fem analysis of surface acoustic wave resonators of piezoelectric gallium nitride on silicon...

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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 2012

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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

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Index

IntroductionTheory of SAW devicesSimulations (finite element method)FabricationCharacterizationResults

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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

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Piezoelectric materials

• Charge accumulates when force is applied• Deforms when electrical field is applied

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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

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SAW propagation animationIntroduction Theory SimulationFabrication Characterization ResultsIntroduction Theory SimulationFabrication Characterization Results

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Using SAW

Frequency controlf = υ/λ

• Dimensions of IDTs Wavelength λ

• Material properties Wave propagation speed υ

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SAW Devices

• SAW filters - Frequency filter

Used in telecommunications and wireless applications

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SAW Filters– Mobile

telephones– Radio

receivers

SAW Resonators

– Radio Transmitters

– Remote controls

– Radio links– No

channelization devices

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SAW Sensors– Chemical– Optical– Thermal– Pressure– Acceleration– Torque– Biological

SAW devicesIntroduction Theory SimulationFabrication Characterization ResultsIntroduction Theory SimulationFabrication Characterization Results

• 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

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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

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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

MaterialsIntroduction Theory SimulationFabrication Characterization ResultsIntroduction Theory SimulationFabrication Characterization Results

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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

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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

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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)

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Stress and Strain

T=cS c = elastic stiffness, Young’s modulus (N/m²) tensor equation, , j denotes direction of force F, k direction of vector of area ALikewise deformation directions defined similarly.

• 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 ΔL of solid length L

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Piezoelectric interactionsThe E established by V will distort the molecular charge distribution and result in accumulation of surface charge. Electrical displacement density matrix equationpiezoelectric constant, electric field intensity, dielectric permittivity

[𝑒 ]=( 0 0 00 0 0𝑒31 𝑒31 𝑒33

0 𝑒15 0𝑒15 0 00 0 0)

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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

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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

λ0/8

λ0/4

Split-electrode pair

0

270

180

- 270

ο

ο

ο

ο

λ0/8

λ0/2

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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

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Finite Element Method

• Nanosized SAW devices require numerical simulations

Initial values of the variablesequations new values over small Δt• 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 platformSolves a set of differential equations on grid using FEM

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Geometry design• Non-linear model with high computational

requirementsFor typical 2-port SAW resonator, delay line 1000λ, aperture 500λ, depth 10λ, minimum 20 first order elements per wavelength = 108 elementsFour degrees of freedom, displacement (Ux,Uy,Uz) and potential (φ)Total number of unknowns = 4×108

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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 μmo GaN piezoelectric layer 1.6

μmo IDT electrode height 80 nmo IDT width, p=130 nm , 200

nm

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Complete/Unit cell model

• Comparing the two modelsFor 1 hour of simulation of the compact model50 years of simulations are needed for the complete model

Compact model used 4 GB of RAMFor the complete model 2 PB of RAM would be needed.

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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

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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

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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

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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-electrodemodel

Split-electrodemodel

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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.

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

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

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• Resonance at 2.08 GHz, of DART type IDT with 200 nm finger width.

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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

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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

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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

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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)

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Post fabrication images of the devices

Complete IDT structure with connecting pads at magnification x130IDT fingers with reflectors at magnification x3000Single electrode IDT type magnification x50000

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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=0.5

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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

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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. S21 means response at port 2 due to signal at port 1

• For 2-port network, incident voltage denoted by “a”, leaving by “b”

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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 = YV Y is an N × N matrix2-port network transformation from S-parameters to Y-parameters

Y0 characteristic admittance

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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

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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.

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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.

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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.

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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.

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Conclusions

• Efficient numerical methodology for determination of fs

• SAW devices (GaN/Si) designed and implemented with fs up to 9GHz

• Measured fs to predicted fs deviation in the order of 3%

• Further improvement of the predictability of resonant frequency with reasonable cost in computational time

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Acknowledgements

• I would like to thank– Alexandra

Stefanescu– Dan Neculoiu – Mircea Dragoman– Adrian Dinescu

– George Konstantinidis

– Eleftherios Iliopoulos – Alexandros Pantazis– Panos Tzanetakis– Alexandros

GeorgakilasΠΑΡ00195-1 for the financial support

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End of slide show, click to bananas.

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Fabrication process

(1100)

[1120]

[11,0][0110][12,0]

[121

0]

[01,

0]

Si[1

12]

[110

0]

[11,

0]

(101

0)(0

110)

(112

0) [2110][10,0]

[1010]

[21,0]

Si[1

12]

Si(111)

Si[110]

• GaN/Si wafers grown by MOCVD

• Epitaxial relationship of GaN(0001) c-axis on Si(111) with ~17% mismatch

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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

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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.

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