近場掃描微波顯微鏡的研發製作

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(1)國立台灣師範大學物理學系碩士論文. 指導教授：盧志權博士. 近場掃描微波顯微鏡的研發製作 Development of Near-field Scanning Microwave Microscope (NSMM). 研究生: 賴奎元撰中華民國一零四年十二月.

(2) Table of Contents Acknowledgement ................................................................................................ V Abstract ................................................................................................................VI List of Figures .................................................................................................... VII 1 Preface................................................................................................................ 1 2 Principle ............................................................................................................. 3 2.1. 2.2. Scanning tunneling microscope (STM) ............................................. 3 2.1.1. History and overview ................................................................. 3. 2.1.2. Tunneling effect ......................................................................... 6. 2.1.3. Vibration isolation theory ........................................................ 10. 2.1.4. Signal ground techniques ......................................................... 13. Near-field scanning microwave microscope (NSMM) .................... 17 2.2.1. Historical review ...................................................................... 18. 2.2.2. Transmission line theory .......................................................... 19. 2.2.3. Near-field interaction ............................................................... 25. 2.2.4. Correlation between S11 and surface impedance ..................... 27. 3 Instrumentation ................................................................................................ 29 3.1. Introduction ...................................................................................... 29. 3.2. STM ................................................................................................. 30. I.

(3) 3.3. 3.2.1. SPM controller and current preamplifier ................................. 30. 3.2.2. Piezoelectric stage and controller ............................................ 32. 3.2.3. Stepper motor and motor drive ................................................ 33. 3.2.4. Sample stage ............................................................................ 34. 3.2.5. Tip holder ................................................................................. 35. 3.2.6. Tip and tip-fabricating equipment ........................................... 36. NSMM ............................................................................................. 38 3.3.1. Network analyzer ..................................................................... 38. 3.3.2. Bias tee ..................................................................................... 39. 3.3.3. Diode detector .......................................................................... 42. 3.3.4. Circulator ................................................................................. 43. 3.3.5. NI my DAQ.............................................................................. 44. 3.3.6. Electromagnet .......................................................................... 45. 4 Developmental Process and Result .................................................................. 46 4.1. Introduction ...................................................................................... 46. 4.2. Build the STM.................................................................................. 47 4.2.1. Main body ................................................................................ 48. 4.2.2. Automatic approach system ..................................................... 50. 4.2.3. Vibration isolation ................................................................... 53. II.

(4) 4.3. Seek for the best tip-etching parameter ........................................... 56 4.3.1. 6M KOH .................................................................................. 56. 4.3.2. 4M KOH .................................................................................. 58. 4.4. STM test sample fabrication ............................................................ 59. 4.5. Noise reduction ................................................................................ 60. 4.6. NSMM test sample fabrication ........................................................ 63. 4.7. Transform STM into NSMM ........................................................... 65. 4.8. 4.7.1. Introduction .............................................................................. 65. 4.7.2. Narrowband bias tee, diode detector and circulator................. 66. 4.7.3. Broadband bias tee, NI my DAQ and PC ................................ 69. Results of measurement and demonstration of instruments ............ 72 4.8.1 Introduction ................................................................................. 72 4.8.2 STM ............................................................................................ 73 4.8.3 NSMM ........................................................................................ 76. 5 Conclusions and Outlook ................................................................................. 81 5.1. Conclusions ...................................................................................... 81. 5.2. Outlook ............................................................................................ 82. Reference ............................................................................................................. 83 Appendix A. Rev9 dashboard and IHDL workbench .......................................... 86. III.

(5) Appendix B. LabVIEW program ......................................................................... 88 B.1 Stepper motor control for automatic approach (ori R9Vi.vi) ................ 88 B.2 Incorporation for VNA and R9 SPM controller (new SCAN test.vi) ... 89 Appendix C. Experimental Steps for Operating Instruments .............................. 92 C.1 Experimental steps for the STM............................................................ 92 C.2 Experimental steps for NSMM ............................................................. 96 Appendix D. SolidWorks drawings ..................................................................... 98. IV.

(6) Acknowledgement Immeasurable appreciation and deepest gratitude for the support and help are extended to a number of people, particularly to those in the following. I express my deepest sense of gratitude to Prof. C. K., Lo, my mentor and research advisor, for the guidance, timely support and scholarly advise, and for providing me with a freewheeling ambience to soar, stumble, and stand up from failures, which were of great influence to not only my academic studies, but also to my philosophy and attitude toward life. I am sincerely thankful that I am offered this research opportunity to practice the three abilities, independent thinking, self-learning, and programming, which he mentioned for the first time we met. I indebt the most grateful thanks to Mr. Ken Kollin, the product manager of the RHK technologies, for providing me all technical support respecting the R9 SPM controller. His prompt inspirations, suggestions with kindness and dynamism have enabled me to complete my research work. It is my privilege to gratefully appreciate Dr. Pavel Kabos, veteran researcher from the NIST, for kindly, patiently and enthusiastically discussing with my enquiries. He had showed me what makes an esteemed researcher. I thank Mr. R. W., Zhang and Yi-Da manufacturer enterprise for machining all hardware parts of the research and bringing my design drawings into real objects. My sincere appreciation are given to B.Y., Xie and T. L., Su from ARML with expertise in STM tip fabrication for generously and kindly imparting me the knowledge of tip fabrication as well as suggestions on the tip-fabricating equipment building. Also, I thank my friends, K. J., Huang for countless technical advises and support; W. X., Wang for handling my test sample and giving general assistance and suggestion during the last but most critical stage of my research; Z. W., Huang and H.Z., Chen for the cheer-up, relaxing chatting and encouragement. Finally, I would like to acknowledge with gratitude, the support and love of my families and my girlfriend Meredith. They all kept me going. This research wouldn’t have been completed without them.. V.

(7) Abstract In order to achieve surface impedance topography and submicron level magnetic domain image as well as extend our greatest interest and expertise of spin dynamic measurement, so called ferromagnetic resonance (FMR), to local ferromagnetic resonance measurement(LFMR), we are dedicated to developing a near-field scanning microwave microscope (NSMM). Self-configured scanning tunneling microscope (STM) and NSMM employing RHK R9 SPM controller, n.point C.300 piezoelectric stage and Agilent N5230C network analyzer are demonstrated in this dissertation. Developmental processes can be mainly divided into STM part and NSMM part. In STM part, designs of main body, vibration isolation, automatic approach system, and tip fabrication are demonstrated. In NSMM part, two different configurations adopting microwave components, vector network analyzer (VNA), and NI my DAQ, are discussed. Finishing constructing, various samples were employed to test performance of the instruments. Cu-coated 4.7 GB DVD fabricated by pulse laser deposition (PLD) was used as STM test sample. For NSMM’s test samples, Au/Si alternatively stripped samples with three different dimensions, 25 um/ 25 um, 10 um/ 10 um, and 2 um/ 18 um, were fabricated by electron beam lithography (EBL) and vacuum thermal evaporation deposition (VTED). An AFM standard silicon test sample with dimensions of 5 um in x, y and 180 nm in z was also scanned to discriminate the influence of 100-nm thickness of Au strips from surface impedance. Hundred-nanometer spatial resolution has been achieved by our STM with setpoint current 0.8 nA and bias voltage 1.5 V. A set of chemically-etching equipment are also developed and are capable of producing sharp tips with apex diameter less than 100 nm under parameters of 4 V KOH, 8 V etching voltage, and 2 V cut-off voltage. This apex is very ideal for scanning probe microscope (SPM) uses. Most critically, the self-developed NSMM configuration using VNA, PC and NI my DAQ. This novel yet simple configuration enables our NSMM to miraculously accomplish λ/10000wavelength-relative resolution as well as sensitivity less than 0.01 dB while working over 13 GHz. Keyword: near-field, microwave, microscope, surface impedance, scanning tunneling microscope (STM), local ferromagnetic resonance (LFMR) 關鍵字: 近場、微波、顯微鏡、表面阻抗、掃描穿隧電子顯微鏡、局域鐵磁共振. VI.

(8) List of Figures FIG. 2-1 SCHEMATIC DIAGRAM OF STM. [13] ................................................................. 3 FIG. 2-2 TWO PRIMARY OPERATIONAL MODE OF IMAGING. [UPPER]: CONSTANT HEIGHT MODE. [BOTTOM]: CONSTANT CURRENT MODE. ...................................................... 4 FIG. 2-3 ONE-DIMENSIONAL MODEL FOR TUNNELING EFFECT. ........................................ 6 FIG. 2-4 A SYSTEM INFLUENCED BY AN EXCITATION FREQUENCY Ω. ............................ 10 FIG. 2-5 STM IS EXCITED BY A FREQUENCY Ω............................................................. 12 FIG. 2-6 SIGNAL GROUNDING TECHNIQUE COMPRISES FOUR METHODS. ........................ 13 FIG. 2-7 SCHEME OF SINGLE POINT GROUND. ................................................................ 14 FIG. 2-8 SCHEME OF MULTIPLE POINT GROUND ............................................................. 14 FIG. 2-9 SCHEME OF MIX GROUND. ................................................................................ 15 FIG. 2-10 SCHEME OF FLOATING GROUND. .................................................................... 16 FIG. 2-11 MODEL FOR TRANSMISSION LINE THEORY ..................................................... 19 FIG. 2-12 TRANSMISSION LINE MODEL COMPRISED OF PER-UNIT-LENGTH RESISTANCE, INDUCTANCE, CAPACITANCE, AND PARASITIC CONDUCTANCE. ............................. 20 FIG. 2-13 A LOSSLESS TRANSMISSION LINE CONNECTED TO A LOAD WITH IMPEDANCE ZL. ..................................................................................................... 23. FIG. 2-14 WAVE IMPEDANCE VERSUS RELEVANT DISTANCE .......................................... 26 FIG. 2-15 WAVE ATTENUATION VERSUS RELEVANT DISTANCE...................................... 26 FIG. 2-16 PROBE-SAMPLE MODEL IN TRANSMISSION LINE THEORY................................ 27 FIG. 3-1 RHK R9 CONTROLLER (REAR) ........................................................................ 30 FIG. 3-2 RHK R9 CONTROLLER (FRONT) ..................................................................... 30 FIG. 3-3 CURRENT PREAMPLIFIER. IVP-200 [RIGHT]. IVP-R9 [LEFT]. .......................... 31 FIG. 3-4 N.POINT C.300 DSP CONTROLLER. .................................................................. 32 FIG. 3-5 N.POINT NPXY100Z25-102 THREE DIMENSIONAL PIEZOELECTRIC STAGE. ..... 32 FIG. 3-6 SIGMA KOKI SHOT-102 MOTOR DRIVE [RIGHT] AND SIGMA KOKI SGSP40-5ZF FIVE PHASE STEPPER MOTOR STAGE [LEFT]. .................................... 33 FIG. 3-7 ACRYLIC-MADE SAMPLE STAGE ....................................................................... 34 FIG. 3-8 ALUMINUM-MADE SAMPLE STAGE ................................................................... 34 FIG. 3-9 DRAWING OF TIP HOLDER. ............................................................................... 35 FIG. 3-10 TAPERED TIP SHAPE AND CORRESPONDING IMAGE [26]. ................................ 36 FIG. 3-11 TIP-FABRICATING EQUIPMENT. ...................................................................... 37 FIG. 3-12 AGILENT N5230C PNA-L. ............................................................................ 38 FIG. 3-13 SKETCH OF INNER STRUCTURE OF BIAS TEE. .................................................. 39 FIG. 3-14 DRAWING AND SPECIFICATION OF BT-A04-S-2 BIAS TEE. ............................ 40 FIG. 3-15 VSWR DIAGRAM OF IMMET BROADBAND BIAS TEE. ................................... 41 FIG. 3-16 INSERTION LOSS DIAGRAM OF IMMET BROADBAND BIAS TEE. ..................... 41 FIG. 3-17 FAIRVIEW SMA M/F 2 GHZ-18GHZ DETECTOR. ..................................... 42 VII.

(9) FIG. 3-18 PERFORMANCE DIAGRAM OF THE DIODE DETECTOR. ..................................... 42 FIG. 3-19 CONCEPTUAL WORKING SCHEME FOR THE CIRCULATOR. ............................... 43 FIG. 3-20 FAIRVIEW SMA F’S 2 GHZ-4 GHZ CIRCULATOR .......................................... 43 FIG. 3-21 NI MY DAQ ............................................................................................... 44 FIG. 3-22 NI MY DAQ CONTAINS MULTIPLE I/O AND POWER SUPPLIES......................... 44 FIG. 3-23 HORSESHOE ELECTROMAGNET WITH 200OE MAXIMUM MAGNETIC FIELD. .... 45 FIG. 3-24 SORENSEN DSC150-8E POWER SUPPLY. ....................................................... 45 F IG . 4-1 F LOW CHART OF EXPERIMENTAL PROCESSES . .......................................... 46 FIG. 4-2 STM SCHEMATIC DIAGRAM. ............................................................................ 47 FIG. 4-3 STM’S MAIN BODY .......................................................................................... 48 FIG. 4-4 INDIVIDUAL PART OF THE MAIN BODY. ............................................................ 49 FIG. 4-5 PROGRAM FOR AUTOMATIC APPROACH PROCEDURE ........................................ 51 FIG. 4-6 EASY LABVIEW PROGRAM FOR STEPPER MOTOR STAGE CONTROL ................. 51 FIG. 4-7 FRONT PANEL [RIGHT]. BLOCK DIAGRAM [LEFT]. ............................................ 52 FIG. 4-8 PIEZOELECTRIC STAGE’S STEP RESPONSE IN X[TOP], Y[MIDDLE], AND Z[BOTTOM]............................................................................................................ 53 FIG. 4-9 VIBRATION ISOLATION SYSTEM OF STM. ........................................................ 54 FIG. 4-10 OVER SMALL CUT-OFF VOLTAGE RESULTS IN A BROKEN AND TORN TIP END. . 56 FIG. 4-11 CUT-OFF VOLTAGES ARE COMPARED. 4V-426 NM [TOP]. 2V-100 NM [MIDDLE]. 1V-36NM [BOTTOM]............................................................................. 57 FIG.4-12 A 30-NM-DIAMTER TIP FABRICATED UNDER OUR BEST PARAMETER. .............. 58 FIG. 4-13 AN CU-COATED 4.7 GB DVD RECORDING LAYER FABRICATED BY PLD....... 59 FIG. 4-14 GROUND SCHEME OF OUR INSTRUMENTS ....................................................... 60 FIG. 4-15 BEFORE GROUND [TOP]. AFTER GROUND [BOTTOM]. ..................................... 61 FIG. 4-16 14 HZ MECHANICAL NOISE AND ITS HARMONIES. ........................................... 62 FIG. 4-17 NSMM TEST SAMPLES. AU/SI (25UM/25UM) [UPPER-LEFT]. AU/SI (10UM/10UM) [UPPER-RIGHT]. AU/SI (2UM/18UM) [BOTTOM-LEFT]. AFM TEST SAMPLE [BOTTOM-RIGHT]. .................................................................................... 64 FIG. 4-18 SCHEMATIC DIAGRAM OF AN STM-ASSISTED NSMM PUBLISHED IN 2003 [22]. .............................................................................................................................. 65 FIG. 4-19 FIRST NSMM SCHEME ADAPTED FROM THE PAPER PUBLISHED IN 2003. ....... 66 FIG. 4-20 AU/SI (25UM/25UM) TEST SAMPLE. WITH FOIL[LEFT] V.S. WITHOUT FOIL [RIGHT]. ................................................................................................................ 67 FIG. 4-21 SEVERE POWER LOSS SHOWN ON S11 TRACE DIAGRAM. .................................. 68 FIG. 4-22 REMODELED NSMM SCHEME DEVELOPED OURSELVES. ................................ 69 FIG. 4-23 LABVIEW PROGRAM ORGANIZING REMODLED NSMM CONFIGURATION. .... 70 FIG. 4-24 LARGE ELECTRICAL NOISES AT 34 HZ AND ITS HARMONIC FREQUENCIES DUE TO THE BROADBAND BIAS TEE. FFT SPECTRUM [TOP]. OSCILLOSCOPE [BOTTOM]. 71. VIII.

(10) FIG. 4-25 8UM X 8 UM. SET-POINT = 0.8 NA, BIAS VOLTAGE = 0.8 V............................. 73 FIG. 4-26 4 UM X 4 UM. SET-POINT = 0.8 NA, BIAS VOLTAGE = 0.8 V ............................ 73 FIG. 4-27 4 UM X 4 UM. SET-POINT = 0.8 NA, BIAS VOLTAGE = 1.5 V ............................ 74 FIG. 4-28 2 UM X 2 UM. SET-POINT = 0.8 NA, BIAS VOLTAGE = 1.5 V ............................ 74 FIG. 4-29 800 NM X 800 NM. SET-POINT = 0.8 NA, BIAS VOLTAGE = 1.5 V. ................... 75 FIG. 4-30 AU/SI (25 UM/25 UM). Q = 557. F = 13.86 GHZ. ......................................... 76 FIG. 4-31 CROSS SECTION VIEW OF PICTURE ABOVE. ..................................................... 76 FIG. 4-32 AU/SI (10 UM/10 UM). Q = 628. F = 19.97 GHZ .......................................... 77 FIG. 4-33 CROSS SECTION VIEW OF PICTURE ABOVE. ..................................................... 77 FIG. 4-34 AU/SI (10 UM/10 UM). Q = 557. F = 13.86 GHZ .......................................... 78 FIG. 4-35 CROSS SECTION VIEW OF PICTURE ABOVE. ..................................................... 78 FIG. 4-36 AU/SI (2 UM/18 UM). Q = 213. F = 13.53 GHZ ............................................ 79 FIG. 4-37 CROSS SECTION VIEW OF PICTURE ABOVE. ..................................................... 79 FIG. 4-38 AFM TEST IS A NEGATIVE EVIDENCE VERIFYING THE AUTHENTICITY OF NSMM IMAGES. ................................................................................................... 80 FIG. 0-1 IHDL WORKBENCH, WHERE WE CREATE STM SOFTWARE PART. ..................... 86 FIG. 0-2 DASHBOARD IN REV 9, WHERE WE EXECUTE THE EXPERIMENT. ...................... 87 FIG. 0-1 STEPPER MOTOR CONTROL PROGRAM FOR INCLUDING IN R9’S IHDL AUTOMATIC PROCEDURE. [TOP]: BLOCK DIAGRAM. [BOTTOM]: FRONT PANEL. .... 88 FIG. 0-2 FIRST PART OF THE PROGRAM. PRE-EXPERIMENT PARAMETERS SUCH AS SOURCE POWER, AVERAGE TIMES, SWEEP POINTS, MARK LOCATION AND FREQUENCY ARE SET. ....................................................................................................................... 89 FIG. 0-3 SECOND PART OF THE PROGRAM. ASK S11 DATA IN UNIT OF DB FROM THE VNA, CONVERTING IT INTO VOLTAGE VALUES BY CARRYING OUT INTERPOLATION METHOD. BOTH S11 DATA IN DB AND VOLTAGE ARE DISPLAYED ON THE FRONT PANEL. ................................................................................................................ 90 FIG. 0-4 FINAL PART OF THE PROGRAM. COMMAND THE NI MY DAQ OUTPUT ASSIGNED VOLTAGE VALUES, AND RESET VOLTAGE VALUES TO ZERO WHEN PROGRAM TERMINATED. ........................................................................................................ 90 FIG. 0-5 A FRONT PANEL OF THE PROGRAM. FREQUENCY SPAN AND AVERAGE TIMES CAN BE SET, AND THE S11 IN BOTH DB AND VOLTAGE CAN BE TIMELY AND SIMULTANEOUSLY MONITORED ON SCREEN. TO TERMINATE TO EXPERIMENT, PRESS STOP AND THE VOLTAGE VALUE WOULD BE SET BACK TO ZERO, PREVENTING THE NI MY DAQ FROM CONSTANTLY OUTPUTTING VOLTAGES WHILE NOT USING. ...... 91. IX.

(11) 1. Preface. As increasing demand of higher memory storage capacity has extended singledomain region to submicron distance scale, breeding a need to not only visualize the magnetic domain in fine resolution, but also quantitative spin dynamic measurements. Magnetic domains are microstructural elements of magnetic materials revealing the basic physical properties with its macroscopic properties and applications [1]. In 1907, Weiss first suggested the existence of magnetic domain and pointed out that spontaneous magnetization takes different directions in different domains in ferromagnetic material [2]. A decade later, Barkhausen in 1919 discovered that magnetization process is discontinuous, giving rise to a characteristic noise made audible by an amplifier [3]. This was the first confirmation of domain concept and led to plenty of further pursuits [1]. In 1935, the modern theory basis took shape as Landau and Liftshitz proposing a well-known theoretical explanation of domain structure which stated domains are formed to minimize the total energy [4]. The first attempt to observe the domain can date back to Bitter patterns [5]. A variety of techniques such as transmission electron microscopy (TEM) [6], magnetooptical microscopy (MOM) [7], scanning electron microscopy (SEM) [8], X-ray, neutron are also exploited to meet individual needs [1]. Nowadays, the most powerful and common techniques for magnetic domain observation have been typically investigated by magnetic resonance force microscopy (MFM) [9] magnetic force microscopy (MRFM) [10]. The former enables the magnetic domain observation down to 10-100 nanometer-scale, the latter, even better, can magically achieve single-spin measurement [11], however; both of their ferromagnetic detecting tip and cantilever forbid the spin dynamic measurement in high magnetic field. Thus, in order to achieve submicron level magnetic domain image as well as extend our greatest interest and expertise of spin dynamic measurement, so called ferromagnetic resonance (FMR), to local ferromagnetic resonance (LFMR), we are dedicated to developing a new apparatus inspired by near-field scanning microwave microscope (NSMM) [12]. This apparatus, named local ferromagnetic resonance (LFMR), combines scanning tunneling microscopy (STM), vector network analyzer (VNA), high Q factor resonator and electromagnet, giving us the access to acquire impedance topography image, visualization of magnetic domain and the most important. 1.

(12) part, LFMR measurement which allows precise investigation of magnetic properties such as g factor, magnetization of single domain region of certain topographic pattern on the sample, rather than a bulk sample in the past. The entire construction work can be divided into three stages, STM, NSMM, and LFMR. Whereas, in this thesis, we present the first two stages, and leave the third stage to future work.. 2.

(13) 2. Principle. 2.1 Scanning tunneling microscope (STM) 2.1.1 History and overview The scanning tunneling microscope (STM) was invented by Gerd Binnig and Heinrich Rohrer in 1982, and earned inventors the Nobel Prize on Physics in 1986. The essential elements consist of probe tip, piezoelectric scanner, and feedback circuit…etc. (Fig. 2-1). When the tip-sample distance is in nanometer regime and a bias voltage is applied in between, electrons have the ability to break the potential barrier of air gap and bring about a tunneling current. Next, launch the piezoelectric scanner along x, y direction to acquire the image.. Fig. 2-1 Schematic diagram of STM. [13]. Fixing the bias, based on quantum mechanics, the tunneling current is exponentially proportional to the gap between tip and sample, shown as, I ∝ 𝑒 ∆𝑧 leading to two primary operational modes (Fig. 2-2),. 3. (2.1).

(14) 1. Constant height mode (CHM) In this mode, tunnrling current feedback loop is turned off in order to keep the piezoelectric scanner in constant height. Due to surface topography, different tipsample distance results in different value of tunneling current while scanning. Using tunneling current feedback, the surface contour can be mapped. CHM has faster scanning speed while it is more suitable to work under a relatively flat surface to prevent the tip from crashing. 2. Constant current mode (CCM) On contrary to CHM mode, the tunneling current is set constant, so called setpoint. While scanning, the PID feedback loop continously compares set-point with transient tunneling current. If the transient current is larger than the set-point, the piezoelectric drive retracts to increase the tip-sample distance; vice versa, if the transient current is smaller than the set-point, the piezoelectric drive extends to reduce the tip-sample distance. Therefore, the feedback loop keeps the tip-sample distance constant. Using z-axial movement feedback, the surface contour can be acquired. This mode possesses slower scanning speed but it is better for a rougher surface.. Fig. 2-2 Two primary operational mode of imaging. [Upper]: constant height mode. [Bottom]: constant current mode.. 4.

(15) As the tip-sample distance is within several Å in operational condition, the vibration isolation thus plays a critical role for achieving atomic resolution. Vibrations come from miscellaneous sources, for example, building, ground, wind, cooling pump, walk, talk, air-conditioning…etc. However, the most harmful vibration for STM results from building and ground which is at the frequency of 10~100 Hz. Consequently, optimizing vibration isolation system is also an imperative task for STM. Thanks to the simplicity of the principle, non-destructive imaging, and the high resilience of configuration, the STM has become a very powerful tool in variety of fields such as chemistry, biology, condense matter physics, nanotechnology and so on. Moreover, the greatest feature is, it can perform in various ambiences no matter in air, in gas, in ultrahigh vacuum or in liquid, and the operating temperature ranges from absolute zero to a few hundred degrees centigrade [13].. 5.

(16) 2.1.2 Tunneling effect In this section we introduce tunneling effect, the core concept of STM, using onedimensional model as (Fig. 2-3). Region 1, 2, and 3 stand for sample, air gap and metallic tip respectively. Considering an elastic tunneling, which the electron energy is equal in the sample and the tip. The air gap, or the potential barrier is V0 larger than other two regions.. Fig. 2-3 One-dimensional model for tunneling effect.. In classical mechanics, an electron with energy E moving in a potential V0 is described by. 𝑝𝑧2 2𝑚. + 𝑉0 = E. (2.2) [13]. 𝑝𝑧2 2𝑚. + 𝑉0 = E. (2.2). where m is the electron mass. In regions where E > V0, the electron has a momentum pz. This equation indicates that electron cannot penetrate into any region with E < V0. Thus, the electron is impossible to penetrate the air gap and cause a tunneling current. In quantum mechanics, however, the state of electron is described by a wave ℏ2 𝑑 2. function ψ(z) satisfying the time-independent Schrödinger’s equation − 2𝑚 𝑑𝑧 2 ψ(z) + U(z)ψ(z) = Eψ(z) (2.3),. 6.

(17) ℏ2 𝑑 2. − 2𝑚 𝑑𝑧 2 ψ(z) + U(z)ψ(z) = Eψ(z). (2.3). where m is the electron mass, U(z) is the potential barrier function, E is the electron energy, and ℏ is Plank’s constant h divided by 2π. Let’s start to derive the wave function ψ(z) in each region. In three regions shown in (Fig. 2-3), (2.3) can be respectively expanded as below, ℏ2 𝑑 2. − 2𝑚 𝑑𝑧 2 ψ1 (z) = Eψ1 (z). (2.4). ℏ2 𝑑 2. − 2𝑚 𝑑𝑧 2 ψ2 (z) + 𝑉0 ψ2 (z) = Eψ2 (z). ℏ2 𝑑 2. − 2𝑚 𝑑𝑧 2 ψ3 (z) = Eψ3 (z). (2.5). (2.6). The wave functions of electron are, 2𝑚𝐸. 𝜓1 = 𝑒 𝑖𝑘𝑧 + 𝐴𝑒 −𝑖𝑘𝑧 ,. 𝜓2 = 𝐵𝑒 𝜘𝑧 + 𝐶𝑒 −𝜘𝑧 ,. 𝜓3 = D𝑒 𝑖𝑘𝑧 ,. 𝑤𝑖𝑡ℎ 𝑘 = √. ℏ. 2𝑚(𝑉0 −𝐸). 𝑤𝑖𝑡ℎ 𝜘 = √. ℏ. 2𝑚𝐸. 𝑤𝑖𝑡ℎ 𝑘 = √. ℏ. (2.7). (2.8). (2.9). K, κ are the wave vectors. We are interested in potential barrier transmission coefficient T, which is the ratio of the transmitted current density 𝐽𝑡 and the incident current density 𝐽𝑖 that are given by,. 𝐽𝑡 =. −𝑖ℏ. [𝜓3∗ 2𝑚. 𝑑𝜓3 𝑑𝑧. − 𝜓3. 7. 𝑑𝜓3∗ 𝑑𝑧. ]=. ℏ𝑘 𝑚. |𝐷|2. (2.10).

(18) ℏ𝑘. 𝐽𝑖 =. (2.11). 𝑚. therefore, 𝐽. T = 𝐽𝑡 = |𝐷|2. (2.12). 𝑖. By applying the boundary condition 𝜓1 (0) = 𝜓2 (0) (2.13), 𝜓3 (𝑠) = 𝜓2 (𝑠) (2.14), 𝑑𝜓1 (𝑧) 𝑑𝑧. |. 𝑧=0. =. 𝑑𝜓2 (𝑧) 𝑑𝑧. |. 𝑧=0. (2.15) and. 𝑑𝜓2 (𝑧) 𝑑𝑧. |. 𝑧=𝑠. =. 𝑑𝜓3 (𝑧) 𝑑𝑧. |. 𝑧=𝑠. (2.16) to (2.7), (2.8), and. (2.9), 𝜓1 (0) = 𝜓2 (0). (2.13). 𝜓3 (𝑠) = 𝜓2 (𝑠). (2.14). 𝑑𝜓1 (𝑧) 𝑑𝑧. |. 𝑧=0. 𝑑𝜓2 (𝑧) 𝑑𝑧. |. 𝑧=𝑠. =. =. 𝑑𝜓2 (𝑧) 𝑑𝑧. |. 𝑧=0. 𝑑𝜓3 (𝑧) 𝑑𝑧. |. 𝑧=𝑠. (2.15). (2.16). the coefficient A, B, C, D can be solved, and transmission coefficient T can be derived, 16k2 κ2. T = (k2 +κ2)2 𝑒 −2𝜅𝑠 ∝ 𝑒 −2𝜅𝑠. (2.17). The tunneling current also suggested, I ∝ 𝑒 −2𝜅𝑠. with κ =. √(𝑉0 −𝐸) ℏ. , where √(𝑉0 − 𝐸) is the square root of effective barrier height, so is. the potential barrier width.. 8.

(19) Therefore, the transmission coefficient T shows even the potential barrier V0 is higher than the electron energy E, electrons still have the probability to penetrate the potential barrier. Given that e−2𝜅𝑠 is the dominant contribution of T and I, which are exponentially dependent on the barrier width s. This accounts for an extremely sensitive tunneling current, to which an order of magnitude variation can be led when changing the tip-sample distance by 1 Å .. 9.

(20) 2.1.3 Vibration isolation theory . Considering a one-dimensional system influenced by an excitation frequencyω. The system consists of a mass M, a spring and a damper. The stiffness of the spring is k, the damping constant is c, and displacement of the mass and the frame are respectively x(t) and X(t) (Fig. 2-4).. Fig. 2-4 A system influenced by an excitation frequency ω.. According to Newton’s equation, 𝑥̈ + 2γ𝑥̇ + 𝜔02 𝑥 = 2𝛾𝑋̇ + 𝜔02 𝑋. (2.18). where 𝑐. γ = 2𝑀. (2.19) 𝑘. 𝜔0 = 2𝜋𝑓0 = √𝑀. (2.20). 𝜔0 is natural resonance frequency. The displacement of the mass and the frame can be derived, x(t) = 𝑥0 𝑒 𝑖𝜔𝑡. 10. (2.21).

(21) X(t) = 𝑋0 𝑒 𝑖𝜔𝑡. (2.22). Substituting eq. (2.21) and eq. (2.22) into eq. (2.18), we define the ratio of the amplitudes a transfer function, 𝜔 2 +4𝛾2 𝜔2. 𝑥. 0 K(ω) ≡ |𝑋0 | = √(𝜔2 −𝜔 2 )2 +4𝛾 2 𝜔2 0. (2.23). 0. Smaller K(ω) stands for better vibration isolation. Three special cases are discussed in the following, (1) At a ultra-high excitation frequency (𝛚 ≫ 𝝎𝟎 ), damping is negligible, 𝜛. 2. 𝑓. 2. K(ω) ≈ ( 𝜛0 ) = ( 𝑓0 ). (2.24). which suggests ultra-high external frequency makes barely effect on the system. (2) Excitation frequency is close to natural resonance frequency (𝛚 ≈ 𝝎𝟎 ), 𝜛2. K(ω) = √1 + 4𝛾02 ≈. 𝜔0 2𝛾. ≡𝑄. (2.25). Q is the quality factor. Normally, higher Q means better isolation. In this case, the compromise between K(ω) and Q suggests proper damping must be applied to avoid resonant excitation frequency. (3) Excitation frequency is higher than natural resonance frequency (𝛚 > 𝐐𝝎𝟎 ), 𝟏 𝒇𝟎. 𝐊(𝛚) = 𝑸. 𝒇. (2.26). the transfer function K(ω) is again affected by the quality factor Q, suggesting the larger Q, the better isolation. However, take both (2), (3) into consideration, Q shouldn’t be too large or too small. Hence, the compromise between the suppression of resonance and the suppression of. 11.

(22) high excitation frequency has to be made by choosing an appropriate Q. Research investigated that Q value of 3~10 is the best [13]. In STM internal structure analysis, assuming the STM is excited by a frequency ω. The displacement of the tip and the sample are X(t), x(t), as shown in (Fig. 2-5). (2.23) can be reduced to, 𝑥0 −𝑋0 𝑥0. ≈. 𝜛2 𝜛02. =. 𝑓2 𝑓02. (2.27). (2.27) shows that when the external frequency is much lower than the STM natural frequency, the relative motion of the tip versus the sample moves consistently with the sample.. Fig. 2-5. STM is excited by a frequency ω.. In conclusion, from (2.25) and (2.26), we learn that a design for a good vibration isolation system can be achieved by choosing an appropriate Q ranging from 3 to 10. From (2.24) and (2.27), it is suggested that a rigid STM construction with low resonance frequency of the vibration isolation system is the most efficient way for isolating vibrations.. 12.

(23) 2.1.4 Signal ground techniques Depending on different purposes, the ground can be generally clustered to power safe ground and signal ground. The former protects the instrument from being damaged by the power leak, and the latter prevents the signal from being contaminated. In this section, the signal ground is our focus, which comprises four different methods in case of different situations, e.g. single point ground, multiple point ground, mix ground, and floating ground [14] (Fig. 2-6).. Fig. 2-6 Signal grounding technique comprises four methods.. 1.. Single point ground. Connect instruments independently to a shared point on a co-grounded plane (Fig. 2-7). Normally, the length of the ground wire is not supposed to be longer than a twentieth of the signal wavelength. This method is only suitable for low-frequency signals with frequencies no higher than 1 MHz, otherwise it would radiate as if an antenna according to transmission line theory. Instruments do not interfere with each other as their ground wires independently connect to the co-grounded point. While this may results in longer ground wire needed and higher impedance, rendering the coupling with other ground wires.. 13.

(24) Fig. 2-7 Scheme of single point ground.. 2.. Multiple point ground Connect each instrument to the nearest points on the co-grounded plane(Fig.. 2-8).. Fig. 2-8 Scheme of multiple point ground. The basic idea is to reduce the length of ground wire as much as possible to lower the wire impedance. This method suits for high-frequency signals with frequencies higher than 10 MHz as it uses shorter ground wires which brings about lower impedance. In high-frequency circuit, the longer the transmission line, the larger the capacitance as well as the inductance. However, the ground loops are be created and the high-frequency instruments might influence lower-frequency ones.. 14.

(25) 3.. Mix ground. Simultaneously connect instruments at a co-grounded point in series and at different points on the same co-grounded plane in parallel (Fig. 2-9).. Fig. 2-9 Scheme of mix ground.. Combining advantages of single ground and multiple ground, this approach is commonly applied on instruments with wide working frequency across from lowfrequency regime to high-frequency regime. Working in low frequencies, it is regarded as a single point ground connecting ground wires from instruments at a co-grounded point in series. While working in high frequencies, it is seemed to be a multiple point ground connecting instruments to different points on the co-grounded plane via capacitors. Mix ground is often used for a low-frequency cable to resist the highfrequency noise. 4.. Floating ground. Separate the power safe ground and signal ground to individual reference plane(Fig. 2-10). The main purpose of this method is to isolate sensitive signals from either dirty gorunds or being coupled with the power leak of the metallic case of instruments by connecting the signal ground wires together as a joint reference point. However, this method is subject to suffer a discharging or charge accumulation, so it is often disregarded.. 15.

(26) Fig. 2-10 Scheme of floating ground.. 16.

(27) 2.2 Near-field scanning microwave microscope (NSMM) The NSMM is characterized by scanning scattering parameter 𝑆11 on a sample surface under near-field condition in order to map surface impedance. A sharp tip is employed as a probe to emit microwave to a sample as well as collect the reflected microwave back from the sample. To fully understand physics and mechanism of NSMM, we introduce the historical review, transmission line theory, near-field interaction and correlation between 𝑆11 and surface impedance.. 17.

(28) 2.2.1 Historical review The original idea of the near-field microscope is mostly attributed to Synge [15] in 1928, who proposed that the super resolution could be achieved by creating a subwavelength sized hole(~10 nm in diameter) in a metal film, illuminating it from the backside and scanning it about 10 nm above the sample. The light is collected in a pixelby-pixel scan. However, this theoretical proposal had not been carried out until 1959, when Frait [16] developed the first ferromagnetic resonance (FMR) microscope in microwave regime by means of placing the sample outside a cavity with a 500-μm diameter hole in the cavity face and operating at a wavelength of 3 cm (10 GHz). A magnetic thinfilm sample was scanned closely beneath the hole and showed local changes in magnetic properties. Similar results were also obtained at 5.5 GHz by Soohoo in 1962 [17]. The first use of non-resonant scanned coaxial probes dates back to 1965 when Bryant and Gunn [18] used a tapered open-ended coaxial tip to measure local resistivity of semiconductor samples at 450 MHz with millimeter resolution. The subwavelength resolution was not presented until 1972, Ash and Nicholls [19], who demonstrated λ/60 wavelength-relative resolution using 3 cm microwaves confined to a sub-micro wavelength aperture. This is a profound influence for modern NSMM. In order to increase resolution from centimeters to millimeters or less, two principal aspects of probes must be improved. First, the probe-sample distance control which must be less than the resolution sought. Second, the resolution of the probe itself should also be increased, namely, a sharpen tip or a smaller aperture. In 1989, Fee, Chu and Hänsch [20], achieved λ/4000 resolution by using 12 cm (2.5 GHz) microwaves, a coaxial cable and a sharpened tip with 30-μm-radius apex, despite without probedistance distance control. With the advent of STM and AFM, the solution to these two major concerns become possible. The first STM-assisted near –field microwave microscope is accomplished by Karamer in 1996 [21], when the topographical features as small as 15 nm was observed. Since then, near-field microscopy has spread through a wealth of techniques and applications to form a diverse field of research [22] [23] [24].. 18.

(29) 2.2.2 Transmission line theory In microwave regime, namely alternating current (AC), the lumped constant circuit theory for direct current (DC) is far from addressable, instead, a distributed constant circuit should be introduced. To be more specific, when the propagating wavelength exceeds over a hundredth of the length of transmission line, the characteristics of electrical parameters such as voltage, current, and phase vary from point to point, which discriminates “distributed” from “lumped”, because the stray capacitance and the self-inductance can no longer be disregarded. A naïve wire in DC circuit turns into an inductor; a pair of parallel wires in DC are independent, while in AC the stray capacitance between should be taken into consideration. Therefore, in order to govern much more complicated electrical characteristics in AC circuit, we learn transmission line theory [25]. A pair of parallel transmission lines can be analogous to a model composed of the resistor, the inductor, the static capacitor, and the parasitic conductance which evenly distributed along the wire (Fig. 2-11).. Fig. 2-11 Model for transmission line theory. 19.

(30) Dividing the transmission line into infinitesimal unit length, and assuming the electronic elements per unit length are the resistance R(Ω/m), the inductance L(H/m), the leak conductance G(S/m), and the parasitic capacitance between two parallel wires C(F/m)(Fig. 2-12), the series impedance Z and parallel admittance Y per unit length can accordingly be described as, Z = R + jωL. (2.28). Y = G + jωC. (2.29). Fig. 2-12 Transmission line model comprised of per-unit-length resistance, inductance, capacitance, and parasitic conductance.. According to (Fig. 2-12), the voltage and current can be expressed as, 𝑑𝑉. 𝑉𝑥+𝑑𝑥 = 𝑉𝑥 + ( 𝑑𝑥𝑥 ) 𝑑𝑥. 𝑑𝐼. 𝐼𝑥+𝑑𝑥 = 𝐼𝑥 + ( 𝑑𝑥𝑥 ) 𝑑𝑥. (2.30). (2.31). The voltage and current between P, Q are given by, 𝑉𝑥 − 𝑉𝑥+𝑑𝑥 = (𝑅𝑑𝑥 + 𝑗ωLdx)𝐼𝑥. 20. (2.32).

(31) 𝐼𝑥 − 𝐼𝑥+𝑑𝑥 = (𝐺𝑑𝑥 + 𝑗ωCdx)𝑉𝑥. (2.33). Substitute (2.28), (2.29), (2.30), (2.31) into (2.32) and (2.33), d𝑉𝑥. = −𝑍𝐼𝑥. (2.34). = −𝑌𝑉𝑥. (2.35). dx. d𝐼𝑥 dx. Differentiate both (2.34) and (2.35), 𝑑2 𝑉𝑥. 𝑑𝐼. = −𝑍 𝑑𝑥𝑥. 𝑑𝑥 2. 𝑑2 𝐼𝑥 𝑑𝑥 2. = −𝑌. (2.36). 𝑑𝑉𝑥. (2.37). 𝑑𝑥. Insert (2.34) into (2.37), and (2.35) into (2.36) plus letting 𝛾 2 = 𝑍𝑌,γ = α + jβ where γ is propagating constant, α is attenuation constant, and β is phase constant, turning (2.36) and (2.37) into, 𝑑2 𝑉𝑥 𝑑𝑥 2. 𝑑2 𝐼𝑥 𝑑𝑥 2. = 𝛾 2 𝑉𝑥. (2.38). = 𝛾 2 𝐼𝑥. (2.39). Let 𝑉𝑥 = A𝑒 𝜆𝑥 with some equation substitutions, (2.38) and (2.39) can be solved. As a result, the distribution of voltage and current on transmission line can be formulated, 𝑉𝑥 = 𝑉0+ 𝑒 −𝛾𝑥 + 𝑉0− 𝑒 𝛾𝑥. 𝐼𝑥 =. 𝑉0+ 𝑍0. 𝑒 −𝛾𝑥 −. 21. 𝑉0− 𝑍0. 𝑒 𝛾𝑥. (2.40). (2.41).

(32) where 𝑒 −𝛾𝑥 represents the wave travelling toward x, 𝑒 𝛾𝑥 represents the wave travelling toward -x, and 𝑉0+ , 𝑉0− represent the voltage amplitude depending on the boundary condition. 𝑍0 is the characteristic impedance, which can be expanded as, 𝑍. 𝑍. 𝑅+𝑗𝜔𝐿. 𝑍0 = 𝛾 = √𝑌 = √𝐺+𝑗𝜔𝐶. (2.42). Lossless Transmission Line Theory In most realistic cases, the loss is low enough to be deemed so much as lossless (R = G = 0), where (2.40), (2.41) can be further simplified. By substituting 0 for R and G in 𝛾 2 = 𝑍𝑌 and (2.42), the propagating constant γ turns into, γ = α + jβ = jω√𝐿𝐶. (2.43). as expected, the attenuation constant α equals 0. The characteristic impedance 𝑍0 becomes, 𝐿. 𝑍0 = √𝐶. (2.44). Putting (2.43), (2.44) into (2.40) and (2.41), the voltage and current equations for lossless transmission line are acquired, 𝑉𝑥 = 𝑉0+ 𝑒 −𝑗𝛽𝑥 + 𝑉0− 𝑒 𝑗𝛽𝑥. 𝐼𝑥 =. 𝑉0+ 𝑍0. 𝑒 −𝑗𝛽𝑥 −. 𝑉0− 𝑍0. 𝑒 𝑗𝛽𝑥. (2.45). (2.46). Considering connecting a load to the end of the transmission line, the impedance of the load is 𝑍𝐿 (Fig. 2-13). At x = 0, by replacing x with 0, we can find a relation between 𝑍0 and 𝑍𝐿 described by voltage and current as (2.47),. 22.

(33) Fig. 2-13 A lossless transmission line connected to a load with impedance 𝑍𝐿 .. 𝑍𝐿 =. 𝑉(0) 𝐼(0). 𝑉 + +𝑉 −. = 𝑉0+ −𝑉0− 𝑍0. (2.47). 0. 0. Here, we introduce a reflective coefficient Г, which is defined as the ratio of the voltage amplitude of reflective wave and incident wave, 𝑉−. Г = 𝑉0+. (2.48). 0. Combine (2.47) and (2.48), 𝑉−. 𝑍 −𝑍. Г = 𝑉0+ = 𝑍𝐿 +𝑍0 𝐿. 0. 0. (2.49). Last but not least, scattering parameterS𝑖𝑗 , a powerful yet instinctive scattering parameter is introduced on account of that voltage and current are of difficulty to be measured in microwave circuit, 𝑉−. S𝑖𝑗 = 𝑉𝑖+ |𝑉𝑘+ =0 𝑎𝑛𝑑 𝑘≠𝑗. (2.50). 𝑗. (2.50) characterizes incident, reflective and transmission wave in microwave network, from which other related parameters such as impedance, standing wave ratio (SWR), reflective loss, phase delay, and so forth, can be derived. To be more specifically, in our case, we measure S11 by a 2-port vector network analyzer (VNA), it can be expanded as,. 23.

(34) 𝑉−. (1). S11 = 𝑉1+ |𝑉2+ =0 = Г 1. |𝑉2+=0 =. 𝑍1 −𝑍0. | 𝑍1 +𝑍0 𝑤ℎ𝑒𝑛 𝑝𝑜𝑟𝑡 2 𝑖𝑠 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑 𝑡𝑜 𝑍0. ( 2.51). where 𝑍0 = 50𝛺. Again, 𝑍0 is the characteristic impedance. From (2.51), clearly can (1). we find that scattering parameter S11 has not only become reflective coefficient Г. at port 1, but also been formulated with the impedance 𝑍1 of the load connected to port 1.. 24.

(35) 2.2.3 Near-field interaction In general definition, near-field zone can be realized when the relevant distance (d) is much smaller than the wavelength of electromagnetic wave (λ) and in the meantime the size of scatter (r) is much smaller than the wavelength of electromagnetic wave. That is r ≪ d ≪ λ [26]. However, in NSMM, we lay the focus on r ≤ d ≪ λ, where r is the diameter of tip apex, d is the tip-sample distance, andλ is the wavelength of microwave. In near-field zone, the spatial resolution of NSMM is no longer restricted by Abbe’s diffraction limit, which states that the spatial resolution cannot exceed λ/2. On the other hand, near-field zone provides a non-radiative environment, where is the best for reactive energy storage and dissipation in tiny volume of the sample. Two perspectives accounting for this non-radiative phenomenon are given in the following. In terms of classical electrodynamic, the interaction between electromagnetic waves and material can be illustrated by Maxwell’s equations supplemented with boundary conditions. By solving Hertzian dipole model, the solutions show that both electric and magnetic fields in near-filed zone can be considered quasi-static [27] because they are similar to electrostatic and magnetostatic fields generated by dipoles. This give rise to a non-radiative environment. Another perspective according to microwave engineering, impedance mismatch is a useful concept to explain this non-radiative behavior. The free space impedance can be calculated, 𝜇. 𝑍0 = √ 𝜀 0 ≈ 377Ω 0. (2.52). where 𝜇0 and 𝜀0 are the magnetic permeability and dielectric permittivity. The wave impedance Z is widely known as E/H, where E is the magnitude of electric field and H is the magnitude of magnetic field. For a sharp tip as if a rod antenna, E >> H leads to an extremely high wave impedance Z, which is much greater than the free space impedance 𝑍0 until entering far-field region [28](Fig. 2-14). This tremendously large impedance mismatch prohibits microwave from radiating. Therefore, the power of. 25.

(36) microwave remains unchanged in the near-field zone (Fig. 2-15) unless dissipated in the sample. Noted that the critical distance between far-field zone and near-field zone is λ/2π, where λ is the wavelength of the electromagnetic wave. In other words, far-field zone is where the relevant distance is greater than λ/2π, whereas the near-field zone is where the relevant distance is smaller than λ/2π.. Fig. 2-14 Wave impedance versus relevant distance. Fig. 2-15 Wave attenuation versus relevant distance. 26.

(37) 2.2.4 Correlation between S11 and surface impedance In this section we explain the correlation between reflective scattering parameter S11 and surface impedance by using a probe-sample model (Fig. 2-16). The sample is considered as a one-layer thin film on a bulk substrate [26]. According to microwave engineering, S11 can be formulated as (2.53) [25],. Fig. 2-16 Probe-sample model in transmission line theory. 𝑉. 𝑍 −𝑍. 𝑆11 = 20logΓ = 20log |𝑉+ | = 20log |𝑍𝑖𝑛+𝑍0 | −. 𝑖𝑛. 0. (2.53). where Γ is the reflection coefficient, V+ ,V- is respectively the incident and reflecting voltages of electromagnetic wave, 𝑍𝑖𝑛 is the input impedance and 𝑍0 is the characteristic impedance of the probe. The input impedance is affected by thin film impedance, substrate impedance, film thickness, and wave number as (2.54) shows, 𝑍𝑠 +𝑖𝑍𝑓 𝑡𝑎𝑛(𝑘𝑓 𝑡𝑓 ). 𝑍𝑖𝑛 = 𝑍𝑓 𝑍. 𝑓 +𝑖𝑍𝑠 𝑡𝑎𝑛(𝑘𝑓 𝑡𝑓 ). (2.54). where 𝑖 2 = −1 is the imaginary unit, Z𝑓 , 𝑘𝑓 , 𝑡𝑓 is respectively the thin film impedance, wave number, thickness of the thin film, 𝑍𝑠 is the impedance of the substrate. Hence, (2.53) and (2.54) explicitly suggest that S11 is affected by factors including thin film thickness, thin film impedance, substrate impedance, and wave number.. 27.

(38) Furthermore, the impedance and wave number of the thin film are defined as (2.55),. (2.56) [25],. 𝜇𝑓 𝜇0. 𝑍𝑓 = {. √𝜀. 𝑓 𝜀0. 𝜇. = 𝑍𝑎 √ 𝜀 𝑓. 𝑓𝑜𝑟 𝑑𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑠. 𝑓. (2.55). 1. (1 + 𝑖)√𝜋𝑓𝜇𝑓 𝜇0 𝜎𝑓 = (1 + 𝑖) 𝛿. 𝑓𝑜𝑟 𝑚𝑒𝑡𝑎𝑙𝑠. 𝑓. 2𝜋𝑖𝑓 √𝜇𝑓 𝜇0 𝜀𝑓 𝜀0 = 𝑘𝑎 √𝜇𝑓 𝜀𝑓 𝑘𝑓 = {. 𝜋𝑓𝜇𝑓 𝜇0. (1 + 𝑖)√. = (1 + 𝑖) 𝜎. 𝜎𝑓. 𝑓𝑜𝑟 𝑑𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑠 1. 𝑓 𝛿𝑓. 𝑓𝑜𝑟 𝑚𝑒𝑡𝑎𝑙𝑠. (2.56). where Z𝑎 , 𝑘𝑎 are the impedance and wave number of free space. 𝜇0 and 𝜀0 are respectively the magnetic permeability and dielectric permittivity of free space. 𝜇𝑓 , 𝜀𝑓 , 𝜎𝑓 are respectively the relative magnetic permeability, relative dielectric permittivity and the conductivity of the thin film. f is the frequency of electromagnetic wave. 𝛿𝑓 is the skin depth of electromagnetic wave penetrating through the thin film. Assuming metallic thin film is chosen, after inserting (2.55), (2.56) into (2.54), and performing some mathematic transformations, we get (2.57), 1. 2𝑡𝑓. 𝑠 𝑠. 2 𝑓 𝛿𝑓. 𝑍𝑖𝑛 = (𝜎 𝛿 − 𝜎. 1. 2𝑡𝑓2. 𝑠 𝑠. 2 𝑠 𝑠 𝛿𝑓. ) + 𝑖 (𝜎 𝛿 + 𝜎 𝛿. ). (2.57). then substitute (2.57) into (2.53), the 𝑆11 can be expressed as (2.58),. 𝑆11 = 20log {−𝑒𝑥𝑝 (−. 2−4𝜋𝑓𝜇0 𝜇𝑓 𝑡𝑓 𝜎𝑠 𝛿𝑠 𝜎𝑠 𝛿𝑠 𝑍0. ) × 𝑒𝑥𝑝 (−𝑖. 2+4𝜋𝑓𝜇0 𝜇𝑓 𝜎𝑓 𝑡𝑓 𝜎𝑠 𝛿𝑠 𝑍0. )} (2.58). (2.58) involves valuable electric and magnetic properties such as impedance, electric permittivity and magnetic permeability of the thin film. These can be further investigated by measuring reflective scattering parameter S11. Moreover, either magnetic field-sweeping mode or frequency-sweeping mode makes the influence on S11. The smaller S11 refers to the more energy absorbed by the sample.. 28.

(39) 3. Instrumentation. 3.1 Introduction The near-field scanning microwave microscope (NSMM) incorporates scanning tunneling microscope (STM) with vector network analyzer (VNA), NI my DAQ, PC and multiple microwave components such as bias tee, circulator, diode detector, and so forth. The basic scheme is to create a near-field environment by getting the tip-sample distance down to nanometer scale, emit the microwave via a sharp tip, and scan the surface impedance topography. In this chapter, we introduce critical features and specifications of every single part used for developing STM and NSMM, and detailed configration works will be presented and discussed in Chapter 4. Experimental Processes and Results.. 29.

(40) 3.2 STM 3.2.1 SPM controller and current preamplifier SPM controller is a brain of STM and NSMM. Our RHK R9 SPM controller (Fig. 3-1) (Fig. 3-2) plays multiple roles as power supply, high voltage amplifier, PI feedback control, piezoelectric stage driving, current preamplifier, data acquisition and data postprocessing. We take numbers of advantages from its high flexibility of hardware configuration ADC, DAC I/Os, LabView VI support and ultra-low noise performance of electronics.. Fig. 3-1 RHK R9 controller (rear). Fig. 3-2 RHK R9 controller (front). 30.

(41) Tunneling current in STM is extremely tiny, typically range from 0.01 to 50 nA. Current preamplifier is thus an essential component to convert tunneling current into voltage and feed back to R9 SPM controller. Our IVP-200 and IVP-R9 (Fig. 3-3) are two-stage high performance current preamplifiers from the RHK technology. The first stage, IVP-200 has a gain of 109 (10nA/V) with 30 kHz (50 kHz) bandwidth at 0 pF (100 pF) input capacitance. IVP-R9, as the second stage, provides a selectable gain and bandwidth, and it is also responsible for outputting bias voltage to the sample. In practice, the distance between tip and input port of the first-stage preamplifier should be as short as possible. The shorter traveling distance, the less equivalent stray capacitance, the smaller electrically coupling noise.. Fig. 3-3 Current preamplifier. IVP-200 [right]. IVP-R9 [left].. 31.

(42) 3.2.2 Piezoelectric stage and controller To handle nanometer-scale movement including fine approach and scaning task, we exploited n.point NPXY100Z25-102 three dimensional piezoelectric stage (Fig. 3-5) controlled by n.point C.300 series DSP controller (Fig. 3-4). In x, y, and z, the piezoelectric stage features a maximum translation range of 100 μm, 100 μm and 25 μm and position noises are respectively 0.3 nm, 0.3 nm and 0.1 nm. PID mode and AFM scan mode are both supported.. Fig. 3-4 n.point C.300 DSP controller.. Fig. 3-5 n.point NPXY100Z25-102 three dimensional piezoelectric stage.. 32.

(43) 3.2.3 Stepper motor and motor drive SGSP40-5ZF stepper motor stage and SHOT-102 stepper motor drive (Fig. 3-6) are used to practice coarse approach. This is a five-phase stepper motor stage featuring 0.5 μm per step resolution, 5 mm maximum travel distance and 2 kg maximum loading weight.. Fig. 3-6 SIGMA KOKI SHOT-102 motor drive [right] and SIGMA KOKI SGSP405ZF five phase stepper motor stage [left].. 33.

(44) 3.2.4 Sample stage Our acrylic-made sample stage (Fig. 3-7) was then revolutionized into an aluminum-made one (Fig. 3-8 Aluminum-made sample stage. The remodeled aluminum-made one has better sample-attaching design, more secure bias volatge attachment as well as larger and more flexible scanning area. The height of the sample stage was deliberately modeled for LFMR to work under an in-plane magnetic field in the future.. Fig. 3-7 Acrylic-made sample stage. Fig. 3-8 Aluminum-made sample stage. 34.

(45) 3.2.5 Tip holder Tip holder is responsible for firmly holding the tip and transmitting both tunneling current and microwave. SMA connector is typically and widely used for coaxial transmission line with signal frequency available from DC to 18 GHz microwave. Thus, we tailored a SMA connector by drilling a 0.4-mm-diameter and 3-mm-depth hole on SMA Jack, turning the jack into a tube to hold a 0.25-mm-diameter tip (Fig. 3-9). Also, this tip holder features 50Ω impedance and excellent electrical shielding to prevent from coupling with electrical noise.. Fig. 3-9 Drawing of tip holder.. 35.

(46) 3.2.6 Tip and tip-fabricating equipment The importance of tip treatment is recognized by Binning and Rohrer in the very beginning of the STM’s birth. The tip is suggested as sharp as possible to achieve better spatial resolution. In addition, for NSMM, tip shape is of the most primary factor for spatial resolution and sensitivity [26]. (Fig. 3-10) illustrates that image quality affected by different shape of the tip. Sharp tip (a) performs high spatial resolution but low sensitivity. Blunt tip (b) performs low spatial resolution but high sensitivity. Hybrid tip (c) with decreasing tapered angle gives the image with both high spatial resolution and high sensitivity. Therefore, tip fabrication is a critical and imperative technique for a high-quality image, and apparently the hybrid tip is the most wanted.. Fig. 3-10 Tapered tip shape and corresponding image [26].. In our experiment, the tip was fabricated by electrochemically etching a 0.25-mmdiameter tungsten wire in 4M KOH solution. First, we sandpapered the oxide layer off the tungsten wire surface, cut the tungsten wire into roughly 0.7-cm-length clips before a 5-minute ultrasonic cleaning in methyl alcohol and acetone respectively. Second, we had a tungsten clip clamped as anode and submerged into KOH with 2-3 mm out the surface, and a copper wire was connected as cathode. Once the set-up is ready, turn on the DC power supply and increase the voltage slowly from 2 V to 8 V. To avoid the asymmetry of etching caused by absorbing foam on the tungsten wire, the voltage can be adjusted in above range to control the etching speed, and the two electrodes should be separated as far as possible to prevent bubbles of hydrogen gas from interfering the observation. The tungsten clip under KOH surface would be considerably sharpened. Not until the bottom portion is about to drop off, decrease the voltage down to 2 V and. 36.

(47) give intermittent pulses. Cut-off timing is significantly critical for the sharpness of tip. The quicker the electrochemical reaction can be stopped as soon as the wire breaks, the sharper tip apex will be shaped [29]. Chemical formulas of electrochemical reaction for tip etching are shown as below, Anode:. W + 8OH − → 𝑊𝑂4−2 + 4𝐻2 𝑂 + 6𝑒 −. Cathode:. 6𝐻2 𝑂 + 6𝑒 − → 3𝐻2 + 6𝑂𝐻 −. (3.1) (3.2). Our tip-etching equipment consists of a TOE 8704 DC power supply, a momentary switch, wires, a vertical displacement stage, a tip-fixing stage, a beaker, a LED light, a clip of copper wire as the anthode, and a long-len microscope (Fig. 3-11).. Fig. 3-11 Tip-fabricating equipment.. 37.

(48) 3.3 NSMM 3.3.1 Network analyzer Network analyzer is a powerful instrument used primarily for testing linear electrical characterization of microwave components. Some of which are capable of simultaneously acquiring magnitude and phase characterization from devices under test are called vector network analyzer (VNA), hence VNA becomes the most common abbreviation for network analyzers. Agilent N5230C PNA-L (Fig. 3-12) is a two port network analyzer allowing the measurement of four different S-parameter, S11, S22, S12, and S21 with frequencies ranging from 10 MHz to 20 GHz. This VNA serves as our microwave source and S11 trace diagram monitor, and plays a pivotal role in NSMM. Microwave is emitted from port 1 to the sample through coaxial cable, microwave components, and tip, and reflected from the sample back to the port 1 all the way reversed.. Fig. 3-12 Agilent N5230C PNA-L.. 38.

(49) 3.3.2 Bias tee Bias tee was put after the tip for decoupling the DC and microwave, so called radio frequency (RF) signals, preventing the STM part from interfered by RF signals. This three-port component is made with an inductor port which allows DC but RF, a capacitor port allowing RF but DC, and a combined port allows both DC and RF, shown as (Fig. 3-13).. Fig. 3-13 Sketch of inner structure of bias tee.. 39.

(50) 1. Narrowband bias tee Taylor BT-A04-S-2 manufacture grade bias tee (Fig. 3-14) is designed for frequencies between 500 MHz to 4 GHz, featuring the maximum insertion loss 0.5 dB, VSWR 1:1.31, minimum isolation 40 dB. The lower insertion loss and VSWR indicate the better quality of the microwave component.. Fig. 3-14 Drawing and specification of BT-A04-S-2 bias Tee.. 40.

(51) 2. Broadband bias tee Aeroflex IMMET 8812KMM-26 military grade bias tee is a broadband bias tee with working frequencies ranging from 12 kHz to 26.5 GHz, max current 150 mA. VSWR (Fig. 3-15) and insertion less (Fig. 3-16) vary from different frequency ranges.. Fig. 3-15 VSWR diagram of IMMET broadband bias tee.. Fig. 3-16 Insertion loss diagram of IMMET broadband bias tee.. 41.

(52) 3.3.3 Diode detector Diode detector is an ADC adapter converting the power of microwave signal into voltage for analog input of R9 SPM controller. We utilized a Fairview SMA M/F ZERO BIAS DIODE 2 GHz - 18 GHz diode detector (Fig. 3-17) which features max VSWR 1:1.5, 100-mW max input power, and sensitivity of 500mV/mW. As (Fig. 3-18) indicates, the output voltage (mV) is linearly proportional to the input microwave power (dB) when the power is no weaker than -35 dBm. If the power decays to less than -35 dBm, the performance of higher frequencies is better than those below 1 GHz.. Fig. 3-17 Fairview SMA M/F 2 GHz-18GHz detector.. Fig. 3-18 Performance diagram of the diode detector.. 42.

(53) 3.3.4 Circulator Circulator is a three-port device used to transfer the microwave from one port to one another in rotation with theoretically no power loss. More specifically, a signal entering port 1 comes out of port 2; a signal entering port 2 comes out of port 3; a signal entering port 3 comes out of port 1(Fig. 3-19). Reversal rotation is forbidden.. Fig. 3-19 Conceptual working scheme for the circulator.. This is a Fairview SMA F’S 2 GHz - 4GHz circulator (Fig. 3-20) with insertion loss 0.5 dB, VSWR 1:1.4. The reflective microwave signal is intended to be passed to the R9 SPM controller as a feedback to image the impedance topography of the sample. The microwave sourced from the VNA inputs to the port 1, the port 2 is responsible for the microwave go to and come back from the sample, and the reflective microwave is directed to the R9 SPM controller from the port 3 via a diode detector.. Fig. 3-20 Fairview SMA F’S 2 GHz-4 GHz circulator. 43.

(54) 3.3.5 NI my DAQ NI my DAQ (Fig. 3-21) is a data acquisition (DAQ) device. It is a LabVIEWbased instrument and mainly created for facilitating the real-world signals measurement and analysis. Analog I/O, digital I/O, audio I/O, and +5 V, +15 V, -15 V power supplies up to 500 mW are supported (Fig. 3-22). Configured with LabVIEW on PC, IEEE 488 GPIB-USB cable, and BNC cable, we bridged VNA and R9 SPM controller by tranforming VNA data, ASCII code, into voltage for analog input on R9 SPM controller.. Fig. 3-21 NI my DAQ. Fig. 3-22 NI my DAQ contains multiple I/O and power supplies.. 44.

(55) 3.3.6 Electromagnet The horseshoe electromagnet (Fig. 3-23) is made of a raw iron and powered by a Sorensen DCS150-8E power supply (Fig. 3-24). The maximum magnitude of magnetic field is up to 200 Oe, linearly proportional to the current increasing from 0 A to 8 A. This electromagnet is made for LFMR in the future, so it will not be included into instruments demonstrated in this thesis.. Fig. 3-23 Horseshoe electromagnet with 200Oe maximum magnetic field.. Fig. 3-24 Sorensen DSC150-8E power supply.. 45.

(56) 4. Developmental Process and Result. 4.1 Introduction Our NSMM‘s developmental processes (Fig. 4-1) can be divided into seven major stages. In sequence, build the STM to meet our particular need, best tip-etching parameter seeking, STM test sample fabrication, modification for noise reduction, transform the STM into NSMM by incorporating with microwave components, fabricate the NSMM test sample, and finally measure NSMM test samples and testify the instrument.. Build the STM. Tip-etching parameter searching. STM Test sample fabrication. Modification for noise reduction. Measure and testify. NSMM test sample fabrication. Transform the STM into NSMM. Fig. 4-1 Flow chart of experimental processes.. 46.

(57) 4.2 Build the STM STM is a prerequisite for NSMM because it helps achieve near-field condition by bringing tip-sample distance down to nanometer regime. Between two most common approaching techniques, AFM mechanical tuning fork and STM tunneling current feedback, we opted for STM on account of its simplicity of construction and adaptability in various working conditions. Schematic diagram below (Fig. 4-2) gives an overview of our STM. The tip is fixed securely on the main body, and the sample is placed on and moved by the piezoelectric stage for fine approach and scanning. The stepper motor stage is in charge of coarse approach. These two stages are commanded by their individual controller and drive. When a bias voltage applied on sample in tunneling range, tunneling current flows from the sample to tip, going back to R9 SPM controller in form of voltage converted by the preamplifier. Comparing the acquired signal with set-point, R9 SPM controller tells piezoelectric stage controller the offset to move. This is called closeloop feedback. R9 SPM controller, piezoelectric stage controller and stepper motor drive are cabled to PC.. Fig. 4-2 STM schematic diagram.. In this section, design of main body structure, automatic approach system, vibration isolation measures, software configuration and tip fabrication will be thoroughly discussed. Different from Chapter 3, we put emphasis on the know-how of developmental processes. Instruments mentioned here are introduced in 3.2 STM. 47.

(58) 4.2.1 Main body Three critical facets must be seriously considered and evaluated when designing STM’s main body, 1 2 3. Convenience and feasibility for incorporation with electromagnet, microwave components, and VNA. Stiffness in order to minimize relative displacement among every single part. Evaluation of geometric symmetry and weigh distribution are indispensable to prevent the main body from flipping over.. Therefore, we utilized an Unice BR0303-1 optical breadboard as a base. The main body (Fig. 4-3) (Fig. 4-4) is combined with columns, mounting bases for instruments, a weigh, and stabilizers. These hardware are all designed by SolidWorks and made of Aluminum 6061. Drawings of which are presented in Appendix D.. Fig. 4-3 STM’s main body. 48.

(59) Fig. 4-4 Individual part of the main body.. 49.

(60) 4.2.2 Automatic approach system Owing to that tunneling current will not emerge until the tip-sample distance reaches to nanometer scale, a nanometer-scale-resolution relative displacement is required for moving sample toward a fixed tip. Therefore, the automatic approach procedure is usually divided into two stages, coarse approach and fine approach. Stepper motor stage, responsible for coarse approach, approaches sample toward the fixed tip until the tip-sample distance is hardly visualized, followed by the piezoelectric stage, as the fine approach, takes over and brings the tip-sample distance into nanometer regime. In brief, the cooperation of stepper motor stage and piezoelectric stage has made our automatic approach system come true. We will demonstrate how to make it happened in this section. A program is the key to integrate fine approach and coarse approach (Fig. 4-5). Noted that, opposite to the reality, we imagine it is the tip and sample are moving for the sake of easier conveying the concept of this program. In our program (Fig. 4-5), the tip is released first to see if feedback signal, the tunneling current, hits set-point after start button is pressed. If the feedback signal hits set-point, message window pops up and shows “Approach completed”. If the feedback signal does not hit the set-point when the tip is fully extended, the tip will be fully retracted before the stepper motor stage brings the sample one step closer to the tip, afterward, the tip will be released again to see if the feedback signal is detected and matched the set-point. By repeating this procedure over and over until the set-point is hit, we will sooner or later complete the approach. Normally, it takes five to ten minutes.. 50.

(61) Fig. 4-5 Program for automatic approach procedure. An easy LabVIEW program simply functioning in step-in (Fig. 4-6) was created in order to be included in the program to collaborate with the piezoelectric stage. Step number per launch can be tuned by changing the digit in the front panel, never bigger than 25 (Fig. 4-7). Normally, for the stability the step number is set to 10.. Fig. 4-6 Easy LabVIEW program for stepper motor stage control. 51.

(62) Fig. 4-7 Front panel [right]. Block diagram [left].. Calibrations for piezoelectric stage is also a must, and can be done by using the user interface of n.point C.300 controller (Fig. 4-8). Position in each axis is shown at the bottom of the window in unit of um. PID mode particularly for STM is chosen. PID control is a feedback mechanism widely used in industrial control system. PID stands for proportional (P), integral (I) and derivative (D), three different action control gains. In practice, however, PI control is the most common because derivative action is rather sensitive to pick up the noise. The calibrations for piezoelectric stage is simply finding out the best combination of proportional gain (P) and integral gain (I) in every axis. Proper setting of the gains can optimize the automatic approach system’s performance. Thus, first we let the derivative gain set to zero. Second, we tried different combinations of P and I. In theory, smaller proportional gain the better stability and the integral gain depends on the compromise between response speed and stability. Our optimum combination of the P, I and D gains in each axis are presented in (Fig. 4-8 Piezoelectric stage’s step response in x[top], y[middle], and z[bottom].).. 52.

(63) Fig. 4-8 Piezoelectric stage’s step response in x[top], y[middle], and z[bottom]. 4.2.3 Vibration isolation. 53.

(64) Introduced in 2.1.3 Vibration isolation theory, suspending high rigidity STM scanning body on a low resonance frequency springs is the most effective and economical solution for vibration isolation. Based on the theory, we designed a set of suspension springs to reduce spring-STM system (Fig. 4-9) resonance frequency to roughly 1 Hz, and hung the system on an aluminum frame. The frame is mounted on the pneumatic Newport research grade pneumatic table in order to suppress the floor vibration, which is the most harmful vibration for the STM.. Fig. 4-9 Vibration isolation system of STM.. To reduce the natural resonance frequency of the system, we expand the frequency 1. 1. 𝑘. 𝑓0 as 𝑓0 = 2𝜋 𝜔0 = 2𝜋 √𝑚. (4.1),. 54.

(65) 1. 1. 𝑘. 𝑓0 = 2𝜋 𝜔0 = 2𝜋 √𝑚. (4.1). where k is the spring constant, m is the mass of the system. According to Hooke’s law,. ∆L =. 𝑚𝑔. (4.2). 𝑘. where ∆L is the elongation of the spring, g is the gravitational acceleration. Combine 𝑓0 =. 1 2𝜋. 𝜔0 =. 1 2𝜋. 𝑘. √. 𝑚. (4.1) and ∆L =. 𝑚𝑔. (4.2). 𝑘. into. 𝑓0 =. 1. 𝑔. 5.0. √ ≈ √∆𝐿 (𝑐𝑚) 2𝜋 ∆L. (4.3), 1. 𝑔. 𝑓0 = 2𝜋 √∆L ≈. 1. 𝑔. with g=9.8 m/𝑠 2 . 𝑓0 = 2𝜋 √∆L ≈. 5.0 √∆𝐿. 5.0 √∆𝐿. (𝑐𝑚). (4.3). (𝑐𝑚) (4.3) suggests the longer elongation of. spring provides the lower natural resonance frequency. If the elongation is 25 cm, the natural resonance frequency can be as low as to 1 Hz. For our 12.8-kg STM main body suspended on eight springs with k=0.0082 kgf/mm, the spring elongation can be estimated as 19.5 cm, lowering the natural resonance frequency down to 1.13 Hz. This relative low natural resonance frequency is presumably good enough for isolating most of external vibrations.. 55.

(66) 4.3 Seek for the best tip-etching parameter Tips are of significant importance for the measurement. Two most common material are Pt / Ir alloy and tungsten, and the tip can be fabricated by mechanical cutting or electrochemical etching. Although many different tip-etching parameters have been published, they actually vary from equipment to equipment, making this parameter-seeking work necessary. Parameters for tip fabrication contain material, dimensions of the wire, chemical solution concentration, etching voltage, cut-off voltage and cut-off timing. First, we found that it makes no detectable difference on the cut-off timing regardless of manually detaching wires or pressing a momentary switch. Second, in our experiment, a 0.25-mm-diameter tungsten wire is cut into roughly 0.7-cm-length clips before chemical etching in KOH. Hence, the rest uncertain parameters are etching voltage, cutoff voltage, and concentration of KOH. We started with 6M KOH and 6V etching voltage reported by AMRL, another lab experienced in STM tip fabrication. 4.3.1 6M KOH By fixing the etching voltage at 6V and comparing tip apexes produced under cutoff voltages at 4V, 2V, and 1V, the tip apexes are relatively 426 nm, 100 nm, and 36 nm in diameter (Fig. 4-11). The smaller cut-off voltage makes the sharper tip apex. However, too small cut-off voltage leads to a broken and torn tip apex because the bottom part’s gravity outweighs shear force caused by etching. It prolongs and tears the tip end (Fig. 4-10). For this reason, we fixed the cut-off voltage at 2V, comparing tips produced under etching voltages at 6V, 4V, 2V, and even 1V. However, these tips shared two common weakness: 1. Tips are severely oxide. 2. The tip-etching process was too aggressive to maintain the tip quality. Therefore, we cannot think of better solution but dilute the concentration of KOH down to 4M, starting the second test.. Fig. 4-10 Over small cut-off voltage results in a broken and torn tip end .. 56.

(67) Fig. 4-11 Cut-off voltages are compared. 4V-426 nm [top]. 2V-100 nm [middle]. 1V-36nm [bottom].. 57.