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FEM analysis of Surface Acoustic Wave resonators of Piezoelectric Gallium Nitride on Silicon substrate for frequencies above 5 GHz Athanasios Margiolakis University of Crete

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Purpose The purpose of this work is to develop an accurate numerical methodology that simulates SAW resonators for use with new technologies on wireless connections and telecommunications above 5 GHz 2

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Index Introduction Theory of SAW devices Simulations (finite element method) Fabrication Characterization Results 3

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Surface Acoustic Wave (SAW) Acoustic wave on surface of a material exhibiting elasticity Amplitude decays exponentially with depth into the substrate Generated by piezoelectric material stimulated by electrodes 4 Introduction TheorySimulationFabrication CharacterizationResults

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Piezoelectric materials Charge accumulates when force is applied Deforms when electrical field is applied 5 IntroductionTheorySimulationFabrication CharacterizationResults

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Interdigital Transducers (electrodes) Alternating electric potential on IDTs is applied Electric field on piezoelectric material under IDTs Piezoelectric deforms creating waves Waves with wavelength similar to IDT dimensions survive 6 IntroductionTheorySimulationFabrication CharacterizationResults

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SAW propagation animation 7 IntroductionTheorySimulationFabrication CharacterizationResults

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Using SAW Frequency controlf = υ/λ Dimensions of IDTs Wavelength λ Material properties Wave propagation speed υ 8 IntroductionTheorySimulationFabrication CharacterizationResults

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SAW Devices SAW filters - Frequency filter Used in telecommunications and wireless applications 9 IntroductionTheorySimulationFabrication CharacterizationResults SAW Filters –Mobile telephones –Radio receivers SAW Resonators –Radio Transmitter s –Remote controls –Radio links –No channelizati on devices

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SAW Sensors –Chemical –Optical –Thermal –Pressure –Acceleration –Torque –Biological SAW devices 10 IntroductionTheorySimulationFabrication CharacterizationResults SAW sensors – using SAW propagation speed

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Advantages SAW have better –Performance –Cost –Size o Compared to other technologies such as quartz crystals LC filters waveguide filters 11 IntroductionTheorySimulationFabrication CharacterizationResults

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Why above 5 GHz Current commercial telecommunication filter technology limited to 5 GHz Need for new technologies above 5 GHz Faster data transfers at higher frequencies Better performance filters (higher Q factor) Commercial products like WiMAX (2-11 GHz) and 4G mobile networks require higher frequencies 12 IntroductionTheorySimulationFabrication CharacterizationResults

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Substrate material –Silicon (Si) with diamond cubic structure, structural and electric properties highly anisotropic. Piezoelectric layer –Gallium Nitride (GaN) is a binary III/V direct bandgap semiconductor with Wurtzite crystal structure Materials 13 IntroductionTheorySimulationFabrication CharacterizationResults

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Material benefits Gallium Nitride (for piezoelectric material) –Can be monolithically fabricated on microelectronic devices –GaN SAW material is superior to other existing materials Silicon (for substrate material) –Most common and low cost material for such applications 14 IntroductionTheorySimulationFabrication CharacterizationResults

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Why Numerical modeling Need to accurately determine resonant frequencies Complex and non-linear problem Analytical methods not accurate Need for higher frequencies lead to dimension reduction –Stronger effects of IDT dimensions and geometry on resonant frequencies Modeling using numerical methods –Finite Element Method (FEM) analysis 15 Introduction TheorySimulationFabrication CharacterizationResults

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Mechanical motion of SAW Physical motion is time dependent elliptical displacement of the surface. The unbounded direction (y-axis) vibrates more than the bounded (x-axis). Amplitudes become negligible for penetration depths greater than few acoustic wavelengths λ(=ν/f) 16 Introduction Theory SimulationFabrication CharacterizationResults

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Stress and Strain T=F/A Stress T is the force F applied per unit area A of the solid. S=ΔL/L Strain S is fractional deformation Δ L of solid length L 17 IntroductionTheorySimulationFabrication CharacterizationResults

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Piezoelectric interactions 18 IntroductionTheorySimulationFabrication CharacterizationResults

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General equations of surface waves Equations of motion From Maxwell’s equations Electric field intensity Piezoelectric mechanical stress Piezoelectric displacement density Linear strain displacement S = Strain T = Stress ρ = mass density u = mechanical displacement D = displacement density E = electric field intensity Φ = electric potential 19 IntroductionTheorySimulationFabrication CharacterizationResults

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IDT types Single-electrode –Basic IDT type Split-electrode –reduce undesirable finger reflection effects –reflections from each split- electrode pair cancel out at center frequency –requires increased lithographic resolution DART (Distributed Acoustic Reflection Transducer) –Variable reflectivity can be achieved to give greater design capability –Reduce pass band ripples 20 IntroductionTheorySimulationFabrication CharacterizationResults

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Modeling SAW device Early SAW filter models (analytical solution) –Delta function –Crossed-Field –Impulse-response Other analytical methods for SAW design –Equivalent circuit model –S-matrix model –P-matrix model –Coupling-of-modes Analytic method Know absolutely how the model will behave Works only for simple models Linearized approximation 21 IntroductionTheory Simulation FabricationCharacterizationResults

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Finite Element Method Nanosized SAW devices require numerical simulations Initial values of the variablesequations new values over small Δ t FEM is dividing up a problem into small elements that can be solved in relation to each other Benefits of FEM for SAW modeling –domain changes, precision varies over the entire domain, solving complex elasticity problems Comsol Multiphysics platform Solves a set of differential equations on grid using FEM 22 IntroductionTheorySimulation FabricationCharacterizationResults

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Geometry design Non-linear model with high computational requirements For typical 2-port SAW resonator, delay line 1000 λ, aperture 500 λ, depth 10 λ, minimum 20 first order elements per wavelength = 10 8 elements Four degrees of freedom, displacement (Ux,Uy,Uz) and potential ( φ ) Total number of unknowns = 4× IntroductionTheorySimulation FabricationCharacterizationResults

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Reducing the size of the models dimensions –Dimension in the direction that the wave propagates is one wavelength –Dimension of perpendicular to motion is discarded due to the shape of IDTs –The depth of the substrate is set to 10 wavelengths of resonance frequency Approach of the model p o Si substrate height 10 μ m o GaN piezoelectric layer 1.6 μ m o IDT electrode height 80 nm o IDT width, p=130 nm, 200 nm 24 IntroductionTheorySimulation FabricationCharacterizationResults

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Complete/Unit cell model Comparing the two models For 1 hour of simulation of the compact model 50 years of simulations are needed for the complete model Compact model used 4 GB of RAM For the complete model 2 PB of RAM would be needed. 25 IntroductionTheorySimulation FabricationCharacterizationResults

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Model Parameters Boundary conditions (b.c.) –Periodic boundary conditions are defined on both sides of the substrate –Stress-free boundary conditions for the surface and the electrodes –Piezoelectric and substrate have “zero charge/symmetry” electric b.c. –Electrodes are grounded or have 1 Volt electric potential Subdomain (material properties) Young’s Modulus, Poisson’s ratio, density, thickness, elasticity matrix, coupling matrix, relative permittivity and electric conductivity of substrate material and piezoelectric layer 26 IntroductionTheorySimulation FabricationCharacterizationResults

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Model Parameters In finite element model problem domain is discretized in smaller regions, called elements, connected at nodes Mesh –Detail of mesh has major effect in simulation time –Finer elements are used closer to the surface for better accuracy –Bulkier elements to the bottom for faster calculations 27 IntroductionTheorySimulation FabricationCharacterizationResults

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Model Parameters Substrate thickness –Small values decrease the accuracy of the simulation –Large values increase the computational time –Values of few wavelengths provide fast and accurate results –Height of 7 wavelengths were used 28 IntroductionTheorySimulation FabricationCharacterizationResults

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Model Parameters IDT width and in between spacing (p) –Define the wavelength of the resonant frequency SAW topologies –Single electrode –Split-electrode –DART p Single-electrode model Split-electrode model 29 IntroductionTheorySimulation FabricationCharacterizationResults

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Resonance at 7.96 GHz with electric potential and total displacement maps plotted respectively, for Single-electrode IDT with 130 nm finger width. 30 IntroductionTheorySimulation FabricationCharacterizationResults

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Resonance at 5.49 GHz, for Single- electrode IDT with 200 nm finger width. 31 IntroductionTheorySimulation FabricationCharacterizationResults

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Resonance at 2.79 GHz, of Split- electrode type IDT with 200 nm finger width. 32 IntroductionTheorySimulation FabricationCharacterizationResults

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Resonance at 2.08 GHz, of DART type IDT with 200 nm finger width. 33 IntroductionTheorySimulation FabricationCharacterizationResults

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Resonance at 5.49 GHz, of DART type IDT with 200 nm finger width. DART array with multiple resonant wavelengths for the same IDT dimensions 34 IntroductionTheorySimulation FabricationCharacterizationResults

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IDT fabrication process a.Employing PMMA resist of 200 nm thickness on a Gallium Nitride wafer b.Direct electron beam lithography writing c.A metal layer of Ti/Au (5 nm/75 nm) was subsequently deposited on wafer using an e-beam evaporator d.Followed by a lift-off procedure to form the interdigitated electrodes(IDTs) e.Materials used for fabrication 35 IntroductionTheorySimulation Fabrication CharacterizationResults

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Photolithography mask Photolithography mask that was used, with different IDT characteristics –Variable delay lines –IDT finger lengths –Crystal orientation –Reflectors exist or not 36 IntroductionTheorySimulationFabrication CharacterizationResults

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Fabrication Mix and Match fabrication IDTs were fabricated in “IMT” using e-beam lithography (gold) Rest of the device elements were fabricated in “FORTH” using conventional optical lithography (green) 37 IntroductionTheorySimulationFabrication CharacterizationResults

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Post fabrication images of the devices Complete IDT structure with connecting pads at magnification x130 IDT fingers with reflectors at magnification x3000 Single electrode IDT type magnification x IntroductionTheorySimulationFabrication CharacterizationResults

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Post fabrication images of the devices Single electrode type IDT array, finger width 130nm and metallization ratio η =0.5 Split electrode type IDT array, finger width 200nm and metallization ratio η =0.5 DART type IDT array, finger width 200nm and metallization ratio η = IntroductionTheorySimulationFabrication CharacterizationResults

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Characterization A couple of three finger probes were placed on the pads of the IDTs The middle electrode was grounded and the upper/bottom were put to 1 Volt electric potential A frequency scan performed from 2 to 9 GHz depending the IDT type. Signal Ground 40 IntroductionTheorySimulationFabrication Characterization Results

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S-parameters Scattering (S) parameters describe the response of an N-port network to voltage signals at each port The first number refers to responding port, while second to incident port. S 21 means response at port 2 due to signal at port 1 For 2-port network, incident voltage denoted by “a”, leaving by “b” 41 IntroductionTheorySimulationFabrication CharacterizationResults

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Y-parameters Admittance (Y) is a measure of how easily a circuit or device will allow a current to flow. It is the inverse of the impedance. Y-parameters describe the small-signal response of non-linear networks. For all ports the currents may be defined in terms of the Y-parameter matrix and the voltages I = YVY is an N × N matrix 2-port network transformation from S- parameters to Y- parameters Y 0 characteristic admittance 42 IntroductionTheorySimulationFabrication CharacterizationResults

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Simulated with measured results comparison The simulations for the Single- electrodes with 200nm width had a frequency drift of 187 MHz to lower frequencies that is 3.29% difference from the characterized device. Ripples occur from interference of the reflections 43 IntroductionTheorySimulationFabrication CharacterizationResults

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Simulated with measured results comparison The simulations for the Single- electrodes with 130nm width had a frequency drift of 184 MHz to lower frequencies that is 2.25% difference from the characterized device. 44 IntroductionTheorySimulationFabrication CharacterizationResults

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Simulated with measured results comparison The simulations for the Split- electrodes with 200nm finger width had a frequency drift of 343 MHz to higher frequencies that is 4.14% difference from the characterized device. 45 IntroductionTheorySimulationFabrication CharacterizationResults

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Simulated with measured results comparison The simulations of the Split- electrodes with 200nm width for a wider frequency spectrum had a harmonic resonance drift of 73 MHz to lower frequencies that is 3.42% difference from the characterized device. The main resonant frequency was compared in the previous figure. 46 IntroductionTheorySimulationFabrication CharacterizationResults

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Simulated with measured results comparison The simulations for the DART electrodes with 200nm width had a frequency drift of 185 MHz to lower frequencies that is 3.25% difference from the characterized device. 47 IntroductionTheorySimulationFabrication CharacterizationResults

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Conclusions Efficient numerical methodology for determination of f s SAW devices (GaN/Si) designed and implemented with f s up to 9GHz Measured f s to predicted f s deviation in the order of 3% Further improvement of the predictability of resonant frequency with reasonable cost in computational time 48 IntroductionTheorySimulationFabrication Characterization Results

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Acknowledgements I would like to thank –Alexandra Stefanescu –Dan Neculoiu –Mircea Dragoman –Adrian Dinescu 49 –George Konstantinidis –Eleftherios Iliopoulos –Alexandros Pantazis –Panos Tzanetakis –Alexandros Georgakilas ΠΑΡ for the financial support

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Fabrication process GaN/Si wafers grown by MOCVD Epitaxial relationship of GaN(0001) c-axis on Si(111) with ~17% mismatch 53 IntroductionTheorySimulationFabrication CharacterizationResults

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Model Parameters IDT height –Greater height has wider cross-section, thus lower resistivity IDTs –A shift in resonance frequency is observed for different heights –Results did not provide any outcome that can be used to optimize the efficiency of the simulation 54 IntroductionTheorySimulation FabricationCharacterizationResults

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Conclusions determine the parameters which affect the bandwidth and center frequencies a series of simulations were done for various IDT structure types like Single-electrode, Split- electrode and DART For two different finger widths the simulated results compared with the experimental presented differences of less than 5% in center resonance frequency of all the tested devices. 55 IntroductionTheorySimulationFabrication CharacterizationResults

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