analysis of resonant frequencies in tungsten tips for ...€¦ · roark's formulas for stress...

Analysis of Resonant Frequencies in Tungsten Tips for Application in STM

Gabriel Pak Arabia Mountain High School Advisor: Dr. Philip First

Side Project: STM Micrometer Replacement § Due to fatigue, the y-translating micrometer failed and needed

replacement § Car jack used to support, but does not allow for precise movement

of equipment § Designed, constructed and installed precision jack

Abstract § Scanning tunneling microscopes (STM) use an extremely fine tungsten

tip to produce quality images § During imaging a background frequency of approximately 400 Hz was

noticed that may produce noise or adversely affect image quality § COMSOL Multi-physics models were built to analyze eigenfrequencies of

various tip lengths to optimize tip dimensions § More detailed Solidworks models were constructed for further analysis

Introduction: Background § Dr. Phillip First research group uses a custom-built LEED/

Auger system that utilizes a STM for the purposes of imaging and understanding the physical properties of graphene

One-atom thick layer of graphite, which is extremely light (1 m2 = .77 mg), highly conductive, transparent and incredibly strong

Potential applications include:

-integrated circuits

-touch screens

-solar cells

-ultracapacitors

Introduction: Motivation for Graphene

Introduction: Motivation

§ What are possible reasons for one picture to be blurry compared to the other?

Introduction: Motivation

§ High quality images are essential in gathering accurate data in characterizing graphene

§ Tips with a low resonant frequency could produce low resolution images as quantum tunneling is spread to multiple atoms at different heights

§ MOTIVATION: optimize tip dimensions and explore mounting or fixture options to decrease resonance effects and minimize noise

Introduction: What’s Been Done? § No recent work has been in the field of resonant frequencies

in tungsten STM tips

Theory § STM uses current (flow of electrons) to tunnel through atoms

on the surface of samples to produce an image § The smallest uncertainties in equipment are magnified,

particularly the movement of the tungsten tip due to resonant frequencies

Theory § Resonance comes from the tendency for a system to

oscillate with a greater amplitude at certain frequencies given a small periodic driving force. These certain frequencies are the resonant frequencies of the system

§ Common example is the breaking of a wine glass given a frequency that matches the resonant frequency of the glass

§  In the case of the tungsten STM tips, if the resonant frequencies of the tips are found to be relatively low then that could be a cause of blurry or inaccurate images produced by the STM

Approach § Upon building a model, run a parametric sweep to gauge

trends in the relationship between frequency and various dimensional components

§ Vary different parameters to optimize tip dimensions to minimize affects of resonance

Experimental Work: COMSOL § COMSOL provides software for multi-physics modeling with

built in geometries, materials and solvers

Experimental Work: COMSOL § Using average dimensions of tips used in STM with a fixed

boundary at one end, a model is built § Relevant material properties for tungsten include:

§ Density = 17800 kg/m3 §  Young’s modulus = 3.6e11 Pa §  Poisson’s ratio = 0.27

Results: Frequency vs Tip Length

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

0 2 4 6 8 10 12 14 16

Freq

uenc

y (H

z)

Cone Length (mm)

Frequency of Various Length Cones

0.30 mm diameter

0.15 mm diameter

0.10 mm diameter

0.05 mm diameter

Results: Frequency vs Tip Length

§ As shown from the previous graphs, the frequency decreases as a power function of tip length

§ The lowest resonant frequencies observed are at the longer cone lengths for the given diameters

§ 400 Hz range reached with lengths of around 14 mm

Results: Frequency vs Tip Base Width

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

3.0E+04

3.5E+04

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Freq

uenc

y (H

z)

Cone Diameter (mm)

Frequency of Various Width Cones

Cone length 4mm

Cone length 8 mm

Cone length 12 mm

Cone length 16 mm

Results: Frequency vs Tip Base Width

§ As shown from the graph, the frequency increases linearly as a function of tip base width

§ With a low cone diameter (0.05-0.1 mm) and high cone length (16 mm), we find resonant frequencies of 323-552.5 Hz which is the range of the background frequency observed

Results: Changing Geometry § Using Solidsworks we more accurately modeled the tips to a tapered

shape where the taper begins at 1 mm and extends for 3 mm § Tapered Length = 3 mm, Resonant frequency = 32630 Hz

Results: Changing Geometry § Solidworks allows for a variety of geometries depending on

the tip being produced § The left shows a typical etched tip with imperfections along

the surface that affect the resonance § Figure on right shows an ideal tip with strong base and sharp

point

Results: Animated Model § Animated models showing the lowest resonant frequency

and simulated motion § Length = 4 mm, Resonant frequency = 28,621 Hz

Discussion::Significance § By establishing, minimum and maximum tip dimensions, the

amount of noise due to resonance can be reduced §  Overall, though resonance does not currently seem to be a

high contributing factor to image quality, the following guidelines are recommended to be followed to minimize such affects

§ MINIMUM WIDTH AT BASE: 0.2 mm § MAXIMUM LENGTH OF TIP: 4.0 mm

Conclusions § Resonance does not seem to be the main contributing factor

for the current tip dimensions but can play a role for lower resolution or distorted images if dimension recommendations are not followed

§ Tip etchers should take into account such dimensions when choosing which tips to work with

Recommendations for Future Work § Automating tip etching process that accounts for dimensions

and uses a current tracker to cut the voltage and stop etching when a sharp tip is created

§ Setting up a vertical orientation of the set up rather than horizontal to allow for gravity to help with the etching process

Classroom implications § Relating with current science research, particularly

introducing students to the nano-scale world and graphene § Nature of science discussion to set the stage for classroom

environment for the year (i.e. importance of uncertainty, precision)

§ Practical application of resonance in science research and

activity dealing with tuning forks to see the natural frequency of every object

Acknowledgements § Dr. Phillip First, Principle Instructor § Dr. Leyla Conrad, Assoc. Director, Education § Yuntao Li, Graduate Student Mentor § Di Chen, Graduate Student Mentor § STEP-UP Fellows

§  Bill Daly §  John Nice §  Kenny Patterson §  Karen Porter

§ Georgia Tech and the National Science Foundation

References § http://www.ieap.uni-kiel.de/surface/ag-kipp/stm/stm.htm § http://www.uta.edu/nano/facility.php?id=55&cat2=STM §  Z.Q. Yu, C.M. Wang, Y. Du, S. Thevuthasan, I. Lyubinetsky

“Reproducible tip fabrication and cleaning for UHV STM”, Environmental Molecular Science Laboratory and Institute for Interfacial Catalysis, Pacific Northwest National Laboratory

§ Roark's Formulas for Stress and Strain, 7th Edition, September 2001

§ M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust et al., A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors

Appendix I: Solver Check §  In order to check for accuracy of the solver, the results for a

simple cantilever was compared with a basic equation

COMSOL   Calculated  Rod Length

[m]  Frequency

[Hz]  Frequency

[Hz]  0.003   1.21E+04 1.19E+04  0.004   6.84E+03 6.71E+03  0.005   4.38E+03 4.29E+03  0.006   3.04E+03 2.98E+03  0.007   2.23E+03 2.19E+03  0.008   1.71E+03 1.68E+03  0.009   1.35E+03 1.33E+03  0.01   1.09E+03 1.07E+03  

𝑓= 𝑡/2𝜋𝐿↑2  √𝐸/𝜌  

t   Beam thickness  L   Beam Length  E   Young's modulus  ρ   Mass density  

0.00E+00

2.00E+03

4.00E+03

6.00E+03

8.00E+03

1.00E+04

1.20E+04

1.40E+04

0 0.002 0.004 0.006 0.008 0.01 0.012

Freq

uenc

y [H

z]

Beam Length [m]

Comparing COMSOL Solver with Calculated Frequencies

COMSOL

Calculated

Appendix II: Table of Values Diameter: 0.30 mm   Diameter: 0.15 mm  Diameter: 0.10 mm  Diameter: 0.05 mm  

Cone Length (mm)   Frequency (Hz)   Frequency (Hz)   Frequency (Hz)   Frequency (Hz)  

2   95812   48360.04   32335.1   15987.6  3   50758.76433   21556.73   14452   7536.4  4   28621.73168   12206.52   7993.8   4355.8  5   18337.32955   7703.28   4869.7   2879.5  6   12746.01968   5225.18   3376.9   2062.9  7   9368.126   3862.02   2533.4   1571.7  8   7173.770072   2825.58   1994.9   1244  9   5672.810903   2251.208   1634.1   1021.7  

10   4595.515316   1846.3   1349   860.9  11   3150.1   1550.6   1122.5   740.4  12   2612.6   1329.9   949.5   642.6  13   2208.5   1161.5   815.4   569  14   1931   1025.1   708.9   404  

Cone Length: 4 mm  

Cone Length: 8 mm  

Cone Length: 12 mm  

Cone Length: 16 mm  

Cone Diameter (mm)   Frequency (Hz)   Frequency (Hz)   Frequency (Hz)   Frequency (Hz)  0.05   3989.7   1104.9   528.8   322.9  0.1   7993.8   1994.9   949.5   552.5  

0.15   12206.5   2825.6   1329.9   793.9  0.2   16167.5   3996.9   1688.4   997.4  

0.25   20172.5   5073.3   2126.3   1195.8  0.3   24180   6103.3   2612.6   1412.8  

0.35   28157.7   7108.2   3145.1   1687.5  0.4   32142.9   8083.8   3613   1998.4