GHz operating frequencies and may exceed one micron for resonators 710 with sub-GHz operating frequencies. The etch depth relative to the thickness of the resonator film determines the contrast of the resulting diffractive acoustic element and therefore has an impact on the strength of the conversion of acoustic waves in the resonator into a Bessel beam-like configuration. The spacing of the circular corrugations is lithographically matched to the natural operating frequency of the resonator. Therefore, in one embodiment, each resonator of a particular size and thickness can have a structure that is optimized to match in terms of ring spacing and ring depth.

[0131] Figure 7B Depicted using Figure 7C and Fig.7D An exemplary cyclic axicon mask for pulse simulation is shown. Fig.7D After the steady-state pattern shown develops, it remains essentially unchanged, indicating very low coupling to the external environment.

[0132] In one embodiment, this design can solve the problem of mechanical film breakup at the center of known circular FBARs. Mechanical breakup is caused by the divergent tendency of the Bessel function's power per unit area at its center. For example, in the case of a Bessel beam, each of the ring-like structures of the beam carries an equal amount of power, and therefore the power density at the center point is high. In one embodiment, this can be solved by changing the height of the center portion of the circular corrugations so that the power is slightly offset from the center of the structure. In one embodiment, the axicon mask (ring set) can be applied to non-circular resonator shapes, such as irregular pentagonal shaped resonators.

[0133] Variations on the cyclic axicon resonator design can use a diffractive structure that intersects a spherical wavefront with a plane, rather than uniformly spaced concentric rings. Such diffraction patterns are known as Newton's rings or continuous or stepped zone plates. The diffraction pattern resembles 7A to 7D A cyclic axicon pattern shown where the spacing of the rings is non-uniform. The spacing of the rings is defined by the wavelength of the wave they construct and the focal length they want to reproduce. Newton's ring variations of diffractive designs are used as a method to impart an acoustic curvature similar to that caused by a spherical surface to the resonator surface. Other variations of diffractive structures that incorporate variations in the speed of sound can be used.

[0134] In the foregoing description, the present invention has been described with reference to specific exemplary embodiments of the present invention. However, it will be apparent that various modifications and changes may be made thereto without departing from the broader spirit and scope of the present invention as set forth in the appended claims. Therefore, the description and drawings are to be regarded as illustrative rather than restrictive.

Claims

1. A resonator, comprising: substrate; a top electrode and a bottom electrode; A piezoelectric film is suspended on a substrate between top and bottom electrodes, the piezoelectric film having a longer acoustic path at a central region of the resonator than at an edge of the resonator for waves perpendicular to a surface of the piezoelectric film, wherein the piezoelectric film is gradient hardened with ion implantation, the ion implantation hardening the edge of the piezoelectric film more than the center of the piezoelectric film.

2. The resonator according to claim 1, wherein The resonator is formed using one or more of the following methods: deposition, etching, milling, and actively stressing the resonator.

3. The resonator according to claim 1, wherein The resonator is shaped by implanting ions near the edge of the resonator, thereby producing a convex lens-like acoustic shape in the ion-implanted region of the piezoelectric membrane.

4. The resonator according to claim 3, wherein: The ions are gradually implanted towards the edge of the resonator.

5. An acoustic resonator, comprising: substrate; a recess in the substrate, the recess having an edge; A resonator film is located above the pit and contacts the substrate on the edge, the resonator film comprising a top electrode and a bottom electrode, the resonator film having a longer acoustic path in a central region of the resonator film than at an edge of the resonator film, wherein ion implantation is used to harden the edge of the resonator film.

6. The acoustic resonator according to claim 5, wherein The resonator film includes a piezoelectric material, and the piezoelectric material is one of aluminum nitride (AlN) and zinc oxide (ZnO).

7. The acoustic resonator according to claim 5, wherein The top electrode is on a top surface of the resonator film, and the bottom electrode is on a bottom surface of the resonator film, the bottom surface facing the recess.

8. An acoustic resonator, comprising: substrate; a depression in the substrate, the depression having an edge; a top electrode and a bottom electrode; a resonator membrane suspended on a substrate between a top electrode and a bottom electrode; The top electrode is on the top surface of the resonator film, and the bottom electrode is on the bottom surface of the substrate below the pit.

9. An acoustic resonator, comprising: substrate; a recess in the substrate, the recess having an edge; a top electrode and a bottom electrode; a resonator membrane suspended on a substrate between a top electrode and a bottom electrode; Wherein, the top electrode is on the top surface of the resonator film, and the bottom electrode is at the bottom of the pit.

10. The acoustic resonator according to claim 5, further comprising: An acoustic Bragg reflector stack is located below the resonator film.

11. The acoustic resonator according to claim 5, further comprising: A lens structure is provided on a top surface of the resonator film below the top electrode, the lens structure thickening a portion of the resonator film.

12. The acoustic resonator according to claim 11, wherein The lens structure is convex.

13. The acoustic resonator according to claim 5, further comprising: A hardening electrode is provided on an edge of the resonator film to harden the edge of the resonator film.

14. The acoustic resonator according to claim 5, wherein The resonator has a non-uniform response to resonance with reduced flexibility at the edges of the resonator film.

15. The acoustic resonator according to claim 14, wherein The inhomogeneous response is due to the implanted ions in the resonator film having a density gradient that increases with distance from the resonator center, such that the concentration of the implanted ions increases at the edge of the resonator film.

16. The acoustic resonator of claim 15, further comprising a second set of implanted ions in the top electrode, a density of the second set of implanted ions being higher at a center of the top electrode.

17. The acoustic resonator of claim 5, further comprising: Circular corrugations on the top surface of the resonator film.

18. The acoustic resonator according to claim 17, wherein The circular corrugations have non-uniform pitches defined by continuous zone plates.

19. The resonator of claim 1 further comprising a second set of implanted ions in the top electrode, the second set of implanted ions having a higher density in a center of the top electrode.

20. The resonator of claim 5, further comprising: The second set of implanted ions in the top electrode has a higher density of the second set of implanted ions in the center of the top electrode.

21. A method of utilizing a thin film acoustic resonator, the thin film acoustic resonator comprising a substrate and a piezoelectric film suspended from the substrate, the piezoelectric film resonating in response to an applied electric field, the method comprising: An electric field is applied to the resonator using electrodes, the electric field being in the piezoelectric film between the electrodes; In response to the electric field, the piezoelectric film resonates in a stimulus response; Based on the injected ions in the piezoelectric film, the excitation response gradually decreases toward the edge of the resonator, and the injection gradient makes the piezoelectric film have a convex lens-shaped piezoelectric response.

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