Micro Assembly for Radio Frequency Electronics: Characterization of Bond Wires

Micro Assembly for Radio Frequency Electronics

Characterization of Bond Wires

YOUJIE CHEN

KTH ROY AL IN STITUTE OF TEC HNO LOGY

E L E C T R I C A L E N G I N E E R I N G A N D C O M P U T E R S C I E N C E IL246X DEGREE PROJECT IN ELECTRICAL ENGINEERING SECOND CYCLE 30 CREDITS

STOCKHOLM, SWEDEN 2019

Micro Assembly for Radio Frequency Electronics

Characterization of Bond Wires

Youjie Chen

2019-07-18

Master’s Thesis

Examiner Gunnar Malm Academic adviser Saul Rodriguez Industrial adviser

Francesc Purroy Martin

KTH Royal Institute of Technology

School of Electrical Engineering and Computer Science (EECS) Department of Electronics

SE-100 44 Stockholm, Sweden

Abstract | i

Abstract

Due to the increasing number of components involved in Radio Frequency design, integration and packaging become an important topic of developing power-efficient and cost-effective solutions.

Furthermore, interconnections are a key factor in such a topic because they are heavily used in Radio Frequency engineering, especially in the Fifth Generation. Among the interconnections, bond wires are one of the most commonly used.

In micro assembly design, it is crucial to understand and model the behavior of each component, including interconnections. Radio Frequency engineers usually use the bond wire models in the software directly without questioning if the model actually has the same behavior as the fabricated one. Therefore, how to accurately model and characterize the bond wires becomes valuable, and furthermore, how the physical dimensions affect the transmission performance. This Master’s thesis project aims to solve this problem by building simple models for single bond wire and double bond wires with coupling, and verifying them by electromagnetic simulation and measurement.

The project has built bond wire models in Matlab and in electromagnetic simulators NI AWR and ANSYS HFSS. The actual test structures are also fabricated using the bonding machine, and measured by vector network analyzer. A sufficient amount of data has been collected from these sources and then analyzed. The proposed analytical model of bond wires is valid after comparing its results with those from simulation and measurement. In addition, the effect of the loop height and separation distance on the transmission performance is studied and has a well verified conclusion.

This thesis work will be helpful to Radio Frequency engineers, who use bond wires in the micro assembly of their design. They would be able to characterize the bond wires more accurately and adjust the physical dimensions in order to achieve the desired performance.

Keywords

Bond wire interconnection, Radio frequency, Analytical model, Electromagnetic simulation,

Electromagnetic measurement

Sammanfattning | iii

Sammanfattning

På grund av det ökande antalet komponenter i radiofrekvensdesign, integration och förpackning blivit ett viktigt ämne för att utveckla energieffektiva och kostnadseffektiva lösningar.

Sammankopplingar är en nyckelfaktor i ett sådant ämne, eftersom de är starkt används i radiofrekvensteknik. Bland dem, bondtrådar är en av de vanligaste.

Det är viktigt att förstå och modellera beteendet hos varje komponent. Därför hur att noggrant modellera och karakterisera bondtrådarna blir ett värdefullt problem, och dessutom, hur de fysiska dimensionerna påverkar överföringsprestanda.

Projektet har byggt bondtrådsmodeller i Matlab och i elektromagnetiska simulatorer NI AWR och ANSYS HFSS. De faktiska teststrukturerna tillverkas också med hjälp av bindningsmaskinen och mäts av vektornätverksanalysatorn. Den föreslagna analysmodellen för bindningstrådar är giltig efter att ha jämfört dess resultat med dem från simulering och mätning. Dessutom studeras effekten av slinghöjden och separationsavståndet på transmissionens prestanda och har en väl verifierad slutsats.

Nyckelord

Bindningstråd sammankoppling, Radiofrekvens, Analytisk modell, Elektromagnetisk simulering,

Elektromagnetisk mätning

Acknowledgments | v

Acknowledgments

I would like to thank my examiner, Gunnar Malm, and supervisor at KTH, Saul Rodriguez, for their advice and constant supervision of this project. Thanks to my supervisor at Huawei Technologies Sweden AB, Francesc Purroy Martin, who has been giving me valuable insights and help throughout this journey. In addition, I would like to express my gratitude to my manager Dr.

Shi Cheng, and my colleagues at the company, Igor Blednov, Peng Li, Qingzhao Du, and Tomasz Kaczkowski for welcoming me to the team and offering all the help I need along the way.

I would like to thank my family and friends for all the love and moral support that they always give me. This thesis project could not have been completed without the assistance and guidance that I received from all these people, to whom I am deeply grateful.

Stockholm, July 2019

Youjie

Table of contents | vii

Table of contents

Abstract ... i

Keywords ... i

Sammanfattning... iii

Nyckelord ... iii

Acknowledgments ... v

Table of contents ... vii

List of Figures ... ix

List of Tables... xi

List of acronyms and abbreviations ... xiii

1 Introduction ... 1

1.1 Background ... 1

1.2 Problem ... 1

1.3 Purpose ... 1

1.4 Goals ... 2

1.5 Research Methodology ... 2

1.6 Delimitations ... 2

1.7 Structure of the thesis ... 2

2 Background ... 5

2.1 Transmission Line Theory ... 5

2.2 Bond Wire ... 6

2.2.1 Bonding methods ... 6

2.2.2 Relation with transmission line theory ... 7

2.3 Microwave Network Analysis ... 7

2.3.1 Impedance and Admittance Matrices ... 8

2.3.2 Scattering Matrices ... 9

2.4 Related work... 10

2.4.1 Transmission performance analysis of single and double bond wires ... 10

2.4.2 Comprehensive performance analysis of single bond wire in simulation ... 11

2.4.3 Modeling and minimizing the self-inductance of bond wire ... 12

2.4.4 Analysis of capacitance compensation structure for bond wire ... 14

2.4.5 Electromagnetic simulation of bond wires and comparison with measurements ... 16

2.4.6 Novel approach to model the packaged RF power transistors ... 17

2.5 Summary ... 18

3 Methodologies and Methods ... 21

3.1 Research Process ... 21

3.2 Research Paradigm ... 21

3.3 Data Collection ... 21

3.3.1 Sample Size ... 21

3.4 Experimental design/Planned Measurements ... 22

viii | Table of contents

3.4.1 Test environment/test bed/model ... 22

3.4.2 Hardware/Software to be used ... 22

3.5 Assessing reliability and validity of the data collected ... 22

3.5.1 Reliability... 22

3.5.2 Validity ... 23

3.6 Planned Data Analysis ... 23

3.6.1 Data Analysis Technique ... 23

3.6.2 Software Tools ... 23

4 Experimental and Modeling Approach ... 25

4.1 Analytical modeling ... 25

4.1.1 Shape model ... 25

4.1.2 Electrical characteristics ... 26

4.1.3 Network analysis ... 27

4.2 Simulation ... 28

4.2.1 Circuit modeling and simulation ... 28

4.2.2 3D modeling and simulation... 30

4.3 Fabrication and measurement ... 31

4.3.1 Bond wire prototyping ... 32

4.3.2 Thru-Reflect-Line (TRL) network analyzer calibration ... 33

4.3.3 Measurement ... 35

5 Results and Analysis ... 37

5.1 Major results... 37

5.1.1 Analytical model results ... 37

5.1.2 Simulation results ... 39

5.1.3 Fabrication and measurement results ... 42

5.2 Reliability Analysis ... 48

5.2.1 Single bond wire ... 48

5.2.2 Double bond wires ... 48

5.3 Validity Analysis... 49

5.4 Discussion ... 49

5.4.1 Analytical model ... 49

5.4.2 Fabrication and measurement ... 49

5.4.3 Loop height ... 50

5.4.4 Separation distance ... 50

6 Conclusions and Future work ... 51

6.1 Conclusions ... 51

6.2 Limitations ... 51

6.3 Future work ... 51

6.4 Reflections ... 52

References ... 53

List of Figures | ix

List of Figures

Figure 2.1.1: Equivalent electric circuit of a transmission line [6] ... 5

Figure 2.2.1: Bond wires on chip [8] ... 6

Figure 2.2.2: Ball-wedge bond wire [9] ... 7

Figure 2.2.3: Wedge-wedge bond wire [10] ... 7

Figure 2.3.1: Two-port network... 8

Figure 2.4.1: Simulation results of single bond wires with different height [8] ... 10

Figure 2.4.2: Fabricated single bond wire structure [8] ... 11

Figure 2.4.3: Equivalent circuit for bond wire interconnection [11] ... 11

Figure 2.4.4: Transmission performance of the fabricated single bond wire [11] ... 12

Figure 2.4.5: Bond wire model of Gaussian distribution function [12] ... 13

Figure 2.4.6: Measurement of return loss of bond wires with radius 12.5 µm and 62.5 µm [12] ... 13

Figure 2.4.7: Measurement of insertion loss of bond wires with radius 12.5 µm and 62.5 µm [12] ... 14

Figure 2.4.8: Structure of the interconnection [13] ... 14

Figure 2.4.9: Capacitance compensation model for bond wire [13] ... 14

Figure 2.4.10: 3D capacitive compensation structure [13] ... 15

Figure 2.4.11: Simulated return loss of capacitive compensated and uncompensated structure [13] ... 15

Figure 2.4.12: SEM picture of the bond wire [14] ... 16

Figure 2.4.13: Geometry and corresponding lumped element model of the bond wire [14] ... 16

Figure 2.4.14: SEM picture of the inside of a power transistor [15] ... 17

Figure 2.4.15: Extracted model for electromagnetic simulation of resistance and inductance in FastHenry [15] ... 18

Figure 3.1.1: Research Process ... 21

Figure 4.1.1: Rayleigh distributions [17] ... 26

Figure 4.1.2: Shape model ... 26

Figure 4.1.3: Equivalent p circuit ... 28

Figure 4.1.4: Cascaded p circuits ... 28

Figure 4.2.1: Single bond wire model in AWR... 29

Figure 4.2.2: Double bond wires model in AWR ... 29

Figure 4.2.3: Equivalent circuit for single bond wire ... 29

Figure 4.2.4: Equivalent circuit for two bond wires with coupling ... 30

Figure 4.2.5: Overall test structure in HFSS ... 31

Figure 4.2.6: Close-up view of test structure in HFSS ... 31

Figure 4.3.1: Empty test board ... 32

Figure 4.3.2: Detailed structure of the bond wire in top view ... 33

Figure 4.3.3: VNA measurement of two-port device [6] ... 34

Figure 4.3.4: Board for calibration ... 34

Figure 5.1.1: Comparison of analytical model and Rayleigh distribution function ... 37

Figure 5.1.2: Matlab results of single lossless bond wires with different loop heights ... 38

Figure 5.1.3: S-parameters of single bond wires in AWR simulation and Matlab ... 39

Figure 5.1.4: Return loss of single bond wires in AWR simulation and Matlab ... 40

Figure 5.1.5: Error between single bond wire model in AWR simulation and Matlab ... 40

Figure 5.1.6: S-parameters of single bond wire in HFSS simulation ... 41

Figure 5.1.7: Return loss of single bond wire in HFSS simulation ... 42

Figure 5.1.8: SEM picture of single bond wire with gap = 1 mm, and loop = 1 ... 43

Figure 5.1.9: Errors among single bond wires of loop = 1 ... 44

x | List of Figures

Figure 5.1.10: Errors among single bond wires of loop = 10 ... 44

Figure 5.1.11: S-parameters of fabricated single bond wires with different loop heights ... 45

Figure 5.1.12: Return loss of fabricated single bond wires with different loop heights ... 45

Figure 5.1.13: S-parameters of fabricated double bond wires with different separation ... 46

Figure 5.1.14: Return loss of fabricated double bond wires with different separation ... 47

Figure 5.2.1: Error between two measurements on a single bond wire... 48

Figure 5.2.2: Error between two measurements of double bond wires ... 49

List of Tables | xi

List of Tables

Table 2.5.1: Technical methods of related works ... 18

Table 4.3.1: Test board structure ... 32

Table 5.1.1: Bond wire parameters in Matlab ... 38

Table 5.1.2: Optimized values for single bond wire ... 41

Table 5.1.3: Coupling coefficient of double bond wires with different separation ... 42

Table 5.1.4: Single bond wires with 1 mm gap ... 43

Table 5.1.5: Optimized electrical characteristics for single bond wires ... 46

Table 5.1.6: Optimized coupling coefficients of measured double bond wires with

different separation ... 47

List of acronyms and abbreviations | xiii

List of acronyms and abbreviations

2D Two Dimensional

3D Three Dimensional

5G Fifth Generation

AAU Active Antenna Unit

DUT Device under Test

EM Electromagnetic

FEM Front End Module

FDTD Finite Difference Time Domain HMIC Hybrid Microwave Integrated Circuit

IC Integrated Circuit

LNA Low Noise Amplifier

MIMO Multiple-Input and Multiple-Output

PA Power Amplifier

PCB Printed Circuit Board

RF Radio Frequency

SEM Scanning Electron Microscope S-parameter Scattering Parameter

TRL Thru-Reflect-Line

VNA Vector Network Analyzer

Introduction | 1

1 Introduction

Bond wire is one of the most commonly used interconnections in integrated circuit (IC) fabrication and packaging [1]. This is because it is a reliable, cost-effective and flexible technology. One of the common usages of bond wire is to connect the chip and its packaging. In the Fifth Generation (5G) technology, the increasing data transmission rate and the number of components in the device make the transmission performance of the interconnections more and more crucial. This gives rise to studies into the electrical behavior of the bond wires, such as how to accurately model and

characterize the bond wires, and how the physical dimensions affect the transmission performance.

1.1 Background

Phased-arrays are one of the most fundamental blocks in the 5G multiple-input and multiple-output (MIMO) active Antenna units (AAUs) [2]. Each sub-array is fed by a Front-End Module (FEM), which typically consists of a Power Amplifier (PA), a switch and a Low Noise Amplifier (LNA) [3].

Because of the wide frequency range in 5G, there are a large number of components in Radio Frequency (RF) design. Therefore, integration and packaging become an important aspect of developing power-efficient and cost-effective solutions. This project focuses on the Power Amplifier integration.

1.2 Problem

For sub 6 GHz frequency, the Power Amplifier integration design is implemented by using a hybrid microwave integrated circuit (HMIC) [3]. There are a lot of components and interconnections used in the HMIC. Bond wire is one of the most frequently used interconnections in RF design, and its behavior can affect the performance of the system significantly [1]. In order to understand the behavior of the system better, all the components used in HMIC Micro Assembly should be able to be correctly characterized and modeled in terms of basic electromagnetic components. For bond wire, its transmission performance under different frequency and with different physical parameters is of interest. The problem in this project is how to accurately characterize bond wires, and how the physical dimensions influence the transmission performance.

1.3 Purpose

This project is meant to research the characterization of bond wires, and to gain insights into how parameterizing the physical dimensions would impact its transmission performance in a certain frequency range.

This thesis will be beneficial to engineers, who need to use bond wires in their designs and want to get a better sense of the characterization of the bond wires. Once this thesis is successfully completed, the engineers can use the model proposed in this project for bond wires, and the results and conclusions of this thesis will help them understand better how the model in the software actually behaves in real hardware, and choose the most suitable shape of bond wire for their specific design requirements.

As this thesis is based on the bigger goal of developing and implementing power-efficient and cost-effective solutions by looking into the integration and packaging, it is meant to be

environmentally friendly and sustainable.

2 | Introduction

1.4 Goals

The goal of this project is to accurately characterize both single bond wire and double bond wires with coupling, and to draw conclusion about how the physical dimensions influence the

transmission performance. This is divided into the following four sub-goals:

1. Build mathematical models for single bond wire and for double bond wires with coupling 2. Design and simulate test structures in simulation

3. Build test structures on bond wire prototype machine, and perform Vector Network Analyzer (VNA) measurement

4. Investigate the effect of different loop height and separation distance on the transmission performance

Deliverables: simple models for single bond wire and for double bond wires with coupling Results:

1. The transmission performance of the analytical models should be consistent with simulation and measurement results

2. Conclusion about the effect of loop height and separation distance on the transmission performance

1.5 Research Methodology

This project is a quantitative research, because it is meant to prove that the proposed model is consistent with the real bond wire by experiments and measurements. Due to the “experimental and testing character” of this project, the philosophical assumption is positivism [4]. As this project also includes studying the relationships between the physical dimension parameters and the

electromagnetic performance, it needs to employ an experimental research method.

1.6 Delimitations

Due to the limited resource of physical wires, this project would only use one specific kind of wire.

This means that this project would not be able to study the effect of other factors, such as different material or diameter of the wire. The measurement device Vector Network Analyzer only gives accurate calibration results under 15 GHz. Therefore, the frequency domain will be from 1 GHz to 15 GHz in theoretical calculation, simulation environment and the physical measurement. For

simplicity reasons, only ball-wedge bond wires will be used, and this project would not study the impact of different bonding method.

1.7 Structure of the thesis

• Chapter 2 introduces relevant background information about transmission line theory, bond wires and network analysis. It also contains a selection of valuable related work that other researchers have done in this area.

• Chapter 3 presents the methodology and method that are used in this degree project in order to solve the problem.

• Chapter 4 shows how the research is designed and implemented in detail, which includes mathematical modeling, simulation, fabrication and measurement.

• Chapter 5 presents the data and results that are obtained from these three sources, and the

reliability and validity analysis of the data. In addition, it discusses briefly about the

Introduction | 3

3 analytical model and fabrication, and draws a conclusion about the effect of loop height and separation distance.

• Chapter 6 is a final summary and conclusion of the work, including advantages,

shortcomings and limitations. It also suggests what can and should be done in the future

based on the results of this thesis project.

Background | 5

2 Background

This chapter provides some basic background information about transmission line theory and bond wire to help readers understand the subject this project deals with. It also introduces how to perform network analysis, which is applied in this project. Several related works on modeling and characterizing bond wires are also discussed in this chapter.

2.1 Transmission Line Theory

Transmission lines are commonly used for transmitting electrical power and information in electrical engineering [5]. As a transmission line can have a considerable length compared to wavelengths, it can be treated as a distributed parameter network [6]. From the perspective of electric circuit theory, a two-wire transmission line can be represented as a cascade of N segments of the structure shown in Figure 2.1.1.

For a segment of length Δ𝑧, it is modeled as an equivalent circuit consisting of series resistance, series inductance, shunt conductance and shunt capacitance. R is the series resistance of the wire per unit length; L is the series inductance of the wire per unit length; G is the shunt conductance between two conductors per unit length; C is the shunt capacitance between two conductors per unit length. Due to the nature of R and G, they both indicate loss in the circuit [6]. The values of these parameters are dependent of the geometric dimensions and material of the transmission line.

Figure 2.1.1: Equivalent electric circuit of a transmission line [6]

When analyzing this circuit, Kirchhoff’s law can be applied here and will get [6]

𝑣(𝑧, 𝑡) − 𝑅 Δ𝑧 𝑖(𝑧, 𝑡) − 𝐿 Δ𝑧 𝜕𝑖(𝑧, 𝑡)

𝜕𝑡 − 𝑣(𝑧 + Δ𝑧, 𝑡) = 0 𝑖(𝑧, 𝑡) − 𝐺 Δ𝑧 𝑣(𝑧 + Δ𝑧, 𝑡) − 𝐶 Δ𝑧 𝜕𝑣(𝑧, 𝑡)

𝜕𝑡 − 𝑖(𝑧 + Δ𝑧, 𝑡) = 0 These can be derived to

𝑑

𝑉(𝑧)

𝑑𝑧

− 𝛾

𝑉(𝑧) = 0

𝑑

𝐼(𝑧)

𝑑𝑧

− 𝛾

𝐼(𝑧) = 0

where

6 | Background

𝛾 = 𝛼 + 𝑗𝛽 = ;(𝑅 + 𝑗𝜔𝐿)(𝐺 + 𝑗𝜔𝐶)

is the complex propagation constant, 𝛼 is the attenuation constant and 𝛽 is propagation constant [6].

The solutions to these traveling wave equations are [6]

𝑉(𝑧) = 𝑉

𝑒

+ 𝑉

𝑒

𝐼(𝑧) = 𝐼

𝑒

+ 𝐼

𝑒

The characteristic impedance of the transmission line is defined as 𝑍

= 𝑉

𝐼

= −𝑉

𝐼

= 𝑅 + 𝑗𝜔𝐿

𝛾 = D 𝑅 + 𝑗𝜔𝐿 𝐺 + 𝑗𝜔𝐶

In the case of lossless transmission line, 𝑅 = 𝐺 = 0 and the corresponding propagation constant is 𝛾 = 𝛼 + 𝑗𝛽 = 𝑗𝜔√𝐿𝐶. The characteristic impedance will be 𝑍

= F

.

2.2 Bond Wire

Bond wires are typically used to form interconnections between a chip and its package, and there are also other bond wires like crossovers and printed circuit board (PCB) bonds [3]. It is a flexible and cost-effective type of interconnection technique, and it had been used for more than 90%

interconnections in semiconductor packages by 2013 [7]. Figure 2.2.1 is a picture showing that a number of bond wires connect the chip in the middle with its packaging on the surrounding.

Figure 2.2.1: Bond wires on chip [8]

2.2.1 Bonding methods

There are two bonding techniques: ball bonding and wedge bonding. Ball bonding method

begins with forming a free air ball at the tip of the wire by creating a spark, and then applying force

and ultrasonic energy on the ball against the bond pad until a ball bond is formed. While for wedge

bonding, it uses the foot of the wedge to deform the wire and applies force and ultrasonic energy at

the same time until the bond is made.

Background | 7

7 There are two types of bond wires in terms of techniques: ball-wedge wire and wedge-wedge wire [7]. In Figure 2.2.2 is a ball-wedge gold bond wire. The first bond is a ball bonding made on the bond pad of the die, and the second one is a wedge bonding on the lead frame of the packaging. This is the type of bond wires that this project studies.

Figure 2.2.2: Ball-wedge bond wire [9]

In Figure 2.2.3 is a wedge-wedge bond wire. Both of the bonds are formed by wedge bonding method.

Figure 2.2.3: Wedge-wedge bond wire [10]

2.2.2 Relation with transmission line theory

A bond wire can be interpreted by the transmission line theory with some variations. Applying the model of Figure 2.1.1 to the case of single bond wire, R is the resistance of the wire per unit length; L is the inductance of the wire per unit length; C is the capacitance between the wire and the ground per unit length. G should be the shunt conductance between two conductors, and it is not applicable in this case, which simply means G=0.

Among all the electrical parameters, inductance is the one that makes most difference in the transmission performance. Hence, it is one of the evaluation metrics in this project.

2.3 Microwave Network Analysis

There are mainly two ways to perform analysis on a microwave problem, which are (1) circuit or

network analysis and (2) field analysis using Maxwell’s equations [5]. Circuit analysis is a quite

intuitive and basic method to solve microwave problems, but it gives limited information and it

8 | Background

could be too simplified for certain problems. Field analysis, on the other hand, provides comprehensive solutions, but it is very complicated, difficult and time-consuming to apply. Most of the electromagnetic simulation software would use field analysis to get a full picture of the electromagnetic fields around the test structure.

Network analysis is more suitable for analytical modeling in the cases when only the voltage and current at the terminals are needed. In order to perform network analysis, the values of the basic components, for example, the characteristic impedance, of the circuit need to be derived first. Then, connect all the components properly and apply electric circuit theory or transmission line theory to assess the behavior of the system [6].

2.3.1 Impedance and Admittance Matrices

Impedance and admittance matrices show the relationship of total voltages and currents at all terminals, which becomes a description of the whole network [6]. Here, consider a simple two-port network as in Figure 2.3.1. 𝑡

and 𝑡

are the terminal plane defined for the first and second port, respectively. (𝑉

, 𝐼

) and (𝑉

, 𝐼

) are the equivalent voltages and currents for the incident waves to the port 1 and port 2, respectively. (𝑉

, 𝐼

) and (𝑉

, 𝐼

) are those for the reflected waves.

Figure 2.3.1: Two-port network

The impedance matrix [Z] relates the voltages with currents by J 𝑉

𝑉

K = J 𝑍

𝑍

𝑍

𝑍

K J 𝐼

𝐼

K and the corresponding admittance matrix [Y] will be

J 𝐼

𝐼

K = J 𝑌

𝑌

𝑌

𝑌

K J 𝑉

𝑉

K

The relationship between impedance and admittance matrices is [𝑌] = [𝑍]

The element Z

and Y

can be found by [6]

𝑍

= 𝑉

𝐼

Q

R_ST= UVW XYP

𝑌

= 𝐼

𝑉

Q

Z_ST= UVW XYP

Background | 9

9 2.3.2 Scattering Matrices

Different from the impedance and admittance matrix, the scattering matrix indicates the relationship of the voltages of the incident and reflected waves on all ports [6]. It can be obtained by calculations, or measurement performed on a Vector Network Analyzer.

In the same case as Figure 2.3.1, 𝑉

and 𝑉

are the amplitude of the voltage of the wave incident and reflected at port 𝑛. The scattering matrix [𝑆] can be expressed as

J 𝑉

𝑉

K = J 𝑆

𝑆

𝑆

𝑆

K ^ 𝑉

𝑉

_ The element 𝑆

can be directly found by [6]

𝑆

= 𝑉

𝑉

Q

Z_S^`T= UVW XYP

which means that

can be calculated by driving port 𝑗 with

and measuring

at port 𝑖. As a result, 𝑆

is the voltage reflection coefficient (G) at port 𝑖 when other ports are all terminated with matched load, and the return loss at port 𝑖 will be 𝑅𝐿 = −20 log(|Γ|) dB = −20 log(|𝑆

|) dB . Similarly,

is the transmission coefficient (Τ = 1 + Γ) from port 𝑗 to port 𝑖 when other ports are all terminated with matched load, and the insertion loss will be 𝐼𝐿 = −20 log(|Τ|) dB =

−20 logkl𝑆

lm dB.

Another way to calculate the scattering matrix is from the impedance matrix or admittance matrix, which is easier to manage in some cases [6]

[𝑆] = ([𝑍] + 𝑍

[𝑈])

([𝑍] − 𝑍

[𝑈])

The scattering parameters are one of the metrics used in this project to evaluate the transmission performance of the bond wires, including the return loss and insertion loss.

2.3.2.1 Reciprocal network and lossless network

A reciprocal network is one that the transmission of signal does not depend on the direction of propagation, or in other words, the input and output ports can exchange and the transmission performance would still be the same [6]. The scattering matrix of such network is symmetric, which means

𝑆

= 𝑆

For a lossless network, no real power is actually delivered to the network, which indicates that the incident power is equal to the reflected power. The scattering matrix of a lossless network is unitary, which can be written as [6]

[𝑆] oooo ∙ [𝑆]

= [𝑈] or [𝑆] ∙ [𝑆]

= [𝑈]

where [𝑆] oooo is the conjugate matrix of [𝑆], [𝑆]

is the transpose matrix, [𝑆]

is the conjugate transpose and [𝑈] is the identity matrix. This equation can be expressed as

s 𝑆

∙ 𝑆 oooo

XTI

= 1, for 𝑖 = 𝑗 and

s 𝑆

∙ 𝑆 oooo

uT4

XTI

= 0, for 𝑖 ≠ 𝑗

10 | Background

If more explicitly,

|𝑆

|

+ |𝑆

|

= 1

|𝑆

|

+ |𝑆

|

= 1 𝑆

∙ 𝑆 oooo + 𝑆

∙ 𝑆 oooo = 0

𝑆

∙ 𝑆 oooo + 𝑆

∙ 𝑆 oooo = 0

These two conditions can be used to check if the scattering matrix obtained from the analytical model is fundamentally correct.

2.4 Related work

There have been a considerable number of studies regarding how to model and characterize bond wires and also how the physical parameters affect the transmission performance in the last two decades. They all have shown satisfying results, and are quite helpful for the development of this project. This section will introduce six pieces of work of this topic.

2.4.1 Transmission performance analysis of single and double bond wires

This work [8] studies the relationship between the height and the transmission performance of single bond wire, and the crosstalk or coupling between double bond wires. It approximates the shape of the bond wire as an arc of a circle with a radius of 0.5 mm, and then simulates the model in electromagnetic analysis software CST MWS 2015 to get its scattering parameters in the frequency range from 0 Hz to 43.5 GHz [8]. After comparing the performance of different loop heights ranging from 0.4 mm to 0.8 mm in simulation as in Figure 2.4.1, it concludes that a lower loop height gets a better return loss and a better performance.

Figure 2.4.1: Simulation results of single bond wires with different height [8]

It designs and fabricates the test structure of single bond wire on PCB shown in Figure 2.4.2 and

performs VNA measurement. The simulated and measured results agree with each other. This work

Background | 11

11 also fabricated the double bond wires with the pitch of 8 mm to observe the crosstalk between them.

Compared to simulation results, the crosstalk is quite severe in the frequency range of 0 Hz to 10 GHz, and the measured results are more consistent with simulation in higher frequency.

Figure 2.4.2: Fabricated single bond wire structure [8]

2.4.2 Comprehensive performance analysis of single bond wire in simulation

The paper [11] performs a comprehensive electrical performance analysis of bond wire interconnection in the frequency up to 170 GHz. The bond wire is simplified as an arc of a circle. It proposes an electrical model for the entire bonding, including the series inductance L of the bond wire, and the shunt capacitance C for the bond pad and ball, as shown in Figure 2.4.3. The work then derives the transfer function of the two-port network [11]

It studies the effect of the inductance and capacitance in the transfer function of the bond wire, and finds out that there is a trade-off between them in terms of achieving a better performance for the system. Note that it does not derive the values of the elements according to the shape profile of bond wire.

Figure 2.4.3: Equivalent circuit for bond wire interconnection [11]

12 | Background

3D simulation software is also to study the impact of different gap distances, pad areas and loop heights on the transmission behavior. The simulation results demonstrate that the electrical performance of the single bond wire can be improved by a shorter bond wire length and a bonding pad of proper size. This paper also emphasizes the process-related limitations and variations of the loop height, ball size and bonding pad distance, which is of great value when it comes to realistic analysis. It fabricates bond wire test structures on the PCB, and measures the distance between two bonding positions and scattering parameters (S-parameters). It performs simulation of the bond wire, and compares it with the measured result, shown in Figure 2.4.4.

Figure 2.4.4: Transmission performance of the fabricated single bond wire [11]

The results can be considered consistent up to around 130 GHz, and after that the parasitic is beyond the scope of simulation. It is also indicated in this paper that the bond wire profile in the simulation is not a perfect match for the fabricated one.

2.4.3 Modeling and minimizing the self-inductance of bond wire

In the work [12], it presents an analytical calculation for the partial self-inductance of single bond wire. It proposes a novel way to calculate the partial self-inductance, including internal and external ones, which uses the bonding geometric parameters as variables in the functions. These parameters include the loop height, distance between two bonding bumps and the thickness of metallization.

The shape of the bond wire is approximated to follow the Gaussian distribution function in Figure

2.4.5, because the paper [12] considers this as a realistic and accurate representation of the bond

wire profile. It uses Matlab to obtain the values of all the elements in the analytical model and

validates the model by performing simulation in Ansys Q3D.

Background | 13

13

Figure 2.4.5: Bond wire model of Gaussian distribution function [12]

This paper [12] also looks into possible ways to minimize the partial self-inductance by examining the analytical model, and discovers that increasing the radius can reduce the partial self- inductance. This is also verified in simulation, and it takes a further step by quantifying the impact of the radius through fabrication and measurement. The results in the following two figures are consistent with that from analytical modeling and simulation.

Figure 2.4.6: Measurement of return loss of bond wires with radius 12.5 µm and 62.5 µm [12]

14 | Background

Figure 2.4.7: Measurement of insertion loss of bond wires with radius 12.5 µm and 62.5 µm [12]

2.4.4 Analysis of capacitance compensation structure for bond wire

In this work [13], a capacitance compensation structure for bond wire in multiple-chip module is studied. It approximates the bond wire structure as in Figure 2.4.8, and proposes an equivalent circuit for bond wire as shown in Figure 2.4.9. In the equivalent circuit, L is the series inductance, R is the series resistance, and C is the parallel capacitance between the bond pad and the ground. It analytically derives the expressions of all these three elements in terms of the geometric parameters of the bond wire.

Figure 2.4.8: Structure of the interconnection [13]

Figure 2.4.9: Capacitance compensation model for bond wire [13]

Background | 15

15 It investigates the relationship between the geometric parameters and the behavior of the bond wire using the analytical model. The parameters are the diameter, loop height and the number of bond wires in parallel, and the key to improve the performance is to decrease the inductance. Then, it builds the entire capacitive compensation structure in the 3D electromagnetic simulator ANSYS HFSS, shown in Figure 2.4.10. There are two pads added on the edge of the microstrips, and two striplines underneath them.

Figure 2.4.10: 3D capacitive compensation structure [13]

This capacitance compensated structure is compared with the uncompensated one, whose results are in Figure 2.4.11. The conclusion is that the compensated structure can minimize the parasitic effects and improve the return loss [13].

Figure 2.4.11: Simulated return loss of capacitive compensated and uncompensated structure [13]

16 | Background

2.4.5 Electromagnetic simulation of bond wires and comparison with measurements

The work [14] looks into different techniques to perform analysis on bond wires in wide band frequency domain. It utilizes a scanning electron microscope (SEM) to take close and clear pictures of the long bond wires (shown in Figure 2.4.12), discretizes them by an edge detection algorithm, and then generates suitable orthogonal grids for electromagnetic simulation. This method gives a very accurate and realistic profile of the bond wire.

Figure 2.4.12: SEM picture of the bond wire [14]

A numerical technique, full wave finite difference time domain (FDTD) simulation, is performed to obtain the function of the scattering parameters in the frequency domain under 20 GHz. In order to extract the lumped elements, an analytical model in Figure 2.4.13 is considered, where the capacitance is the one between the bond wire and the ground plane. It uses the Monte Carlo technique and FastHenry to calculate the inductance, and the finite element method for the capacitance.

Figure 2.4.13: Geometry and corresponding lumped element model of the bond wire [14]

Background | 17

17 These results from FDTD, Monte Carlo and FastHenry are all compared with measurements.

They are further analyzed by dividing the results into high frequency range and low frequency range.

The computational effort of different techniques is discussed as well. [14] gives a summary of the advantages and disadvantages of all the techniques it uses.

2.4.6 Novel approach to model the packaged RF power transistors

This work [15] uses three-dimensional electromagnetic simulator and SPICE to model the packaged radio frequency power transistors. The key problem is the model accuracy of the bond wires and package. To solve this problem, [15] first calculates the inductance and resistance of the systems of bond wires, including building an equivalent model for the package. In order to get a realistic and accurate profile of the bond wires inside the power transistor, the novel approach used here is to take scanning electron microscope micrographs, as in Figure 2.4.14, and run software in Java to extract the three-dimensional geometries of the bond wires.

Figure 2.4.14: SEM picture of the inside of a power transistor [15]

The 3D electromagnetic simulator FastHenry is used for the simulation of inductance and resistance, with the input of the geometrical extraction from the Java program as in Figure 2.4.15.

FastCap is used to estimate the capacitance of the package, and the capacitance model is simplified.

18 | Background

Figure 2.4.15: Extracted model for electromagnetic simulation of resistance and inductance in FastHenry [15]

In the result part, [15] discusses different options and factors that have different impacts on the model accuracy, such as simple model, frequency-dependent model, skin effect, mutual inductance and package capacitance.

2.5 Summary

All the works mentioned in this chapter are a great value to the research design planning of this project. Even though there are already many studies regarding bond wires, they have different techniques and research focuses. Table 2.5.1 is a summary of the technical methods that related works use in terms of how they approximate the shape of the bond wire, if they build a mathematical model and what elements they include in it, if they simulate the model and if they perform fabrication and measurement on the test structure.

Table 2.5.1: Technical methods of related works

The work [8] studies the relationship of the loop height and the transmission performance in simulation, and the crosstalk between two bond wires in measurement. [11] uses analytical modeling and simulation to conclude the effects of gap distances, pad areas and loop heights.

However, it does not extract the inductance or capacitance of the bond wire, and measurement is used to see how it differs from simulation results at different frequency. [12] puts emphasis on the analytical calculation of inductance, and investigates its dependency on gap distance and loop

2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6

Shape model Arc Arc Gaussian

distribution

- Extraction from SEM

Extraction from SEM Mathematical

model

No Yes Yes Yes Yes Yes

Elements - L, C L L, C, R L, C, R L, R

Simulation Yes Yes Yes Yes Yes Yes

Fabrication and measurement

Yes Yes Yes No Yes Yes

Background | 19

19 height in calculation and simulation, and metallization thickness in measurement. [13] compares the capacitance compensated structure and the uncompensated in simulation, and also studies the impact of different diameter, loop height and number of bond wires in mathematical modeling. But it doesn’t perform lumped element extraction. Unlike all the papers mentioned previously, [14] and [15] focus more on the techniques and methods rather than simply studying the behavior of bond wires. They all use the scanning electron microscope to extract the realistic geometrical profile of the bond wire, and perform electromagnetic simulation, inductance and capacitance extraction using different methods.

As shown previously, a few studies have investigated the relationship between certain physical dimension parameters and the transmission performance of bond wires. Almost all of them model the bond wire in terms of a simple equivalent electrical circuit, which usually consists of one inductor and/or two capacitors and/or one resistor. They, more or less, use the means of mathematical modeling, simulation, fabrication and measurement to verify their results.

In light of these, this project would try to build a more accurate analytical model of the bond

wires and apply all three techniques to verify the accuracy of the proposed model.

Methodologies and Methods | 21

3 Methodologies and Methods

This chapter introduces the research methods used in this project. It includes the research process, research paradigm, data collection techniques, experimental design, how to evaluate the reliability and validity of the data collected, and data analysis.

3.1 Research Process

This project follows the steps in Figure 3.1.1 to conduct the research.

Figure 3.1.1: Research Process

3.2 Research Paradigm

The research paradigm or philosophical assumption for this project is positivism. It assumes that the reality is objective and does not depend on the researcher or instrument [4]. This project is quantitative because of its purpose to prove that a certain model fits the behavior of bond wire. The behavior is assumed to follow the fundamental electromagnetic theory and transmission line theory, and they are objective given any circumstances.

3.3 Data Collection

This project uses experiments to collect data of the scattering parameters of the network. The data would include the return loss, insertion loss and the angles, and it would come from three different sources: calculation, simulation and measurement. With the scattering parameters, the corresponding values for inductance, capacitance and resistance can be obtained as well. In the scope of the project, no human participant is involved, which means that it is not subject to privacy or human right issues. No violation of ethics is present in the research process.

3.3.1 Sample Size

In mathematical calculation, at least three samples of different loop height are taken. In simulation,

three samples are taken to verify the results from calculation, and three samples of different

separation are needed as well. Because the calculation and simulation are always theoretically

correct and certain, it is not necessary to take multiple samples of the same test structure.

22 | Methodologies and Methods

For measurement, two different loop height and three different separation are needed. Each of these cases should have three test structures fabricated, and each test structures should be

measured for at least twice, and three times if necessary.

3.4 Experimental design/Planned Measurements

This project would combine mathematical modeling, simulation, fabrication, measurement and analysis to solve the problem. This process involves a lot of different technologies. This section introduces all the technologies and conditions needed for the experimental design.

3.4.1 Test environment/test bed/model

All the tests are performed in a professional laboratory, and should not have strong electromagnetic interference in the surrounding. The test bed involves the floating table, VNA, WinCal XE 4.6 and the test board. The test model is fabricated with the bond wires on an original test board.

3.4.2 Hardware/Software to be used

For hardware, there are in total twenty empty test boards available to build test structures and perform calibration. The bond wire prototype machine MP iBond 5000 is used to fabricate test structures, and vector network analyzer N5242A by Agilent Technologies to perform S-parameter measurements. The three-pin probes from Cascade Microtech are used for connection with the test structure. The regular optical microscope is necessary to observe and measure the dimensions of the bond wires. The scanning electron microscope is used to take micrographs of the fabricated bond wires.

There are mainly four kinds of software used in this project. Matlab is used to build

mathematical model. National Instruments AWR software is used to perform 2D simulation of the bond wire models and equivalent circuits. Its optimization functionality can extract the values of electrical elements in the equivalent circuit. This project also uses a 3D electromagnetic simulator ANSYS HFSS to simulate the entire test structures and test environment. WinCal XE 4.6 by Cascade Microtech is connected with the VNA and passes the commands to the VNA in order to perform calibration and measurement. The measurement results from the VNA is then transmitted back to the software WinCal XE 4.6.

3.5 Assessing reliability and validity of the data collected

As a part of quality assurance, it is important to assess whether every test is measuring the right content and whether it is measuring accurately, which means reliability and validity respectively.

This section talks about the fundamentals of such assessment.

3.5.1 Reliability

Reliability is the consistency of the results. This will be guaranteed by performing multiple

measurements on the same test structure. Test it twice at the beginning, and if the two results agree

with each other, then the result is reliable; if not, it is necessary to do a third one, and rule out the

problematic one.

Methodologies and Methods | 23

23 3.5.2 Validity

Validity can be achieved by comparing the measurement results with the simulation or calculation results. If the measurement shows the same behavior as the simulation, then it is valid; if not, the testing procedures, simulation and analytical model need to be examined again and find out the possible source of error.

3.6 Planned Data Analysis

The collected data will be analyzed in order to draw conclusions about the model, simulation and fabrication. This section shows the data analysis method and the corresponding tools used in this project. The evaluation metrics in this project are the scattering parameters and the inductance of the bond wires.

3.6.1 Data Analysis Technique

In order to check if two sets of scattering parameters are close enough, the average L2 norm would be calculated and evaluated. This weighted difference is the “average squared magnitude of the difference between each element of the S-parameter matrix” [16]

Average L2 norm error = ∑

∑

kl𝑆

− 𝑆

lm

𝑁

where N is the number of ports of the network, and the error will be calculated in the unit of dB.

In order to compare simpler numeric data, such as coupling coefficient, the percent error is calculated according to

Percent error = |Experimental − Expected|

Expected × 100%

3.6.2 Software Tools

NI AWR is used to show the graphs of scattering parameters obtained from measurement, perform

optimization to get element values, and to calculate and display the average L2 norm.

Experimental and Modeling Approach | 25

4 Experimental and Modeling Approach

This chapter presents how the research is designed and implemented. After studying the related works, a comprehensive research is designed in accordance of the goals of this project, which includes building an analytical model in Matlab, performing electromagnetic simulation in NI AWR and ANSYS HFSS, and hardware fabrication and measurement.

A mathematical model is helpful to understand the fundamentals of the bond wire, and it needs to be validated in simulation. In this case, two simulators are employed, with AWR for two-

dimensional and HFSS for three-dimensional simulation. The model is also compared with the measurement to see if they have the same behavior. This kind of comprehensive design would give reliable and trustable results regarding the purpose of this project.

With the techniques mentioned above, the project would investigate how accurate the model is by comparing the results from mathematical modeling with those from simulation and

measurement. Furthermore, it would look into how the loop height affects the transmission

performance of the single bond wire, and the separation distance influences that of the double bond wire with coupling.

4.1 Analytical modeling

This section explains how to build a mathematical model of the bond wire in Matlab. It is based on the lump-element model of the transmission line. Both single bond wire and double bond wires with coupling are considered.

One single bond wire can be considered as a cascade of N segments of wires. Each segment can be treated as a transmission line, and has the equivalent circuit as shown in Figure 2.1.1. In lossless situation, R would be considered neglectable.

4.1.1 Shape model

In Section 2.4, two works use the arc of a circle to model the shape of the bond wire, [12] use the Gaussian distribution function, and [14] and [15] extract the discretized shape from the photo taken by SEM. [14] and [15] have the most realistic and accurate profile of the wire, but it is also difficult and complicated to obtain. A compromising solution is to use a certain mathematical function to model the shape of the bond wire. By observation, the shape of the wire can be better approximated as a Rayleigh distribution function than a Gaussian distribution function [17]:

𝑓(𝑥; 𝜎) = 𝑥 𝜎

𝑒

•

4•^•

, 𝑥 ≥ 0

The probability density function for Rayleigh distribution has the shape shown in Figure 4.1.1.

26 | Experimental and Modeling Approach

Figure 4.1.1: Rayleigh distributions [17]

In order to build a quantifiable model, divide the gap evenly into N sections along the x axis, and take the height of the middle point as the equivalent height for this section of wire. The length of each section is estimated as the distance between two middle points. The case with 𝑁 = 10 is illustrated in Figure 4.1.2. The dashed line is the bond wire outline following a Rayleigh distribution, and the red solid line is the approximated segmented line. Each section will be considered as parallel to the ground when evaluating their electrical characteristics.

Figure 4.1.2: Shape model

4.1.2 Electrical characteristics

In the equivalent circuit, there are series inductance, series resistance and parallel capacitance.

Among these three elements, the inductance is the one that can influence the transmission performance the most.

4.1.2.1 Inductance

The inductance of each section normally consists of the self-inductance of the round wire and the mutual inductance between the wire and the ground. Here, the mutual inductance is small enough to be negligible. The self-inductance can be calculated by [18]

𝐿

= 2 •𝑙 log ^ 𝑙 + √𝑙

+ 𝑟

𝑟 _ − ;𝑙

+ 𝑟

+ 𝑙

4 + 𝑟™

Experimental and Modeling Approach | 27

27 where 𝑟 is the radius, and 𝑙 is the length of the wire.

In case of two parallel bond wires, the inductive coupling between them needs to be considered as well. The mutual inductance can be found analytically by [18]

𝑀

= 2 •𝑙 log ^ 𝑙 + √𝑙

+ 𝑑

𝑑 _ − ;𝑙

+ 𝑑

+ 𝑑™

where 𝑑 is the distance between two bond wires. Another way to get the mutual inductance is through the coupling coefficient

𝑀

= 𝑘;𝐿

∙ 𝐿

in which 𝐿

and 𝐿

are the inductance of the two conductors, and 𝑘 is the coupling coefficient between these two inductances. In the ideal case that the two bond wires are identical, 𝐿

should be equal to 𝐿

.

The total inductance of the double bond wires with coupling will be 𝐿

= 𝐿

∙ 𝐿

− 𝑀

𝐿

+ 𝐿

− 2𝑀 4.1.2.2 Capacitance

As mentioned previously, each section of the bond wire is considered as a straight line or a very thin metal plate parallel to and over the ground. The surface facing the ground would be in the shape of a rectangle, and its area can be calculated as 2𝑟𝑙 . The capacitance between this section of bond wire and the ground plane can be found by [19]

C = 𝜀

𝐴 ℎ ≈ 𝜀

2𝑟𝑙 ℎ

where 𝜀

is the electric constant and ℎ is the equivalent height from the ground plane.

4.1.2.3 Resistance

The resistance of a conductor can be calculated by [19]

R = 𝜌 𝑙 𝐴

in which 𝜌 is the resistivity of the material of the bond wire, which is gold in this case. The resistance of the bond wires in this case is extremely small.

4.1.3 Network analysis

As introduced in Section 2.1, the characteristic impedance of each segment of transmission line can be found by

𝑍

= D 𝑅 + 𝑗𝜔𝐿 𝐺 + 𝑗𝜔𝐶

The Y matrix for each section is [5]

[𝑌] = − 𝑗

𝑍

∙ J 𝑐𝑜𝑡 (𝜃) −𝑐𝑠𝑐(𝜃)

−𝑐𝑠𝑐(𝜃) cot (𝜃) K

where 𝜃 = 𝛽𝑙.

28 | Experimental and Modeling Approach

Each section can be converted to a 𝜋 equivalent circuit, shown in Figure 4.1.3, with each element represented by the admittance parameters

Figure 4.1.3: Equivalent p circuit

where 𝑧

= 𝑧

=

¬¬>«_¬•

, and 𝑧

= −

¥

.

As the entire bond wire is a cascade of all N segments, it also means that it is a cascade of all N equivalent 𝜋 circuits as Figure 4.1.4. In order to obtain the scattering parameters of the entire bond wire, the easier way is to find the impedance parameters first. The impedance matrix can be found by definition, and then transform it into the scattering matrix using the formula mentioned in Section 2.3.2.

Figure 4.1.4: Cascaded p circuits

The whole analytical model has been done in Matlab, and this gives a theoretically ideal results of the transmission performance of bond wires.

4.2 Simulation

One way to verify the mathematical model is to perform electromagnetic simulation. This project would use two simulators to investigate the behavior of the bond wires: NI AWR and ANSYS HFSS.

NI AWR is a tool for RF and microwave circuit design and simulation, and ANSYS HFSS is used to perform 3D electromagnetic simulation which takes the whole test environment around the test structure into account.

4.2.1 Circuit modeling and simulation

In NI AWR, there are existing bond wire models that can be used directly as a component in a

design. Figure 4.2.3 is the model for single bond wire, and Figure 4.2.4 for double bond wires. Since

the bond wire studied in this thesis project is quite short, it cannot achieve very accurate results if it

is divided into too many segments in simulation. In fact, the attempt to use more segments in the

model failed due to the warning message in AWR. Therefore, a simpler three-segment bond wire

component is used in AWR simulation. This requires approximating the ten-segment shape used in

Experimental and Modeling Approach | 29

29 Matlab to a three-segment one. The general rule for such approximation is maintaining the similar shape profile and total length.

The ports used in this project all have the impedance of 𝑍 = 50 Ω.

Figure 4.2.1: Single bond wire model in AWR

Figure 4.2.2: Double bond wires model in AWR

The bond wire model with the approximated physical dimensions is then compared to the equivalent circuit with element values calculated in Matlab. For equivalent circuits, the single bond wire is modeled by an inductor, a resistor and two capacitors in Figure 4.2.3. The resistance would simply be zero in the lossless case.

Figure 4.2.3: Equivalent circuit for single bond wire

For double bond wires with coupling, the circuit in Figure 4.2.4 is used. This fundamentally

consists of two of the circuits from Figure 4.2.3 in parallel, and coupling between the inductors as

well.

30 | Experimental and Modeling Approach

Figure 4.2.4: Equivalent circuit for two bond wires with coupling

In NI AWR, the optimization functionality is used to fit the bond wire model to the equivalent circuit by minimizing the average L2 norm difference between the scattering parameters of the model and the circuit. The optimization process can obtain the optimized values for all the elements in the circuit, which are inductance, capacitance and resistance in the single bond wire, and coupling coefficient in the double bond wires. The corresponding values for the elements in the circuit can then be compared with the ones from Matlab calculations.

4.2.2 3D modeling and simulation

In ANSYS HFSS, the whole testing environment with the test model can be constructed and

simulated, and this should give very accurate results as well. As presented in Figure 4.2.5, the box

on the outside is the environment of air or vacuum and also the radiation boundary for

electromagnetic simulation; the plane inside is the copper ground plane, where the bond wire is

built on.

Experimental and Modeling Approach | 31

31

Figure 4.2.5: Overall test structure in HFSS

From a closer view of the test structure in Figure 4.2.6, on the edges of the single bond wire are the lumped ports for excitation. All these components are required in order to build a complete test structure and achieve better results in the 3D simulator. The bond wire model used in HFSS should also be a three-segment model which has the same parameters and shape as the one used in AWR.

Figure 4.2.6: Close-up view of test structure in HFSS

4.3 Fabrication and measurement

The last section of the design and implementation is to build the test structures by using the bond

wire prototype machine, and to perform scattering parameter measurement on them via Vector

Network Analyzer. The fabrication is done on a two layered board with microstrips on the top,

shown in Figure 4.3.1. The detailed information of the board from the top to the bottom is listed in

Table 4.3.1.