Probing heat transport in nanowires using a focused electron beam heating technique

PROBING HEAT TRANSPORT IN NANOWIRES USING A FOCUSED ELECTRON BEAM HEATING TECHNIQUE LIU DAN (B. Eng. (Hons.), National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NUS GRADUATE SCHOOL FOR INTEGRATIVE SCIENCES AND ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. __________________________________ LIU DAN ACKNOWLEDGEMENTS I would like to express my greatest gratitude to my supervisor Assoc. Prof. John T. L. Thong, who is a gentleman and a tremendous supervisor. His broad knowledge scope, quick mind and clear thought inspired me; his patient downto-detail guidance and continuous encouragement drove me. Without his supervision and constant help this dissertation would not have been possible. I would also like to thank my co-supervisor Prof. Li Baowen. I was attracted to this research group by his words during one group meeting “What is a Ph.D.? A Ph.D. is not about how many papers you publish, but it is about understanding what you so well that nobody else in the world can understand it better than you, and in order to tell others about your understanding, you write some papers. Papers are natural outcomes but not the aim of a Ph.D.” This became the guiding principle in carrying out my research. I thank the remaining members of my thesis advisory committee, Prof. Adekunle Adeyeye and Dr. Koh Yee Kan for their kind advice and help. I would also like to thank the CICFAR lab officers, Mrs. Ho Chiow Mooi, Mr. Koo Chee Keong and Ms. Linn Linn. Your regulations and fast response accelerated my research progress. I specially thank Dr. Xie Rongguo, who conceptualized the electron beam heating technique and worked on its early development. I learned a lot from him, not only about how to use the equipment but more importantly, about the attitude in doing experiments: being both bold and cautious, which I will always bear in mind. Much appreciation goes to my past and present colleagues, Dr. Chen Jie, for the MD simulation and comments in Chapter 4; Dr. Yang Nuo, Dr. Zhu Liyan, for the numerical calculations in Chapter and Chapter 6; Dr. Yang Yue, for the advice in the simulation work in Chapter 3. Dr. Wang Rui, who advised me to work 16 hours per day; Dr. Liu Sha and Dr. Xu Xiangfan, for those long discussions until midnight; Dr. Wang Ziqian, Dr. Pi Can, Dr. Wong Chee Leong, Dr. Ren Yi, Dr. Wang jiayi, Dr. Huang Jinquan, for those days we had lunch together; Dr. Ren jie, Dr.Zhang Lifa, Dr. Zhu Liyan, for fruitful discussions; Dr. Hao Yufeng, Dr. Feng Ling, Dr. Zhu Guimei, Dr. Bui Cong Tinh, Dr. Li Yida, Zhao Xiangming, Meng Lei, Yang Lina, Bai Xue, Yu Ya, Zhao Yunshan, and Liu Yi. I love all of you. Last but not least, I am very grateful to my beloved parents. Their constant support and unconditional love make my life meaningful. i Table of contents Acknowledgements i Table of contents ii Summary v List of Figures vii List of Symbols xvi List of Abbreviations Chapter xviii Introduction 1.1. Motivation and objectives .1 1.2. Organization of thesis .5 Chapter Literature review 2.1. Background .8 2.1.1. Harmonic approximation, normal modes and phonon 2.1.2. Transport of phonons 10 2.1.3. Molecular dynamics (MD) simulations 14 2.1.4. Effect of nanowire diameter 15 2.1.5. Effect of rough surface 18 2.1.6. Binary and alloyed nanowire 23 2.1.7. Phonon confinement effect .26 2.1.8. Epitaxial interfaces embedded in the nanowires .28 2.2. Measurement techniques of thermal transport in nanowires 29 2.2.1. 3ω method for nanowires 30 2.2.2. Scanning thermal microscopy (SThM) .33 2.2.3. Raman thermography 36 2.2.4. Thermal bridge method .37 ii 2.3. Summary .42 Chapter Electron beam heating technique 44 3.1. Working principle .44 3.2. Electron beam - sample interaction .47 3.2.1. Energy absorption from the incident electrons .48 3.2.2. Energy relaxation from excited hot electrons to phonons 54 3.3. Experimental set-up 62 3.3.1. Improving measurement sensitivity 64 3.3.2. Other technical considerations 68 3.4. Summary .72 Chapter Thermal conductivity of helium ion damaged Si nanowires 74 4.1. Sample preparation .74 4.1.1. Fixing Si nanowire on the suspended METS device 74 4.1.2. Irradiating Si nanowire using helium ions 76 4.2. Lattice disorder created by helium ions 77 4.3. Experimental results and discussions 83 4.3.1. Calculating Ri(x) .83 4.3.2. Crystalline to amorphous transition 86 4.3.3. Phonon scattering by point defects and NEMD simulation 88 4.3.4. Effect of annealing on point defects .93 4.4. Summary .96 Chapter Spatially resolved thermal conductivity of Si1xGex/NiSi1-xGex bamboo-structured nanowires 98 5.1. Sample fabrication 99 5.2. Results and discussion 102 5.3. Summary .105 Chapter Interfacial thermal resistance (ITR) of Si/NixSiy bamboo-structured nanowires 106 6.1. Sample fabrication 107 6.1.1. Formation of NixSiy/Si interface .108 iii 6.1.2. Formation of NiSi2 fillet with two Si/NiSi2 interfaces 110 6.2. Results and discussion 114 6.2.1. ITR across Si/NixSiy interface .114 6.2.2. ITR across a NiSi2 fillet with two Si/NixSiy interfaces .118 6.2.2.1. ITR across a single Si/NiSi2 interface and the spatial resolution .118 6.2.2.2. ITR across NiSi2 fillets with different thickness and diameter .125 6.2.3. ITR across a Si fillet .128 6.3. Summary .133 Chapter Conclusion and Future Works 135 7.1. Conclusion 135 7.2. Exploring new material systems .138 7.2.1. Spatially resolved thermal conductivity of rough/porous Si nanowires .138 7.2.2. Nanophononic Si nanowire: reducing thermal conductivity by local resonance .141 7.2.3. Effect of strain on the thermal conductivity of Si nanowires .142 7.3. Further development of the technique 143 7.3.1. Instrumentation improvement .143 7.3.2. Spatially-resolved measurement of thermal rectification effect .144 7.3.3. Measurement of non-diffusive thermal transport .146 Appendices 150 Appendix I. Setup of Casino simulation regarding the electron beam scattering energy .150 List of Publications 153 List of References 154 iv SUMMARY The understanding of nanoscale thermal transport plays an important role in the thermal management of modern micro/nano-sized devices and in the development of thermoelectric materials. Numerous experimental and theoretical works have emerged during the past 1-2 decades, deepening the understanding of how heat flows in nanostructures. However the tools available to the experimentalist to probe thermal transport at the nanoscale are still quite limited. In this thesis, a new thermal measurement technique that is capable of profiling nanowire thermal resistance with a spatial resolution of nanometers was developed. The technique uses a focused electron beam as a localized heat source to establish a temperature gradient along the nanowire. The heat fluxes from the two ends of the nanowire are measured using platinum resistance thermometers on two suspended thermally-isolated islands from which the local thermal conductivity can be derived. Three material systems were studied using the electron beam heating technique. Firstly, an individual Si nanowire was irradiated by high energy helium ions with position-dependent dose, and the effect of lattice disorder created by helium ion irradiation on the thermal conductivity of the Si nanowire was studied. From the spatially-resolved thermal conductivity along a single Si nanowire, we observed a clear transition from crystalline Si to amorphous phase above a critical dose. Moreover, within the dose regime in v which only point defects are created, we observed that the Si nanowire thermal conductivity decreases almost exponentially as the dose increases, and only 4% point defects could reduce the thermal conductivity by ~70%, indicating a strong phonon scattering effect by point defects. Finally, the annealing effect on the recovery of thermal conductivity of the damaged portion is reported. The second material system is a Si1-xGex/NiSi1-xGex bamboo-structured nanowire, on which we measured the thermal conductivities of both Si1-xGex and NiSi1-xGex portions, the latter being much larger than the former. The third material system is a Si/NixSiy bamboo-structured nanowire. The thermal conductivities of both Si and NixSiy are measured. Moreover, one Si/NixSiy bamboo-structured nanowire contains several interfaces, and the interfacial thermal resistance (ITR) of each interface could be probed. The influence of NixSiy phase, the nanowire diameter, the distance between two interfaces and the material embedded between two adjacent interfaces on the ITR was studied. From the measurement in the vicinity of the nearly-abrupt interface between the Si and NiSi2 phases, we inferred the spatial resolution to be better than 20 nm. The electron beam heating technique developed provides powerful means to elucidate the underlying physics of thermal transport in nanostructures, which will in turn improve the thermal models adopted in the design of nano-devices, and inform the fabrication of nanostructured thermoelectric materials with enhanced performance. vi List of Figures Figure 2.1 Study notes on the concept of phonons, the theories of phonon transport, and the influence of nanostructures. The figure in the top right quadrant illustrates the phonon dispersion in linear diatomic chain. . 14 Figure 2.2 (a) Measured thermal conductivity of different diameter Si nanowires27 using Thermal Bridge method. The number beside each curve denotes the corresponding wire diameter. (b) Thermal conductivities vs temperature calculated using the complete dispersions transmission function26, for Fl = 1.05 × 37nm (solid), 1.3 × 56nm (dotted) and 1.15 × 115nm (dashed). Dots: experimental results27. Inset: thermal conductivity of bulk Si. 17 Figure 2.3 Schematic illustration of phonon scattering processes in nanowires29. . 19 Figure 2.4 (a) Thermal conductivity accumulation as a function of wavelength at 300 and 1000 K36. Roughly 80% of contribution to thermal conductivity at room temperature comes from phonons with wavelengths between and 100 nm. (b) Roughness power spectrum at the selected length scales (1−100 nm). While the actual power spectrum is shown in blue, the Lorentzian fit used to extract σ and L is shown in red to be a poor fit at the relevant length scales. The power law fit shown in black captures the roughness better. . 22 Figure 2.5 Quantifying surface roughness effects on phonon transport in silicon nanowires35. (a) Thermal conductivity as a function of roughness factor αp. As αp increases, the wires are rougher, with wavelengths in the 1−100 nm range and the thermal conductivity drops significantly. (b) Colored TEM image of the nanowire profiles representing points in (a). . 23 Figure 2.6 Theoretical predictions of thermal conductivity of Si1-xGex nanowires43 (a) Thermal conductivity vs diameter, (b) Thermal conductivity vs Ge concentration. . 26 Figure 2.7 (a) Illustration of the rod- or filament-like specimen connecting by four-probe configuration73. Sapphire substrate with high thermal conductivity is used as an effective heat sink. (b) Block diagram of the measurement73 . 31 vii Figure 2.8 Schematic diagram of a cantilever probe used for scanning thermal microscopy. The heat transfer mechanisms between the tip, the cantilever and the sample are also indicated. Ta, Tt , and Ts are the temperatures of the ambient, the tip, and the sample, respectively. Rc and Rts are the thermal resistances of the cantilever and the tip-sample junction, respectively81 . 34 Figure 2.9 (a) Image of the probe Pd/SiO2 probe used in 3ω-SThM measurement83-85. (b) Bi2Te3 nanowires (~40 µm long, ~200 nm diameter) are embedded in anodic alumina oxide (AAO) filters. The probe is put on top of the nanowires. By passing electrical current with frequency ω through the probe, a temperature fluctuation with 2ω frequency is triggered, inducing a voltage fluctuation with frequency of 3ω. The tip is connected with an individual nanowire due to its small contact area85. (c) Equivalent thermal schema of the thermal flux passing from the tip to a NW. RC: the tip-to-sample contact thermal resistance; RTip-NW: the constriction resistance of the heat flux between the tip and the nanowire; RNW: the sample intrinsic thermal resistance; RNW-Sub: the constriction resistance of the heat flux between the nanowire and the substrate on which the nanowire is deposited85 . 35 Figure 2.10 Raman measurement of single-walled carbon nanotubes91 (a) SEM image of carbon nanotubes suspended over a 4.7 µm trench. The white circles illustrate the size and location of the laser spot. (b) G band Raman frequency measured along the length of the nanotube in (a) at different laser powers. (c) Laser heating profile of the suspended nanotube shown in (a). Error bars reflect the uncertainties in the G. . 37 Figure 2.11 (a)-(e) Fabrication process of the microfabricated device. (f), (g) Schematic diagram and thermal resistance circuit of the experimental set-up7. 38 Figure 3.1 Working principle for electron beam heating technique. (a) Schematic of the micro-electro-thermal system device, showing the left and right platinum resistance sensor islands. A focused electron beam (purple cone) is used as a heat source. (b) Equivalent thermal resistance circuit, showing Ri, the cumulative thermal resistance from the left island to the heating spot, and the temperature rise of left and right sensors ( TL and TR ). . 45 Figure 3.2 A classical (particle) view of electron scattering by a single atom (carbon)111. (a) Elastic scattering is caused by Coulomb attraction by the nucleus. Inelastic scattering results from Coulomb repulsion by (b) inner-, or (c) outer-shell electrons, which are excited to a higher energy state. The reverse transitions (de-excitation) are shown by broken arrows. 49 viii Figure A 3. The physical model used for the simulation. ss 152 List of Publications Liu, D., Xie, R., Yang, N., Li, B., Thong, J. T. L., Profiling Nanowire Thermal Resistance with a Spatial Resolution of Nanometers. Nano Letters 14, 806-812 (2014). Wang, Z., Xie, R., Bui, C. T., Liu, D., Ni, X., Li, B., Thong, J. T. L., Thermal transport in suspended and supported few-layer graphene. Nano Letters 11, 113-8 (2011). Liu, D., Chen, J., Hao, H., Li, B., Thong, J. T. L., Effect of lattice disorder created by helium ion irradiation on the thermal conductivity of Si nanowires (under preparation). Conference Presentations Liu, D., Xie, R., Li, B., Thong, J. T. L., Effect of lattice disorder created by helium ion irradiation on the thermal conductivity of Si nanowires. Poster presented at the Advanced Workshop on Energy Transport in Low Dimensional Systems, Trieste Italy (2012). Thong, J. T. L., Liu, D., Xie, R., Li, B., Spatially-resolved profiling of thermal resistance within individual nanowires. Invited presentation at 2013 MRS Spring Meeting & Exhibition, San Francisco, USA (2013). Liu, D., Xie, R., Li, B., Thong, J. T. 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Science 314, 1121-1124 (2006). 167 [...]... possible to measure the resistance change across epitaxial material interfaces in the nanowire and relate it to the local morphology of the interface Because a focused electron beam is used as a non-contact heating source, we simply named it the electron beam heating technique 4 1.2 Organization of thesis This thesis is organized as seven chapters, with Chapter 1 being the introduction Chapter 2 covers... embedded in nanostructured materials undergo additional scattering, which give rise to interfacial thermal resistance (ITR) Apart from introducing additional phonon scattering, nanostructured materials such as thin nanowires1 , nanomesh films2 and nanophononic metamaterials3 also affect the phonon transport by altering the phonon dispersion, which in turn either induces a phononic band gap or reduces... materials For example, phonons – the main heat carrier in semiconductor and dielectric materials – are predominately scattered by the surface of nanowires and thin films whose dimensions are comparable to the phonon mean free path This phonon boundary scattering reduces the thermal conductivity of a material when it is in nanowire and thin-film form Phonons traveling across the interfaces embedded in. .. literature review The background of the concept and transport of phonons is first introduced before focusing specifically on phonon transport in nanowires Several techniques to probe heat flow in nanowires are then described, namely the 3ω method, scanning thermal microscopy (SThM), Raman thermography, and the thermal bridge method Chapter 3 introduces the electron beam heating technique, starting with... temperature gradient is measured22 14 Besides calculating the thermal conductivity directly, MD simulation can also provide information about phonon relaxation times, which is a crucial but difficult task20 Moreover, phonon dispersions can also be calculated by MD calculation14 Compared with Boltzmann Transport modeling, MD has an advantage in being able to investigate materials with realistic crystalline structures... 6 Chapter 2 Literature review In non-conducting materials, heat is mainly carried by lattice vibrations whose quantized modes are called phonons In this chapter we will briefly introduce the transport and scattering of phonons, from which the thermal properties of nanowires can be understood more systematically Besides calculating phonon transport in an explicit manner, atomic level simulation using. .. PRT Platinum resistance thermometer RTA Rapid thermal annealing SAED Selected area electron diffraction SEM Scanning electron microscope SMRT Single mode relaxation time SThM Scanning thermal microscopy TDTR Time-domain thermoreflectance TEM Transmission electron microscope xviii Chapter 1 Introduction 1.1 Motivation and objectives Heat transport in nanostructures differs significantly from that in bulk... is the time-domain thermoreflectance (TDTR) method, which has a unique strength in measuring the ITR between a thin film and its substrate8 In a TDTR measurement, a thin film (usually aluminum film) is deposited to act as thermo-transducer A pump laser beam is used to heat up the transducer, and a probe laser beam with varying delay times is used to measure the transducer film’s optical reflectivity,... followed by a review of experimental techniques to measure thermal transport in nanowires: 3ω method, scanning thermal microscopy (SThM), Raman thermography, and in particular the thermal bridge method Lastly, a comparison of these techniques addressing both pros and cons will be given 7 2.1 Background 2.1.1 Harmonic approximation, normal modes and phonon Heat transport in non-metallic systems is generally... Total recombination rate Substantial amount of EHPs recombine at the interface, which release heat and distort the heating volume from its symmetric shape 60 Figure 3.11 (a) Same as Figure 3.10 (a) , just to illustrate the relative dimensions for (b) and (c) (b) and (c): electron and hole concentrations 61 ix Figure 3.12 Normalized heat generation at the interface due to EHP recombination as . PROBING HEAT TRANSPORT IN NANOWIRES USING A FOCUSED ELECTRON BEAM HEATING TECHNIQUE LIU DAN (B. Eng. (Hons.), National University of Singapore) A THESIS SUBMITTED. probe thermal transport at the nanoscale are still quite limited. In this thesis, a new thermal measurement technique that is capable of profiling nanowire thermal resistance with a spatial resolution. Temperature discontinuity at the interface /QA Heat flow per unit area INT h Interfacial thermal conductance R NW Nanowire thermal resistance R Thermal resistance of the sample T h