Evaluation of length scale effects for micro and nano-sized cantilevered structures

Transcription

1 University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 2010 Evaluation of length scale effects for micro and nano-sized cantilevered structures Chenzhi Tang University of Wollongong Recommended Citation Tang, Chenzhi, Evaluation of length scale effects for micro and nano-sized cantilevered structures, Master of Engineering - Research thesis, University of Wollongong. Faculty of Engineering, University of Wollongong, Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: research-pubs@uow.edu.au

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3 Evaluation of Length Scale Effects for Micro and Nano-sized Cantilevered Structures A thesis submitted for the fulfillment of the requirements for the award of the degree of Master of Engineering Research by Chenzhi TANG from Faculty of Engineering, University of Wollongong July 2010 Wollongong, New South Wales, Australia

4 CERTIFICATION CERTIFICATION I, Chenzhi TANG, declare that this thesis, submitted in partial fulfillment of the requirements for the award of Master of Engineering research, in the School of Mechanical, Materials and Mechatronic Engineering, Faculty of Engineering, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution. Chenzhi TANG 30 th June 2010

5 ACKNOWLEDGEMENTS ACKNOWLEDGEMENTS I wish to thank my supervisors, Prof. Gursel Alici and Dr. Yue Zhao, for their enthusiastic support, professional direction, and constant encouragement that inspire me to overcome the challenges on my road of life and study. Pure-hearted appreciations are also due to Dr. Buyung Kosasih, for his helpful direction on micro and nano-indentation process for this study. Particular thanks are extended to Greg Tillman and Dr. Michael Higgins for their help on the operation of atomic force microscopy and AFM cantilever calibration. Thanks are also extended to Guillaume Michal for his kind assistance and discussions. Finally, I specially would like to thank my parents for their understanding, patience and unwavering support during my study period. i

6 TABLE OF CONTENTS TABLE OF CONTENTS ACKNOWLEDGEMENTS...i TABLE OF CONTENTS...ii LIST OF FIGURES...v LIST OF TABLES...viii LIST OF SYMBOLS...x Abstract...1 Chapter 1 Introduction Background and motivation Aims and objectives Thesis outline...5 Chapter 2 Literature Review Introduction A brief introduction about MEMS and silicon The development of MEMS Mechanical properties of silicon The size effect phenomenon and modelling methods Size effect Modelling methods Length scale factor estimate methods The fabrication methods of micro cantilever beams Surface micromachining of silicon cantilever Other Fabrication Techniques Spring constant of atomic force microscopy Micro electro mechanical systems applications...25 ii

7 TABLE OF CONTENTS Medical technology Environmental and bio-technology Automation technology Conclusions 29 Chapter 3 Indentation Test Theory and Model Formulation Introduction Nanoindentation theory Nanoindentation introduction Tip selection and calibration Multi-scale modeling framework Data analysis method Frequency and deflection models formulation Conclusions 40 Chapter 4 Micro/Nano Indentation Results and Estimation of Length Scale Factor Introduction Experimental procedure Experimental results Micro-sized indentation Nano-sized indentation Length scale factor and modified models Length scale factor estimation The deflection and frequency modified models Conclusions...65 Chapter 5 Fabrication Process for Micro Silicon Cantilevers Introduction The dimension of micro silicon cantilevers Preparation for fabrication process...67 iii

8 TABLE OF CONTENTS Photomask design and fabrication Photoresist and developer selection Substrate selection and fabrication Fabrication process of micro silicon cantilevers Optical lithography process Pulsed laser deposition process Remove process Transfer process Conclusions...85 Chapter 6 AFM Calibration Method and Validation of Modified Models Introduction Experimental setup AFM cantilever deflection measurement Calibration the AFM cantilever Principle of deflection measurement Experimental results Nano-sized cantilever deflection results Micro-sized cantilever deflection results Comparison of deflection results Comparison of frequency results Conclusions Chapter 7 Conclusions and Recommendations for Future Work Summary Recommendations for Future Research REFERENCES.108 iv

9 LIST OF FIGURES LIST OF FIGURES Figure 1.1 Relationships of the different chapters.. 6 Figure 2.1 Multiscale, hierarchical framework of MSG theory...16 Figure.2.2 Schematic illustration of the geometrically necessary dislocations...18 Figure 2.3 Surface machining process of silicon cantilever...20 Figure 2.4 The configuration of a PLD deposition chamber 21 Figure 2.5 Lithography method...22 Figure 2.6 Calibrate spring constant of AFM cantilever by large cantilever...24 Figure 2.7 New patch and a common hypodermic needle illustration...26 Figure 2.8 DNA microinjection 28 Figure 3.1 Nanoindentation test result..31 Figure 3.2 Schematic representation of the unloading process...32 Figure 3.3 The reflection of a Berkovich indenter...33 Figure 3.4 Schematic illustration of multi-scale framework.34 Figure 3.5 Concentrate force at the end of silicon beam..39 Figure 4.1 The schematic diagram of IBIS nanoindenter.42 Figure 4.2 Nanoindentation scheme...43 Figure 4.3 Hardness versus residual depth for micro indentation (first time)..45 Figure 4.4 Square of indentation hardness versus the reciprocal of residual depth.45 Figure 4.5 Hardness versus residual depth for micro indentation (second time).46 Figure 4.6 Square of indentation hardness versus the reciprocal of residual depth.47 Figure 4.7 Hardness versus residual depth for micro indentation (third time).47 Figure 4.8 Square of indentation hardness versus the reciprocal of residual depth.48 Figure 4.9 Hardness versus residual depth for micro indentation (fourth time)..49 Figure 4.10 Square of indentation hardness versus the reciprocal of residual depth...49 Figure 4.11 Relationship between micro hardness test and residual depth...50 v

10 LISI OF FIGURES Figure 4.12 Relationship between micro hardness test and residual depth...53 Figure 4.13 Hardness versus residual depth for nano indentation (first time)...54 Figure 4.14 Square of indentation hardness versus the reciprocal of residual depth...55 Figure 4.15 Hardness versus residual depth for nano indentation (second time)...55 Figure 4.16 Square of indentation hardness versus the reciprocal of residual depth...55 Figure 4.17 Hardness versus residual depth for nano indentation (third time) Figure 4.18 Square of indentation hardness versus the reciprocal of residual depth...57 Figure 4.19 Hardness versus residual depth for nano indentation (fourth time)...58 Figure 4.20 Square of indentation hardness versus the reciprocal of residual depth...58 Figure 4.21 Relationship between nano hardness test and residual depth...59 Figure 4.22 Relationship between nano hardness test and residual depth...61 Figure 4.23 Size effect on natural frequency and deflection 65 Figure 5.1 The dimensions of silicon cantilever pedestals...67 Figure 5.2 Spin Speed Curve for AZ 1500 Resist Products...69 Figure 5.3 Salt substrate covered by photoresist and pattern on the salt substrate..71 Figure 5.4 The process of transferring a micro cantilever to a silicon substrate..72 Figure 5.5 Numerical aperture of a thin lens 74 Figure 5.6 Exposure system...75 Figure 5.7 Pattern on the silicon substrate, exposure time is 3 minutes...76 Figure 5.8 Pattern on the silicon substrate, exposure time is 1 minutes...76 Figure 5.9 Pattern on the silicon substrate, exposure time is 40 seconds Figure 5.10 Pattern on the silicon substrate, exposure time is 30 seconds...77 Figure 5.11 Pattern on the silicon substrate, exposure time is 20 seconds...78 Figure 5.12 PLD system and its components..79 Figure 5.13 Cantilever pattern after exposure.80 Figure 5.14 Cantilever pattern image under the AFM Figure 5.15 Inclined plane C under AFM Figure 5.16 The section of the inclined planes...82 vi

11 LISI OF FIGURES Figure 5.17 The change of silicon substrate during PLD process...83 Figure 5.18 The cantilever pattern after PLD process...84 Figure 6.1 View of cantilever in Atomic Force Microscope Figure 6.2 AFM deflection detection system...88 Figure 6.3 Experimental system...88 Figure 6.4 AFM cantilever...89 Figure 6.5 The interface of Lab View...90 Figure 6.6 Calibration grating under AFM scanning Figure 6.7 Force-distance curve to compute the sensitivity Figure 6.8 Force curve Figure 6.9 Power spectrum density curve Figure 6.10 Power spectrum density Figure 6.11 Force curve and Lorentzian fit curve Figure 6.12 The pictures of silicon cantilevers Figure 6.13 Deflections of Nano-sized cantilevers Figure 6.14 Deflections of Micro-sized cantilevers vii

12 LISI OF TABLES LIST OF TABLES Table 2.1 Differences between positive and negative photoresist.22 Table 3.1 Size regime and appropriate theory...35 Table 4.1 Hardness and residual depth measurements...44 Table 4.2 A new set of experimental hardness and residual depth data...46 Table 4.3 The third set of the experimental hardness and residual depth data.47 Table 4.4 The fourth set of the hardness and residual depth data 48 Table 4.5 H * 0micro, h and A data from the four measurements...51 Table 4.6 Hardness and residual depth data for the silicon sample B...52 Table 4.7 First set of the hardness and residual depth data...53 Table 4.8 The second set of the hardness and residual depth data Table 4.9 The third set of the hardness and residual depth data..56 Table 4.10 The fourth set of the hardness and residual depth data..57 Table 4.11 Four types of numerical values of viii H * 0Nano, h and A data...60 Table 4.12 The hardness and residual depth for silicon sample B...61 Table 4.13 The numerical values of the parameters in the micro and nano scales..63 Table 5.1 Silicon cantilevers with different dimensions..66 Table 5.2 Specifications of the photomask..68 Table 5.3 Place on the photomask 68 Table 5.4 Physical and chemical properties of AZ Table 5.5 Spin speed and thickness of photoresists.70 Table 5.6 Thickness of photoresist, the time of every step and the corresponding rotational speed...73 Table 5.7 Technical specifications of the PLD system employed in this study..80 Table 6.1 Data that obtained by programs...94

13 LISI OF TABLES Table 6.2 The dimensions of experimental silicon cantilevers 95 Table 6.3 The value in nano-sized cantilever deflection..96 Table 6.4 The results in nano-sized cantilever deflection 97 Table 6.5 Calibration data of strong cantilever Table 6.6 The value in micro-sized cantilever deflection 97 Table 6.7 The results in micro-sized cantilever deflection.. 98 Table 6.8 The deflection results of nano-sized cantilevers and errors.99 Table 6.9 The deflection results of micro-sized cantilevers and errors..101 ix

14 LISI OF SYMBOLS LIST OF SYMBOLS d P max H A s grain size maximum applied load in indentation Traditional hardness size of the residual deformation h r plastic deformation after load removal in indentation test h max depth under a maximum load in indentation test h c E φ h * h surface displacement at the contact perimeter in indentation test Young s Modulus half of the indentation angle of Berkovich indenter residual depth characteristic length parameter H 0micro macro hardness that is estimated by micro-sized indentation test H 0nano macro hardness that is estimated by nano-sized indentation test b α μ θ σ 0 χ ˆl Burgers vector a constant of face-centered cubic materials shear modulus complementary angles of half of the indentation angle yield stress average strain gradient length scale factor x

15 LISI OF SYMBOLS ρ s L s density of the statistically stored dislocations mean spacing between statistically stored dislocations ω 0 ω l w t F m s υ A T NA n k 1, k 2 λ CD D F classical frequency modified frequency length of cantilever beam width of cantilever beam thickness of the cantilever beam concentrated load at the tip of cantilever mass of the uniform beam Poisson s ratio a parameter depends on the Burgers vector temperature numerical aperture index of refraction process-related coefficients in lithography process wavelength critical dimensions depth of focus k A stiffness of AFM cantilever δ A deflection of AFM cantilever F S concentrated force on silicon cantilever F A concentrated force on AFM cantilever δ S deflection of silicon cantilever k S spring constant of silicon cantilever xi

16 LISI OF SYMBOLS δ P deflection of pizeo Δ V voltage V 1 initial voltage V 2 Sb final voltage sensitivity of AFM cantilever xii

17 ABSTRACT ABSTRACT This thesis focuses on evaluating the length scale effects for micro and nano-sized silicon cantilever experimentally, and incorporating the length scale effects into the conventional natural frequency and static deflection models of these cantilevers. Experiments were conducted to demonstrate that the models incorporating length-scale effect estimate the natural frequency and static deflection of the cantilevers more accurately. Micro and nano indentation experiments were conducted to determine the length-scale factors for micro and nano-sized silicon cantilevers. Geometrically necessary dislocations (GND) and the strain gradient theory is used to analyze the experimental data and subsequently to calculate the micro and nano length-scale factors using two different length-scale factor estimation methods reported in the literature. The factors match well with each other that both methods are equally valid to estimate the factors of silicon micro and nano cantilevers. Optical lithography and pulsed laser deposition methods were attempted to fabricate the micro silicon cantilevers with encouraging outcomes to use these techniques to make the cantilevers. AFM cantilevers were used as the micro and nano cantilevers to measure their static deflection in order to compare the results calculated from the analytical model incorporating the length-scale factor. The stiffness of the experimental cantilevers were determined experimentally using an AFM in order to determine the real natural frequency of the micro and nano cantilevers. The results presented demonstrate that the length scale-factor should be considered in estimating the natural frequency, static deflection and stiffness of the micro and nanosized cantilevers more accurately, which are the building blocks of micro and nanoelectromechanical systems (MEMS and NEMS). One application of such cantilevers is 1

18 ABSTRACT to use them as chemical, medical, gas or force sensors based on measuring their static deflection and the change in their resonant frequency. 2