Nanopatterned Phase-Change Materials for High-Speed, Continuous

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NANOPATTERNED PHASE-CHANGE MATERIALS FOR HIGH-SPEED, CONTINUOUS

PHASE MODULATION

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulﬁllment of the Requirements for

The Degree of

Master of Science in Electrical Engineering

Andrea E. Aboujaoude

Dayton, Ohio

December, 2018 NANOPATTERNED PHASE-CHANGE MATERIALS FOR HIGH-SPEED, CONTINUOUS

PHASE MODULATION

Name: Aboujaoude, Andrea E.

APPROVED BY:

Joseph W. Haus, Ph.D. Imad Agha, Ph.D. Advisor Committee Chairman Committee Member Professor, Electro-Optics and Photonics Assistant Professor, Physics, Electro-Optics and Photonics

Andrew Sarangan, Ph.D. Joshua Hendrickson, Ph.D. Committee Member Committee Member Professor, Electro-Optics and Photonics Senior Research Physicist, AFRL, Sensors Directorate

Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean, School of Engineering School of Engineering

ii © Copyright by

Andrea E. Aboujaoude

2018 ABSTRACT

NANOPATTERNED PHASE-CHANGE MATERIALS FOR HIGH-SPEED, CONTINUOUS

PHASE MODULATION

Name: Aboujaoude, Andrea E. University of Dayton

Advisor: Dr. Joseph W. Haus

The project explores the vastly different opto-electronic properties of GST in two different phases: amorphous and FCC crystalline. The eventual goal is to design and fabricate photonic devices whose functionality depends on the distinct material properties of the two phases of GST.

A prototypical device structure was designed with a lattice of GST nanorods grown on a Silicon substrate. The GST nanorods are surrounded by a thermally conductive material, such as Boron

Nitride, that rapidly quenches the nanorods during the phase change. An electrical contract on top of the device is used to initiate the GST phase transition. Simulations for this device design are used to explore the range of values needed for nanorod dimensions and applied voltages to control the phase transitions, as well as determine the effectiveness of the material surrounding the nanorod.

Preliminary experiments are conducted to characterize the resistivity and sheet resistance of the

GST samples and contact resistance between different GST phases and the contact metals, Tung- sten and Molybdenum. The measured contact resistances and calculated sheet resistances for the two metals are comparable.

iii For my parents, Elias and Hilda, for teaching me that Not all things worthwhile come easy; for

Mariana, for Always being Two steps ahead of me and Guiding me on my way through life; for

Nicole, for showing me what Neverending determination can Actually Bring; and for Ayesha, for

Being a True friend and my unwavering Support for all matters big and small.

Thank you all for being in my life.

iv ACKNOWLEDGMENTS

I would like to thank Dr. Joseph Haus and Dr. Imad Agha for being my advisers and Dr. Joshua

Hendrickson for being my DAGSI sponsor. Thank you for your support through my proposal and masters project.

I would like to thank Joshua Burrow for his work on the sample fabrication, the contact resistance measurements, and the SEM image for the contact resistance test sample, as well as taking the time to train me on the sputtering tool and answer my many questions on the fabrication process.

I would also like to thank Gary Sevison for his work on the experimental setup and his assistance with gathering experimental data. Thank you to David Lombardo for training me on the lithography machine and for offering his insight into the lithography process. Also, thank you to Pengfei Guo for the GST resistance measurements.

Finally, I would like to thank my family and friends for their endless support and love throughout my college career and especially over the past year.

v TABLE OF CONTENTS

ABSTRACT...... iii

DEDICATION ...... iv

ACKNOWLEDGMENTS ...... v

LIST OF FIGURES ...... viii

LIST OF TABLES ...... xi

I. INTRODUCTION ...... 1

1.1 History of Phase-Change Materials...... 1 1.2 Project Objectives ...... 4 1.3 Thesis Overview ...... 4

II. THEORY...... 5

2.1 GeSbTe...... 5 2.2 Materials Explored ...... 8 2.3 Effective Medium Theory ...... 10 2.4 Effects of Convection ...... 12 2.5 Electrical Resistance ...... 14 2.6 Temperature and Quenching Time Goals ...... 19

III. SIMULATIONS ...... 21

3.1 Model Setups ...... 21 3.2 Single Rod and Array Results ...... 25 3.3 Effects of Nanorod Radius and Height ...... 30 3.4 Effects of Different Materials ...... 31 3.5 Conclusions ...... 32

IV. EXPERIMENTAL SETUPS ...... 34

4.1 Optical Setup ...... 34 4.2 Electrical Setup ...... 37 4.3 Preliminary Experiments ...... 38

V. SAMPLE FABRICATION ...... 41

5.1 Deposition of Metal Contacts ...... 41 5.2 Deposition of GST Test Areas ...... 44

vi VI. EXPERIMENTAL RESULTS...... 47

6.1 GST Resistivity Measurements ...... 47 6.2 Contact Resistance Measurements ...... 49 6.3 Optical Switching Experimentation ...... 53

VII. CONCLUSIONS AND FUTURE WORK ...... 54

7.1 Conclusions ...... 54 7.2 Future Work ...... 55

BIBLIOGRAPHY ...... 57

APPENDICES

A. Matlab Code For Nanorod Height Calculations ...... 62

B. Matlab Code For Impedance Matching Calculations ...... 65

C. Select Model Dimensions ...... 67

D. Select Material Properties ...... 68

E. Array Model Results ...... 72

vii LIST OF FIGURES

1.1 Cross-sectional View of Basic Optical Disk...... 3

2.1 GeTe–Sb2Te3 Pseudobinary Phase Diagram...... 5

2.2 Atomic Structure of the FCC Crystalline GST Phase...... 6

2.3 n and κ values of GST...... 7

2.4 Atomic Structure of GST During Phase Change...... 8

2.5 Boundary Layer Caused by Convection...... 13

2.6 Diagram of Four–Point Probe Setup...... 15

2.7 Simpliﬁed Side and Top Views of One Nanorod...... 17

2.8 Circuit Equivalent of Device...... 17

2.9 Temperature Requirements for Crystallization and Amorphization...... 20

3.1 Single Rod Simulation Model...... 22

3.2 Array Simulation Model...... 23

3.3 Input Voltage Pulse for Amorphous to Crystalline Phase Change...... 24

3.4 Input Voltage Pulse for Crystalline to Amorphous Phase Change...... 24

3.5 Amorphous GST with BN and W contacts (Horizontal View)...... 26

3.6 Amorphous GST with BN and W contacts (Vertical View)...... 26

3.7 Crystalline GST with BN and W contacts (Horizontal View)...... 27

3.8 Crystalline GST with BN and W contacts (Vertical View)...... 27

3.9 Temperature at Center of Amorphous GST Nanorod vs. Time (Single Rod Model). . . . . 28

viii 3.10 Temperature at Center of Crystalline GST Nanorod vs. Time (Single Rod Model)...... 29

3.11 Temperature at Center of Amorphous GST Nanorod vs. Time (Different Radii)...... 30

3.12 Temperature at Center of Crystalline GST Nanorod vs. Time (Different Radii)...... 31

3.13 Temperature at Center of Crystalline GST Nanorod vs. Time (Different Materials). . . . . 32

4.1 Input Pulses for Experimentation...... 35

4.2 Tentative Optical Switching Setup...... 37

4.3 Tentative Electrical Switching Setup...... 38

4.4 Test Cell (Not Drawn to Scale)...... 39

4.5 Mask Design (Not Drawn to Scale)...... 40

5.1 Si Substrate with layer of SiO2 and Photoresist...... 42

5.2 After Image Reversal and Development, Only Exposed Photoresist Remains...... 43

5.3 Metal Deposition...... 43

5.4 Lift-off to Remove Photoresist...... 44

5.5 Spin Coat Photoresist...... 44

5.6 After Development, Only Unexposed Photoresist Remains...... 45

5.7 GST Deposition...... 45

5.8 Final Sample...... 46

6.1 Temperature vs. GST Resistivity...... 48

6.2 Temperature vs. GST Resistance...... 49

6.3 SEM Image of Contact Resistance Sample...... 49

6.4 Distance between Contacts vs. Contact Resistance (Amorphous GST)...... 50

6.5 Distance between Contacts vs. Contact Resistance (Crystalline GST)...... 51

6.6 Distance between Contacts vs. Sheet Resistance (Amorphous GST)...... 52

6.7 Distance between Contacts vs. Sheet Resistance (Crystalline GST)...... 53

ix E.1 Amorphous GST with BN and W contacts for Array Model (Horizontal View)...... 72

E.2 Amorphous GST with BN and W contacts for Array Model (Vertical View)...... 73

E.3 Crystalline GST with BN and W contacts for Array Model (Horizontal View)...... 73

E.4 Crystalline GST with BN and W contacts for Array Model (Vertical View)...... 74

E.5 Temperature at Center of Amorphous GST Nanorod vs. Time (Array Model)...... 74

E.6 Temperature at Center of Crystalline GST Nanorod vs. Time (Array Model)...... 75

x LIST OF TABLES

2.1 GST Material Data...... 7

2.2 Values of n and κ for BN and GST, with Calculated Relative Permittivities...... 10

2.3 Radius and Height Values for a π Phase Shift...... 12

2.4 Model Dimensions...... 16

2.5 Calculated Resistance Values...... 19

3.1 Summary of Single Rod and Array Model Results...... 29

6.1 Calculated Contact Resistances...... 51

C.1 COMSOL Input Values for Single Rod and Array Model Simulations...... 67

D.1 Select Amorphous GST Material Data...... 68

D.2 Select Crystalline GST Material Data...... 68

D.3 Select Si Material Data...... 69

D.4 Select BN Material Data...... 69

D.5 Select W Material Data...... 70

D.6 Select Al Material Data...... 70

D.7 Select SiO2 Material Data...... 71

D.8 Select ZnO Material Data...... 71

xi CHAPTER I

INTRODUCTION

1.1 History of Phase-Change Materials

Phase change materials (PCMs) have been in the spotlight for memory storage devices for decades and have increased in importance as the need for larger memory capacity grows. There are several ways to increase how much storage a device can hold. One method, for example, involves decreasing the wavelength of the laser used to read and write the data [1, 2]. Another method would be doping the material holding the saved data [3]. In this project, modiﬁcation of the device structure is explored with the goal of exploiting the large difference in the opto-electronic properties of PCMs due to their change in phase.

PCMs are materials that can be cycled between at least two phases (an amorphous phase and one or more crystalline phases) that exhibit material properties significantly different enough so they can easily be identified by their interactions with light or electrical current [4]. The amorphous phase exhibits low optical reflectivity and high electrical resistivity, while the crystalline phase(s) exhibit various degrees of high optical reflectivity and low electrical resistivity, in comparison to the amorphous state. Differences in reflectivity can be up to 30 percent; differences in resistivity can be up to 5 orders of magnitude [4]. These vastly different properties allow easy identification between the different phases of a PCM. This translates well for data storage, where amorphous can represent a binary ”0” and crystalline can represent a binary ”1”; with data saved according to the phase, no energy or charge is needed to keep the memory stored [2, 5, 6].

1 Initial investigations of PCMs began in the late 1960s, when Dr. Stanford Ovshinsky published his research highlighting their potential use as chalcogenide amorphous semiconductor materials

[7]. A chalcogenide material consists of at least one chalcogen ion, which include elements from

Column VI of the periodic table that share similar valence electron conﬁgurations and, therefore, chemical behavior [8]. In this project, the chalcogenide material GeSbTe, or GST, is used, though there are several other PCMs available with similar characteristics, such as Ag-In-Sb-Te (AIST),

GeTe, and AgSbSe2 [4].

In the 1980s, GST was discovered and used in the first rewritable optical disk, a side cut of which is shown in Figure 1.1 [9]. This particular optical disk has an active layer of GST sand- wiched by Zinc Sulfide (ZnS) acting as protective layers, and the GST phase is determined through changes in reflectivity. By 1990, these compact disks (CDs) were commercialized, and with each new generation, storage space and read/write speed were improved [10]. Soon afterwards, digital versatile discs (DVDs) were invented, which increased data storage capabilities from 650MB for

CDs to 4.7GB [11]. Storage increased further with the development of Blu-Ray disks that are able to hold between 23.3 and 50GB of memory [11]. Over time, the laser wavelength also decreased, going from 780nm for CDs, to 650nm for DVDs, and ﬁnally, 405nm for Blu-Rays [11, 12]. Despite the difference in wavelengths, storage size, and design, the core operation for these three types of optical disks is the same, using the vast difference in reﬂectance between amorphous and crystalline phases of the PCM to store and read data [2].

Aside from phase-change memory and optical disks, GST has also been used in other applications. For example, GST can be used as the working mechanism of an optical latch or switch, where the amorphous and crystalline phases mark either the on or off state [13]. It can also be used as a buffer layer in a conductive-bridging random access memory (CBRAM) design to decrease the residual conductive ﬁlament (CF) and allow for better control of ion injection [14]. As a thermal

2 Figure 1.1: Cross-sectional View of Basic Optical Disk.

barrier, GST assists in reducing write power in magnetic tunnel junctions; this property is dependent on the thickness of the GST, but its effectiveness is limited to devices with a small area [15].

In order for this device to be successful, the material used must meet certain requirements: the amorphous state must be stable; the transition between phases must be fast; the material properties for each phase must be significantly different; and it must allow for a large number of cycles between the phases [10]. GST is an excellent candidate for this device. GST is able to crystallize in less than 50ns, while also staying in the amorphous state for years [16]. In both optical and electrical properties, the different phases of GST exhibit vastly different values which allows for easy identification of which phase is present. For reflectance, the difference can be up to 30 percent, while the resistivities vary by several orders of magnitude [4, 17, 18]. The cyclability values differ for each report but is at least in the tens of thousands cycles [4, 11, 19, 20, 21]. These properties of

GST are further explored in this project with the goal of developing photonic devices with superior performance compared to those available on the market today.

3 1.2 Project Objectives

This project explores the basis for the development of a GST phase-change device for data storage, with the ﬁnal goal being to switch between the amorphous and crystalline phases of GST using an applied voltage and read the current phase using resistance. Simulations are conducted to explore the effects of different materials and the device dimensions, as well as estimate the applied voltage that would be needed to switch the GST between its amorphous and crystalline phases.

GST resistance is also explored, as it will become more important as the project progresses forward.

Preliminary experiments are planned, with the use of a laser to trigger a phase switch.

1.3 Thesis Overview

Chapter II lays out the theory behind GST’s phase change properites, what other materials are needed in the device, how dimensions for the device can be determined, the potential effects of convection, the different types of resistance that must be considered, and what conditions need to be met so that this device can be considered practical for application. Simulation setups and results are introduced in Chapter III, giving an outline for what input parameters such as voltage are needed to successfully transition between GST’s phases. Chapter IV introduces the optical and electrical setups used to collect experimental data, while the sample fabrication process is outlined in Chatper

V. The experimental results are explained in Chapter VI. Finally, Chapter VII gives conclusions and future work for this project.

4 CHAPTER II

THEORY

2.1 GeSbTe

The material at the focus of this project is GeSbTe, or GST. GST comes in many different compounds with different material properties, though the intermediate ternary compound of Ge2Sb2Te5 in particular is often employed due to its status as a ”standard material” for optical disks since its use for the ﬁrst rewritable phase-change optical disk in 1990 [10]. There are other compounds that exist for this system, like GeSb2Te4, Ge3Sb2Te6, and GeSb4Te7, as can be seen in Figure 2.1, though

only Ge2Sb2Te5 is used in this project [10, 22].

Figure 2.1: GeTe–Sb2Te3 Pseudobinary Phase Diagram.

GST is known to have three different phases in the solid state: amorphous, face-centered cubic (FCC) crystalline, and hexagonal close-packed (HCP) crystalline. This project focuses on the

5 switch between the amorphous and FCC crystalline phases. A representation of GST’s FCC crystal structure can be found in Figure 2.2 [6]. This FCC structure, also called a distorted NaCl structure, differs from the ideal case due to the large number of vacancies (approximately 20 percent) present in the structure [6, 12, 21].

Figure 2.2: Atomic Structure of the FCC Crystalline GST Phase.

GST has several interesting qualities which make it a promising candidate for the given application. First, GST is able to crystallize less than 50ns [9]. It is theorized that this is due to the small amount of atomic motion that needs to occur to switch between amorphous and crystlline, especially in comparison to the original materials used for phase change [7, 16, 21]. GST is also able to maintain its amorphous state for years and can be deposited on virtually any substrate or

ﬁlm at low temperatures [16, 23]. The amorphous and crystalline phases of GST also exhibit vastly different optical properties, which may be caused by the large change in density (5-10%) between the two phases [2, 11, 24]. The n and κ values for GST are shown in Figure 2.3 [23]. Similarly, the difference in resistivities for the two phases is in the orders of magnitude. This property could cause problems in the future for impedance matching, which is explored later on in this chapter.

6 Figure 2.3: n and κ values of GST.

Relevant material property values used for GST in this project are summarized in Table 2.1.

These properties are highly dependent on the method of deposition; in this project, lithography and sputtering are used for making the samples. Other values used in the simulations in Chapter III can be found in Appendix D. Note the large differences between the amorphous and crystalline phases, especially for the electrical conductivity.

Table 2.1: GST Material Data.

Property Amorphous Value Crystalline Value Relative Permittivity (ϵr) 16.0 [25] 33.3 [25] Thermal Conductivity (k) 0.17 W/m/K [26] 0.5 W/m/K [26] Electrical Conductivity (σ) 3 S/m [26] 2770 S/m [26]

A visual representation of the phase change mechanism in GST can be found in Figure 2.4 [10,

27]. In order to crystallize from the amorphous phase, the GST is heated up above the crystallization temperature but below the melting temperature. If given enough time, the bonds will rearrange themselves without melting. Slow quenching allows the bonds to properly form, resulting in the

7 crystalline phase. To return back to the amorphous state, the GST must be heated above the melting temperature and quenched quickly so that the bonds cannot rearrange themselves. GST does not have to be in the liquid state in order to reform into amorphous; it only needs to be heated enough for the weaker bonds to be broken [21].

Figure 2.4: Atomic Structure of GST During Phase Change.

2.2 Materials Explored

Besides GST, three other materials are needed to manufacture this device: the substrate on which the device is placed, the electrical contact to connect the device to the rest of the circuit, and the material that surrounds the GST to assist with quenching. For the substrate, only Silicon

(Si) is explored, though other options such as Sapphire and Quartz are available; it is not clear how the substrate would affect the functionality of the device in this application beyond the change in material properties [28, 29]. Tungsten (W) is used as the electrical contact due to availability.

Use of Cubic Boron Nitride (c-BN, or simply BN) as the material surrounding the GST would be the ideal case for this device, thanks to its high electical resistivity and thermal conductivity,

8 making it a good electrical insulator and thermal conductor [30]. It is also one of the hardest materials known and is chemically inert, which is why it is often used as a coating material [31, 32].

It is speculated that these properties are linked to its crystal structure and low number of atoms per unit cell [33]. In this application, BN works well to quickly quench the heat from the GST nanorod, which is essential for proper phase transitions.

However, in terms of manufacturing, BN is very difﬁcult to deposit in its cubic state. Amorphous

BN (a-BN) does not possess the same appealing properties as c-BN does, in which case, it would be more logical to go with a material easier to deposit that would have properties better for the application. BN also has other problematic properties. It reacts with water, and its hardness also leads to internal stresses that cause cracking and peeling off the substrate [31]. These issues are beyond the scope of the project at present but will need to be explored in the future, if BN is going to be used in the ﬁnal device.

For these reasons, different materials are explored for both the device contacts and the material surrounding the GST. For the contacts, the other material explored is Aluminum (Al), and for the material surrounding the GST, they include Silicon Dioxide (SiO2) and Zinc Oxide (ZnO) to replace

BN. These materials, while easier to manufacture, may not have the properties needed to accomplish the temperature and quenching time goals laid out in Section 2.6. For example, in the case of

SiO2, its thermal conductivity at 300K is severely lacking in comparison to c-BN, potentially due to its crystal structure [33]. How well these materials act in the device and whether they would be reasonable replacements for the original material choices is discussed in Chapter III. Tables with material properties can be found in Appendix D.

9 2.3 Effective Medium Theory

One of the ﬁrst steps in designing the GST device is determining the target dimensions for the nanorod and surrounding material. This is done using the effective medium theory, which uses the relative permittivity of materials in a mixed layer and homogenizes it to give an equivalent permittivity [34]. This requires an assumption that the wavelength is bigger than the layer being homogenized. For this case, the wavelength used is 1.55µm; the calculated height of the BN-GST layer of the device must be smaller than this wavelength for the effective medium theory to be valid.

First, the n and κ values of BN and GST are found at the given wavelength, summarized in

Table 2.2. Since these values change for GST with respect to temperature, several points are used and calculated separately. The results are later averaged together to get a single height value. These value pairs are each put in Equation 2.1 to get the relative permittivity of each material:

ϵ = (n + jκ)2 (2.1)

Table 2.2: Values of n and κ for BN and GST, with Calculated Relative Permittivities.

Material n k ϵ BN [35] 1.6102 0.0549 2.5897+j0.1767 GST as-deposited [23] 4.1807 0.0658 17.5247+j0.7240 GST at 100°C [23] 4.1871 0.0865 36.6406+j25.9443 GST at 200°C [23] 6.3850 2.0317 34.3911+j20.9247 GST at 300°C [23] 6.1093 1.7125 17.4738+j0.5505

These values then put into Equation 2.2

10 ( ) ϵGST − ϵBN ϵeff = ϵBN 1 + 2f , (2.2) ϵGST + ϵBN − f(ϵGST − ϵBN )

where ϵeff is the effective permittivity of the entire layer and f is the fraction of the total volume that is taken up by the inclusion material, in this case GST, which is calculated using

V πr2 f = GST = GST , (2.3) Vtotal wl

where VGST is the volume of the GST, Vtotal is the total volume, rGST is the radius of the GST nanorod calculated for 10nm to 50nm, and w and l are the width and length of the BN block, both set equal to 100nm [34].

The square root of this effective permittivity is then taken, the real part of which is the effective n value. The phase shift or path difference equation shown in Equation 2.4 is used next, rearranged to solve for the height of the GST/BN layer:

Φλ h = (2.4) 2πneff

In this equation, Φ is the phase difference, which would normally be set to 2π. However, this causes some practical issues, as there are natural limitations to how tall a nanorod can be with a given radius. For this reason, a reﬂective coating can be applied under the GST/BN layer, allowing the phase shift to be halfed. With Φ now equal to π, the height of the GST nanorod is calculated and rounded for a range of radius values, as is summarized in Table 2.3. Note that the heights calculated are all less than the wavelength used, making the effective medium theory valid. These values are

11 used in the device simulations for a parametric sweep, as is explained in Chapter III. The Matlab code used for these calculations can be found in Appendix B.

Table 2.3: Radius and Height Values for a π Phase Shift.

rGST hGST 10nm 470nm 15nm 460nm 20nm 440nm 25nm 420nm 30nm 390nm 35nm 360nm 40nm 330nm 45nm 300nm 50nm 265nm

These dimensions are very important for the operation of the device. Balancing the radius and height is needed for the volume-surface area ratio, which is closely related to the quenching rate.

The higher the surface area and lower the volume, the faster the GST is quenched. However, if the quenching rate is too fast, the nanorod will need a higher input voltage to reach the required temperatures for phase change. The effects of the nanorod radius and height are explored in the simulations in Chapter III.

2.4 Effects of Convection

Convection is the method of heat transfer which occurs between a moving ﬂuid and a surface that are at different temperatures. Convection is governed by Newton’s law of cooling, deﬁned as

′′ q = h(Ts − T∞), (2.5)

12 2 where q''is the heat ﬂux (W/m ), Ts is the surface temperature (K), T∞ is the ﬂuid temperature

(K), and h is the convection heat transfer coefﬁcient (W/m2/K) [36]. A visual representation of

convection is shown in Figure 2.5 [36]. In the case portrayed in the diagram, the velocity of the

ﬂuid (u∞) moves horizontal to the adjacent surface. The resulting temperature distribution is shown

on the right (T∞), where the heat ﬂux q''is positive exitting the surface.

Figure 2.5: Boundary Layer Caused by Convection.

There are two types of convection: forced convection and free convection. Forced convection comes from external sources, like fans or wind, while free convection is caused by buoyancy forces, where changes in temperature also affect density and naturally induce motion within the ﬂuid [36].

The difference between these two forms of convection can be seen in h. For free convection, h can range between 2 and 25 W/m2/K for a gas, while forced convection can bring values between 25 and 250 W/m2/K [36].

Convection occurs on the outside surfaces of the device; for the simulations outlined in Chapter

II, an assumed value of 5 W/m2/K is used. Experimentation would need to be conducted to ﬁnd a more accurate value for h, since it is highly dependent on surface geometry, device dimensions,

13 and environmental conditions. This value also assumes that only free convection is applied on the device boundaries; depending on how much convection overall affects the device, it may be helpful to implement a cooling system such as a fan, which would increase h and decrease quenching time.

2.5 Electrical Resistance

In this section, three views of resistance are explored: sheet resistance measurements and resistivity calculations for GST, contact resistance between GST and W contacts, and ﬁnally, how to make a ﬁnal device impedance match to 50Ω.

The resistivity of GST, experimentally determined and summarized in Chapter VI, is calculated using measurements taken by a four-point probe setup similar to the one shown in Figure 2.6 [37].

This setup works by applying a known current to the sample between the outermost probes. The resulting voltage is measured using the inner two probes, and since the distance between the probes is known and equal to one another, the resistivity of the sample can be calculated using

( ) π ρ = tR , (2.6) GST ln(2) measured

where ρGST is the resistivity of GST, Rmeasured is the resistance value given by the probes, and t is the thickness of the GST sample [38].

Another form of resistance that affects the device is the contact resistance between the different materials, especially with the GST and its metal contacts. At the nanoscale, the contact resistance starts playing a bigger role; in some cases, it becomes dominant in the total resistance [39]. There- fore, it is important to explore the effects of the contact resistance on the device.

14 Figure 2.6: Diagram of Four–Point Probe Setup.

The contact resistance is measured using the Transmission Line Measurement (TLM) technique.

Using a probe station, current is passed through the W contacts and GST, with the distance between the contacts varied for each resistance measurement. Equation 2.7 uses the total resistance (RT )

measured to calculate the contact resistance [38].

RT = 2RW + RGST + 2Rcontact (2.7)

Since the contacts are made of metal and therefore have a lower resistance, RW is considered neg- ligible for this calculation. Putting RGST in terms of the sheet resistance and the distance between the W contacts gives

( ) R R = GST sheet d + 2R , (2.8) T W contact where W is the width of the contacts and d is the distance between them [38]. Plotting the total resistance RT against the contact distance d with a line of ﬁt gives the value for 2Rcontact as

15 the y-intercept, half of which is the contact resistance per electrical contact. Equation 2.8 can be rearranged to calculate the sheet resistance RGST sheet from the contact resistance, which gives

( ) R − 2R R = T contact W. (2.9) GST sheet d

Finally, impedance matching is an important point to keep in mind for the future of the device within certain applications. Impedance matching involves adjusting the impedance of the load to be as close to the impedance of the voltage source in order to maximize the output power from the circuit. In many cases, especially with lab equipment, the input impedance is 50Ω, so this is the

assumed input impedance for the calculations to follow. As a ﬁrst step to impedance matching, the

individual resistance contribution of each material is calculated according to Equation 2.10 using

the dimensions summarized in Table 2.4. These resistances are then used to calculate the total

resistance of the device.

( ) h R = ρ (2.10) sheet A

Table 2.4: Model Dimensions.

Variable Name Value Description rGST 50nm Radius of GST nanorod hSi 1µm Height of Silicon hGST 265nm Height of GST nanorod hW 50nm Height of Tungsten w (single rod) 110nm Width and Length of Block (single rod)

The resistances of each material cannot simply be added together to get the total resistance of the device. As can be seen in the simpliﬁed sideview of a single nanorod in Figure 2.7, the current

16 ﬁrst passes through the metal contact, then goes through both the GST and BN layer at the same time, and ﬁnally exits through the Si substrate. These four materials are not simply in series; the

GST and BN portions are in parallel to one another. The equivalent circuit portraying the path of the current can be found in Figure 2.8.

Figure 2.7: Simpliﬁed Side and Top Views of One Nanorod.

Figure 2.8: Circuit Equivalent of Device.

17 From Figure 2.8, the equation for the total resistance of the block can be derived. With RW and

RSi in series with the parallel set RBN and RGST , the block’s total resistance is

( ) 1 1 −1 Rblock = RW + + + RSi. (2.11) RBN RGST

This equation is used twice: once to calculate the resistance of the device when the GST is in the amorphous phase, and then again for when the GST is crystallne. If this block, with the GST nanorod, surrounding BN, Si substrate, and W contact, is considered a unit, then the full device would be made up of an array of these nanorod units. These nanorods are all in parallel with one another, which leads to the equation for the total resistance of the device to be

( )− 1 1 1 1 Rtotal = + + + ... . (2.12) Rblock Rblock Rblock

If there are n number of nanorods, this equation can be simpliﬁed to

( ) −1 n Rblock Rtotal = = . (2.13) Rblock n

Since the simulations in Chapter III use an array of 10 nanorods by 10 nanorods, the n value used is

100 nanorods. The calculated resistance values are summarized in Table 2.5. Two observations can be made from these results. First, the total resistances are still much higher than the input impedance of 50Ω. This can be solved by increasing the number of nanorods in the array, but the amorphous

GST resistance is still orders of magnitude greater than the crystalline GST. Careful adjustment of the dimensions of the device can help reduce this large difference, though this is left to be explored in a future project.

18 Table 2.5: Calculated Resistance Values.

Material Resistance Amorphous GST (unit) 11.26 MΩ Crystalline GST (unit) 20.45 kΩ Amorphous GST (total) 112.6 kΩ Crystalline GST (total) 204.455 Ω

2.6 Temperature and Quenching Time Goals

Certain temperature and quenching time goals must be met in order for this device to function properly. The main concern is for the internal temperature of the GST nanorod to follow the graph shown in Figure 2.9 [26]. Crystallization, marked as the SET pulse in the graph, requires that the

GST slowly heat up to a temperature between the crystallization (or glass) temperature and the melting temperature and remain there for a period of time before slowly quenching back to room temperature. The quenching rate can be controled by slowly lowering the input voltage, as opposed to completely shutting it off all at once. On the other hand, for amorphization, the temperature must follow that of the RESET pulse, rapidly heating up to above the melting temperature and quenching quickly. The quenching rate is mostly dependent on how quickly the input voltage can be shut off and the heat from the GST dissipated by the surrounding BN.

There are many disagreements on what the crystallization and melting temperatures are required to switch GST between its different phases. This is likely due to the methods of deposition used to produce GST samples, as the method and environmental conditions can greatly affect the properties of the material [17, 40]. For the transition from amorphous to FCC crystalline, a range of 130 to

150°C is found in literature [16, 23, 41, 42, 43]. The range for the transition from FCC crystalline to HCP crystalline is much larger, from 200 to 300°C [16, 23, 41, 42, 43]. However, since the intent is not to reach the HCP crystalline phase anyway, the exact temperature where this transition occurs

19 Figure 2.9: Temperature Requirements for Crystallization and Amorphization.

does not matter; staying above 150°C and below 200°C ensures that the phase achieved is FCC crystalline. As for the melting temperature, most agree that GST transitions into the liquid phase above 600°C [2, 9, 16]. This, with a rapid quench, is the temperature goal for amorphization.

The quenching rate is a very important factor for a successful transition back into the amorphous state. If quenching does not occur fast enough, the GST will revert back into its crystalline state.

According to most literature, the quenching rate should fall in the range of 1-10°C/ns [44, 45]. One study claims this rate should be even faster, around 100°C/ns [26]. To compromise these varying numbers, a quenching rate of around 10°C/ns is set as the goal.

The input voltage needed to reach these goals is another important factor to the success of the device. The required power must be low enough to be run with other devices in a circuit or other application. This point has been kept in mind throughout the project, but the actual optimization of the device dimensions and material properties to minimize the required voltage has been left to future work.

20 CHAPTER III

SIMULATIONS

As the ﬁrst step of this project, simulations are conducted using COMSOL 5.2a. COMSOL is a comprehensive software capable of combining multiple disciplines into a single simulation. For this project, the multiphysics for Joule Heating is used, which couples the Heat Transfer in Solids and Electric Current modules using three multiphysics: Electromagnetic Heat Source, Boundary

Electromagnetic Heat Source, and Temperature Coupling. In this way, the simulation is able to show how the device is directly heating up as a result of a current passing through it.

3.1 Model Setups

Due to the shear number of nanorods which would be present in the final device, two different modeling methods are used for the simulations. The first model is a single GST nanorod surrounded by Boron Nitride (BN), with a substrate of Silicon (Si) and a top layer of Tungsten (W) as the electrical contact. The side boundaries of this cube shape are defined using periodic conditions for both the Heat Transfer in Solids module and the Electric Current module; this essentially simulates a nanorod array with infinite dimensions. Assuming the array dimensions are in the thousands in the fabricated device, this model accurately estimates the effects of the surrounding nanorods to the one being analyzed without dramatically increasing the calculation time. Figure 3.1 shows the angled view of the single rod model.

The second model is of a similar design, but instead of a single nanorod, there is a small-scale nanorod array. The array dimensions are set to 10 nanorods by 10 nanorods so that the simulations

21 Figure 3.1: Single Rod Simulation Model.

can be run in a reasonable amount of time. Theoretically, the number of nanorods in the array is signiﬁcantly larger than this, but due to the limitations of the computer being used to run the simulations, the dimensions cannot be increased. Therefore, the array models are only used to conﬁrm the results from the single nanorod models and better visualize how the nanorods are affecting one another. Figure 3.2 shows the angled view of the array model.

In both models, the bottom of the Si substrate is deﬁned as ground, and the top of the W contact is set as the location of the input voltage. The bottom of the device has been set to a constant temperature of 25.0°C. There is also a convection boundary set for each model. For the single nanorod model, the sides of the cube are already covered by periodic conditions, so the convection boundary is only set for the top of the device. For the array model, the convection boundary covers both the top of the block and its sides, the parts of the device that would be exposed to the air during experimental testing.

22 Figure 3.2: Array Simulation Model.

Each simluation is run twice: once for amorphous GST and once for crystalline GST. For the amorphous to crystalline transition, the pulse duration is set to 100ns with a 50ns ramp down period at a maximum input voltage of 25V, while for the crystalline to amorphous transiiton, the pulse duration is for 50ns with essentially no ramp down time at an input voltage of 3V. These pulses are started 5ns after the simulation begins in order to avoid errors due to initial conditions. Figures 3.3 and 3.4 show the input voltage pulses.

Table 2.4 from Section 2.5 summarizes the model dimensions used for both the single rod and array simulation models. The temperatures of the device and of the surroundings are initially set to

2 20°C. The variable hair, chosen as 5 W/m /K, is the convection heat transfer coefﬁcient and used for the convection boundary condition in the Heat Transfer in Solids module, as is explained in Section

2.4 [36]. A more complete table of COMSOL input values can be found in Appendix C.

23 Figure 3.3: Input Voltage Pulse for Amorphous to Crystalline Phase Change.

Figure 3.4: Input Voltage Pulse for Crystalline to Amorphous Phase Change.

24 A parametric sweep of the radius and height of the GST nanorods is also conducted. As explained in Chapter II, the dimensions for the nanorods are calculated using the effective medium theory. In particular, possible nanorod radius values are summarized in Table 2.3 with their corre- sponding heights for the needed π phase shift. Doing a parametric sweep with these values assists in determining the best radius-height combination for the temperature, voltage, and quenching time requirements outlined in Section 2.6.

3.2 Single Rod and Array Results

Figure 3.5 shows the horizontal cut through the single rod model for amorphous GST surrounded by BN and with W contacts. With an input voltage of 25V, a maximum internal temperature of approximately 180°C is reached at the center of the nanorod. The BN surrounding the nanorod stays relatively cool in comparison, staying around 90°C all the way up to where it makes contact with the nanorod. This is similarly shown in Figure 3.6, which shows the vertical cut through the model. Also, the W contacts heat up to around 100°C, while the Si substrate remains well under

80°C. Note that these results are taken 100ns after the voltage is applied to the top of the block, the last moment before the voltage is switched off and the device begins to quench.

In a similar fashion, Figure 3.7 shows the horizontal cut through the single rod model for crystalline GST with BN and W contacts. The input voltage is 3V, which brings the center of the nanorod to a maximum temperature of approximately 600°C. In this model, the BN surrounding the rod heats up signiﬁcantly more to around 470°C. As shown in Figure 3.8, the W contact reaches

500°C, and the Si substrate experiences a much more signiﬁcant temperature gradient, ranging from around 350°C down to less than 100°C. Note that for the crystalline models, the pulse is only on for

50ns, which is when the data was taken for these ﬁgures.

25 Figure 3.5: Amorphous GST with BN and W contacts (Horizontal View).

Figure 3.6: Amorphous GST with BN and W contacts (Vertical View).

26 Figure 3.7: Crystalline GST with BN and W contacts (Horizontal View).

Figure 3.8: Crystalline GST with BN and W contacts (Vertical View).

27 Temperature data for each model is taken and plotted against time, as shown in Figures 3.9 and

3.10. These plots clearly show the heating and quenching process as the voltage is applied and then removed. For the amorphous GST model, a steady-state temperature is reached by 70ns. There is no deﬁnitive temperature to reach for the GST to be considered quenched other than it being close to the initial temperature. By deﬁning the quench temperature as 30°C, the quench time can be approximated as 60ns. This translates to a quenching rate of 2.5°C/ns. As for the the crystalline

GST model, a steady-state temperature is not reached before the voltage is shut off. The quench time can be approximated at 50ns with a quenching rate of 11.5°C/ns.

Figure 3.9: Temperature at Center of Amorphous GST Nanorod vs. Time (Single Rod Model).

28 Figure 3.10: Temperature at Center of Crystalline GST Nanorod vs. Time (Single Rod Model).

These results are compared against those from the array models, which can be found in Ap- pendix E. The side and top views for the array models show similar temperature results to those of the single rod models, while the temperature vs. time graphs show nearly the exact same response.

This conﬁrms that the single rod models with periodic boundary conditions reproduce accurate results as compared an array with many nanorods without dramatically increasing computation time.

A summary of the single rod and array simulation results can be found in Table 3.1.

Table 3.1: Summary of Single Rod and Array Model Results.

Model Input Voltage Max Temperature Quench Time Quench Rate Single Rod, Amorphous 25V 183°C 60ns 2.5°C/ns Array, Amorphous 25V 184°C 60ns 2.5°C/ns Single Rod, Crystalline 3V 608°C 50ns 11.5°C/ns Array,Crystalline 3V 609°C 50ns 11.5°C/ns

29 3.3 Effects of Nanorod Radius and Height

A parametric sweep is conducted for the single rod models to explore the effects of the nanorod radius-height combinations. The values summarized in Table 2.3 are taken and put into COMSOL.

The results for a nanorod radius of 20nm and 50nm are shown in Figures 3.11 and 3.12. For the nanorod radius of 20nm, the height used is 440nm, while for 50nm, the height used is 265nm.

Generally speaking, it is better for devices to be smaller. However, for this device design, the dramatic drop in temperature when the radius is lowered to 20nm and the nanorod height increase to 440nm would prove to be problematic in a practical device and in fabrication. While quenching occurs much faster in a smaller device, in this case, the quenching effects overwhelm the heating from the applied voltage, preventing the device from heating up to the needed temperature for a phase change. A much higher voltage would be needed to trigger a phase change, which would be especially problematic for the amorphous state, where 25V are already being applied.

Figure 3.11: Temperature at Center of Amorphous GST Nanorod vs. Time (Different Radii).

30 Figure 3.12: Temperature at Center of Crystalline GST Nanorod vs. Time (Different Radii).

3.4 Effects of Different Materials

The materials used around the GST have a dramatic effect on the device. As explained in

Chapter II, alternate materials considered in these simulations include Aluminum (Al) to replace W and Silicon Dioxide (SiO2) and Zinc Oxide (ZnO) to replace BN. The results of these simulations are shown in Figure 3.13 for the crystalline GST models. Note that these simulations all have the same input values for dimensions and voltage.

The BN-W and BN-Al models follow nearly the exact same path in the graph, which means that as far as Joule Heating is concerned, there is not much difference between the two materials for electrical contacts. At the same time, the temperature change for ZnO and SiO2 compared to

BN is rather signiﬁcant. The ZnO simulation reaches a maximum temperature of around 800°C,

200°C higher than needed, and takes nearly twice as long to quench (90ns), with a rate of 9.2°C/ns.

31 Figure 3.13: Temperature at Center of Crystalline GST Nanorod vs. Time (Different Materials).

Adjusting the input voltage would make ZnO a possible replacement for BN, despite the sacriﬁce in speed.

On the other hand, for SiO2, a maximum temperature of over 1300°C is reached, and quenching takes longer than 150ns. A quenched temperature of 30°C is not reached during the set time for the simulation; by the time the simulation ﬁnished, the internal temperature of the GST nanorod is still at 200°C. The quenching rate is approximated at 7.9°C/ns. Even with an input voltage adjustment, the speed of the device is signiﬁcantly slowed compared to BN.

3.5 Conclusions

These simulations give great insight into how dimensions, materials, and input values affect the functionality of the device. Comparing the single rod models to the array models show that the single rod models sufﬁciently show the effects of the nanorods on one another without dramatically

32 increasing computation time. For the BN/W models, the quenching time for the crystalline simulations is approximately 11.5°C/ns, which fulﬁlls the goal set in Section 2.6. The temperature goals of 600°for amorphization and 150 to 200°for crystallization are also met, with the internal heating and cooling matching Figure 2.9.

Due to the rapid quenching of BN, there is a limit to how much the radius of the GST nanorod can be decreased; a radius of 50nm and height of 265nm allow the nanorod to both heat to the needed temperatures with a reasonable voltage and quench quickly once the voltage is removed.

Finally, while BN would be the ideal material choice to quench the GST nanorod, ZnO can be considered a possible alternative due to ease of manufacturability and a reasonable quenching rate of 9.2°C/ns. There is no obvious difference between W and Al as far as Joule Heating is concerned for the electrical contacts.

33 CHAPTER IV

EXPERIMENTAL SETUPS

4.1 Optical Setup

The optical switching setup in Figure 4.2 involves the use of lasers to switch the GST between its amorphous and crystalline states, where the phase transition can be determined by examining the change in the refractive index. The setup starts with a continuous-wave (CW) laser with wavelength

1550nm. The beam ﬁrst goes into an 80/20 beamsplitter. Eighty percent of the beam goes into the phase change branch of the setup that actually triggers the phase change, while the remaining twenty percent of the beam goes into the interferometer, which is used to read and visually show the phase change in the GST on an oscilloscope.

The beamsplitter output beam in the phase change branch passes through a polarization controller before coupling into a fiber-coupled Electro-Optic Modulator (EOM). This EOM has two electrical inputs: a DC power supply inputting 6-8V to power the EOM and an arbitrary waveform generator passing a signal through an amplifier (14-20V). The waveform generator creates the optical pulses shown in Figure 4.1. The first pulse is used to switch the GST from crystalline to amorphous, while the second pulse 50µs later switches the GST to crystalline. This waveform generator is not used while the interferometer is being tested.

The output of the EOM passes through a 50/50 beamsplitter. One channel of the beamsplitter sends ﬁfty percent of the optical energy to an optical detector with its electrical output connected to an oscilloscope. This output channel is used to verify that the pulses have the right shape and to ad-

34 Figure 4.1: Input Pulses for Experimentation.

just the polarization using the ﬁrst polarization controller, such that the pulse energy is maximized, rather than the DC signal noise. The other output channel goes into a second polarization controller, which is used later to maximize the beam path output.

The beam then passes through an Erbium-Doped Fiber Ampliﬁer (EDFA), an output coupler, and a linear polarizer that picks out either only vertical or only horizontal polarizations, depending on its orientation. Two mirrors follow to turn the beam on the optical table, introducing some noise into the system. The beam then goes into a free-space EOM. This EOM is set so that when it is on, the polarization of the light is rotated by 90 degrees; when it is off, the light passes through the device unaffected. Next, there is a linear polarizer and then a third mirror, followed by a dichroic mirror. The dichroic mirror reﬂects the 1550nm wavelength beam, while allowing a second laser beam with a wavelength of 405nm to pass through. This second laser is not directly involved in the phase change of the GST. Its beam is only used for the alignment of the invisible 1550nm beam so

35 that the latter can be easily adjusted and positioned as needed. These two laser beams propagate together through two more mirrors before going into the microscope, where the GST sample is placed. A camera and computer are connected to the microscope so that visual changes in the sample can be viewed.

In the microscope, the output beam transmitted through the sample is collimated and passed through two mirrors, followed by an Acousto-Optic Modulator (AOM). This AOM deﬂects the pulses generated earlier in the setup, leaving the CW laser beam unaffected. The beam then goes into a ﬁber coupler followed by a beam combiner, denoted in Figure 4.2 with a plus sign. This beam combiner combines the beam coming from the GST sample with the unaltered twenty percent beam split directly from the 1550nm laser earlier in the setup. The output of the combiner goes into an optical detector with its electrical output connected to an oscilloscope. The phase is recorded before and after the pulse initiating the phase change; the phase difference between the two beams is direct evidence that a phase change has occurred in the GST.

36 Figure 4.2: Tentative Optical Switching Setup.

4.2 Electrical Setup

The electrical switching setup is shown in Figure 4.3. Compared to the optical switching setup described in the previous section, the electrical setup is much simpler. The beam from the 1550nm wavelength laser passes through a 50/50 beamsplitter, each branch of which continues into a polarization controller. One branch goes into an output coupler, which is reﬂected onto the sample.

During this time, an arbitrary waveform generator attached to the sample electrically switches the

37 GST between amorphous and crystalline phases. Since amorphous GST and crystalline GST have different reﬂectance values, the reﬂected beam off the sample experiences a change of phase. This beam passes through an input coupler and is combined with the laser beam from the other branch.

It then goes to an optical detector, and the output is viewed on an oscilloscope.

Figure 4.3: Tentative Electrical Switching Setup.

4.3 Preliminary Experiments

Due to the complexity of the optical and electrical setups, preliminary experiments are conducted using a laser to optically switch the GST between amorphous and crystalline, with the changes read electrically. The basic test cell design used to accomplish this is shown in Figure

4.4. The large squares on either side with leads are Tungsten (W) or Molybdenum (Mo) contacts, used due to availability, and the square in the center is the 10µm by 10µm GST test area. The total width of this test cell is 2mm and is repeated four times with the distance between the contact leads, labeled as d, varied between 2 and 5µm. Varying this distance allows for comparison between the phase change characteristics and how far the current travels through the GST.

38 Figure 4.4: Test Cell (Not Drawn to Scale).

The set of four test cells, shown in Figure 4.5, is repeated several times in an array so that multiple experiments can be conducted on the same GST sample. The d labels below each test cell deﬁne the distance between the contact leads, while the x and y labels above each column mark which test cell set in the array is being viewed. The fabrication process for these samples is outlined in Chapter V. For experimentation, the same optical setup from Figure 4.2 is utilized, minus the interferometer. Instead of the interferometer, electrical readout is done using a two-point probe station that simply sends a current through the sample and measures the resulting resistance.

39 Figure 4.5: Mask Design (Not Drawn to Scale).

40 CHAPTER V

SAMPLE FABRICATION

Preliminary experimental samples are fabricated in the clean room at the University of Dayton using a two-step lithography method explained below. The ﬁrst step is to deposit the metal contacts that are used to electrically determine whether a phase change has occurred in the GST, while the second step is to deposit the GST squares that act as test areas for the phase change. One test sample is made with Molybdenum (Mo) contacts, while the second is made with Tungsten (W). An image of this sample setup can be found in Figures 4.4 and 4.5.

For each deposition done, an extra glass slide, called a companion piece, is included in the chamber. The companion piece is simply used to conﬁrm the thicknesses of the material being deposited (Mo, W, or GST) using a profelometer to perform a step height measurement. Spots on the companion piece are marked off so that after deposition, the material easily be removed, which allows for the step height measurement to be taken.

5.1 Deposition of Metal Contacts

Sample fabrication starts with a Silicon (Si) substrate. First, Plasma-Enhanced Chemical Vapor

Deposition (PECVD) is performed on the substrate to grow a layer of Silicon Dioxide (SiO2), which electrically isolates the substrate from the GST test areas and metal contacts. Next, the substrate is spin coated with Megapost SPR-955 photoresist at 2000 RPM until it is uniform over the whole substrate and prebaked at 100°C for 90 seconds. The side view of the sample thus far is shown in

Figure 5.1. The sample is then loaded into the lithography machine.

41 Figure 5.1: Si Substrate with layer of SiO2 and Photoresist.

The lithography machine used in this process is a SUSS Mask Aligner MA6 that uses a 1000W mercury vapor lamp at a wavelength of 365nm to expose samples using contact masks. After being loaded into the machine, the sample is exposed for 20 seconds with a power of 20mW. At this point, the polarity of the photoresist must be reversed so that the parts not exposed by the mask are removed by the developer, as opposed to the parts that are exposed. This is done through Image Reversal [46].

The sample is placed in a convection oven ﬁlled with ammonia (NH3) for 45 minutes. The NH3 reacts with the photoresist, neutralizing the acid generated during the initial exposure. Afterwards, a

ﬁve-minute ﬂood exposure without the mask effectively reverses the polarity of the photoresist. The developer (MF-319) is applied to the sample for 45 seconds, during which the sections of photoresist not exposed by the mask are removed. The sample thus far is shown in Figure 5.2.

42 Figure 5.2: After Image Reversal and Development, Only Exposed Photoresist Remains.

Next comes the deposition of Mo or W as is shown in Figure 5.3. This is done through sputtering. At ﬁrst, this process proved to be problematic because the lift-off process to remove the photoresist was causing the leads that would connected the GST test area to the electrical contacts to peel off the sample. This is due to the nature of sputtering deposition, which is conformal and therefore also covers the sides of the photoresist. The leads are so thin that they easily peeled off with the photoresist during lift-off. This problem was solved by decreasing the thickness to 50nm.

Mo is deposited at a rate of 0.74 A˚ /s with a power of 100W, and W is deposited at a rate of 0.45 A˚ /s with a power of 75W. Both metal depositions are done starting at a base pressure of 1.4µT that is raised to a working pressure of 4mT using Argon. The sample after lift-off is shown in Figure 5.4.

Figure 5.3: Metal Deposition.

43 Figure 5.4: Lift-off to Remove Photoresist.

5.2 Deposition of GST Test Areas

Starting with the sample as shown in Figure 5.4, another layer of Megapost SPR-955 photoresist is spin coated onto the sample, which is again prebaked at 100°C for 90 seconds before being loaded into the lithography machine. This step is shown in Figure 5.5.

Figure 5.5: Spin Coat Photoresist.

The sample is then exposed. Unlike with the metal contacts, Image Reversal is not needed before the GST deposition. The developer is applied and removes the exposed photoresist, with the result shown in Figure 5.6.

44 Figure 5.6: After Development, Only Unexposed Photoresist Remains.

RF sputtering is used to deposit approximately 100nm of GST onto the sample at a rate of 2.63

A˚ /s with a power of 100W. Argon is used to bring the chamber from the baseline pressure of 1µT to the working pressure of 4mT. The result of this deposition is shown in Figure 5.7. Lift-off is done to remove the photoresist, so that only the GST test areas remain on the sample with the metal contacts. The ﬁnal device can be found in Figure 5.8. A sealing layer of SiO2 covers the sample to prevent material loss during switching.

Figure 5.7: GST Deposition.

45 Figure 5.8: Final Sample.

46 CHAPTER VI

EXPERIMENTAL RESULTS

Preliminary experimental results fall under three categories: the resistivity of GST as measured using a four-point probe, the contact resistance between GST and the electrical contact, and ﬁnally, the resistivity of GST after optical switching has taken place.

6.1 GST Resistivity Measurements

The resistance of GST is measured using a four-point probe station and converted to resistivity as explained in Section 2.5. The samples used are simply GST with a thickness of 405nm deposited on an SiO2/Si substrate. Starting with a measurement of the as-deposited resistance, the samples are then heated on a hot plate up to 340°C, and their resistances are remeasured at interval temperatures.

These resistance measurements are converted to resistivity using Equation 2.6. The ﬁnal results are shown in Figure 6.1.

The resistivity of GST shows a clear decrease as the annealing temperature increases. From around 130 to 150°C, there is a transition period, which corresponds with the transition from amorphous to FCC given in literature [16, 23, 41, 42, 43]. This stays moderately constant for around

30°C, after which it begins to drop again as the GST transitions to the HCP phase. This process is completed around 210°C, after which the resistivity is constant. This is on the lower end of the range given in literature [16, 23, 41, 42, 43]. The highest measured resistivity is 213Ωm at 25°C for the amorphous state, and the lowest measured resistivity is 4.036E-05 Ωm at 300°C for the HCP

47 Figure 6.1: Temperature vs. GST Resistivity.

state, which gives a different of around 7 orders of magnitude. For the FCC state, the measured resistivity is around 4.5E-03 Ωm.

Using Equation 2.10 and the dimensions in Table 2.4, the resistivity can be converted to sheet resistance, the results of which are shown in Figure 6.2. The sheet resistance for the amorphous state is calculated as approximately 7.19GΩ, while for the FCC state, it is approximately 129.9kΩ. This large difference between the two GST phases could prove to be problematic later in the development of the device.

48 Figure 6.2: Temperature vs. GST Resistance.

6.2 Contact Resistance Measurements

The samples used to measure the contact resistances between GST and metal contacts are fabricated using a similar process described in Chapter V. Figure 6.3 shows the scanning electron microscore (SEM) image of this sample, where the darker squares are the metal contacts. The dis- tances between these contacts are varied from 10µm to 60µm. Both Tungsten (W) and Molybdenum

(Mo) are measured as potential electrical contacts for the ﬁnal device.

Figure 6.3: SEM Image of Contact Resistance Sample.

49 Figures 6.4 and 6.5 show the contact resistance between the metal contacts and GST as a function of the distance between the contacts. The equations for the line of fit can be found in the lower righthand corners, where the distance between contacts d is in µm and the contact resistance R is in MΩ for the amorphous phase and Ω for the crystalline phase. As explained in Chapter II, the value of the contact resistance for each contact is half of the y-intercept from the line of fit. They are summarized in Table 6.1. Each graph shows a general increase of the resistance as the distance increases. For the amorphous GST samples, the resistances match the line of fit better than the crystalline GST samples do. This could be due to incomplete crystallization or a mix of FCC and

HCP crystalline being present in the sample.

Figure 6.4: Distance between Contacts vs. Contact Resistance (Amorphous GST).

50 Figure 6.5: Distance between Contacts vs. Contact Resistance (Crystalline GST).

Table 6.1: Calculated Contact Resistances.

GST phase W value Mo value Amorphous GST 4.38MΩ 3.23MΩ Crystalline GST 64.0Ω 89.1Ω

To understand the effect of the contact resistance, the sheet resistance must also be calculated, which is done using Equation 2.9. Note that the contact width W is equal to 80µm. The results are shown in Figures 6.6 and 6.7. The calculated sheet resistance values decrease as the distance between the contacts increases for the amorphous phase and is generally inconsistent for the crystalline phase. The difference between the contact resistance and sheet resistance is not signiﬁcant enough for the contact resistance to be ignored completely. For example, at a distance of 60µm, the contact resistance between the Mo and crystalline GST is over 10 percent that of the sheet re-

51 sistance. This suggests that the contact resistance at the nanoscale is a major source of resistance within the device.

Figure 6.6: Distance between Contacts vs. Sheet Resistance (Amorphous GST).

52 Figure 6.7: Distance between Contacts vs. Sheet Resistance (Crystalline GST).

6.3 Optical Switching Experimentation

Preliminary samples and experiments are described in Chapters IV and V and are meant to show switching of the GST phase using a laser. However, due to downed equipment in the clean room, the samples could not be fabricated at this time. As a result, experiments could not be conducted.

They have been left for a future project to explore.

53 CHAPTER VII

CONCLUSIONS AND FUTURE WORK

7.1 Conclusions

The simulations for the amorphous-to-crystalline phase transition give a reasonable 25V input voltage in order to achieve an internal temperature of 180°C with a quenching time of 60ns. For the crystalline-to-amorphous transition, the input voltage needed is 3V, which gives an internal temperature of 600°C and a quenching time of 50ns. These results suggest that an electrically- induced phase change can be achieved with W contacts and BN surrounding the GST nanorod on a

Si substrate.

The parametric sweep of the nanorod radius and height suggest that the smaller the nanorod radius is, the quicker the quenching is, which means a higher voltage is needed to reach the internal temperature required for a phase change. For this reason, 50nm is selected as the target radius for the GST nanorod, balancing between the required voltage and the desire to maximize the speed of the GST phase transition.

BN is considered the ideal material with which to surround the GST nanorod, though the simulations show that ZnO is a reasonable replacement, should fabrication fail with BN. Replacing BN with SiO2 is another option, though it would result in a signiﬁcant drop in the quenching rate, from

11.5°C/ns to 7.9°C/ns. As far as the temperature and voltage goals are concerned, the material for the electrical contacts does not make a major impact; the simulations for both Al and W contacts followed nearly the exact same heating and quenching path.

54 The GST resistivity results approximately line up with literature with respect to the temperatures at which phase transitions occur. The resistivity values exhibit several orders of magnitude difference between the amorphous and crystalline phases, which measured 213Ωm for amorphous GST,

4.5E-03 Ωm for FCC crystalline GST, and 4.036E-05 Ωm HCP crystalline GST. However, these values are higher than what is found in literature [26]. This could be due to the difference in deposition methods and environmental conditions. These resistivities are converted to sheet resistance, giving 7.19GΩ for the amorphous state and 129.9kΩ for the FCC crystalline state.

The contact resistance measurements show surprisingly large values for both W and Mo contacts, proving that at the nanoscale, contact resistance contributes a major portion of the device’s total resistance, especially compared to the sheet resistance. As electrical contacts, W and Mo are equally problematic due to their high contact resistance. The contact resistance must be reduced for the ﬁnal device to function with a reasonable voltage.

The preliminary samples described in Chapter IV could not be fabricated due to downed equipment in the clean room. As a result, preliminary optical switching experiments, as described in

Chapter V, could not be conducted at this time.

7.2 Future Work

There are many aspects of the project that still need to be explored. For the device simulations, the models can be made more accurate by adding electrical and thermal interface resistances [26].

This could have a major impact on the target input voltages for electrical switching of GST. Con- vection has been accounted for to a degree within the current models, but it may be worth exploring further how much convection affects the device and whether it can be used to assist with quenching. There is also the concept of threshold voltage, which could mean that the required voltages

55 for switching GST are much less than those found through simulations [2, 6, 7]. It may be worth exploring different substrates and electrical contacts for the device and seeing how it would change the device functionality.

Fabricating the ﬁnal device has several obstacles that need to be overcome as well. The method of growing GST nanorods needs to be perfected, as well as how the Boron Nitride (BN) will be deposited. BN is a very hard material and therefore can cause some difﬁculties with deposition.

It has the tendency to crack and peel off the substrate, which is likely due to internal stress and reactions with water [31]. Combining this with GST’s amorphous phase having a greater volume than its crystalline phase, internal stresses and pressure could cause a major issue with the cyclability of the device [2].

Another issue to keep in mind is the possibilty of data loss. The distance between the nanorods needs to be carefully chosen, as having nanorods too close together can cause a nearby amorphous

GST nanorod to unintentionally crystallize when another is being programmed. This assisted by a low crystallization temperature; in scaled-down devices, the crystallization temperature is supposed to be higher as well, which will help prevent data loss [4, 47].

Once a binary device has been achieved, there is also the possibility of making the device analog.

This would be dependent on how much of the GST volume is in the amorphous or crystalline phase.

Difﬁculties will arise with how to measure the amount of amorphrous or crystalline is present.

Exploration of this concept has been left to future projects.

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61 APPENDIX A

Matlab Code For Nanorod Height Calculations

1 %Andrea Aboujaoude 2 %4 / 2 / 2 0 1 8 3 c l e a r a l l ; c l o s e a l l ; c l c ;

6 %C o n s t a n t s : 7 r GST=10e −9:5e −9:50e −9; %r a d i u s of nanorods (m) . 8 d GST=2*r GST ; %d i a m e t e r of nanorods (m) . 9 w=110e −9; l =w; %width and l e n g t h of BN bl o ck (m) . 10 lambda = 1 . 5 5 0 ; %wavelength (um) . 11 p h a s e d i f f = p i ; %phase d i f f e r e n c e of p i ( with ARC) . 12 f = p i *r GST . ˆ 2 . / w ./ l ; %f r a c t i o n of volume . 13

15 %Import n and k v a l u e s from e x c e l f i l e s : 16 BNfilename= ’BN d a t a from handbook of o p t i c a l c o n s t a n t s of s o l i d s volume 3 ’ ; 17 GSTfilename= ’GST n and k v a l u e s ’ ; 18 BN= x l s r e a d ( BNfilename ); GST= x l s r e a d ( GSTfilename );

21 %S e p a r a t e t h e wavelength (um) , n , and k v e c t o r s : − 22 lambda BN=BN( : , 1 ) ; lambda GST=GST ( : , 1 ) *10ˆ( 3) ; 23 n BN=BN( : , 2 ) ; k BN=BN( : , 3 ) ; 24 n GST100=GST ( : , 3) ; k GST100=−GST ( : , 4) ; 25 n GST200=GST ( : , 4 8 ) ; k GST200=−GST ( : , 4 9 ) ; 26 n GST300=GST ( : , 5 8 ) ; k GST300=−GST ( : , 5 9 ) ; 27 n GST AD=GST ( : , 6 3 ) ; k GST AD=−GST ( : , 6 4 ) ;

30 %P l o t n and k vs . wavelength . 31 f i g u r e ; p l o t ( lambda BN , n BN ); t i t l e ( ’ n B N vs . \ lambda B N ’ ); 32 x l a b e l ( ’ \ lambda B N (\mum) ’ ); y l a b e l ( ’ n B N ’ );

34 f i g u r e ; p l o t ( lambda BN , k BN ); t i t l e ( ’ k B N vs . \ lambda B N ’ ); 35 x l a b e l ( ’ \ lambda B N (\mum) ’ ); y l a b e l ( ’ k B N ’ );

37 f i g u r e ; p l o t ( lambda GST , n GST AD , lambda GST , n GST100 , lambda GST ,...

62 38 n GST200 , lambda GST , n GST300 ); t i t l e ( ’ n G S T vs . \ lambda G S T ’ ); 39 l e g e n d ( ’GST ( as d e p o s i t e d ) ’ , ’GST a t 100C ’ , ’GST a t 200C ’ ,... 40 ’GST a t 300C ’ , ’ L o c a t i o n ’ , ’ e a s t ’ ); 41 x l a b e l ( ’ \ lambda G S T (nm) ’ ); y l a b e l ( ’ n G S T ’ ); a x i s ( [ 1 . 2 2 . 6 3 . 8 6 . 5 ] ) ;

43 f i g u r e ; p l o t ( lambda GST , k GST AD , lambda GST , k GST100 , lambda GST ,... 44 k GST200 , lambda GST , k GST300 ); t i t l e ( ’ k G S T vs . \ lambda G S T ’ ); 45 l e g e n d ( ’GST ( as d e p o s i t e d ) ’ , ’GST a t 100C ’ , ’GST a t 200C ’ ,... 46 ’GST a t 300C ’ , ’ L o c a t i o n ’ , ’ s o u t h e a s t ’ ); 47 x l a b e l ( ’ \ lambda G S T (nm) ’ ); y l a b e l ( ’ k G S T ’ );

50 %Interpolate t o g e t n and k v a l u e s a t gi v en wavelength . 51 n BNc= i n t e r p 1 ( lambda BN , n BN , lambda ); 52 n GST ADc= i n t e r p 1 ( lambda GST , n GST AD , lambda ); 53 n GST100c= i n t e r p 1 ( lambda GST , n GST100 , lambda ); 54 n GST200c= i n t e r p 1 ( lambda GST , n GST200 , lambda ); 55 n GST300c= i n t e r p 1 ( lambda GST , n GST300 , lambda );

57 k BNc= i n t e r p 1 ( lambda BN , k BN , lambda ); 58 k GST ADc= i n t e r p 1 ( lambda GST , k GST AD , lambda ); 59 k GST100c= i n t e r p 1 ( lambda GST , k GST100 , lambda ); 60 k GST200c= i n t e r p 1 ( lambda GST , k GST200 , lambda ); 61 k GST300c= i n t e r p 1 ( lambda GST , k GST300 , lambda );

64 %E p s i l o n calculations from n and k f o r t h e h o s t m a t e r i a l (BN) and t h e 65 %i n c l u s i o n m a t e r i a l (GST a t 100C , 200C , and 300C) : 66 epsilon BN =( n BNc+1 i *k BNc ) . ˆ 2 ; 67 epsilon GST AD =( n GST ADc+1 i *k GST ADc ) . ˆ 2 ; 68 epsilon GST100 =( n GST100c+1 i *k GST100c ) . ˆ 2 ; 69 epsilon GST200 =( n GST200c+1 i *k GST200c ) . ˆ 2 ; 70 epsilon GST300 =( n GST300c+1 i *k GST300c ) . ˆ 2 ; 71

73 %C a l c u l a t e e f f e c t i v e e p s i l o n as a f u n c t i o n of t h e nanorod r a d i u s : − 74 epsilon AD = epsilon BN . * ( 1 + 2 * f . * ( epsilon GST AD epsilon BN )./... − − 75 ( epsilon GST AD+ epsilon BN f . * ( epsilon GST AD epsilon BN ))); − 76 e p s i l o n 1 0 0 = epsilon BN . * ( 1 + 2 * f . * ( epsilon GST100 epsilon BN )./... − − 77 ( epsilon GST100 + epsilon BN f . * ( epsilon GST100 epsilon BN ))); − 78 e p s i l o n 2 0 0 = epsilon BN . * ( 1 + 2 * f . * ( epsilon GST200 epsilon BN )./... − − 79 ( epsilon GST200 + epsilon BN f . * ( epsilon GST200 epsilon BN )));

63 − 80 e p s i l o n 3 0 0 = epsilon BN . * ( 1 + 2 * f . * ( epsilon GST300 epsilon BN )./... − − 81 ( epsilon GST300 + epsilon BN f . * ( epsilon GST300 epsilon BN ))); 82

84 %C a l c u l a t e t h e e f f e c t i v e n u s i n g t h e r e a l p a r t of t h e s q r t of t h e e p s i l o n s : 85 neff AD= r e a l ( s q r t ( epsilon AD )); 86 n e f f 1 0 0 = r e a l ( s q r t ( e p s i l o n 1 0 0 )); 87 n e f f 2 0 0 = r e a l ( s q r t ( e p s i l o n 2 0 0 )); 88 n e f f 3 0 0 = r e a l ( s q r t ( e p s i l o n 3 0 0 ));

91 %P l o t e f f e c t i v e n vs . nanorod r a d i u s : 92 f i g u r e ; p l o t ( r GST . * 1 0 ˆ 9 , neff AD , r GST . * 1 0 ˆ 9 , n e f f 1 0 0 , r GST . * 1 0 ˆ 9 , . . . 93 n e f f 2 0 0 , r GST . * 1 0 ˆ 9 , n e f f 3 0 0 ); 94 t i t l e ( ’ n e f f , G S T vs . \ lambda G S T ’ ); 95 l e g e n d ( ’GST ( as d e p o s i t e d ) ’ , ’GST a t 100C ’ , ’GST a t 200C ’ ,... 96 ’GST a t 300C ’ , ’ L o c a t i o n ’ , ’ n o r t h w e s t ’ ); 97 x l a b e l ( ’ r G S T (nm) ’ ); y l a b e l ( ’ n e f f , G S T ’ );

100 %C a l c u l a t e h e i g h t (um) a c c o r d i n g t o e f f e c t i v e n and phase d i f f e r e n c e : 101 h AD= p h a s e d i f f * lambda / 2 / p i ./ neff AD ; 102 h 100= p h a s e d i f f * lambda / 2 / p i ./ n e f f 1 0 0 ; 103 h 200= p h a s e d i f f * lambda / 2 / p i ./ n e f f 2 0 0 ; 104 h 300= p h a s e d i f f * lambda / 2 / p i ./ n e f f 3 0 0 ; 105 h =[h AD ; h 100 ; h 200 ; h 300 ]; avg h =mean ( h );

64 APPENDIX B

Matlab Code For Impedance Matching Calculations

1 %Andrea Aboujaoude 2 %5 / 3 1 / 2 0 1 8 3 c l e a r a l l ; c l o s e a l l ; c l c ;

5 6 n =10*10; %number of nanorods . 7

8 %GST Data : 9 r GST=50e −9; %r a d i u s of nanorod (m) . 10 t GST =265e −9; %t h i c k n e s s of GST s t r i p s (m) . 11 A GST= p i *r GST ˆ 2 ; %a r e a of GST p e r u n i t bl o ck (mˆ 2 ) . 12

13 sigma amor =3; %conductivity of GST i n amorphous s t a t e ( S /m) . 14 s i g m a c r y s =2770; %conductivity of GST i n crystalline s t a t e ( S /m) . 15 rho amor =1/ sigma amor ; %resistivity of GST i n amorphous s t a t e ( ohm m) . 16 r h o c r y s =1/ s i g m a c r y s ; %resistivity of GST i n crystalline s t a t e ( ohm m) .

17 18 R GST amor=t GST / A GST* rho amor ; %r e s i s t a n c e of amorphous GST ( ohms ) . 19 R GST crys=t GST / A GST* r h o c r y s ; %r e s i s t a n c e of crystalline GST ( ohms ) .

22 %BN Data : 23 l BN =110e −9; %l e n g t h of BN l a y e r (m) . 24 w BN=l BN ; %width of BN l a y e r p e r u n i t bl oc k (m) . 25 t BN=t GST ; %t h i c k n e s s of BN l a y e r (m) . − − 26 A BN=l BN*w BN A GST ; %c r o s s s e c t i o n a l a r e a of BN p e r u n i t bl o ck (mˆ 2 ) . 27 rho BN=2 e12 ; %resistivity of BN a t 23C ( ohm m) .

28 29 R BN=t BN / A BN*rho BN ; %r e s i s t a n c e of BN ( ohms ) . 30

65 32 %W Data : 33 l W=l BN ; %l e n g t h of W c o n t a c t s (m) . 34 w W=l W ; %width of W c o n t a c t p e r GST s t r i p (m) . 35 t W=50e −9; %t h i c k n e s s of W c o n t a c t s (m) . − 36 A W=l W*w W; %c r o s s s e c t i o n a l a r e a of W c o n t a c t p e r u n i t bl o ck (mˆ 2 ) . 37 rho W =5.39 e −8; %resistivity of W a t 25C ( ohm m) .

38 39 R W=t W /A W*rho W ; %r e s i s t a n c e of W ( ohms ) . 40

42 %Si Data : 43 l S i =l BN ; %l e n g t h of Si s u b s t r a t e (m) . 44 w Si=w W; %width of Si s u b s t r a t e p e r GST s t r i p (m) . 45 t S i =1e −6; %t h i c k n e s s of Si wafer (m) . 46 A Si= l S i * w Si ; %a r e a of Si p e r u n i t bl o ck (mˆ 2 ) . 47 r h o S i = 0 . 0 0 0 1 ; %resistivity of Si ( ohm m) .

48 49 R Si= t S i / A Si * r h o S i ; %r e s i s t a n c e of Si ( ohms ) . 50

52 %Unit Resistivity ( ohms ) : 53 R a m o r u n i t =R W+ ( 1 / R BN+1/ R GST amor ) ˆ( −1)+R Si ; 54 R c r y s u n i t =R W+ ( 1 / R BN+1/ R GST crys ) ˆ( −1)+R Si ;

56 %T o t a l Resistivity ( ohms ) : 57 R a m o r t o t a l = R a m o r u n i t / n 58 R c r y s t o t a l = R c r y s u n i t / n

66 APPENDIX C

Select Model Dimensions

Table C.1: COMSOL Input Values for Single Rod and Array Model Simulations.

Variable Name Expression Value Description rGST 50nm 5e-8 m Radius of GST nanorod dGST 2*rGST 1e-7 m Diameter of GST nanorod hbase 1µm 1e-6 m Height of Silicon hGST 265nm 2.65e-7 m Height of GST nanorod htop 50nm 5e-8 m Height of Tungsten htotal hbase+hGST +htop 1.301e-6 m Total Height 2 2 hair 5 W/m /K 5 W/m /K Heat Transfer Coefﬁcient of Air Tinitial 20°C 293.15K Initial Temperature Tsurr 20°C 293.15K Temperature of Surroundings Tplate 25°C 298.15K Temperature of Hot Plate w 110nm 1.1e-7 m Width of Block l w 1.1e-7 m Length of Block

67 APPENDIX D

Select Material Properties

Table D.1: Select Amorphous GST Material Data.

Property Value ρ 5995 kg/m3 [48] ϵr 16.0 [25] c 218 J/kg/K [48] k 0.17 W/m/K [26] σ 3 S/m [26]

Table D.2: Select Crystalline GST Material Data.

Property Value ρ 5995 kg/m3 [48] ϵr 33.3 [25] c 218 J/kg/K [48] k 0.5 W/m/K [26] σ 2770 S/m [26]

68 Table D.3: Select Si Material Data.

Property Value ρ 2329.0 kg/m3 at T=25.0°C 2326.9 kg/m3 at T=127°C 2319.2 kg/m3 at T=427°C 2313.6 kg/m3 at T=627°C 2307.7 kg/m3 at T=827°C 2301.6 kg/m3 at T=1027°C [49] ϵr 12.1 [50] c 713 J/kg/K at T=27°C 785 J/kg/K at T=127°C 832 J/kg/K at T=227°C 849 J/kg/K at T=327°C 866 J/kg/K at T=427°C 883 J/kg/K at T=527°C 899 J/kg/K at T=627°C 916 J/kg/K at T=727°C 933 J/kg/K at T=827°C 950 J/kg/K at T=927°C 967 J/kg/K at T=1027°C 983 J/kg/K at T=1127°C 1000 J/kg/K at T=1227°C [49] k 124 W/m/K at T=20°C 105 W/m/K at T=100°C 79.5 W/m/K at T=200°C 52.3 W/m/K at T=400°C 37.7 W/m/K at T=600°C [49] ρelec 0.0001 Ω m [49]

Table D.4: Select BN Material Data.

Property Value ρ 2180 kg/m3 [50] ϵr 7.1 [50] c 793 J/kg/K [50] k 36.2 W/m/K at T=774°C 22.7 W/m/K at T=1202°C 21.9 W/m/K at T=1655°C 18.5 W/m/K at T=1838°C [50] ρelec 2e12 Ω m at T=23.0°C 3e10 Ω m at T=150°C [51]

69 Table D.5: Select W Material Data.

Property Value ρ 19300 kg/m3 [50] ϵr 1 c 132 J/kg/K [50] k 174 W/m/K [50] ρelec 4.82e-8 Ω m at T=0°C 5.28e-8 Ω m at T=20°C 5.39e-8 Ω m at T=25°C 5.44e-8 Ω m at T=27°C 7.83e-8 Ω m at T=127°C 10.3e-8 Ω m at T=227°C 13.0e-8 Ω m at T=327°C 15.7e-8 Ω m at T=427°C 18.6e-8 Ω m at T=527°C 21.5e-8 Ω m at T=627°C [50]

Table D.6: Select Al Material Data.

Property Value ρ 2700 kg/m3 [50] ϵr 1 c 897 J/kg/K [50] k 237 W/m/K [50] ρelec 2.417e-8 Ω m at T=0°C 2.650e-8 Ω m at T=20°C 2.709e-8 Ω m at T=25°C 2.733e-8 Ω m at T=27°C 3.87e-8 Ω m at T=127°C 4.99e-8 Ω m at T=227°C 6.13e-8 Ω m at T=327°C 7.35e-8 Ω m at T=427°C 8.70e-8 Ω m at T=527°C 10.18e-8 Ω m at T=627°C [50]

70 Table D.7: Select SiO2 Material Data.

Property Value ρ 2330 kg/m3 [50] ϵr 4.2 [52] c 1000 J/kg/K [53] k 1.2 W/m/K at T=-79°C 1.4 W/m/K at T=0°C 1.6 W/m/K at T=100°C 1.8 W/m/K at T=400°C [50] ρelec 1e15 Ω m [53]

Table D.8: Select ZnO Material Data.

Property Value ρ 5675 kg/m3 [50] ϵr 8.15 [50] c 494 J/kg/K [50] k 23.4 W/m/K at T=27°C 17 W/m/K at T=200°C 5.3 W/m/K at T=800°C [50] ρelec 0.003 Ω m [54]

71 APPENDIX E

Array Model Results

Figure E.1: Amorphous GST with BN and W contacts for Array Model (Horizontal View).

72 Figure E.2: Amorphous GST with BN and W contacts for Array Model (Vertical View).

Figure E.3: Crystalline GST with BN and W contacts for Array Model (Horizontal View).

73 Figure E.4: Crystalline GST with BN and W contacts for Array Model (Vertical View).

Figure E.5: Temperature at Center of Amorphous GST Nanorod vs. Time (Array Model).

74 Figure E.6: Temperature at Center of Crystalline GST Nanorod vs. Time (Array Model).