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A dilution refrigerator based scanning tunneling microscope for high resolution nanoscale spectroscopy Delaney, Robert 2016

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A Dilution Refrigerator BasedScanning Tunneling Microscope forHigh Resolution NanoscaleSpectroscopybyRobert DelaneyB.Sc., The University of British Columbia, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2016c© Robert Delaney 2016AbstractThis thesis describes the design, construction and fabrication of a completeultra-high vacuum (UHV) Dilution refrigerator based scanning tunnelingmicroscope (STM). Data taken at a base temperature of 114 mK is pre-sented and electrical, mechanical and vacuum design features are describedfor both the STM and the UHV system. Topographic images and spec-troscopy on Au(111), graphene and other materials are presented to detailthe performance of the STM. Techniques involving coherence and finite el-ement analysis are used to address acousto-mechanical interaction betweenthe STM and an acoustic room mode. The design and fabrication of an elec-tron beam heater sample plate and complete UHV sputtering and annealingstage are presented.iiPrefaceThis thesis is based upon the design and use of a dilution refrigerator basedscanning tunneling microscope in the laboratory for atomic imaging research(LAIR).Ben Macleod completed the first design of the Pan style STM Head, anddiscovered the influence of the acoustic room mode on the inertia block.While Yan Pennec and Graeme Adamson were responsible for the design ofthe UHV system.The redesign and construction of the current version of the STM headin Chapter 3 was completed by myself and Dr. James Day. I designed theUHV sputtering and annealing station in Chapter 4, but with significantinput from Dr. James Day, Pinder Dosanh and Dr. Sarah Burke.In Chapter 5 the STM results were taken by myself and James Day,while I was responsible for all calibrations and data processing.The design of the RF tight low-pass filter boxes in Chapter 6 was com-pleted by Damien Quentin, and the entire implementation of the commercialfilters we used was based upon measurements and research he performed oncustom low pass powder based filters.All measurements and calculations in Chapter 7 were performed by my-self, but with input from Ben Macleod.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Low Temperature Scanning Tunneling Microscopy . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Principle of Operation of a Scanning Tunneling Microscope . 21.3 Dilution Refrigeration . . . . . . . . . . . . . . . . . . . . . . 91.4 Low Temperature Scanning Tunneling Microscopy . . . . . . 122 Construction of the STM Head . . . . . . . . . . . . . . . . . 142.1 Redesign of the STM Head . . . . . . . . . . . . . . . . . . . 142.2 Coarse Approach Motors . . . . . . . . . . . . . . . . . . . . 202.3 Capacitive Sensor and Coarse Approach . . . . . . . . . . . . 222.4 STM Grounding . . . . . . . . . . . . . . . . . . . . . . . . . 233 Dilution Refrigerator Performance . . . . . . . . . . . . . . . 283.1 Performance of UBC DR-STM . . . . . . . . . . . . . . . . . 303.1.1 Still Calibration . . . . . . . . . . . . . . . . . . . . . 324 Design and Construction of an Ultra-High Vacuum SamplePreparation Stage . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 The Need for a Clean Surface . . . . . . . . . . . . . . . . . 374.1.1 Annealing . . . . . . . . . . . . . . . . . . . . . . . . 374.1.2 Sputtering . . . . . . . . . . . . . . . . . . . . . . . . 38iv4.1.3 Design of a Sputtering and Annealing Stage . . . . . 384.2 Sample Plate Construction . . . . . . . . . . . . . . . . . . . 424.3 Sample Plate Performance . . . . . . . . . . . . . . . . . . . 435 STM Results and Data . . . . . . . . . . . . . . . . . . . . . . 465.1 Calibration of STM . . . . . . . . . . . . . . . . . . . . . . . 465.1.1 Calibration of Z-piezo with Au(111) . . . . . . . . . . 465.1.2 Calibration of the XY Piezos with Au(111) . . . . . . 485.1.3 Calibration of the XY Piezos with Highly OrientedPyrolytic Graphite . . . . . . . . . . . . . . . . . . . 495.2 Graphene on SiC . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 Implementation of Lowpass Filters for High Resolution Spec-troscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 Towards Reducing Tunnel Junction Noise . . . . . . . . . . 657.1 Reducing Motion Between the Tip and Sample via VibrationIsolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.2 Spectral Density and Coherence . . . . . . . . . . . . . . . . 667.3 Acceleration and Coherence Measurements . . . . . . . . . . 677.4 Modeling of Acoustic Response of the Room . . . . . . . . . 717.4.1 Characteristic Frequencies of the Room . . . . . . . . 717.4.2 Acoustic Forcing of the Inertia Block . . . . . . . . . 797.4.3 Mechanical Noise in Our STM Experiments . . . . . 838 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A Guidelines for Cooling Down the DR-STM . . . . . . . . . 96B Tuning the Block via Acceleration Measurements . . . . . 100vList of Tables2.1 Thermal conductivity and specific heat at 4.2K for commonlyused cryogenic materials. . . . . . . . . . . . . . . . . . . . . 183.1 Comparison of selected Dilution Refrigerator and 3He sorp-tion pump based STMs and their differing temperatures. Teis the electron temperature. . . . . . . . . . . . . . . . . . . 295.1 List of piezo calibration coefficients as a function of temper-ature for the current DR-STM. . . . . . . . . . . . . . . . . . 497.1 Characteristic eigenfrequencies as calculated by COMSOL.The block and the aluminum floor have a large effect on boththe mode shape and frequency of the room eigenfrequencies. . 77viList of Figures1.1 Basic schematic of an STM feedback loop . . . . . . . . . . . 31.2 Demonstration of how the density of states gets convolvedwith −dF (E−eV )dV when making STS measurements . . . . . . 81.3 Schematic of the DR-STM’s dilution refrigerator . . . . . . . 112.1 Exploded view of redesigned tip holder. See the scale bar onthe left to get an idea of the size of the tip assembly. Theremovable tip holder can nominally be pulled out of the tipreceptacle during normal operation of the STM to change thetip. The tip receptacle can be unthreaded from the piezotube(when the UHV chamber is vented) if maintenance on theball bearings or leaf springs is required. . . . . . . . . . . . . 162.2 Side by side views of the old and new STM heads. . . . . . . 172.3 Block diagram of coarse piezo electronics. An initial trape-zoidal waveform is generated by the NI PCI-6229 DAQ cardand amplified to 220V by high voltage amplifier. The trape-zoidal waveform is then fed into the VHSRD1 piezo driverthat essentially chops the waveform in half allowing the volt-age to drop or rise with a very high slew rate for the slipportion of the waveform. Six separate waveforms are deliv-ered to the coarse piezos, and all timing of the waveforms iscontrolled by both the DAQ card and an Arduino microcon-troller. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4 Diagram of the capacitive sensor used for determining the zheight of the tip. . . . . . . . . . . . . . . . . . . . . . . . . . 242.5 Plot of capacitive encoder data and fits. . . . . . . . . . . . . 252.6 Schematic of electronics used for STM measurement and thegrounding scheme that provides the lowest tunneling currentnoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.7 Zero bias anomally arising from Nanonis controller . . . . . . 27vii3.1 Plot showing the lack of correlation between STM base tem-perature and electron temperature at low temperature. . . . . 303.2 The STM cooling after placing a 300 K sample into the STM.It takes about 4 hours to cool the sample from 300K to 5 K.The large increase in temperature is due to the warm samplebeing placed into the STM. . . . . . . . . . . . . . . . . . . . 313.3 The new STM head cooling from 5 K to the base temperatureof 150 mK. You can see that it takes ≈ 4 hours to get from5 K to the base temperature. . . . . . . . . . . . . . . . . . . 323.4 The old STM head with a large low thermal conductivitymacor tube being cooled from 300 K straight down to dilutiontemperature. You can see that the sample takes ≈ 5.5 hoursto cool to from 300 K to 5 K, it takes almost 12 hours to coolthe sample from 300 K to a base temperature of 475 mK . . . 333.5 Cooling down the sample to the absolute base temperatureof 114 mK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.6 There is a clear minimum temperature of the mixing chamberat 170 µmol s−1 as a function of flow rate . . . . . . . . . . . 353.7 On the STM an increase in flow rate (increase in still tem-perature) only corresponds to a greater STM temperature.Thus there must be a heat leak between the STM and thestill that is cancelling out the additional cooling power fromthe mixing chamber . . . . . . . . . . . . . . . . . . . . . . . 364.1 Full heater assembly. By attaching the electrical wiring tothe upper translation stage that has limited (< 15 cm of mo-tion) the wiring could easily be attached, freeing up the x-arm to move through it’s ≈ 1.5 m travel. Spring loaded con-tacts pivot stainless steel contacts into the four molybdenumelectrical contacts on the sample plate allowing for multipleconfigurations of heating and temperature measurement viathermocouple. . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Sample boat portion of heater assembly. The sample getstwist locked into the sample boat where four 316SS pivotcontacts engage with the four molybdenum contacts on thesample plate. The spring loaded electrical contacts push onthe pivot contacts to ensure solid electrical contact to thesample plate during heating. . . . . . . . . . . . . . . . . . . 404.3 Custom built heater sample plate. . . . . . . . . . . . . . . . 41viii4.4 Testing the sample heater in a separate vacuum chamber be-fore installing it in the UHV chamber. A thermocouple wasattached directly to the sample and the sample heater wasbeing used in radiative heating mode. The blue curve showsa smaller diameter of filament failing before getting to therequired temperature of 600 ◦C. The red curve shows theminimum time it can take to get the sample up to it’s highesttemperature–about 30 minutes. . . . . . . . . . . . . . . . . 444.5 Testing the sample heater in the UHV chamber on a coppertest piece. Here the sample is glowing and at well over 700 ◦C.When the sample is at 600 ◦C it is not possible to see thesample glowing. . . . . . . . . . . . . . . . . . . . . . . . . . . 455.1 A large scale image of Au(111) clearly showing many atomicterraces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2 Au(111) clearly showing many atomic terraces and the 22 ×√3 reconstruction. The reconstruction shows up as the faintdouble striped features that are mainly running vertically inthis image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.3 Highly oriented pyrolytic graphite; first test of new STM atroom temperature. . . . . . . . . . . . . . . . . . . . . . . . . 505.4 Fourier transform of figure 5.3, used to calibrate the STM at300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.5 Calibration of piezotube as a function of temperature. Thelarge decrease in piezotube displacement at liquid helium tem-peratures matches well with the manufacturer’s specifications. 525.6 Graphene on SiC atomic resolution . . . . . . . . . . . . . . . 545.7 Graphene on SiC showing moire pattern as well as many ad-sorbates that are likely both underneath and overtop of thegraphene. As can be seen from the many lines/tip changes inthe image the tip was not very stable of the duration of thismeasurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.8 Comparison between lock-in amplifier and numerical deriva-tive. The numerical derivative was Gaussian smoothed withσ = 15 mV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.9 Typical spectroscopy showing the Au(111) surface state. Thiswas measured using numerical dIdV with a Gaussian smoothingparameter of σ = 15 mV . . . . . . . . . . . . . . . . . . . . . 59ix6.1 Transmission function of high voltage filters. The attenuationis flat because the cutoff frequency is ≈ 5 MHz for these filtersand the network analyzer can only measure above 10 MHz.Forthese filters the transmission was measured with water bottlesplaced inside the RF tight box. . . . . . . . . . . . . . . . . . 616.2 Transmission function of low voltage filters. The attentuationis flat because the cutoff frequency is ≈ 1 MHz for these filtersand the network analyzer can only measure above 10 MHz. . 626.3 Opened filter box showing the filtered and unfiltered sides ofthe box along with all wiring going to filters. The filters arescrewed into the dividing plate in the middle of the box. Thisseparates the unfiltered side of the box from the filtered sideof the box. Shielded mil connectors are used on either side ofthe box. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.1 Power spectral density of block acceleration in the low fre-quency regime. . . . . . . . . . . . . . . . . . . . . . . . . . . 687.2 Linear spectral density of tunneling current with tunnelingfeedback engaged, 20 Hz noise is generally the only remainingimportant noise source that shows up in the tunneling currentafter the rebuild of the STM head . . . . . . . . . . . . . . . 697.3 Coherence between the current and the block acceleration inthe North-South direction in the low frequency regime. Notethe large broad peak at 19 Hz; suggesting that the motion inthe North-South axis at this frequency is primarily responsi-ble for the noise in the tunneling current at ≈ 20 Hz . . . . . 727.4 Coherence between the current and the block acceleration inthe East-West direction in the low frequency regime. . . . . . 737.5 Coherence between the current and the block acceleration inthe up-down direction in the low frequency regime. . . . . . . 747.6 Model of the room, block and STM that was used for FEAcalculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.7 The lowest eigenfrequency of the room is 15.15 Hz and actsprimarily in the up-down direction. . . . . . . . . . . . . . . . 767.8 The second lowest eigenfrequency of the room is 19.65 Hz andacts primarily in the North-South direction. . . . . . . . . . . 787.9 Top view of hexagonal inertia block. Horizontal eigenfrequen-cies will couple to move the block in both the North-Southand East-West directions . . . . . . . . . . . . . . . . . . . . 80x7.10 Calculated acoustic force on the block in the up-down direc-tion (right axis, red line) along with the coherence betweenblock acceleration in the up-down direction and the tunnelingcurrent. For additional comparison the relevant eigenfrequen-cies are plotted as dashed magenta lines. . . . . . . . . . . . . 817.11 Calculated acoustic force on the block in the East-West di-rection (right axis, blue line) along with the coherence be-tween the block acceleration in the East-West Direction andthe tunneling current. For additional comparison the relevanteigenfrequencies are plotted as dashed magenta lines . . . . . 827.12 Calculated acoustic force on the block in the North-South di-rection (right axis, blue line) along with points of large coher-ence along with points of large coherence between the blockacceleration in the North-South direction and the tunnelingcurrent. For additional comparison the relevant eigenfrequen-cies are plotted as dashed magenta lines . . . . . . . . . . . . 847.13 Comparison between calculated and measured acceleration ofthe block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.14 There is a clear shift in the 20 Hz noise peak showing up thetunneling current noise spectra (amplitude spectral density)when the heatswitch is engaged and stiffens the DR insert. . . 867.15 There is a well defined phase relation between the tunnelingcurrent and the block acceleration in the North-South andEast-West directions around approximately 18-19 Hz. . . . . 87B.1 Comparison of block floated properly vs block partially rest-ing on its levelators . . . . . . . . . . . . . . . . . . . . . . . . 101xiAcknowledgementsFor my entire MSc (and part of my undergrad) I worked directly with, orin consultation with, James Day on the design, construction, debugging,running and operation of the DR-STM. He was always available to providea critical eye when designing something new or debugging instruments, whilealso being incredibly supportive and understanding at the same time.Pinder Dosanjh has years of experience with low temperature physicsand a large portion of his advice went, in some way or another, into theredesign and construction of the STM. Even with his busy schedule he alwaysmade time to provide his ideas for designs, construction techniques andtroubleshooting.Harish Gautam was always happy to give advice on machining my ownparts, and machined many of the parts designed in this thesis that requiredthe use of a CNC mill or lathe.Ben Macleod did the initial design of the STM head, all of the work onmeasuring the acoustics of the room and the performance of the vibrationisolators. In many ways I have simply worked to expand upon the thingshe has already done for the DR-STM project, and he was one of the mainpeople driving this project forward.Thanks to Sarah Burke for always setting aside time from her busyschedule for James and I to ask her pretty much anything we could thinkup about STM, UHV and low temperature physics.I’d like to acknowledge the NSERC CREATE QuEST program, and theQuantum Matter Institute for providing funding for my graduate studies.My supervisor, Doug Bonn, has been a pleasure to work with, and pro-vided me with a great combination of freedom to pursue my ideas, whilealso providing lots of guidance.Thanks to Tanya for all of her love and support, but also for lots of helpwith physics and engineering.Finally, I’d like to thank the entire current LAIR group for making thepast couple of years in the lab a great supportive place to work and doresearch. It has really been enjoyable to work with all of you. Thanks forall of the advice, help and shared cryogens!xiiChapter 1Low Temperature ScanningTunneling Microscopy1.1 IntroductionSpectroscopy is a very old field that has been around since it was discov-ered that a prism was capable of dispersing light into a rainbow of colours.With the advent of quantum mechanics it was postulated by Einstein thatlight was actually formed by wave packets called photons and if one is ableto measure the wavelength of this photon then the energy of the photon isdetermined by E = hcλ . If the photon is emitted as the result of an atomictransition then the change in energy of the electron can be mapped ontothe wavelength of the photon, and from this more modern techniques ofspectroscopy were born. Many optical techniques can be used to achievevery high spectroscopic (energy) resolution, sometimes limited only by thelifetime of the energy state, but they are always limited spatially by thewavelength of light. Thus optical spectroscopy must average over a diffrac-tion limited area which can simply average out or obscure the rich physicsthat occurs on the nanoscale.Scanning tunneling microscopy was invented in 1982 by Binning andRohrer [1] and relies on quantum mechanical tunneling of electrons throughan atomically sharp tip to make topographic maps of conducting or semi-conducting surfaces with sub-A˚ngstrom resolution. Furthermore, it providesaccess to spectroscopic information–specifically the local density of states(LDOS)– with sub nanometer resolution, and energy resolution limited onlyby the temperature of the tunneling junction and the lifetime of the energystate. In the past 30 years the scanning tunneling microscope (STM) hasbecome a ubiquitous tool for studying the topography and spectroscopy ofcondensed matter systems. It has been used on a wide variety of systemsthat range from confirming the existence of surface states [2] in metals suchas gold, providing strong evidence for the symmetry of the superconductingorder parameter of unconventional superconductors [3, 4] and many other1phenomena.This thesis describes the design, construction and commissioning of ascanning tunneling microscope (STM) that is attached to a dilution refrig-erator capable of cooling the microscope to a base temperature of ≈ 120mK and applying up to 7 T magnetic fields to the sample. The goal of thisSTM is to make high resolution (< 100 µeV) spectroscopic measurements onnovel materials such as iron pnictide superconductors, with sub-A˚ngstromresolution.There are several different limits on the resolution of an STM. The spatialresolution is only fundamentally limited by the size of the tunneling junction,and this resolution can be highly variable. With a tip that cannot maintaina stable configuration one cannot resolve anything, and it is not possible tomeasure any properties of the surface. In contrast a tip with a single atomsitting stably on the end of it can provide resolution on the order of the sizeof the atom: about 1 A˚. In reality this resolution is highly dependent uponthe orbital character of the atom on the tip. An s-wave orbital has a largerspatial extent and will not provide exceptionally high resolution, while anatom with d-wave orbital character, where a sharp lobe of the orbital jutsout, will have a much smaller spatial extent and can sometimes providesub angstrom resolution [5]. On metals it is extremely common (assumingyou have a very stable STM) to apply a short voltage pulse to the tip andachieve atomic resolution [6]. It is hypothesized that this occurs due toreconfiguration of the atomic orbital on the end of the tip to a sharper d-wave state. Thus, once a single atom is sitting on the end of the tip thespatial resolution of the STM is only limited by the quantum mechanicalnature of atomic orbitals and their spatial extent. Spectroscopic (energy)resolution is limited fundamentally by the thermal distribution of electrons(as dictated by the Fermi-Dirac distribution), the electronic noise at thetunnel junction and can also be fundamentally limited by the lifetime of theenergy state. This is why great effort has been made to reduce/eliminatethese sources of noise by both cooling the STM to millikelvin temperaturesand filtering out as much electronic noise as possible.1.2 Principle of Operation of a ScanningTunneling MicroscopeThe basic principle of operation is that a sharp metallic tip is brought towithin less than a nanometer of the surface of the sample. A small voltageis applied between the sample and tip on the order of mV up to a couple of2Feedback LoopCurrentAmplifierFigure 1.1: Basic schematic of an STM feedback loopV. This causes electrons to tunnel through the vacuum barrier between thetip and sample. A tunneling current can be measured, and is exponentiallydependent on the tip sample separation, thus a slight variation in surfaceheight yields a large change in tunnel current. Typically a PID controller isused to adjust the height of the tip above the sample to hold the tunnelingcurrent constant. The tip is then rastered over the surface in order to mapout the surface topography by recording the height of the tip.To achieve the required spatial positioning of the tip, piezoelectric crys-tals are used to control the motion of the tip, and a high gain transimpedanceamplifier with G = 109 is used to measure the tunneling current as shown infigure 1.1. Due to the 1-1000pA tunneling currents that typically must bemeasured and the high gain of the amplifier, both grounding and filteringof the STM electronics are extremely important for high resolution STMmeasurements. Furthermore, due to the exponential dependence of the tun-neling current on z-height, it is also very important to eliminate or dampout all outside sources of vibration that can affect the tip-sample separation.An equation for one dimensional tunneling was first written down byBardeen in 1961 [7] using perturbation theory. The use of pertubation theoryis valid when the tip (sample) is far enough away from the sample (tip) thatit’s wavefunction is only slightly changed by the presence of the sample (tip).3It was originally applied to uniform planar tunneling junctions, but if theSTM tip is assumed to be symmetric it can be applied equally accurately totip-sample tunneling junctions. The tunneling current is given by:I =4pieh¯∫ ∞−∞|M |2ρtip(E + f )ρsample(E − eV + f )[f(E − eV + f , T )− f(E + f )]dE(1.1)M =h¯22m∫junction(ψ∗sample∂ψtip∂z− ψ∂ψ∗sample∂z)dS (1.2)where ρtip and ρsample are the tip and sample densities of states respectively.|M |2 is the transmission function which decays exponentially as a functionof Z. Since the work function of a metal is typically on order of 3-10 eV [8],and a typical tip-sample bias is < 100 meV for our experiments it is to beexpected that the transmission function is roughly constant over the samplebias range of interest. If one wants to record STM data at a bias of up toseveral volts (as is commonly done when measuring molecular orbital states[9]) then the transmission function can vary significantly over that energyrange.Since the tip is metallic, its density of states is constant over severalelectron volts surrounding the Fermi level, so it is possible to remove ρtipfrom the integral. In practice the tip is not always metallic and can even beinsulating, but we shape the tip and measure its density of states until it isactually metallic. This is a good assumption so long as the tip density ofstates remains constant over the course of the measurement. This assump-tion is violated if the tip changes configuration during a given measurement.Whenever a tip reconfiguration occurs the density of states will generallyshift to a different constant. Thus if one is imaging or performing spectro-scopic measurements a discontinuous jump will be seen in the image or datadue to the tip change. Much effort in STM is put into maintaining the samestable tip for long periods of time so that the density of states of the tiptruly remains constant over a long measurement period. Vibration isolationfor the purpose of keeping the tip-sample separation constant is importantnot only for reducing current noise, but also for being able to maintain thestability of the tip, since a tip that varies in height with respect to the sur-face is more likely to drift close enough to the surface to interact with it andmodify the structure of the tip.It can also be useful to simplify further, and treat the tunneling matrixelement (transmission function) as constant. This approximation is not4uniformly a good one, and is always a poor approximation when measuringat voltages that begin to approach the work function of the tip or sample(several V). However, this is not usually a problem since the high energyresolution afforded by a DR-STM is usually only a benefit for energy levelsclose to the Fermi energy. This can be explained with Fermi Liquid theory(proposed by Landau [10]) where the lifetime of a quasiparticle–a particlethat is described with a single particle wavefunction that is dressed by it’sinteractions with other particles– is given by:1τ∝ (k − f )2 (1.3)This is true in almost all metals and is based upon a phase space argu-ment. For T < TFermi (which is any temperature for a solid metal since eventhe melting temperature is well below the Fermi temperature in a metal)electrons will behave similarly to how they behave at low temperature. Moststates below the Fermi energy will be occupied, while most states above theFermi energy will be unoccupied. For an excited electron just above theFermi surface, if it scatters with an electron from below the Fermi surfacethen at very low temperature (T << TFermi) the energy levels of the twoelectrons after scattering must be very close to the Fermi surface by conser-vation of energy. Thus scattering can only occur in a narrow energy bandsurrounding the Fermi energy, reducing the total phase space for scattering,exactly equivalent to increasing the lifetime of the particle which can be seenfrom the energy-time uncertainty relation:∆E∆T ≥ h¯2(1.4)Except in the case of strongly correlated systems or topologically pro-tected states [11] where Fermi liquid theory breaks down, the lifetime ofan excited state is usually only long enough to require exceptionally highenergy resolution very close to the Fermi level. Thus for all systems obeyingFermi liquid theory, approximating the transmission function as constantand measuring only very close to the Fermi level will be a very good approx-imation.In the constant transmission approximation this gives:I ∝∫ ∞−∞ρsample(E − eV + f )[f(E − eV + f , T )− f(E + f )]dE (1.5)From 1.1 we can make several approximations that reveal the spectro-scopic power of STM and the factors that limit its resolution. STM is always5referenced to the the Fermi level of the sample. The Fermi-Dirac distribu-tion becomes increasingly like a step function around the Fermi-level at lowtemperature. Since we usually operate our STM at a maximum temperatureof about 10 K the Fermi-Dirac distribution becomes well approximated bya step function:F (E, T, f ) =1exp (E − f )/kBT + 1 (1.6)F (E, T, f ) ≈{1 E ≤ f0 E ≥ f(1.7)Where the sharpness of the approximate step function is determined bythe thermal broadening kBT . Carrying out the step function approximationgives:I ∝∫ ∞0ρsample(E + f )dE−∫ ∞−eVρsample(E + f )dESubtracting the two common parts of these integrals gives:I ∝∫ −eV0ρsample(E − eV + f )dE (1.8)Shifting bounds to give a more intuitive representation of the tunnelingcurrent gives:I ∝∫ −eV+ffρsample(E)dE (1.9)This means when we apply a positive or negative voltage to the samplewith respect to the tip we are either the removing electron or holes of en-ergy e|V | away from the Fermi level. At finite temperature this removal ofelectrons or holes gets smeared out on order of energy kBT , and also by anyother remaining electronic noise in the system.Using 1.9 we can see that the fundamental theorem of calculus gives:dIdV∣∣∣∣−eV∝ ρsample(f − eV ) (1.10)Thus we can determine the local density of states of the sample with sub-A˚ngstrom spatial resolution, and energy resolution that is only limited by6the temperature of our tip-sample junction. If we approach zero temperature1.10 approaches the actual (k-space integrated 1 ) local density of states ofthe sample.To get an idea of what the actual thermal broadening is we can go backto 1.1 and differentiate it:dIdV=4pie2h¯|M |2∫ ∞−∞ρtip(E+f )ρsample(E−eV+f )(−df(E − eV + f , T )dV)dE(1.11)where the Fermi-Dirac derivative is given by:df(E − eV + f , T )dV=βeeβ(E−eV+f )(eβ(E−eV+f ) + 1)2(1.12)At zero temperature the derivative of the Fermi-Dirac distribution 1.12goes to:limT→0df(E − eV + f , T )dV= limT→0βeeβ(E−eV+f )(eβ(E−eV+f ) + 1)2= δ(E−eV +f ) (1.13)At zero temperature dIdV is directly proportional to the density of states.At finite temperature the density of states is broadened by the Fermi-Diracderivativedf(E − eV + f , T )dV. One can estimate the amount of thermalbroadening by finding the full width half maximum of 1.12 which gives:σthermal ≈ 3.5kBT (1.14)Thus at a temperature of 4.2 K you can get an energy resolution at best of1.2 meV, while at 50 mK one can achieve 15 µeV resolution, allowing accessto physics on completely different energy scales. So great effort has been puttowards lowering the temperature of STMs to improve energy resolution byorders of magnitude.A classic example of how thermal broadening can influence the resultsof STM measurements is the superconducting gap of a clean BCS supercon-ductor [7]. Aluminum is a common example with a superconducting criticaltemperature of 1.2 K, which at T = 0 corresponds to a gap size of 176 µeV.As a result, we would like to see the spectroscopic shape of features that areon the order of 100 µeV, which would be impossible at higher temperatures.1The exact weighting of different k-states in integration depends on the symmetry ofthe wavefunctions of the tip and sample and is always largely weighted to the Γ point atthe center of the first Brillouin zone7−600 −400 −200 0 200 400 600Energy µeV0246810121416Densityofstates(A.U.)BCS DOS for AluminumFermi-Dirac Derivative, T= 50mKFermi-Dirac Derivative, T= 500mKFermi-Dirac Derivative, T= 1K(a) Gap Density of states at T=0 displayed along with the normalizedFermi-Dirac derivative at T = 50 mK . These two functions get con-volved together when measuring the differential conductance at finitetemperature−600 −400 −200 0 200 400 600Energy µeV0246810121416Densityofstates(A.U.)BCS DOS for AluminumT = 50.0mKT = 500.0mKT = 1.0K(b) Gap density of states as measured by STM at various tem-peratures. Note the large amount of broadening of the mea-sured density of states as temperature increases.Figure 1.2: Demonstration of how the density of states gets convolved with−dF (E−eV )dV when making STS measurements8Figure 1.2b simulates the broadening of the density of states that occursat finite temperature. This demonstrates how sharp spectroscopic featurescan be masked by thermal noise, and thus decreasing temperature will in-crease resolution of the STM for spectroscopic measurements.Thus the benefits of low temperature dilution temperature STM (DR-STM) are two-fold. Firstly, the fundamental spectroscopic resolution is im-proved by several orders of magnitude. Secondly, physics that only occurson temperature scales well below 1 K such as heavy fermion superconduc-tivity, quantum Hall effect, and topologically protected systems all becomepossible systems for measurement.1.3 Dilution RefrigerationLow temperature physicists love to point out that making things extremelycold is one of the few things that humans are better at than nature. Thecosmic microwave background sits at a balmy 2.75 K [12], while simplyhooking up a pump and reducing the pressure of helium gas above a bath ofliquid helium can get to a temperature of ≈ 1 K. If you want to go to evenlower temperatures the next step is probably to attach your experiment toa dilution refrigerator. Dilution refrigeration is a technique that relies onthe quantum mechanical properties of mixtures of 3He and 4He. Since 3Henuclei are fermions while 4He nuclei are bosons, they behave very differentlyat low temperatures.At low temperature the behavior of fermions is dictated largely by thePauli exclusion principle causing particles to mainly fill energy levels upto the Fermi energy, with only a small deviation from this due to thermalexcitations. In contrast, at low temperatures bosonic 4He nuclei will tendto gravitate towards the lowest energy state. This is why pure 4He enters abosonic superfluid state where the 4He nuclei cannot scatter off the walls ofa tube if they are travelling below a critical velocity [13].At high temperatures it is possible for 4He and 3He to mix spontaneously,but as temperature is lowered below the λ point at 2.2 K bosonic 4He nucleiwill tend towards a superfluid state where 4He has zero viscosity. In contrastfor 3He the fermionic atoms will eventually form Cooper pairs and also entera superfluid-like state. The opposite quantum nature of 3He and 4He makesthem immiscible below 870 mK and the two isotopes spontaneously separateinto two phases.This separation takes two forms, a 3He-rich phase that is almost entirely3He and a dilute phase of 6.6%3He and 93.4%4He. Since 3He is lighter9than 4He the 3He-rich phase sits on top of the dilute phase. The dilutionrefrigerator operates by forcing 3He across the phase boundary. This phasetransition, or mixing of the two phases requires energy, which is taken fromthe walls of the mixing chamber pot that holds the two 3He-rich and dilutephases and causes cooling of the mixing chamber.Forcing the 3He-rich phase across the phase boundary into the 3He-poorphase (dilute phase) is done by heating and pumping on the still pot, causing3He to evaporate from the still. The evaporation of 3He from the still createsan osmotic pressure between the still and the mixing chamber, causing more3He to leave the dilute phase allowing 3He to cross the phase boundaryand create more useful cooling power. Silver-sintered heat exchangers withenormous surface areas efficiently transfer heat from other parts of the fridgeto the mixing chamber. Figure 1.3 shows a general schematic of our fridge.Note that the entire dilution refrigerator is immersed in a bath of liquid 4Heat 4.2 K. Gas is then sent in through a Joule-Thompson expansion stagewhere it is pre-cooled to 1.5 K. The gas is then cooled by heat exchangerswith the still (which is cooled by evaporating 3He) and then enters themixing chamber where dilution occurs. The exact details of the pre-coolingmechanism and heat exchange in fridges can vary, but the principle of forcing3He across the phase boundary is always used.A dilution refrigerator’s effective cooling power and temperature willdepend on how well the mixing chamber is thermally decoupled from itsenvironment, and also the rate at which 3He is forced across the phaseboundary. Radiative coupling and thermal conduction both can serve asheat leaks to counteract the cooling from the mixing chamber. Typicallydilution refrigerators have several poorly thermally coupled stages that areconnected by thin wall, low thermal conductivity stainless steel tubes. Theseusually consist of a 4.2 K stage that is thermalized to the liquid heliumbath, a 1 K stage which contains the still and cools the radiation shieldthat is thermalized to ≈ 1 K. The radiation shield surrounds the dilutionrefrigerator and all things attached to it to protect it from 4 K radiation.This is extremely important due to the Stefan-Boltzmann law in which theemmissive power is given by:j = σT 4 (1.15)Thus radiation at 4 K has 256 times more power than radiation at 1 K,and can be a significant source of heating if exposed to the mixing chamber.10StillMixingChamberJouleThompsonImpedanceHe-3 gas returnsto pump for recirculationHe-3 gas sent in at ~300 mbarfrom circulation pumpFigure 1.3: Schematic of the DR-STM’s dilution refrigerator111.4 Low Temperature Scanning TunnelingMicroscopyIn section 1.2 it was shown that the spectroscopic resolution of a scanningtunneling microscope is fundamentally limited by the temperature of thetunnel junction. So attaching an STM to a dilution refrigerator and mea-suring at 50 mK should instantly achieve 15 µeV resolution! Unfortunatelythings are never this simple. A dilution refrigerator contains a complexseries of tubes and pumps that generate significant amounts of vibrationand acoustic noise. Furthermore, due to the interfacial thermal resistance(Kapitza resistance [14]), that increasingly impedes heat transport at lowtemperature, the microscope must be attached rigidly with as much force aspossible to allow for thermal conduction of heat out of the microscope. At-taching one of the most vibration sensitive instruments in the world to a vi-brating series of tubes presents many experimental problems. Furthermore,microwave radiation can easily travel down wires from room temperature toour experiment and cause noise that is equivalent to being at a temperaturemuch greater than the temperature of the fridge. To see how other formsof noise can equate to an increase in effective temperature we can computethe variance in energy due to thermal noise ET and microwave noise En:V ar(ET + En) = 〈(ET + En − 〈ET + En〉)2〉 (1.16)V ar(ET + En) = V ar(ET ) + V ar(En)− 2Cov(Et, En) (1.17)Since microwave noise and thermal noise are of course uncorrelated:V ar(ET + En) = V ar(ET ) + V ar(En) (1.18)Thus the total energy broadening at the tunnel junction is:σE =√σ2T + σ2n (1.19)σE =√(3.5kbT )2 + σ2n (1.20)So equation 1.20 shows that we must add all noise sources that reachthe tunnel junction in quadrature, and equal importance must be placedupon filtering out high frequency noise and dropping the temperature of theSTM. Generally speaking it is high frequency noise, not temperature thatlimits the performance of a dilution refrigerator based STM [15]. Noise in thedisplacement of the tip (mechanical noise) also shows up in spectroscopy, but12does not fundamentally affect the behavior of electrons, so it can generallybe averaged out if it is not large enough to perturb the configuration of thetip. However, mechanical noise may require averaging times so long that itis impractical to measure. In contrast, noise in energy fundamentally affectsthe physics being measured, for example, noise on the scale of of 200 µeV islarge enough to break all Cooper pairs in aluminum and completely eliminatethe 176 µeV energy gap.There are many technical challenges that all need to be solved in par-allel for the microscope to achieve its thermally limited resolution. Most4.2 K STMs reduce their susceptibility to mechanical vibrations by hangingoff of very compliant springs to prevent mechanical vibrations from beingtransmitted to the STM. This is not possible with a DR-STM since themicroscope must be rigidly connected with high thermal conductivity ma-terials to the mixing chamber plate. As a result one must make the STMas rigid as possible so that any vibrations that are transmitted to the STMsimply cause the entire STM to move together coherently. If this is achievedthen in the frame of the tip-sample junction there is no relative motion andhigh resolution STM measurements can be achieved. Furthermore, the el-evated temperature of a 4.2 K STM places less stringent requirements onthe removal of high frequency noise for the achievement of thermally limitedresolution.It is these two requirements, solid thermal contact with the vibratingmixing chamber and low relative motion of the tip-sample junction thatconflict with each other and make constructing a DR-STM particularly chal-lenging. This thesis describes how we have tried to overcome these obstacles.13Chapter 2Construction of the STMHeadThe first iteration of the STM head was originally designed by Ben Macleodand was assembled by Yan Pennec and Kirill Sapchuk [16]. There weremultiple issues with the old STM head including a piezo tube that was cutin half and glued back together, massive 28 AWG wires that could easilycouple vibrational noise to the STM tip and a large macor tube connectingthe STM to the mixing chamber plate that limited the sample temperatureto 475 mK. Due to these issues we decided that the STM needed to becompletely rebuilt. This chapter documents the design decisions that wentinto the rebuild of the STM head.2.1 Redesign of the STM HeadThe STM head is based on the standard Pan style [17] which is commonlyused in applications where mechanical rigidity is required [18], thus essen-tially all dilution temperature or pumped 3He refrigeration STMs make useof this type of head.The tip is controlled by a piezotube and a set of six shear stacks, whilethe sample is held above the tip. A piezotube typically has four quadrantson the outside that are labelled x+, y+, x-, y- with the positive quadrantsbeing physically opposite the negative quadrants. There is also an inner zelectrode that acts as a reference for the four outer quadrants. If a voltageis applied across x or y it will shear the piezo tube in that direction. If anequal voltage is applied across both sets of electrodes then the piezotubeexpands or contracts in the z direction. This allows for the tip to be movedover a small ≈ 2 × 2 µm2 area, and the tip can be extended by roughly500 nm in height.The piezotube is mounted in a sapphire prism that is held in place by thesix shear stacks. Bringing the tip to within tunneling range of the sampleis done by the shear stacks, which essentially shuffle the tip towards the14sample via a stick-slip motion that is described in section 2.2.Ben Macleod was responsible for the initial design of the head [19] whichincludes a macor body and six piezo shear stacks from Physik Instrumente(P-121.01T) [20]. These were epoxied to a macor body using Epotek R© H20E[21] electrically insulating epoxy. Upon removing the old STM head it wasdecided that the construction of the shear stacks was acceptable, and thatthey could be re-used in the next iteration of the head. The fine z-piezo wasentirely replaced and the entire tip holder assembly was re-designed. Wealso made significant changes to the wiring of the head. Instead of havinga connector near the base of the STM that is susceptible to vibrations fromthe radiation shield that encloses the entire STM, we brought wires straightdown from the mixing chamber plate directly to the STM.Figure 2.1 shows the redesigned tip holder assembly. The macor cup wasepoxied along with the insulating spacer into the piezotube. Epotek R© H20Econductive silver epoxy and H77 insulating epoxy were used to assemble thez-piezo and tip holder assembly. The phosphor bronze tip receptacle has anM2 thread on the bottom and screws into the titanium threaded insert whichis epoxied into the macor cup. This was threaded instead of epoxied sincethe design of the tip holder was new and not completely tested, allowingfor the entire tip holder assembly to be replaced if needed. There are three1/16” ball bearing cups that allow the titanium ball bearings to protrudepartially into the center hole of the tip receptacle. Be-Cu leaf springs pushthe titanium balls inwards so that the removable tip holder is held snuglyin place at all times, even when significant thermal contraction occurs. Theremovable tip holder was inserted/removed several hundred times manuallyto test the efficacy of the tip holder and no visible wear or change in clampingforce appeared. The leaf springs and their 0-80 retaining screws were thenepoxied in place permanently using H77 epoxy.The threaded insert that the tip holder threads into was made out oftitanium since its relatively low coefficient of thermal expansion matchesmacor better than other metals [22]. It should be noted that titaniumgoes superconducting at 390 mK [23]. When ramping the magnetic fieldcurrents can get trapped in the superconductor, which can then subsequentlychange the actual magnetic field at the tip-sample junction. This couldcause inaccuracies for small magnetic field measurements, but it is alwayspossible to eliminate these by warming the microscope up above 400 mK andquenching superconductivity in the titanium, and then cooling back downin the new magnetic field.This setup nominally allows for blind tip transfer, though it has not beenattempted with the current setup because the current transfer arm claw that15TipRemovable Tip HolderTip ReceptacleBe-Cu Leaf springsTitanium Ball BearingsTi Threaded InsertMacor CupInsulating SpacerGold Coated Macor2 mmFigure 2.1: Exploded view of redesigned tip holder. See the scale bar on theleft to get an idea of the size of the tip assembly. The removable tip holdercan nominally be pulled out of the tip receptacle during normal operationof the STM to change the tip. The tip receptacle can be unthreaded fromthe piezotube (when the UHV chamber is vented) if maintenance on the ballbearings or leaf springs is required.16(a) Old STM mounted on the fridge.Note the large amount of macor and 28AWG wires going into the bottom of theSTM.(b) New STM mounted on the fridge.The amount of macor was greatly re-duced, and much smaller gauge wire wasused.Figure 2.2: Side by side views of the old and new STM heads.we use is designed in such a way that it is quite possible for the claws toput large lateral forces on the piezotube that may be large enough to breakit. However, with an appropriate grabber design that cannot apply lateralforces this setup should allow for clean tip transfer.Figures 2.2a, 2.2b show the old and new STM heads. The amount ofmacor has been greatly reduced which was in large part responsible for ourbase temperature going from 475 mK to below 150 mK. Note that exceptfor the tunnel wire the 36 AWG wires are barely visible in the image of thenew STM head, while the wires contain significant mass on the old STMhead and are much more capable of disturbing or mechanically exciting thepiezotube/tip assembly.The macor tube that fixes the STM to the mixing chamber and positionsit in the bore of the 7T magnet was replaced with a gold plated phosphorbronze tube. If one considers raw ability to transfer cooling power from themixing chamber plate to the STM then oxygen-free copper (well actuallysilver, but cost is a big issue with that) is the clear winner. However, we17Material Thermal Conductivity (W m−1 K) Specific Heat (J K−1 m−3)Oxygen-Free Copper 183 815Phosphor Bronze 6.25 ??Sapphire 410 31.8Macor 0.08 100Table 2.1: Thermal conductivity and specific heat at 4.2K for commonlyused cryogenic materials.would also like to be able to measure in magnetic fields of up to 7 T. FromFaraday’s law of induction and Ohm’s law in a conductor it is clear thatwhenever we change the magnetic field eddy currents will be generated. Inthe case of just ramping the magnet up and down this will result in heating ofthe conductor, and possibly long wait times for the fridge to cool back downto base temperature. In the worst case the superconducting magnet cango normal (either due to a lack of cryogens or due to exceeding the criticalcurrent of the superconducting wire in the coil) and quench. This can causethe magnetic field to drop very quickly, only limited by the inductance ofthe coil and the resistance of the magnet. So a magnet quench can causemassive eddy currents in any conductor inside of the bore of the magnet.This induced current creates its own magnetic field resulting in extremelylarge forces on the STM head. To estimate these forces we can use:J = σE (2.1)∇×E = −∂B∂t(2.2)m =12∫x× Jd3r (2.3)To estimate the force we can approximate the current distribution aslocalized [24]:F = ∇(m ·B) (2.4)Assuming that the∂B∂tis constant for a cylinder of inner radius a andouter radius b we get:18J =−σ2∂B∂trφˆ (2.5)Assuming the magnetic field is largely pointing in the z direction (thisis the dominant contribution) we only need to calculate mz:mz = −σhpi(b4 − a4)16∂Bz∂t(2.6)This gives our estimate of the field as:F =pihσ(b4 − a4)8∣∣∣∣∂Bz∂t∣∣∣∣ |∇B| (2.7)We are looking for the peak force on the tube during a quench, so wecan use the low temperature value of the conductivity for copper [25] (witha residual resistivity ratio of 200) of σ = 7.7 · 109 S and estimate |∇B| = 0.1T cm−1. The ramp time can be estimated from the LR circuit formed bythe superconducting magnet going normal. I(t) = Ioe−LRt. This gives:Bsolenoid = µoηI = µoηIoe−LRt = Boe−LRt. (2.8)Thus the maximum possible change in field is given by:∂B∂t Max= −LRBo. (2.9)We can estimate the maximum change in field with the inductance ofthe magnet L = 10 H and Rnormal ≈ 14 Ω giving ∂B∂t Max≈ 5 T s−1. Thecopper tube has a maximum outer radius of b = 25 mm and an inner radiusof a = 18 mm and a height h = 18 cm. Putting all this together we find thatthe peak force Fmax ≈ 7800 N during a quench. This likely overestimatesthe forces during a quench since the copper will heat up significantly dueto the large induced currents and its conductivity will decrease as a result.Regardless, the forces involved during a quench are possibly large enoughthat your cryostat or experiment could be destroyed. The above derivationis similar (though for a different geometry) to that found in [26] for theirmillikelvin temperature scanning gate microscope.In contrast, the low temperature electrical conductivity of phosphorbronze is σ = 1.25 · 107 S which would reduce the maximum force on theSTM during a quench to Fmax ≈ 8 N which is much less likely to causedamage. This will also reduce the prevalence of eddy current heating as19the lower conductivity reduces the magnitude of the currents induced in thetube during a magnet ramp.Referring back to table 2.1 it becomes clear that sapphire is an excellentchoice due to it’s high thermal conductivity and low specific heat. Also,as an insulator sapphire is completely unsusceptible to eddy currents. It ispossible to get large artificial single crystals of sapphire and grind them, butthis was prohibitively expensive and time consuming for a tube of that sizeso we decided not to go that route. Furthermore, it is important to notethat if one gets to a low enough temperature all phonons will eventuallyfreeze out in any material, and virtually all remaining heat transport will bedone by conduction electrons. It can be shown via the Debye model–whichat low temperatures is quite accurate– that the phonon specific heat goesas Cphonon ∝ (T/TD)3 where TD is the so called Debye temperature of amaterial. Whereas from the Sommerfeld model the electronic specific heatgoes as Celectron ∝ T . From these two relations it’s clear that when T <TD the phonon specific heat drops off very quickly, whereas the electronicspecific heat drops much more slowly at low temperature. Thus at verylow temperatures almost all heat transfer occurs through mobile conductionelectrons and at low enough temperatures sapphire may not be the optimalchoice of material.2.2 Coarse Approach MotorsThe coarse approach motors are responsible for moving the tip towards thesample from a starting point of ≈ 5 mm tip-sample separation. The coarseapproach motors can be run in so-called stick-slip, or inchworm mode de-pending on which software settings are used. The basic principle of operationinvolves the use of 6 shear stack piezos. The voltage is slowly ramped overmilliseconds from 0 to up to 220 V; this causes the stacks to shear on the or-der of about half a micron. Due to the relatively slow nature of this processthe sapphire prism that holds the fine piezo and the tip is thrust forwardby frictional contact with the shear piezos. The piezos are then dischargedvery quickly on the order of 500 ns which causes the piezos to slip alongthe sapphire prism. This process is repeated thousands of times in order toapproach the tip towards the sample. Retracting the tip works exactly thesame, but the waveform is reversed in time; in other words V (t)→ V (−t).Combined with the fine piezo, which can extend further than the distancetraveled during a coarse step, a feedback loop is used to approach via a huntand peck mechanism. First a tunneling current set-point is chosen, and20VHSRD1Nanonis HVA4 AmplifierArduinoControllerCoarse PiezosNanonisSPM ControllerPCI-6229 DAQCapacitive EncoderLock-in measurementof coarse piezo displacementvia capacitive sensorG=22The VHSRD1 allows the signal from the DAC card/amplifier through when the digital line is HIGHCurrent Setup Each of the six coarse piezos is ~ a 2nF capacitive load.  Figure 2.3: Block diagram of coarse piezo electronics. An initial trapezoidalwaveform is generated by the NI PCI-6229 DAQ card and amplified to 220Vby high voltage amplifier. The trapezoidal waveform is then fed into theVHSRD1 piezo driver that essentially chops the waveform in half allowingthe voltage to drop or rise with a very high slew rate for the slip portionof the waveform. Six separate waveforms are delivered to the coarse piezos,and all timing of the waveforms is controlled by both the DAQ card and anArduino microcontroller.21then one measures the tunneling current, which should be slightly less than1 pA when not tunneling due to the inherent Johnson noise of the tunnelingcurrent amplifier. The z-piezo extends outwards towards the sample, if thetunneling current set-point is reached, the approach stops, if not a coarsestep is taken and the process is repeated again.This hunt and peck method allows for the STM to approach withoutcrashing the tip into the sample which can damage the sample or ruin afreshly prepared tip. This is critical for measuring samples such as graphitebecause carbon flakes stuck on your tip are generally extremely unstableand prevent good tunneling conditions from being achieved.2.3 Capacitive Sensor and Coarse ApproachDuring the operation of the fridge and STM we have no optical access toany cold part of the experiment. Furthermore, the stick-slip coarse approachcan take a very long time to approach in hunt and peck mode since we canonly approach at a rate of a couple Hz. So it is important to know theposition of the tip so that we can move the tip without feedback near tothe sample, and then complete the last part of the approach in hunt andpeck mode. It is also critical to know the location of the tip for verifyingthat the coarse piezos are moving and that the tip has been retracted farenough away for changing the sample. A capacitive sensor is attached to thebottom of the STM to verify the height of the tip and piezo tube assembly.Determining that the piezos are working is actually the main function ofthe capacitive sensor since there have been several thermal cycles of theSTM where the coarse piezos became stuck due to an increase in frictionstopping the stick-slip motion from functioning properly. In fact, we now settension on the coarse peizos so low at room temperature that the sapphireprism holding the z-piezo cannot move. Only once you cool the microscopedown, and thermal contraction increases friction do the motors start workingconsistently again.It was possible to fit the capacitive sensor data quite well as a functionof height. A simple model of:C(z) = Co + az +bz(2.10)was used to fit the data.The constant term accounts for parasitic capacitance, the linear term isdue to the cylindrical capacitors and the 1z term is due to the bottom of the22electrode forming a parallel plate capacitor. We measure the voltage dropover the capacitor so:V = IZ ∝ 1jωC(z)(2.11)Since the parasitic capacitance is so much larger than the capacitancebetween the sensor electrodes:|V | ∝ 1ωCo11 + 1Co (az +bz )(2.12)|V | ≈ 1ωCo(1− aCoz +bCo1z)(2.13)From equation 2.13 we can fit the capacitive sensor data as a functionof height as shown in figure 2.5. The fit agreed almost perfectly before therebuild of the microscope. After rebuilding the microscope it appears thatwe have metallized different parts of the macor and the capacitance deviatesfrom the fit near the top of the piezo motor range. This non-monotonicityis highly undesirable, so we tuned the voltage of the waveforms deliveredto the upper and lower electrodes until the measured voltage drop over thecapacitor was monotonic as a function of z.Even though the calibration is excellent for a given set of measurements,the parasitic capacitance of the whole capacitive sensor is very easily changedby moving wires and changing grounding of the STM electronics. This causesjumps in the calibration that make it difficult to measure the capacitance re-peatably. As a result we cannot get an absolute calibration of the capacitiveencoder currently, but it works very well for determining the direction (andexistence of) piezo motor motion, which is the most important function.The capacitive sensor consists of three gold-coated macor electrodes. Itwas originally meant to be a phase sensitive detector but we quickly foundthat sending two out of phase sine waves into the top and bottom electrodeand measuring the magnitude of the AC signal on the inner electrode wasmore linear and less noisy. Figure 2.4 shows the setup of the capacitiveencoder. Due to the geometry the bottom electrode has larger capacitancewith the inner electrode than the top electrode does.2.4 STM GroundingDue to the high gain transimpedance amplifier required to accurately mea-sure the tunneling current, STM is inherently limited to measurements23V = VoSin(ωt)V = VoSin(ωt+π)VoutUpper electrodeBottom electrodeInner capacitivesensorelectrodeZ-piezoShear piezoFigure 2.4: Diagram of the capacitive sensor used for determining the zheight of the tip.at frequencies well below 1 kHz. Furthermore, the extremely high gain(G = 109) makes the amplifier very sensitive to electrical noise from groundloops or pickup, and it is because of these two factors that an ’audio’ [27]grounding scheme is used where all grounds of all electrical devices used inthe measurement (high voltage amplifiers, bias voltage, tunneling amplifieretc.) get grounded to a single point only once. This contrasts RF groundingwhere coaxial cables must be continually connected to ground to maintainthe shield of the coax at the same potential over it’s entire length.Figure 2.6 shows the grounding scheme for all STM electronics usedduring measurement. Notice that each ground is connected to the centralground point only once. We apply a bias to the tip-sample junction Vbiasfrom output 1 on the Nanonis controller [28], which is responsible for the240 20000 40000 60000 80000 100000Number of Steps50000100000150000200000CapacitiveencoderreadingCapacitive Enocoder Data at 10KAfter microscope rebuildBefore rebuildFigure 2.5: Plot of capacitive encoder data and fits.operation of the STM. We use output 2 from the Nanonis to offset the tran-simpedance amplifier by a voltage −2 V < Voffset < 2 V. This accomplishestwo things. Firstly, it references both the amplifier and the bias to the sameground of the Nanonis controller outputs. Due to the differential natureof op-amps any common mode noise that arises from the Nanonis will beeliminated or reduced by this differential measurement. Secondly, we havealso discovered that at the transition from negative to positive voltages the22-bit Nanonis DAC has an error that creates a zero bias anomaly. Thisanomaly is big enough that it can obscure or ruin small spectral featuresthat we would like to measure via scanning tunneling spectroscopy. Figure2.7 demonstrates the large issue with the DAC very close to zero bias. Tofix this anomaly we offset the amplifier by some voltage Voffset and thensweep the bias symmetrically around −Voffset in order to do spectroscopyclose to the Fermi energy without ’measuring’ the Nanonis SPM controllerzero bias anomaly.25VoffsetVoutVBiasSampleCryostatAmplifierG= 10^9-+Protection EarthG =  22 HVamplifiersx+ x- y+ y- zto STMfine piezoCoarse piezosgrounded duringSTM MeasurementFigure 2.6: Schematic of electronics used for STM measurement and thegrounding scheme that provides the lowest tunneling current noise26-3000 -2000 -1000 0 1000 2000 3000Energy (µeV)050100150200250300350DifferentialConductance(nSV−1)Figure 2.7: Zero bias anomally arising from Nanonis controller27Chapter 3Dilution RefrigeratorPerformanceThe dilution refrigerator that the DR-STM is connected to was custom de-signed by Janis Research corporation [29]. It is smaller than typical dilutionrefrigerator based STM systems [30–34] that have been built in the past.The advantage of this is that a smaller dewar belly and neck can be used,greatly reducing helium consumption and increasing hold time. Table 3.1shows the electronic temperature of the tip-sample tunnel junction of se-lected comparable low temperature STMs. In terms of base temperaturethe UBC DR-STM clearly is at a disadvantage in comparison to the biggerdilution refrigerator based systems, but outperforms helium-3 based systemssignificantly in terms of achievable base temperature.It is also worth noting that there is very little correlation between thebase temperature (the lattice temperature of the thermometer) of the STMslisted in table 3.1 and the electronic temperature of the tip-sample junction.Firstly, RuO2 thermometers (used by all groups in table 3.1) can only mea-sure the local temperature of the thermometer, and it is quite possible fortemperature gradients to exist in the system making the real temperatureof the tunneling junction significantly higher. The Ast group [33] addressedthis possibility by cooling down their STM with two RuO2 thermometersattached in place of the tip and sample, yielding a junction temperature of20 mK, only slightly above their base temperature. Additionally, as men-tioned in section 1.4, microwave frequency noise can increase the electrontemperature while leaving the lattice temperature relatively low. Microwavefrequency noise has elevated the electron temperature of most other systemsto the 140-250 mK range. Any voltage/energy noise that reaches the tun-neling junction can serve to broaden spectroscopic features used to calibratethe effective temperature of the STM. Since ∆ESTM = 3.5kBT this meansthat 1 µV of energy smearing caused by noise is equivalent to 3 mK ofthermal noise. Great care must be taken to eliminate low frequency noise,ie. noise you can measure with your STM measurement electronics, butmicrowave noise can also easily travel down lines and cross-talk with the28Group η @ 100mK (µW) Te (mK) TSTM (mK) Hold time (days)Max Planck [33] 396 38 20 ShortSt. Andrews [32] 400 140 10 7UMD [34] 400 184 30 ??NIST [30] 350 232 10 11Princeton [31] 400 250 20 4UBC 100 ?? 114 10Cornell [17] N/A 660 240 ??RHK N/A 400 400 ??Table 3.1: Comparison of selected Dilution Refrigerator and 3He sorptionpump based STMs and their differing temperatures. Te is the electron tem-perature.tunnel junction at low temperature to also decrease energy resolution.Not only is it difficult to reach an effective temperature near the basetemperature of the fridge, but measuring the effective temperature is non-trivial as well. The systems measured in [30–33] used the broadening of thesuperconducting gap of aluminum tips or samples to measure their effectivetemperature, while [34] used NbSe2 to calibrate their effective temperature.Some form of either the Dynes equation [35] or the Maki equation[36]–bothmodels of the BCS density of states that include a phenomenological quasi-particle lifetime for fitting purposes–were used to fit the spectroscopic data.It is assumed broadening due to finite lifetime effects is much less than thatdue to finite temperature, but many things can influence this including thestate of the tip [37]. Thus accurate characterization of any dilution refrig-erator based STM’s effective temperature is difficult, and we were not ableto achieve that measurement, but it should be carried out in the future.Table 3.1 clearly shows that the UBC DR-STM is at a disadvantage, interms of base temperature, to the larger dilution refrigerators. However, forspectroscopy it is only the electron temperature that is relevant, and this canpartially be overcome with proper room temperature and low temperaturefiltering, since the major limiting factor in the performance of the UBC DR-STM may be tunnel junction noise, rather than temperature, leaving thepossibility of the UBC DR-STM performing well given the small size of thefridge. Table 3.1 makes it clear that having a fridge with a large amountof cooling power may only give you an effective temperature of 250+ mK ifyou do not filter out microwave frequency noise appropriately.290 50 100 150 200 250 300 350 400 450TST M (mK)0100200300400500600700T electron(mK)Correlation Between Electron Temperatureand STM TemperatureMax PlanckSt. AndrewsUMDNISTPrincetonCornellRHK Commercial SystemFigure 3.1: Plot showing the lack of correlation between STM base temper-ature and electron temperature at low temperature.The small size of our DR-STM causes very little helium consumptionand allows for an exceptionally long hold time. Our dewar holds about 55 Lof LHe while for example Stroscio’s system [30], which has an impressivehold time of 11 days, has a 250 L dewar that significantly increases heliumconsumption and the cost of running experiments. Other systems have 2-3xthe helium consumption while having significantly worse hold times.3.1 Performance of UBC DR-STMIn this section a comparison of the thermal performance of the old andrebuilt STM head is shown. The new phosphor bronze tube that can beseen in figure 2.2b connects the STM head to the mixing chamber andextends the STM into the bore of a 7 T magnet, providing a much betterthermal link than the old macor tube. This is unsurpising since the thermalconductivity at 5 K of macor is 0.08 W m−1 K−1 [38] while the thermalconductivity of phosphor bronze is 1.6 W m−1 K−1 at 5 K.On the newly rebuilt STM head it takes about 8 hours to transfer a roomtemperature sample into the STM and cool it down to the base temperature300 1 2 3 4 5 6 7Time (Hours)051015202530354045Temperature(K)Cooling Sample fromRoom Temperature to 4KFigure 3.2: The STM cooling after placing a 300 K sample into the STM. Ittakes about 4 hours to cool the sample from 300K to 5 K. The large increasein temperature is due to the warm sample being placed into the STM.of the fridge. It is also possible to pre-cool samples to about 10 − 20 Kbefore placing them into the STM. This can be useful for improving thevacuum by cryopumping the UHV chamber to improve vacuum conditionsbefore cleaving a sample. Adding in additional time for sample preparationand approaching the STM tip makes the whole sample transfer process takeabout 12 hours. If the magnet is not being run we generally are capable oftransferring samples several times before needing to refill helium.As shown in figure 3.5 the DR-STM has a base temperature of 114 mKand can be held at that temperature with minimal drift in temperature for 7-10 days. For slightly elevated temperatures over other home built DR-STMswe gain a long hold time. This is extremely useful when trying to completeany STM measurement where a single stable tip configuration is required,such as spectroscopic maps. With a boil off rate of only 6-7 l per day verylittle helium is consumed in comparison to other dilution refrigerator basedSTMs.310 2 4 6 8 10 12 14Time (Hours)10−210−1100101Temperature(K)Cooling Sample from 4K to 150mKSample TemperatureMixing Chamber TemperatureFigure 3.3: The new STM head cooling from 5 K to the base temperatureof 150 mK. You can see that it takes ≈ 4 hours to get from 5 K to the basetemperature.3.1.1 Still CalibrationDilution refrigeration relies upon removing 3He from the dilute phase inthe mixing chamber so that 3He can pass from the 3He rich phase to the3He poor phase and cause more cooling via ’dilution’. The way this isactually achieved is by evaporating 3He from the still pot which createsa chemical gradient of 3He between the still and the dilute phase in themixing chamber causing more 3He to move towards the still from the dilutephase. The evaporation of 3He is accomplished by slightly heating the stillto above its base temperature of 500− 700 mK. Optimally the still and themixing chamber would be completely thermally decoupled, but in realitythat is never the case, and instead there is a weak thermal link betweenthe two stages which comes from both radiation and thermal conductionthrough the thin walled stainless steel tubing connecting the two thermalstages. This means there is some optimum still temperature that facilitatesthe evaporation of 3He–creating more cooling power via dilution–while notsimply heating the full system up.A still calibration was run to find the optimum flow rate of 3He forthe fridge. Figures 3.6 and 3.7 show the results of the still calibration for320 2 4 6 8 10 12 14Time (Hours)10−210−1100101102Temperature(K)Old Head: Room Temperature to 475mKSampleMixing Chamber PlateFigure 3.4: The old STM head with a large low thermal conductivity macortube being cooled from 300 K straight down to dilution temperature. Youcan see that the sample takes ≈ 5.5 hours to cool to from 300 K to 5 K, ittakes almost 12 hours to cool the sample from 300 K to a base temperatureof 475 mK330 1 2 3 4 5Time (Hours)0.00.51.01.52.02.5Temperature(K)Sample base temperature of 114 mKCooling Sample After Approaching TipSampleMixing Chamber PlateFigure 3.5: Cooling down the sample to the absolute base temperature of114 mKthe mixing chamber plate and STM respectively. The still heater powerwas varied between 0 and 10 mW to control the flow, which was measuredby a flow meter connected to the gas handling system pump. The mixingchamber shows a clear minimum temperature as a function of flow in figure3.6, and the cooling power of the mixing chamber is maximized at a flow rateof around 170 µmol s−1. Interestingly the STM does not show any cooling(see figure 3.7) with an increase in 3He flow rate. There are two equallyplausible reasons for this. Firstly, the radiation shield that hangs off thestill plate to protect the STM and mixing chamber from 4 K radiation willheat up when the still heater is turned on. This will increase the radiationload on the STM which may be responsible for the increase in temperature.Secondly, the thermometers on the STM are connected to the outside ofthe STM and are on the order of 5 mm away from the radiation shield,thus they are particularly sensitive to radiation from the radiation shield, sothe STM itself may not be warming, but the thermometer may be warmingsignificantly due to a high radiation load.The cause of this warming could be resolved by placing a thermometerin a solidly radiation protected position within the STM, however the smalldecrease in temperature of the mixing chamber plate suggests that theremay not be much to be gained by ever running the still heater, and indeed3450 100 150 200 250 300Flow µmol s−169.069.570.070.571.071.572.072.573.0MixingChamberTemperature(mK) MC Temperature During Still CalibrationFigure 3.6: There is a clear minimum temperature of the mixing chamberat 170 µmol s−1 as a function of flow ratein practice we rarely use the still heater to increase the cooling power ofthe fridge. Other dilution refrigerator based STMs see only a small changein mixing chamber temperature when running their still heater [33], and ingeneral the few mK drop in temperature is not typically worth the effort ofrunning the still heater.3550 100 150 200 250 300Flow µmol s−1150200250300350400450SampleTemperature(mK)STM Temperature During Still CalibrationCopper RingSample Thermalization PostFigure 3.7: On the STM an increase in flow rate (increase in still tempera-ture) only corresponds to a greater STM temperature. Thus there must be aheat leak between the STM and the still that is cancelling out the additionalcooling power from the mixing chamber36Chapter 4Design and Construction ofan Ultra-High VacuumSample Preparation Stage4.1 The Need for a Clean SurfaceSTM is inherently a surface science technique, and when measuring sur-faces one must make sure that the surface is free of contaminants. At lowtemperature our STM can only measure over a scan area of 2x2 µm2, andover a height of approximately 500 nm, so it is critical that one prepares aclean atomically flat surface. For metals this can be achieved by cycles ofargon sputtering and high temperature annealing. No sample preparationhad originally been designed into the STM because all sample preparationwas supposed to occur on a molecular beam epitaxy system that will even-tually be connected to the STM. Thus the entire sputtering and annealingstage needed to be built into the existing sample preparation chamber of theSTM.4.1.1 AnnealingAnnealing simply involves heating the sample up to a set temperature andholding it there for a set period of time. Annealing serves several purposes.It can aid in the removal of adsorbates by supplying them enough thermalenergy to evaporate or fly off the sample. Secondly, sputtering leaves thesurface pitted and microscopically rough, thus annealing is important to al-low recrystalization of the sample back into its single crystalline form. Exactannealing parameters can vary widely for different materials. For metals,the higher the melting point the higher in temperature one should anneal to.Fortunately, STM is an excellent tool for testing different annealing param-eters, and usually one varies the temperature of the anneal until the sampleis satisfactorily prepared for measurement via STM. For Au(111) crystals itis common to anneal to 500− 600 ◦C for a 10-30 minute period [39],[2].374.1.2 SputteringSputtering is essentially UHV sandblasting, except instead of sand, heavyions are used. In order to sputter, the sample is placed at ground and thevacuum chamber is filled with argon (or a different noble gas) up to a partialpressure of about 1∗10−5 mbar. The argon gets ionized by thermal electronsemitted in a large electric field (we use a potential of approximately 1 kV)and this causes argon ions to accelerate towards the sample with enoughspeed to impact the sample and eject atoms from the surface of the material.It is possible to sputter at higher energies but eventually ion implantationwill occur [40]. Typically the sputtering current is kept high enough so thaton the order of monolayers/second are removed from the sample. This servesto remove any impurities from the sample that were adsorbed on the surfaceand cannot be removed by annealing. For example aluminum oxide Al2O3which instantly coats aluminum when exposed to air has a melting pointof Tm = 2072◦C, while aluminum has Tm = 660 ◦C. Thus it is impossibleto remove the oxide layer without melting the sample. Sputtering serves toremove adsorbates and oxide layers that annealing cannot.4.1.3 Design of a Sputtering and Annealing StageSince the microscope was entirely home built a method of preparing sampleswas needed to reliably sputter anneal samples before placing them into theSTM for measurement. A set of four electrical contacts was designed toprovide electrical contact for both the resistive heater and measurement ofthe sputtering current.Having four contacts also allows for the possibility of thermocouples be-ing attached to the sample or the use of electron beam heating. Electronbeam heating involves heating a filament and applying a large electric fieldbetween the filament and the sample, this accelerates the thermally emittedelectrons towards the sample and can heat the sample to very high tempera-tures (> 1000◦C) in less than a second. E-beam heaters are frequently usedfor flash annealing; necessary for some samples where high temperatures arerequired to remove oxides or reconstruct the sample.38Spring loaded electrical contactsMacor insulation block316 SS rod connected to translation stageExtra sample positionMacor insulation X-arm connection pointFigure 4.1: Full heater assembly. By attaching the electrical wiring to theupper translation stage that has limited (< 15 cm of motion) the wiringcould easily be attached, freeing up the x-arm to move through it’s ≈ 1.5m travel. Spring loaded contacts pivot stainless steel contacts into the fourmolybdenum electrical contacts on the sample plate allowing for multipleconfigurations of heating and temperature measurement via thermocouple.39Heater +Sample contactHeater -Sample contactFigure 4.2: Sample boat portion of heater assembly. The sample gets twistlocked into the sample boat where four 316SS pivot contacts engage with thefour molybdenum contacts on the sample plate. The spring loaded electricalcontacts push on the pivot contacts to ensure solid electrical contact to thesample plate during heating.40Spring WasherRotating Top CapSapphire Ball BearingsBearing RaceMacor BodyMolybdenum feet/electrical contactsSample ClampAlumina Electrically Insulated ScrewsSample(a) Exploded view of heater sample plateHeater + Sample ContactHeater -Sample Contact(b) typical contact configuration of heater sampleplateFigure 4.3: Custom built heater sample plate.41Kapton coated 26 AWG wire was used for the electrical contacts. Thefuse current of 26 AWG wires is < 10 A and up to 5 A of current is requiredto run the button heater at over 600 ◦C so two 26 AWG wires were used inparallel for each heater contact in order to prevent melting of the wire orit’s insulation.4.2 Sample Plate ConstructionFigure 4.3a demonstrates the mechanics of how the sample plate goes to-gether. Initially it was only the eight electrically insulating alumina screwsthat held the sample plate body together. After having alumina screwsbreak twice with the sample plate in the vacuum chamber the entire sampleplate was epoxied together, with Pelco high performance ceramic adhesive[41], an alumina based epoxy that works up to 1650 ◦C. Epoxying the sam-ple plate together virtually eliminates forces on the alumina screws that nowonly serve to hold the sample to the sample plate, and also made the wholesample plate assembly much sturdier.There are three modes in which the sample plate can operate. Thefirst mode is via button heater where a tungsten filament is epoxied into amacor disc (in the shape of a button) that is then pressed against the backof the sample (see figure 4.3a). The heater is physically contacted to thesample, and at close to the same temperature as the sample. The secondmode is radiative mode, where a filament is held behind the sample withoutmaking contact to the back of the sample. Enough current is flowed throughthe filament that, due to radiation, the sample heats up to the desiredtemperature; the filament will be much hotter than the sample. Finally,if a voltage is applied between the filament and the sample, this turns thefilament into an e-beam heater. Again, the filament will be much hotterthan the sample, but it will heat the sample much more efficiently than inradiative mode. Except for the initial test of the sample plate in its radiativeheating mode, the sample plate has always been used in button heater mode.The button heaters are easily made by bending 0.01 inch diameter tung-sten wire into a wave pattern and potting it in the Pelco high performanceceramic adhesive on top of a macor block. A thin molybdenum sheet canbe epoxied on top to provide good thermal contact to the sample. If theheater gets used and the sample gets removed from the vacuum chamber thetungsten wire becomes very brittle and is very easy to break. Fortunatelythe button heaters are very cheap and can be made in a few hours of work.The outside shape of the sample plate conforms to the original shape42of the sample plates that were used with the STM. This leaves us able touse the original solid copper samples plates for cleaved samples that do notrequire further preparation. Sapphire bearings run in a bearing race betweenthe sample top cap and the sample plate body to allow the sample plate topcap to be rotated and wedged into place both in the STM and in the heatingstage of the transfer arm.4.3 Sample Plate PerformanceWe have prepared samples 50+ times with this assembly and the contactassembly has held up through all of these thermal cycles. The heater wastested in a separate vacuum chamber in radiative mode (the least efficientmode of heating) to verify that it could get to the required temperature of600 ◦C and it achieved that without any problems in radiative heating modeas shown in figure 4.4Sputtering has also worked quite well, although after tens of hours ofsputtering, enough material was sputtered off the sample and the sampleplate to deposit enough metal onto the insulating macor sample boat thatthe electrical contacts shorted together. This will be fixed by either analumina collimator or sectioning the macor sample boat into four separatedpieces to prevent the metalization from shorting out electrodes.A two color pyrometer is used to measure the temperature of the samplethrough the vacuum chamber windows. After testing the heater in radiativemode we switched to using button heaters for our sample heating since thepyrometer would pick up the very high temperature of the glowing filament.With button heaters the heater is well thermalized to the sample and thepyrometer measures the approximate temperature of the sample instead ofthe temperature of a glowing filament. This setup has worked well so far,though it does have the drawback of only being able to measure temperaturesabove 500 ◦C. For noble metals this is not a problem, but for samples withlower melting points such as aluminum (Tmelt = 660◦C) this can poseproblems for accurate temperature measurement. Furthermore, this buttonheater heats up the entire sample plate to several hundred ◦C and can causean increase in pressure of the chamber by up to two orders of magnitude ifthe sample plate has not been properly degassed.Switching from the button heater to an e-beam heater configurationwould help keep the pressure in the vacuum chamber low as it will localizethe heating to the sample. This built in functionality of the sample plate iseasy to switch to, though a method of reliably measuring temperature via a430.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Time (s)−1000100200300400500600SampleTemperatureKSample Plate in Radiative Heater Mode0.005” filament that failedSlow Voltage Rampturning filament up very fastFigure 4.4: Testing the sample heater in a separate vacuum chamber beforeinstalling it in the UHV chamber. A thermocouple was attached directly tothe sample and the sample heater was being used in radiative heating mode.The blue curve shows a smaller diameter of filament failing before gettingto the required temperature of 600 ◦C. The red curve shows the minimumtime it can take to get the sample up to it’s highest temperature–about 30minutes.thermocouple would have to be developed.44Figure 4.5: Testing the sample heater in the UHV chamber on a copper testpiece. Here the sample is glowing and at well over 700 ◦C. When the sampleis at 600 ◦C it is not possible to see the sample glowing.45Chapter 5STM Results and DataThis chapter attempts to represent the baseline performance of the DR-STM and shows a variety of topographic and spectroscopic measurementsthat were made over the course of commissioning of the DR-STM. We haveimaged a wide variety of surfaces at temperatures as low as 114 mK. Whentesting the STM we typically use Au(111) which is relatively inert/non-reactive, easy to prepare flat single crystalline surfaces and it contains aneasily measurable surface state for verification of basic spectroscopic perfor-mance.5.1 Calibration of STMAfter construction of the new STM head the fine motion x, y and z piezo allneeded to be calibrated. The z-height can be calibrated via atomic terraceson Au(111) while the x and y piezos can be calibrated either from thespacing of atoms or other features of known separation such as the Au(111)reconstruction.5.1.1 Calibration of Z-piezo with Au(111)The z-piezo was calibrated using the apparent height of atomic terraces.This was the method used to calibrate the STM from room temperaturedown to millikelvin temperatures. Figure 5.1 shows multiple atomic terracesalong with an atomically flat region measured at a temperature of 141 mK.In order to calibrate the z piezo the image was first smoothed with a 4x4box averaging filter to reduce noise. This broadens the apparent width ofthe step edge but will not change the measured step height. Line cuts weretaken, and a linear fit was subtracted from the line cut to flatten out thestep edge. Then a logistic function of the form h(z) = A∗tanh (b(z − zo))+cwas fit to each step edge and the apparent step height was taken as twicethe amplitude A.460 20 40 60 80 100 120 140x nm020406080100120140ynmAu(111) at 141 mK0.00.20.40.60.81.01.21.41.6Z(nm)Figure 5.1: A large scale image of Au(111) clearly showing many atomicterraces.470 5 10 15 20 25 30 35 40x nm0510152025303540ynmAu(111) at 77K0.00.40.81.21.62.02.42.83.2Z(nm)Figure 5.2: Au(111) clearly showing many atomic terraces and the 22×√3reconstruction. The reconstruction shows up as the faint double stripedfeatures that are mainly running vertically in this image.5.1.2 Calibration of the XY Piezos with Au(111)The surface of Au(111) does not mirror that of a bulk Au single crystal.Instead it relaxes and forms a 22 × √3 reconstruction. This shows up assets of double stripes every 22 lattice constants or approximately 63 A˚. At77 K, 4 K and 142 mK the x and y calibration was found via taking linecuts across the Au(111) surface reconstruction. This can be seen clearly infigure 5.2The large corrugations that are decorated with white and black bumps(contaminants of some sort) are the atomic terraces, while the fainter doublelines that run normal to the atomic terraces are the 22×√3 reconstruction.In order to calibrate the apparent distance, multiple line cuts were takenacross multiple reconstruction lines. The distance between every fourthpeak was calculated by a peak finding algorithm (that was also verified byeye to prevent errors) to find the piezo voltage applied corresponding to 2248Temperature K x nm V−1 y nm V−1 z nm V−1300 14.01± 0.04 14.01± 0.04 2.55± 0.0277 8.63± 0.05 8.63± 0.05 1.97± 0.045 4.17± 0.02 4.17± 0.02 1.03± 0.020.142 ?? ?? 0.95± 0.03Table 5.1: List of piezo calibration coefficients as a function of temperaturefor the current DR-STM.atoms. The images at 77 K were of highest quality, but the reconstructionwas easily visible at all three temperatures.5.1.3 Calibration of the XY Piezos with Highly OrientedPyrolytic GraphiteAfter the rebuild of the STM we initially tested it on highly oriented py-rolytic graphite (HOPG). This easily cleavable material (from which thefirst graphene samples were made [42] ) stays clean in air for months whenmeasuring with STM, making it an optimal sample for testing the perfor-mance of the STM quickly and easily. HOPG has a hexagonal lattice andcleaves very easily along the c axis of the crystal. Typically STM only sees3 of the 6 atoms in a HOPG unit cell, though it is possible to see all 6 if thetip obtains the correct configuration.The calibration for HOPG was obtained from taking the fast Fouriertransform of the image to find the hexagonal reciprocal lattice vectors. Fig-ure 5.3 was used for the calibration with figure 5.4 showing the reciprocallattice of the real space image in figure 5.3.5.2 Graphene on SiCThe first experimental isolation of a single graphene sheet occured in 2005[42]. Its unique properties, where electrons behave like massless relativisticparticles inside the 2D lattice, have made it possibly one of the most studiedmaterials in condensed matter physics. Partially this is because the uniqueproperties (including electron mobility at room temperature exceeding thatof any other material) of graphene arise from it’s two dimensional nature,but in the vast majority of cases graphene must be grown on a substrate andmeasured on that substrate, or transferred to another substrate. Even true490.0 0.5 1.0 1.5 2.0x nm0.00.51.01.52.0ynmHOPG at 300K0.000.040.080.120.160.200.240.280.32Z(nm)Figure 5.3: Highly oriented pyrolytic graphite; first test of new STM atroom temperature.50230 240 250 260 270 280kx nm−1230240250260270280k ynm−1FFT of HOPG at 300KA.U.Figure 5.4: Fourier transform of figure 5.3, used to calibrate the STM at300 K5110−1 100 101 102Temperature (K)02468101214PiezoCalibrationCoefficient(nmV−1) Piezo Tube Calibrationsx and y caibrationz-calibrationFigure 5.5: Calibration of piezotube as a function of temperature. The largedecrease in piezotube displacement at liquid helium temperatures matcheswell with the manufacturer’s specifications.52free standing graphene has ripples in it that increase the dimensionality andreduce the prevalence of graphene’s amazing intrinsic properties [43, 44].Thus people have invested an enormous amount of effort trying to find waysto decouple graphene from its substrate and trying to determine the influenceof different substrates on the properties of graphene.Furthermore, in order to do proper transport measurements on graphenecontacts are typically laid down and portions of the sample or substrate getetched away. Samples are then typically cleaned in forming gas to removeimpurities [45]. All of these processes can have unpredictable effects on thecleanliness of the graphene sample and have large influence on the trans-port properties of graphene. For example, the presence of enough magneticimpurities will vastly reduce the conductivity of graphene. Furthermore,people preparing graphene in UHV prepare it very differently than someonewho is preparing it for transport purposes. To be able to compare differentsamples of graphene that are measured by different techniques it is impor-tant to understand if the technique (or preparation for said technique) iscausing any changes in the graphene surface.Although I did not get to complete this comparison of different graphenepreparation methods with STM, we did measure graphene at low tempera-ture. We measured the same sample twice, the first time we annealed thesample to 150 − 250 ◦C and then cooled it down to 5 K. Figure 5.7 showsthe Moire pattern along with many impurities/defects that are still presentlikely due to the low annealing temperature. The tip picked something upfrom the graphene relatively quickly and became quite unstable, so we re-moved the graphene and annealed it to 600 ◦C overnight for about 12 hours.We also performed field emission on the tip at a voltage of 300 V and currentof 5-10 µA. Upon placing the sample back into the STM, the tip seemed tobe significantly cleaner and quite stable and we were able to obtain atomicresolution on graphene. The sample also certainly seemed cleaner due tothe higher annealing temperature but we were not able to scan over largeenough areas to be certain of that statement.5.3 SpectroscopyFrom the beginning, the goal of this microscope has been to make highenergy resolution measurements on novel materials. For a typical spectro-scopic measurement one holds the tip at a fixed height (the feedback isturned off) and then the voltage is swept over the range of interest. Sincespectroscopic measurements are performed with no tunneling feedback it is530.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5x nm0.00.51.01.52.02.53.03.5ynmGraphene at 5.1 K0.000.020.040.060.080.100.120.140.160.18Z(nm)Figure 5.6: Graphene on SiC atomic resolution540 5 10 15x nm051015ynmGraphene at 5.1 K0.000.080.160.240.320.400.480.560.64Z(nm)Figure 5.7: Graphene on SiC showing moire pattern as well as many adsor-bates that are likely both underneath and overtop of the graphene. As canbe seen from the many lines/tip changes in the image the tip was not verystable of the duration of this measurement.55critical to have very little motion between the tip and the sample. Further-more, any electrical noise that gets down either the tunneling or bias linecan serve to broaden any measured spectra and to erase the advantage ofbeing at ≈ 120 mK. As mentioned in the introduction the local density ofstates as measured by STM is approximately given by LDOS ∝ dIdV . Onecan either measure the current, and then take a numerical derivative, or onecan measure the derivative directly via a lock-in amplifier.To measure the derivative of the tunneling current with respect to voltagewe can modulate the bias so that the current has a small modulation atfrequency f = ω2pi :I(V ) = I(〈V 〉) +A sinωt (5.1)I(V ) = I(〈V 〉) + dIdV∣∣∣∣〈V 〉(I − I(〈V 〉)) +O((I − I(〈V 〉))2) (5.2)I(V ) = I(〈V 〉) + dIdV∣∣∣∣〈V 〉A sinωt+O((A sinωt)2). (5.3)Thus if the modulation of the bias is sufficiently small such that thecurrent modulation is small, then putting the I(V) signal into the lock-in and measuring the component in phase with sinωt is, to a very goodapproximation:Ilock−in(V ) ∝ A dIdV∣∣∣∣〈V 〉. (5.4)Now in reality we have converted the tunneling current to voltage withour transimpedance amplifier and the lock-in actually makes a voltage mea-surement that is proportional to the current, but the same measurementtechnique still applies.With a lock-in we are able to measure the local density of states bymodulating the tip-sample bias. This has advantages and disadvantages.The main advantage is that a lock-in is essentially the ultimate bandpassfilter. The signal recovery 7265 lock-in [46] that we use for our dIdV measure-ments has noise of approximately 5 nV/√Hz arising from its FET amplifier.With a time constant of 100 ms and a slope of 12 dB/octave the equiva-lent noise bandwidth is 1.6675 Hz giving a total noise of 6.46 nV. Since ourtransimpedance amplifier uses a resistor with R = 109 Ω at a temperatureof 300 K this causes Johnson Noise [47] of vn =√4kBTR∆f = 5.2 µV. So56the noise from the lock-in is negligible compared to that coming from theJohnson noise limited tunneling current amplifier.The narrow bandpass filtering properties of a lock-in also allow us tomeasure at a frequency where there is little electrical or mechanical noise.This is possibly the main advantage of a lock-in. This contrasts numericalderivatives in which it is possible to apply a low pass filter to remove highfrequency noise, but low frequency noise below several kilohertz is all in-cluded in the measurement because the measurement bandwidth is on theorder of kilohertz instead of 0.1-2 HzThe biggest disadvantages of lock-in amplifiers are the time required tomeasure and the inherent broadening due to modulation of the bias. Lock-ins employ a low pass filter to display the DC voltage that is proportionalto the magnitude of the AC signal at the frequency of interest, and asa result these can require quite large time constants to make a low noisemeasurement. Thus a lock-in measurement may take several minutes torecord, while a fast sweep of numerical dIdV can usually be recorded withinabout 10 seconds even with a significant amount of averaging to removemechanical noise. This limits the total amount of data that one can takewith a lock-in vs taking numerical derivatives. Secondly, the modulation ofthe current serves as another form of thermal broadening. At 4.2 K wherethe energy resolution of an STM is limited to approximately 1.5 mV this isnot so relevant since we can still modulate the bias at 0.5-1 mV and causelittle extra broadening of spectroscopy.However, if we are measuring at millikelvin temperatures, it becomescritical to send in only a very small modulation voltage on the order of1 − 50 µV depending upon the required resolution and temperature of themicroscope. This extends the integration time required to recover a spec-troscopic curve at low temperature.Figure 5.8 shows a comparison between numerical derivative and lock-inmeasurements on Au(111). The kink at −490 meV is the Au(111) surfacestate [48], while it is unknown what exactly the other features are. Thelarge peak frequently shows up in our Au(111) spectroscopy with multipledifferent tips and it may be a tip state from something picked up off thesurface. Regardless it is clear that they both provide roughly the same result,although the lock-in would have taken much longer to measure the samecurve. Figure 5.9 shows the Au(111) surface state without the correspondingpeak feature seen in figure 5.8.57−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6Energy eV−0.50.00.51.01.52.0DifferentialConductancenSV−1Es = −0.49 eVT = 5.7 Kτ = 100 msVmod = 3 mVLock-in vs Numerical dIdVNumerical DerivativeLock-In AmplifierFigure 5.8: Comparison between lock-in amplifier and numerical derivative.The numerical derivative was Gaussian smoothed with σ = 15 mV58−0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4Energy eV0.060.070.080.090.100.110.12DifferentialConductancenSV−1Esur facestate = 0.48 eVT = 402 mKAu(111) Surface StateFigure 5.9: Typical spectroscopy showing the Au(111) surface state. Thiswas measured using numerical dIdV with a Gaussian smoothing parameter ofσ = 15 mV59Chapter 6Implementation of LowpassFilters for High ResolutionSpectroscopyCooling your STM to dilution refrigerator temperatures is a requirement forachieving high energy resolution, but any type of noise in your system thatmakes it onto the tunneling current wire is also equivalent to an effectivetemperature as discussed in section 1.4. Frequently this noise temperaturecan be significantly higher than the actual temperature of the microscope[49]. This is because microwave frequency noise that gets generated byswitching power supplies and a multitude of other sources can easily bepicked up by ’natural’ antennas in the experiment and travel down the wiresconnecting your measurement electronics to your microscope. For exampleif you just hook an unshielded wire up to an oscilloscope you can easily seenoise on the order of millivolts, equivalent to a temperature of 5− 10 K.Thus it is very important to shield the tunnel junction from any formof microwave noise. At microwave frequencies even the capacitance betweentwo wires is a small enough impedance for a microwave frequency signalto jump from one wire to another with little attenuation, so it is importantthat every wire entering the system be low pass filtered to prevent microwavefrequencies from making it down to the tunnel junction.Two types of pi filters were purchased to serve the high voltage lines(wires for piezos) and low voltage lines (all other measurement wires such asthermometers). The high voltage filter is rated to 220 VAC and has a cutofffrequency in the 5 MHz range [50]. The low voltage filters have a cutoff inthe 1 MHz range [51]. The high voltage filters were used on the 12 coarsepiezo wires and the 5 piezo tube wires. All other wires went through a lowvoltage filter (mainly consisting of heaters, thermometry and the capacitivesensor wires).The filters were enclosed in a hermetically sealed RF tight box where thepre and post filtered sections of the wire were separated by a 3/8” thick brass600 5 10 15 20 25 30 35 40 45Frequency (GHz)−130−120−110−100−90−80−70−60Transmission(dB)High Voltage FilterHigh voltage filterwith water in boxHigh voltage filterFigure 6.1: Transmission function of high voltage filters. The attenuation isflat because the cutoff frequency is ≈ 5 MHz for these filters and the networkanalyzer can only measure above 10 MHz.For these filters the transmissionwas measured with water bottles placed inside the RF tight box.610 5 10 15 20 25 30 35 40 45Frequency (GHz)−120−110−100−90−80−70−60−50Transmission(dB)Low Voltage FilterFigure 6.2: Transmission function of low voltage filters. The attentuation isflat because the cutoff frequency is ≈ 1 MHz for these filters and the networkanalyzer can only measure above 10 MHz.62wall. The joints of each box were sealed either by indium soldering or withsilver conductive epoxy. Figures 6.1 and 6.2 show the frequency responseof each type of filter as measured by a network analyzer. The networkanalyzer can only measure to a frequency of 10 MHz and thus does not showthe frequency response at low frequencies where the transmission should goto unity. It is clear that the high voltage filters have higher attenuation thanthe low voltage filters at low frequency so if future filter boxes are to be madeit would likely be preferable to use only the high voltage filters. Howeverthe performance of both types of filters is acceptable for our application anddrops off to the noise floor of the network analyzer by ≈ 30 GHz.The clear resonance at 2 GHz in figure 6.2 results from the cavity modeof the box. This can be eliminated by introducing bottles of water intothe the cavity. Water has an extremely high dielectric loss coefficient inthe 1− 100 GHz range and acts to decrease the transmission of microwaveradiation in that range. For space reasons this could not be implemented inthe low voltage filter box, but was implemented in the high voltage filter box6.1 and caused a broad decrease in transmission of microwave frequenciesby up to 20 dB.The design of the filter box came from that developed by Damien Quentin[52] for use with iron powder based pi filters. The box along with filters isshown in figure 6.3.63Figure 6.3: Opened filter box showing the filtered and unfiltered sides of thebox along with all wiring going to filters. The filters are screwed into thedividing plate in the middle of the box. This separates the unfiltered side ofthe box from the filtered side of the box. Shielded mil connectors are usedon either side of the box.64Chapter 7Towards Reducing TunnelJunction Noise7.1 Reducing Motion Between the Tip andSample via Vibration IsolationIt is typical to hang a scanning tunneling microscope from a very compliantspring stage with magnetic eddy current dampers used to lower the qualityfactor of the stage. If the spring stage has resonant frequency ω =√km thelow spring constant can drive the resonant frequency to the Hertz range.Since the transfer function of a damped driven harmonic oscillator is givenby:|H(ω)| = 1√m2(ω20 − ω2)2 + γ2ω2(7.1)it’s clear that for ω >> ωo, the transfer function falls off as1ω2. Thus push-ing the resonant frequency ωo of the system as low as possible prevents thetransmission of all but the lowest frequency impulses to the STM. Further-more, if the STM head is made sufficiently stiff, then the resonant frequencyof all components in the STM will be sufficiently high that all parts of theSTM will move together coherently at low frequencies – which is not a prob-lem as it is only the difference in tip-sample distance that matters.In the DR-STM thermal requirements dictate that the STM be attacheddirectly to the mixing chamber plate if we want any chance of the STMbeing close to the base temperature of the dilution refrigerator. The STMplus dilution refrigerator are mounted to an inertia block to isolate the STMfrom outside disturbances. If the mass of the block is sufficiently large thenthe transfer function will be negligible at all but the lowest frequencies. Theblock-air-spring system that we use has a resonant frequency of ≈ 1 Hz inthe z direction, and ≈ 0.7 Hz in the x and y directions. Essentially weuse an 80 tonne inertia block to mount the entire UHV system to a ≈ 1 Hzharmonic oscillator. This is the same principle as mounting the STM head to65small compliant springs, except the only issue is that there are many morestructures between the STM and the harmonic oscillator that can causevibrations at the tunnel junction.7.2 Spectral Density and CoherenceTo estimate the power as a function of frequency contained in a time seriessignal the power spectral density can be used, and is estimated numericallyfor a discrete time series by:Sxx =2N∣∣∣∣∣N−1∑n=0x(n)e−2piiNf ·n∣∣∣∣∣2(7.2)The power spectral density can be used to assess the noise remaining inthe tunneling current feedback loop, as well as the frequency componentscontained within an acceleration signal. In both of these cases we’d preferthe power to be zero at all frequencies, but of course there is always residualnoise or acceleration in any system.The cross-spectral density between two different signals, x and y, acts asan estimate of the correlation of the power of two signals as a function offrequency and can be estimated as:Sxy =2NN−1∑n=0N−1∑k=0x(n)y∗(k)e−2piiNn·fe2piiNk·f (7.3)From the cross spectral density it is possible to estimate the coherencebetween two signals x and y:Cxy(f) =|Sxy(f)|2Sxx(f)Syy(f)(7.4)The coherence provides an estimate of the correlation between two sig-nals. In an ideal linear time invariant system a transfer function H(f)can describe the relation between two signals Y (f) and X(f) as Y (f) =H(f)X(f). For this type of system the coherence will be exactly one be-tween the two signals. If noise is involved in the measurement, or the signalsare not linear and time invariant, then the coherence is always in the range0 < Cxy(f) < 1. However, by averaging a series of spectral density measure-ments we can acquire an estimate of the coherence between two signals as afunction of frequency. We can use the points of high coherence to determine66the possible causes of noise in our tunneling current signal by correlatingthat noise with different accelerometry signals.With these signal processing tools it is possible to gain insights intothe exact processes that cause mechanical noise at the tip-sample junction,and guide the implementation of fixes to improve mechanical rigidity anddecrease the overlap of relevant resonant frequencies.7.3 Acceleration and Coherence MeasurementsIn this section measurements are presented to demonstrate the effects of themotion of the inertia block on the separation of the tip sample junction – inother words the effects of inertia block motion on tunneling current noise.This expands on work done by Ben Macleod [19], where it was found that anapproximately 20 Hz acoustic room mode is able to couple fairly efficiently tothe inertia block, causing deviations from an ideal 0.7 Hz resonant frequencyharmonic oscillator in the horizontal direction. Figure 7.1 shows a largebroad 20 Hz peak that is most prominent in the North-South accelerationof the block, but also shows up less prominently in the East-West and up-down directions. Ben Macleod showed that the 20 Hz peak in the blockacceleration was caused by acoustic forcing of the block by an acoustic roommode. This was verified by both acoustic measurements and by modelingof the acoustic modes of the room.Figure 7.2 shows that 20 Hz noise is the main low frequency noise compo-nent that we see in the tunneling current. Low frequency noise is particularlytroubling for STM since it takes a prohibitively long time to average out, andin topography our signals of interest show up at frequencies near 20 Hz. Forexample if one is scanning at 5 nm/s with an atomic spacing of 2.46 A˚ (typ-ical of graphite) the the tip will pass by atoms with a frequency of 20.3 Hzand the 20 Hz noise signal will show up as a similar frequency modulationto that of the atomic frequency in the image, partially obscuring the atomsfrom view.The acoustic measurements in [19] provided a very clean measurementof the 20 Hz acoustic room mode’s effect on the motion of the inertia block.The following measurements serve to characterize the motion of the intertiablock’s effect on the tunneling current. All power spectral density mea-surements and coherence measurements taken in this section were taken byhaving the tip in tunneling above a clean Au(111) sample, using largelythe same tip configuration. We verified that the same tip was maintainedby looking at the average power spectral density of the tunneling current,670 5 10 15 20 25 30Frequency (Hz)10−1510−1410−1310−1210−1110−1010−910−810−7PSD(m2s−4Hz−1 )Block AccelerationNorth-SouthEast-WestUp-DownFigure 7.1: Power spectral density of block acceleration in the low frequencyregime.680 20 40 60 80 100Frequency Hz10−310−210−1100101102103ASDpA/√HzNew STMAu(111) New STMAluminum New STMHOPG Old STMFigure 7.2: Linear spectral density of tunneling current with tunneling feed-back engaged, 20 Hz noise is generally the only remaining important noisesource that shows up in the tunneling current after the rebuild of the STMhead69because a tip change is a sudden impulse that introduces a broad rangeof frequency components at values orders of magnitude above the tunnel-ing noise baseline. The tunneling current feedback was kept on over theduration of the measurement to hold the current approximately constant.Multiple 60 s time series data sets (between 142 and 519) were taken whereZ(t), I(t) and the block acceleration values were recorded simultaneouslyby a National Instruments DAQ card (PCI − 6229 [53]) at a sample rateof 5 kHz giving an initial frequency resolution of 19 mHz. We reduce thisfrequency resolution to 290 mHz by a 15 point wide box averaging proce-dure to reduce noise and reveal the broader mechanical resonances in thesystem more clearly. Since we only have one accelerometer sensitive enoughfor these measurements (Wilcoxon 731a [54]) we ran the experiment threetimes with the accelerometer oriented in the North-South, East-West andup-down direction. The fridge was close to its base temperature at 140−150mK over the duration of the measurements.For the horizontal accelerometer directions there is a very broad peakcentered at 19.3 Hz in the coherence between the acceleration and the tun-neling current that is certainly associated with the broad peak seen in boththe tunneling current spectral density (figure7.2), and the acceleration spec-tral density (figure 7.1) in both the North-South and East-West directions(and slightly in the vertical direction, but this is less pronounced and maybe due to some amount of cross coupling between accelerometer directions).In all three accelerometer orientations there is a prominent peak at 15.4 Hzin the block acceleration. This was not accounted for by modeling in [19],but does appear to be present in the data; this will be explained by a slightlydifferent model in the following section.The coherence tells us that the tunneling current and the accelerationin the ≈ 19 − 20 Hz range are strongly correlated. We have also measureddirectly that the acoustic room mode causes significant motion in the blockat ≈ 19−20 Hz. The combination of these two factors suggests very stronglythat the acoustic room mode is causing (or at the very least, increasingdrastically) the 19− 20 Hz noise seen in the tunneling current.As mentioned in [19] there are two possible ways that the room mode cancouple to the tunnel junction. First, the room mode moves the block anddirectly causes motion in the tip-sample junction due to an unknown transferfunction between the tip-sample junction and the block. Second, the roommode moves the block and the tip-sample junction coherently, but the roommode ’short circuits’ the block and causes noise at the tip-sample junctiondirectly. Modeling the acoustic forces applied to the block in detail, alongwith looking at the phase of cross spectrum data in the following section70will provide clues as to which of these cases is true.7.4 Modeling of Acoustic Response of the Room7.4.1 Characteristic Frequencies of the RoomIdeally the 80 tonne inertia block that the experiment is mounted to shouldhave as low a resonant frequency as possible. The up-down and side to sideresonances of the block’s air springs are roughly 0.7− 1 Hz. There is also arolling mode– due to the six sets of isolators –that has a resonant frequencyof roughly 2.2 Hz where the block rolls like a boat rocking in waves. Non-ideally, as was shown in the previous section, the block is also moved byacoustic resonances of the room. These resonances come from enforcingan air displacement node at the boundaries of the room. For a room inthe form of a rectangular cuboid with dimensions (Lx, Ly, Lz) the lowestacoustic resonant frequency of a room is given by:fxfyfz =c2Lxc2Lyc2Lz (7.5)Higher frequencies show up as integer multiples of the fundamental (low-est) frequency. Rooms that are not highly symmetric (including our, roomwhich contains a large 80 tonne hexagonal block) also have characteristicacoustic frequencies, but these characteristic frequencies cannot be solvedfor analytically. For this, we use finite element analysis (FEA) to determinethe frequency response of the room. These calculations were performedin COMSOL [55], a software suite that allows for FEA calculations to beperformed over customizable geometries.COMSOL solves the wave equation for pressure on a grid of the geometryspecified in 7.6. The governing wave equation for pressure without anysources or damping is given by:1c2∂2p∂t2= ∇2p. (7.6)From the above we can calculate the eigenfrequencies of the room, withthe largest acoustic response occuring at these characteristic eigenfrequen-cies. Table 7.1 shows the seven lowest eigenfrequencies of the room. It isworth noting that the aluminum flooring and block influence the frequency710 5 10 15 20 25 30Frequency (Hz)0.00.20.40.60.81.0CoherenceCurrent and North-South BlockAcceleration CoherenceFigure 7.3: Coherence between the current and the block acceleration in theNorth-South direction in the low frequency regime. Note the large broadpeak at 19 Hz; suggesting that the motion in the North-South axis at thisfrequency is primarily responsible for the noise in the tunneling current at≈ 20 Hz720 5 10 15 20 25 30Frequency (Hz)0.00.20.40.60.81.0CoherenceCurrent and East- West BlockAcceleration CoherenceNorth-South accelerationFigure 7.4: Coherence between the current and the block acceleration in theEast-West direction in the low frequency regime.730 5 10 15 20 25 30Frequency (Hz)0.00.20.40.60.81.0CoherenceCurrent and Up-Down BlockAcceleration CoherenceFigure 7.5: Coherence between the current and the block acceleration in theup-down direction in the low frequency regime.74Figure 7.6: Model of the room, block and STM that was used for FEAcalculations.75Figure 7.7: The lowest eigenfrequency of the room is 15.15 Hz and actsprimarily in the up-down direction.and direction of the resonant modes significantly, while ceiling padding andsmaller features of the room such as furniture have very little influence. Thiswas tested by adding and removing small features to the room during sim-ulations. In [19] FEA calculations were used to estimate the characteristicfrequencies of the room as well, but the aluminum floor and the incut ge-ometry of the floor were neglected in the simulation. This caused the lowestresonant frequency of the room, at 15 Hz, to be missed. The analysis ofthe FEA calculations in [19] was completely correct, but with the additionalfeatures added in this calculation–particularly the aluminum flooring–we areable to look at the acoustic response of the room in much greater detail.What sticks out immediately is that the 15.15 Hz, 19.65 Hz and 29.96 Hzmodes calculated in table 7.1 show up quite strongly in the block accel-eration, and also in the coherence between the block acceleration and thetunneling current (figures 7.3, 7.4, 7.5) and the block acceleration (figure7.1).76Frequency (Hz) Dominant Direction Image15.15 up-down19.65 North-South22.53 East-West25.40 North-South and up-down29.96 East-West31.3 Bottom Corners38.66 Top CornersTable 7.1: Characteristic eigenfrequencies as calculated by COMSOL. Theblock and the aluminum floor have a large effect on both the mode shapeand frequency of the room eigenfrequencies.77Figure 7.8: The second lowest eigenfrequency of the room is 19.65 Hz andacts primarily in the North-South direction.78Figure 7.7 shows the lowest acoustic resonance of the room that actsprimarily in the up-down direction. Notice that this signal shows up inall accelerometer orientations almost equally. This is likely because anyasymmetry of the mode in the horizontal plane will couple vertical motion tohorizontal motion. Figure 7.8 shows the second lowest acoustic resonance at19.65 Hz. It primarily acts in the North-South direction, and is responsiblefor the broad 19-20 Hz peak in the North-South acceleration of the block,and the very strong coherence between North-South motion and noise in thetunneling current.7.4.2 Acoustic Forcing of the Inertia BlockTo further investigate the effects of the acoustics on the block accelerationwe can also calculate the acoustic response of the room as a function offrequency. If we go back to the wave equation for pressure (equation 7.6)and assume a steady state harmonic excitation with time dependence of theform:p(x, t) = p(x)eiωt (7.7)then it is possible to calculate the harmonic response of the room as afunction of frequency f = ω2pi . Plugging equation 7.7 into the wave equation7.6 and performing separation of variables we get for the spatial component:∇2p(x) + ω2c2p(x) = 0, (7.8)which is the Helmholtz equation. Applying boundary conditions and solvingthe Helmholtz equation numerically via FEA allows for us to determine therelative pressure amplitude for a fixed amplitude harmonic excitation as afunction of frequency and spatial location.What we are actually interested in is the interaction of the structure(the inertia block that is isolating our STM) and the acoustic modes. Byintegrating 7.9 over different portions of the block it is possible to estimatethe relative forces that are being applied to the block in the North-Southaxis, East-West axis and up-down axis.F(ω) ∝∮Surfacep(ω) · dA. (7.9)Note, since we are simply calculating the acoustic response for a fixedharmonic amplitude the calculated force is only proportional to the surfaceintegral in equation 7.9, and we can only calculate the force in arbitrary79NorthSouthEastWestFnormalFEWFNSFigure 7.9: Top view of hexagonal inertia block. Horizontal eigenfrequen-cies will couple to move the block in both the North-South and East-Westdirectionsunits. From this, it is also clear that the pressure applies only a force that isnormal to the surface of the block. As shown in figure 7.9 horizontal (North,South, East, West) room modes will couple to each other because the normalcomponents are not acting only along the North-South or East-West axis.Taking this into account, and integrating the pressure over all eight surfaces(the six sides, the top and the bottom) allows us to compute the acousticforce on the block as a function of frequency.Figures 7.10, 7.11 and 7.12 show much more detailed information thansimply looking at the eigenfrequencies of the room. In the up-down direc-tion (figure 7.10) the 15.15 Hz eigenfrequency forces the block more stronglythan at any other frequency. The high value of coherence (0.95) at that fre-quency suggests that the tunneling current is being affected strongly by themotion of the block caused by this acoustic mode. Note that other eigen-frequencies do not appear to explicitly force the block all that much in theup-down direction. This is because these modes act in primarily horizontaldirections. It is also important to note that at 11 Hz there is a small peakin the acoustic forcing of the block, and a region of very high coherencebetween the tunneling current and up-down block motion. This occurs for805 10 15 20 25 30 35 40Frequency0.00.20.40.60.81.0CoherenceUp-Down CoherenceRelevant Eigenfrequencies01234Force(A.U.)Up-Down ForceFigure 7.10: Calculated acoustic force on the block in the up-down direction(right axis, red line) along with the coherence between block acceleration inthe up-down direction and the tunneling current. For additional comparisonthe relevant eigenfrequencies are plotted as dashed magenta lines.815 10 15 20 25 30 35 40Frequency0.00.20.40.60.81.0CoherenceEast-West CoherenceRelevant Eigenfrequencies024681012Force(A.U.)East-West ForceFigure 7.11: Calculated acoustic force on the block in the East-West di-rection (right axis, blue line) along with the coherence between the blockacceleration in the East-West Direction and the tunneling current. For ad-ditional comparison the relevant eigenfrequencies are plotted as dashed ma-genta linestwo separate reasons. Firstly, the transmission function of the block willnot have dropped off very much by 11 Hz, whereas at higher frequencies,the drop-off in the transmission function from the block to the tip-samplejunction will cause small forces on the block to not show up in the tunnel-ing current. Secondly, frequencies below 20 Hz, also known as infrasound,are much more able to penetrate the thick concrete walls of the room thansound at higher frequencies, so the total acoustic power in the room at lowfrequencies is likely much larger than at higher frequencies.In the East-West (figure 7.11) direction we see a slightly different sce-nario. In the 11 Hz and 15.4 Hz frequency range there is again strong coher-ence between the block motion in the East-West direction and the tunnelingcurrent, however the calculated forces are greatly suppressed in comparisonto the the North-South calculation. This discrepancy is likely because verti-82cal block motion can couple to horizontal block motion, due to asymmetriesin either the block or the mode shape causing a rocking motion in the block.At 27.9 Hz we see that there is significant forcing of the block relative toother frequencies, even though 27.9 Hz is not an eigenfrequency of the room.This 27.9 Hz motion seems to also be coupling strongly between the blockand the tunneling current since the coherence is very strong (> 0.9) at thatpoint. This results from the block coupling strongly to the pressure field ofthe room at 27.9 Hz. This strong coupling of the block to the pressure fieldis also likely the cause of motion of the block at 11 Hz.Strong acoustic forcing at an off resonant acoustic frequency of the roomlikely results from the dimensions and shape of the block being able tovery efficiently couple to the shape of the pressure field at that frequency.The FEA calculation predicting successfully the motion of the block at offresonant frequencies suggests that the model is accurately depicting theinteraction of the block with the pressure field of the room.In the North-South direction we see the largest peak in force centeredat the eigenfrequency 19.65 Hz, along with a large cluster of high coherencepoints. This is consistent with the acoustic mode forcing the block causingthe tip-sample junction to oscillate coherently with the block. Given thatwe have seen the tunnel junction coherently respond to the multiple differ-ent forces predicted by our model, including forces that do not correspondto resonant modes of the room it seems likely that the acoustic forcing iscausing the block to move which in turn causes the tip to move relative tothe sample. This is in contrast to the hypothesis that acoustic power ’shortcircuits’ the block and directly moves the tip relative to the sample.Figure 7.13 shows a comparison between the calculated force and themeasured acceleration of the block. Excellent agreement exists betweenmany frequencies. Most strikingly the largest calculated force on the blockmatches almost perfectly with the broad 19.6 Hz peak in the acceleration.Since the peak forcing frequencies seem to match resonances showing upstrongly in the block, this provides strong evidence that acoustic forcing ofthe block is one of the main driving factors of motion in the 10-40 Hz range.7.4.3 Mechanical Noise in Our STM ExperimentsThe previous result is particularly relevant for our STM experiment sinceone of the main noise sources that is present in our STM measurementsshows up in the 19-24 Hz range. The ultimate cause of this noise is the19.6 Hz North-South acoustic mode, but it also results from some unfortu-nate overlaps of other mechanical resonances in the system. We know that835 10 15 20 25 30 35 40Frequency (Hz)0.00.20.40.60.81.0CoherenceNorth-South CoherenceRelevant Eigenfrequencies02468101214Force(A.U.)North-South ForceFigure 7.12: Calculated acoustic force on the block in the North-South di-rection (right axis, blue line) along with points of large coherence along withpoints of large coherence between the block acceleration in the North-Southdirection and the tunneling current. For additional comparison the relevanteigenfrequencies are plotted as dashed magenta lines84024681012Force(A.U.)Up-DownEast-WestNorth-South5 10 15 20 25 30 35 40Frequency (Hz)10−1510−1410−1310−1210−1110−10PSDm2s−4Hz−1Figure 7.13: Comparison between calculated and measured acceleration ofthe block.850 20 40 60 80 100Frequency Hz10−310−210−1100101102ASDpA/√HzMode Shift When Engaging HeatswitchHeatswitch DisengagedFigure 7.14: There is a clear shift in the 20 Hz noise peak showing upthe tunneling current noise spectra (amplitude spectral density) when theheatswitch is engaged and stiffens the DR insert.the DR-STM insert has a roughly 20 Hz resonance because the noise in thetunneling current shifts from roughly 19 Hz to 22-24 Hz whenever the heatswitch is engaged. When the heat switch is firmly engaged it increases thestiffness of the whole dilution refrigerator insert and causes an increase inthe fundamental resonant frequency of the insert. This has been repeat-edly measured by cycles of engaging and disengaging the heat switch andmeasuring STM noise spectra as show in figure 7.14. We have verified byFEA that the lowest resonant frequency of the insert is a swinging mode,or pendulum mode, that is split slightly in frequency in different directionsdue to slight asymmetries in the construction of the fridge.The largest acoustic resonance in our block is centered almost exactlyover the resonant frequency of the DR insert, which is the worst case scenariofor transmitting the acoustic noise background to the tip-sample junction.This excitation of the dilution refrigerator pendulum mode (DRPM) can8617 18 19 20 21 22Frequency Hz−20246810121416PhasePhase of I to A Cross Powersdata North-Southdata East-Westdata Up-Downfit North-SouthFigure 7.15: There is a well defined phase relation between the tunnelingcurrent and the block acceleration in the North-South and East-West direc-tions around approximately 18-19 Hz.87also be demonstrated by calculating the phase of the cross-spectral densitybetween the tunneling current and the accelerometer. Looking at the crossspectrum phase between the tunneling current and the acceleration in theNorth-South direction in figure 7.15 shows a very clear phase relation at19.0 Hz. It is even possible to fit this phase relation to that of a dampeddriven harmonic oscillator:φ = arctan(cmωω2 − ω2o)+ φo (7.10)where ω0 is the resonant frequency of the oscillator, c is the damping co-efficient and φo is a constant phase offset. The quality factor Q from thefit is Q = mcω0 ≈ 850; much higher than the Q of the block at 20 Hz. Theexistence of a well defined damped, driven harmonic oscillator phase rela-tion between the block acceleration in the North-South direction and thetunnel current noise suggests that the block motion is acting as the drivingforce, and the dilution refrigerator insert is acting as the harmonic oscil-lator. This establishes that the acoustic mode excites the block, and theblock motion is what directly excites the insert mode; causing noise at thetunnel junction. Further evidence for this can be seen in the cross spec-trum between the tunneling current and the acceleration in the East-Westdirection, where a less well defined, but still clear phase relation exists atabout 18.2 Hz, which is the same DRPM split slightly from the mode inthe North-South direction. Finally, in the up-down direction there is nowell defined phase relation, which is not surprising because up-down motionshould not be able to excite the fridge to swing side to side. This overlapof the two resonant frequencies at 19-20 Hz is also why the other strongresonant acoustic forces on the block (for example 15.4 Hz) do not show upas strongly in the tunneling current noise.88Chapter 8ConclusionA scanning tunneling microscope that works at a base temperature of 114mK was designed, built and characterized, along with much of the requiredexperimental infrastructure such as UHV sample preparation, and a lownoise electrical wiring scheme. The long hold time at our current base tem-perature will eventually allow for many exciting measurements to be made.However, for the microscope to really start producing results there are atleast three important things that need to be achieved:1. Tip transfer while cold needs to be completed. The redesign of theSTM head allows for tip transfer, but a fear of breaking the piezotubewhen pulling the tip out with the tip transfer claw prevented us fromattempting it. Designing a ’tip transfer sample plate’ that can grab thetip without being able to apply lateral forces to the piezotube shouldbe a priority.Not being able to transfer tips has definitely slowed progress sincesometimes tips get into a state in which they cannot be made stableby either tip shaping techniques or field emission. Since it takes abouttwo weeks to vent and and cool back down, changing the tip is currentlya very slow process.2. The effective temperature needs to be characterized, and the filtersneed to be fully implemented. The later should be relatively simpleas the filters are already built. If the effective temperature of themicroscope is not low enough then a cold filter scheme that is placedcloser to the microscope, such as the ones implemented in [15] shouldbe implemented.3. A fix needs to be implemented to eliminate 20 Hz noise in the tunnelcurrent. This noise is problematic because it shows up very strongly inmost imaging situations, and also causes a lot of noise in spectroscopy;requiring exceptionally long integration times to eliminate it. Luckily Ithink we have characterized the exact causes of the noise in the tunnel-ing current at this frequency. That being the overlap of two resonant89frequencies: the mechanical resonance of the dilution refrigerator in-sert, and the acoustic resonance that forces the block. Low frequencyacoustic room modes are difficult to attenuate, but shifting the res-onant frequency of the dilution refrigerator by stiffening the dilutionrefrigerator insert should help reduce transmission of the acousticallyforced motion of the block to the tip-sample junction; really any mod-ification that shifts the DRPM away from the 19.6 Hz acoustic roommode should vastly improve the performance of the DR-STM.Another possible way to reduce suceptibility to 20 Hz noise is by mak-ing the STM head stiffer. Although FEA modeling suggested that thelowest resonant frequencies of the STM head are in the kilohertz regime[19] it is common for mechanical joints to be looser than solid mechan-ical objects. Specifically, the sample plate gets wedged in place abovethe tip, and with thermal contraction at low temperatures it seemslikely that this is a mechanical weak point. We can see why this isan issue by modeling the stiffness as two springs in series. The springconstant of the structure ks and the spring constant of the joint kj :k−1tot = k−1s + k−1j =kjkskj + ks(8.1)However for kj << ks, which is almost certainly true since the ma-cor structure has a resonant frequency of several kilohertz, ktot ≈ kj .Thus the originally stiff STM head is basically shorted out mechani-cally via the low spring constant of the loose mechanical joint. Thiscan be improved by developing a sample clamping system that morefirmly clamps the sample plate to the STM head and raises the springconstant significantly.The three items above, in my view, are the big things that needs to bedeveloped and resolved for the STM to perform at a high level. It is quitepossible that the microscope is already functioning well enough to generateinteresting results, and this is particularly true for point spectroscopy mea-surements, but the above fixes will certainly improve the performance andusability of the STM.90Bibliography[1] Gerd Binnig, Heinrich Rohrer, Ch Gerber, and E Weibel. Surface stud-ies by scanning tunneling microscopy. Physical review letters, 49(1):57,1982.[2] JV Barth, H Brune, G Ertl, and RJ Behm. Scanning tunneling mi-croscopy observations on the reconstructed au (111) surface: Atomicstructure, long-range superstructure, rotational domains, and surfacedefects. Physical Review B, 42(15):9307, 1990.[3] S Hetal Pan, JP O’neal, RL Badzey, C Chamon, H Ding, JR Engel-brecht, Z Wang, H Eisaki, S Uchida, AK Gupta, et al. Microscopic elec-tronic inhomogeneity in the high-tc superconductor Bi2Sr2CaCu2O8+x .Nature, 413(6853):282–285, 2001.[4] Shun Chi, S Grothe, Ruixing Liang, P Dosanjh, WN Hardy, SA Burke,DA Bonn, and Y Pennec. 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Design and performance of an ultra-high vacuum scanning tun-neling microscope operating at dilution refrigerator temperatures andhigh magnetic fields. Review of Scientific Instruments, 84(10):103903,2013.[32] Udai Raj Singh, Mostafa Enayat, Seth C White, and PeterWahl. Construction and performance of a dilution-refrigerator basedspectroscopic-imaging scanning tunneling microscope. Review of Sci-entific Instruments, 84(1):013708, 2013.[33] Maximilian Assig, Markus Etzkorn, Axel Enders, Wolfgang Stiepany,Christian R Ast, and Klaus Kern. A 10 mK scanning tunneling micro-scope operating in ultra high vacuum and high magnetic fields. Reviewof Scientific Instruments, 84(3):033903, 2013.93[34] Anita Roychowdhury, MA Gubrud, R Dana, JR Anderson, CJ Lobb,FC Wellstood, and M Dreyer. A 30 mK, 13.5 T scanning tunneling mi-croscope with two independent tips. Review of Scientific Instruments,85(4):043706, 2014.[35] RC Dynes, V Narayanamurti, and J Pm Garno. Direct measurement ofquasiparticle-lifetime broadening in a strong-coupled superconductor.Physical Review Letters, 41(21):1509, 1978.[36] Kazumi Maki and Toshihiko Tsuneto. Pauli paramagnetism and su-perconducting state. Progress of Theoretical Physics, 31(6):945–956,1964.[37] Mostafa Enayat, Klaus Kern, and Peter Wahl. Construction and Op-eration of a milli-Kelvin Spectroscopic Imaging STM for the study ofcorrelated electron materials. PhD thesis, EPFL, 2014.[38] EP Roth and AC Anderson. Low-temperature thermal conductivityand specific heat of a machinable ceramic. Journal of Applied Physics,47(8):3644–3647, 1976.[39] RC Jaklevic and L Elie. Scanning-tunneling-microscope observation ofsurface diffusion on an atomic scale: Au on Au (111). Physical reviewletters, 60(2):120, 1988.[40] M Schmid, W Hebenstreit, P Varga, and S Crampin. Quantum wellsand electron interference phenomena in al due to subsurface noble gasbubbles. Physical review letters, 76(13):2298, 1996.[41] High performance ceramic cement. http://www.tedpella.com/adhesive_html/Adhesives-Nonconductive.htm#_16026. Accessed:2016-07-07.[42] KS Novoselov, AK Geim, SV Morozov, D Jiang, M Katsnelson, I Grig-orieva, S Dubonos, and A Firsov. Two-dimensional gas of masslessdirac fermions in graphene. nature, 438(7065):197–200, 2005.[43] Annalisa Fasolino, JH Los, and Mikhail I Katsnelson. Intrinsic ripplesin graphene. Nature materials, 6(11):858–861, 2007.[44] Wenzhong Bao, Feng Miao, Zhen Chen, Hang Zhang, Wanyoung Jang,Chris Dames, and Chun Ning Lau. Controlled ripple texturing of sus-pended graphene and ultrathin graphite membranes. Nature nanotech-nology, 4(9):562–566, 2009.94[45] Li Liu, Sunmin Ryu, Michelle R Tomasik, Elena Stolyarova, NaeyoungJung, Mark S Hybertsen, Michael L Steigerwald, Louis E Brus, andGeorge W Flynn. Graphene oxidation: thickness-dependent etchingand strong chemical doping. Nano letters, 8(7):1965–1970, 2008.[46] Signal recovery model 7265 lock-in amplifier. http://www.signalrecovery.com/our-products/lock-in-amplifiers/7265.aspx. Accessed: 2016-07-06.[47] John Bertrand Johnson. Thermal agitation of electricity in conductors.Physical review, 32(1):97, 1928.[48] W Chen, V Madhavan, T Jamneala, and MF Crommie. Scanning tun-neling microscopy observation of an electronic superlattice at the sur-face of clean gold. Physical review letters, 80(7):1469, 1998.[49] He´le`ne Le Sueur. Cryogenic AFM-STM for mesoscopic physics. PhDthesis, Universite´ Pierre et Marie Curie-Paris VI, 2007.[50] Spectrum control pi subminiature filter. http://www.richardsonrfpd.com/resources/RellDocuments/SYS_29/SLD_SCI3553000.pdf. Accessed: 2016-07-19.[51] API technologies corp pi filter. http://www.digikey.ca/product-detail/en/api-technologies-corp/1293-001/1171-1135-ND/5067619. Accessed: 2016-07-19.[52] Damien Charles Quentin. Powder filters for a dilution fridge scanningtunneling microscope. PhD thesis, University of British Columbia, 2016.[53] NI PCI-6229 daq card. http://sine.ni.com/nips/cds/view/p/lang/en/nid/14136. Accessed: 2016-07-14.[54] 731a sesimic accelerometer. http://www.wilcoxon.com/vi_index.cfm?PD_ID=33. Accessed: 2016-07-14.[55] COMSOL multiphysics. http://www.comsol.com. Accessed: 2016-08-1.[56] Anita Roychowdhury. Development of a dual-tip millikelvin josephsonscanning tunneling microscope. 2014.[57] Ide engineering. http://www.ideworld.com/. Accessed: 2016-07-18.95Appendix AGuidelines for Cooling Downthe DR-STMWe have thermally cycled the DR-STM > 10 times over the course of mywork at UBC and things have held up quite well over those thermal cycles.Due to the rather complex nature of the system a large number of stepsare required to bring the mixing chamber down to its base temperature andbegin measuring. This provides a brief explanation of most of the stepsrequired to cool down the DR-STM.1. The UHV system must be sealed with the pressure of the dilution fridgeUHV space and the central vacuum chamber in the low 10−7 mbar. Ifany work has been done on the STM then Au(111) can be measuredto verify proper STM operation. If significant work has been done onthe STM then the capacitance of all piezos should be checked and theresistance of the thermometers and heaters should be measured.2. If the dewar has not been used for a while ( > 4 months) or you haveother reason to believe that the dewar vacuum jacket may have itsvacuum compromised a turbo pump should be attached to the pump-ing port on the dewar and the vacuum shield should be pumped out.Caution is neccessary when opening the turbo pump to the vacuumshield as rushing gas can shred the delicate super insulation, so theneedle valve opening the vacuum shield to the pump should be crackedvery slowly. The dewar should then be pumped out to ≈ 10−5 mbar3. Next, one should start circulating a small amount of 3He/4He mixture.It is very important to constantly be circulating mixture while coolingthe STM because it helps prevent plugs from occurring in the tinycapillaries in the fridge. This also allows for an impedance test tobe performed. Typically mixture is circulated via the pump until thepressure in front of the pump (G3) is 850 mbar. Then one can close V1(the valve behind the roots pump) and watch the pressure rise on thegauge G1 that measures the pressure on the line that returns mixture96to the pump. Measuring the pressure on G1 over 10 minutes gives ameasure of how much mixture is getting through the capillary tubesin the fridge. If the pressure barely rises this definitely means there isa plug.While doing the impedance test it is a good idea to turn the RGA onto in the UHV system to make sure that there is no Helium mixtureleaking into the UHV space from the fridge. If a signal shows up onthe RGA the leak must be fixed before cooling down as superfluid He-4will leak out orders of magnitude faster when you cool the fridge downbelow 4.2K. Furthermore, introducing noble gases into a system inwhich high voltages are present is rarely a good idea since the voltagesfor dielectric breakdown are vastly reduced with easily ionizable atomssuch as helium. The group at UMD [34, 56] used 3He exchange gasinstead of a heat switch to pre-cool their STM and had severe prob-lems with their coarse piezos arcing due to remnant 3He sorbed ontothe piezos at dilution temperatures. Thus, leaks are a big issue thatneed to be addressed immediately! See past impedance tests at roomtemperature in the log book for approximate ’correct’ impedance testvalues’.4. Assuming all of the previous tests were passed the dewar can be liftedand filled with LN2. It is generally not neccessary to fill the dewarwith LN2 when pre-cooling the STM, but it is not a big deal if thishappens as the nitrogen can be blown out and saved anyways. Theone occassion we did fill the dewar with LN2 and measured for anextended period at 77 K we had a hold time of over 30 days. If you dointend to measure for extended periods of time at 77K it is best to beconservative with your nitrogen level since it is difficult to determinethe amount remaining. With the heat switch firmly engaged (presseddown and held by a clamp firmly) the STM will take approximately3-4 days to cool to 77K. It takes this long since the only good thermalconnection between the stm and the LN2 is through the 8mm diameterheat switch, the entire rest of the fridge is connected only by thinwalled stainless steel tubes – a very poor thermal conductor.5. While cooling the STM, the piezos should be run up and down throughtheir entire range. This is done to prevent them from freezing inplace as junk from the vacuum gets cryo-pumped onto the coarse piezotracks.Currently, we cool down the STM with the piezos tensioned so lightly97that they cannot run at room temperature. So continue to monitorwhether the piezos are able to move as the STM cools. Once they areable to move, start running them up and down.6. Again one should put in an Au(111) sample (or other sample if that’swhat is available, but gold is exceptionally easy to prepare and mea-sure since it does not react with contaminants in the chamber easily)and check that the piezos are running and also that the tip is stillmetallic/stable.7. Once the STM is at 77K and the tip has been checked it is possibleto cool down to LHE temperatures. To do so, all of the LN2 mustbe blown out of the dewar. This is done by pressurizing the dewar toa couple psi. The LN2 blow out tube gets screwed into the transferport on the dewar and LN2 will come out (quickly from the tube).It is important to attach a rubber hose to the end of the tube beforeblowing out the LN2 because otherwise LN2 will spray all over thedelicate measurement electronics. It is best to just blow the LN2 intoa transport dewar for later use.8. It is critical that all LN2 be blown out because freezing LN2 withhelium is extremely inefficient due to the rather large latent heat ofnitrogen and the small heat capacity of helium. It is better to have thedewar warm up well above 77K than to freeze LN2 with LHe. However,once this is done LHE transfer can begin. Make sure that the LHEfill tip (which directs helium to the bottom of the dewar rather thanspraying it in from the top) is used. It will take several hours to startcollecting LHE and then another hour or so to reach 40−60 % full onthe LHe level monitor. Once you have made it to somewhere aroundthat much helium you will notice that things slow down significantlyand eventually stop. The slow down occurs because at 40 % heightthe dewar belly opens up to a larger column and it takes longer tofill. Secondly the transfer will stall because we are forcing helium inthrough the very bottom of the dewar. So in order to transfer heliumwe need Ptransportdewar > pcryostatdewar+ρHegh. Eventually the heliumlevel becomes high enough we cannot transfer helium at a reasonablepressure.In order to solve this you stop the transfer and switch the the heliumrefill nozzle which sprays the helium onto the top of the LHe. Thiseliminates the ρHegh term and makes it much easier to transfer helium.The only reason we ever use the initial transfer tip is that by sending98the helium to the very bottom of the dewar you get a lot of coolingfrom the helium gas rising up through the dewar, whereas this is notneccessary when the dewar is already cold at 4.2 K9. Typically going from 77 K to 4 K is an all day affair, again it isimportant to run your piezos up and down through their entire rangeof motion while cooling the STM to prevent gases from sorbing ontothe piezo tracks. It is important that you get the dewar to greaterthan 60 % LHe level so that there is helium left by the next day.10. The next day the fridge should be below 10 K and one can typicallyprepare a sample and put the sample into the STM. After waiting forthe fridge to cool down it is possible to enter dilution mode and getto the base temperature of the fridge. This pretty much just involvesslowly letting mixture into the circulation loop so that it can condenseinto the mixing chamber. This should only take a few hours. TypicallyI will close the doors to the vibration proof pod and start approachingthe tip at this point.11. If you have made it this far and have a nice sample and tip then youare finally able to do STM at low temperature! Enjoy!99Appendix BTuning the Block viaAcceleration MeasurementsThe air spring isolators were purchased from IDE Engineering [57]. Theisolators have a damping system that allows the quality factor of the block-spring system to be tuned. At one point in the commissioning of the STM wehad the block become tilted by repeatedly floating and unfloating the block.The block was able to ’walk’ into a position so that when it was supposedto be properly floated it contacted the ground. Luckily, by measuring theresonant frequency of the block is is extremely obvious that something iswrong. This can be seen in figure B.1. To tune the damping of the blockthere are detailed instructions in the IDE manual for the isolators.1000 50 100 150 200Frequency Hz10−810−710−610−510−410−3ASDpA/√HzBlock Floating Properly vs NotBlock Resting on a LevelatorBlock Floating ProperlyFigure B.1: Comparison of block floated properly vs block partially restingon its levelators101

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