Cryogen-Free Scanning Probe Microscopy in Silicon Device Physics at Milli-Kelvin Temperatures

Cryogen-Free Scanning Probe Microscopy in Silicon Device Physics at milli-Kelvin temperatures

Seong woo Oh

A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy

Recommended for Acceptance by the Department of Physics Adviser: Jason R. Petta

Spin qubits housed in silicon quantum dots are rapidly emerging as a viable quantum computing platform. In recent years, there have been single- and two-qubit gate demonstrations, which showed high fidelities to the extent that implementing quantum error correction codes appears to be within reach. With the already existing industrial manufacturing infrastructure, semiconductor spin qubits are well poised to bring us ever closer to making quantum computing in everyday application a reality. There do stand a few technical obstacles in the way, however. One prominent issue has been the splitting of the two lowest lying valley states in the silicon band structure. The valley states, when their energy is comparable to the Zeeman splitting, have shown to often lead to spin-relaxation hotspots, which significantly increases the spin relaxation rate. In addition, the valley splittings have shown to vary greatly not only among different wafers but also at different locations across the same wafer. Having a scanning gate microscope to provide spatially resolved data could be key to tackling this problem. In this thesis, we report our progress toward building a scanning gate system probing silicon quantum devices. We have built and operated a custom scanning probe microscope to show that the biasing of the tip of the scanning probe could play the role of a plunger gate even on devices with overlapping gate structure. Given the scanning probe sensor being a quartz crystal tuning fork and the richness of the physics one could probe with a superconducting resonator, we have fabricated and characterized microwave resonators on a quartz crystal to show the microwave resonators can potentially be housed on the resonator to directly port all our existing microwave measurement techniques. We have also etched a quartz crystal in the shape of a tuning fork to show the feasibility of designing and fabricating a custom tuning fork for future microwave impedance measurements.

iii Acknowledgements

First and foremost, I would like to thank Prof. Petta for helping me cross the finish line. His vision and industry have always inspired me to dream bigger. Next, I would like to thank Prof. Yazdani for allowing me to work in his lab prior to my military service. The microscope training that I had received has been invaluable in building a new system in the Petta lab. I would like to thank Dr. Chen for providing the basis of and helping us modify the scanning probe design to make it compatible with our dry dilution refrigerator and Si/SiGe devices. I shudder at the thought of what may have been, had it not been for our chance encounter. I would like to thank Prof. Barnard at the University of Washington for the non-linear vibration damper design and advice on noise isolation technique for microscopy in pulse tube fridges. I would like to thank Dr. Jarosik for meeting with me on multiple occasions to discuss quartz crystal tuning fork and address my general circuitry questions. I would like to thank Prof. Wu for being on my pre-thesis committee and agreeing to be my thesis reader. I would like to thank Prof. Huse and Prof. Tully for agreeing to be on my thesis committee. I also would like to thank Dr. Vengalattore for my first exposure to research in physics as an undergraduate. I would also like to thank Dr. Lengel at SPECS-TII for generously sharing his expertise beyond the scope of the Nanonis technical support. I also would like to thank Mr. Hitchon for generously providing us with BeCu sheets of varying thicknesses for free. Those BeCu sheets were crucial in getting the system up and running. It would be wrong of me not to thank the wonderful staff in the Princeton physics department. I would like to thank Darryl Johnson, Julio Lopez, Ted Lewis, Steve Lowe, Bob Rickett, Bill Dix, Glenn Atkinson, Stanley Chidzik, Kate Brosowski, Lau- ren Callahan, Lisa Scalice, and all others I have failed to mention due to my bad memory. Please understand that your omission is not a reflection of my ingragtitude.

iv I have a lot to thank the people in the Petta lab for. I would like to thank Artem Denisov for being a beast of a physicist in both practical and technical sense. Similar to the way I think of Dr. Chen, I shudder at the thought of what if. I would like to thank Dr. Sigillito, Dr. Schupp, Dr. Croot, Dr. Gullans, and Dr. Ansaloni for being great postdocs in the Petta lab. The lab, including myself, thanks Travis for his lab coordination and management of cleanroom tools. I would like to thank Felix Borjans, Adam Mills, Susanne Zhang, Remy Delva, Mayer Feldman, and Charlie Guinn for being generous with their time to help me and inspiring the rest of the lab with their hard work. I want to thank Dr. Chakram and Dr. Patil for helping me with my undergraduate research projects. Also, it would be wrong of me not to express my gratitude toward Mr. and Mrs. Dare for their help during my high school days in Buffalo, NY. Speaking of Buffalo, I would like to thank Will for staying in touch with me all these years. Finally, I would like to thank Mr. Lew and Mr. Savas for their willingness to stick around within my ever shrinking social circle. Last, I would like to thank my family. I do not know how they have been able to put up with me all these years, albeit remotely. I hope dealing with me from a distance made it more bearable. Of all my family members, I feel most indebted to my father for his financial support for my education. His effort has been Herculean.

v To my family.

vi The work described in this dissertation has been published in the following articles and presented at the following conferences:

Rev. Sci. Instrum. (Submitted)

“Tuning Fork-Based Mobile Microwave Cavity Spectroscopy” Quantum Cavities Workshop by the Institut Quantique at the Universit´ede Sherbrooke and CIFAR, June 2019, Orford, Quebec (poster session)

The work not described in this dissertation has been published in the following articles and presented at the following conferences:

Science 351, 1184 (2016)

vii Contents

Abstract...... iii Acknowledgements...... iv List of Tables...... x List of Figures...... xi

1 Introduction1 1.1 Silicon Device Physics...... 2 1.2 Scanning Probe Microscope...... 7 1.3 Quartz Crystal Tuning Fork and Superconducting Resonator.....7 1.4 Thesis Overview...... 9

2 Microscope Design and Assembly 10 2.1 Design...... 10 2.2 Assembly...... 18

3 Setup and Operation 22 3.1 Initial Testing and Adjustment...... 22 3.2 AFM Operation...... 27 3.3 Noise Isolation and Characterization...... 36

4 Device Imaging 46 4.1 Physics Overview...... 46

viii 4.2 Design...... 51 4.3 Operation and Data...... 52

5 Quartz Tuning Fork Design and Fabrication 62 5.1 Design, Simulation, and Preliminary Test of Resonator on Quartz.. 62

6 Conclusion and Outlook 80

A Cryogen-free scanning gate microscope for the characterization of

Si/Si0.7Ge0.3 quantum devices at milli-Kelvin temperatures 84

B Preliminary Quartz Tuning Fork Etch Recipe 93

C Tuning Fork-Based Mobile Microwave Cavity Spectroscopy (poster) 96

Bibliography 98

ix List of Tables

3.1 Work functions and decay constants for selected materials...... 24 3.2 Geometrical parameters of qPlus sensor...... 30

5.1 Lengths of low and high Q resonators...... 68 5.2 Low Q resonator design frequency comparison...... 68 5.3 High Q resonator design frequency comparison...... 69 5.4 Low Q design Q comparison...... 69 5.5 High Q design Q comparison...... 69

x List of Figures

1.1 Bloch Sphere Representation of Qubit...... 3 1.2 Loss-DiVincenzo Proposal...... 3 1.3 Trapping Single Charges in Silicon...... 4 1.4 Valley Physics in Silicon...... 6

2.1 Schematic Diagrams of Pan Walker...... 12 2.2 Pan Walker Actuation Mechanism...... 13 2.3 Solidworks Renderings of Version 1 Microscope...... 15 2.4 Coarse Positioning Piezo Stacks...... 16 2.5 Scanning Piezo Tube...... 17 2.6 Scanning Piezo Tube After Assembly...... 17 2.7 Scanning Probe Microscope During Assembly...... 19 2.8 Printed Circuit Board Design...... 20 2.9 Printed Circuit Board With Dose Test Chip...... 20 2.10 Device and Probe Tip under Optical Microscope...... 21

3.1 Thermalization and Drift...... 25 3.2 Thermal Drift Tracking...... 26 3.3 Electrochemical Etching Setup...... 28 3.4 SEM Image of Electrochemically Etched Tip...... 29 3.5 AFM Sensor Preparation...... 31

xi 3.6 qPlus Sensor Anatomy...... 32 3.7 Comparison of AM and FM Mode...... 33 3.8 Schematic of the Frequency Modulation Mode Operation...... 33 3.9 Cryogenic AFM Signal Amplifer Testing:...... 35 3.10 HEMT Amplifier Simulation and Measurement Data Comparison... 36 3.11 HEMT Gain Data...... 36 3.12 Bandwidth Characterization...... 37 3.13 Microscope Calibration in AFM mode...... 38 3.14 Mechanical Noise Isolation Outside Vacuum Chamber...... 39 3.15 Mechanical Noise Isolation Inside Vacuum Chamber...... 40 3.16 Effect of Active Damping Unit (vertical)...... 43 3.17 Effect of Active Damping Unit (horizontal)...... 44 3.18 Noise Analysis...... 45

4.1 Signle Quantum Dot...... 49 4.2 Double Quantum Dot Shematic...... 50 4.3 Stability Diagram of DQD...... 50 4.4 Early Device Design Simulation...... 52 4.5 CAD Drawings of Early Device Designs...... 53

4.6 Demonstration of Scanning Gate Microscopy on a Si/Si0.7Ge0.3 Quan- tum Device (QPC design)...... 55 4.7 Stability diagram: Tip voltage versus side gates. (QPC design).... 56 4.8 Double Al Layer Device Design...... 57 4.9 Electron Loading via Biased Probe Tip on Second version of

Si/Si0.7Ge0.3 quantum device (Double Al layer device) - 1...... 58 4.10 Electron Loading via Biased Probe Tip on Second version of

Si/Si0.7Ge0.3 quantum device (Double Al layer device) - 2...... 59 4.11 AFM Reference Image for Kelvin Probe Method...... 60 xii 4.12 Kelvin Probe Imaging...... 61

5.1 High and Low Quality Factor Resonator AutoCAD design...... 64 5.2 AutoCAD Drawing of Hanger Resonators...... 64 5.3 Capacitive junction set up in Maxwell and Sonnet...... 65 5.4 Schematic representation of capacitive junction...... 66

5.5 Typical S21 Spectrum ABCD Matrix Method...... 67 5.6 Image of high Q resonator after wire bonding...... 70 5.7 Schematics of the CIA2 dunker setup...... 71

5.8 S21 of Low and High Q...... 72 5.9 Shorted hanger resonator in second chip...... 72 5.10 Design and Measured Resonance Frequencies-1...... 73 5.11 Design and Measured Resonance Frequencies-2...... 74 5.12 Resonator PCB...... 75

5.13 S21 Spectra...... 75 5.14 Etch Mask and SEM Images...... 78 5.15 High Magniﬁcation SEM Images...... 79 5.16 Tuning Fork Electrode Patterns...... 79

6.1 Tuning Fork Design Proposal...... 82 6.2 Next Microscope Design Iteration...... 82

xiii Chapter 1

Introduction

Attracted to the potential benefits of quantum computing classical computers are unable to access, scientists and engineers have worked tirelessly toward creating a scalable quantum computing platform. Various types of quantum computing platforms have been explored, with each platform having its own strengths and weaknesses. Spin-based quantum computing in silicon has become a strong contender thanks to silicon being an excellent host material for spins and the already existing industrial infrastructure for silicon based microelectronics. Despite the advantages that silicon spin qubits have over other competing platforms, it does have several technical draw- backs. One of the main challenges standing in the way of scaling the silicon qubit architecture is our lack of understanding of the two lowest-lying valley states in silicon. Over the past decade, various measurement schemes were developed and applied to better understand the valley degeneracy. Most of the techniques still fully rely on on-chip gate patterning. All of these approaches require the time-consuming cycling through multiple devices to acquire meaningful statistics. In addition, none of the approaches offers a way to acquire spatially resolved data in a non-invasive manner. A scanning gate microscope has the potential to be a technique that offers a high throughput measurement of valley splitting. We touch on the premise of silicon

1 quantum computing and devices designed and fabricated in connection with scanning gate microscopy, oﬀer a brief overview of the microscope constructed in my time in the lab, and outline the basics of quartz crystal tuning fork and desired modiﬁcations for future experiments.

1.1 Silicon Device Physics

The crux of quantum computing, irrespective of the form of physical realization, is the qubit. Similar to the classical qubit, a quantum bit, upon measurement, has two possible outcomes: 0 and 1 . However, unlike a bit, the general state of a qubit | i | i can be a superposition of both 0 and 1 described by the wavefunction | i | i

ψ = α 0 + β 1 , (1.1) | i | i | i

Such a general qubit state can be represented graphically on the Bloch sphere shown in Figure 1.1( 0 = and 1 = ). | i |↓i | i |↑i In 1998, Loss and DiVincenzo proposed trapping electrons with metal gates de- ﬁned on a silicon chip and operate them as qubits [1]. In this scheme, two qubit gates are implemented by modulating the tunneling barrier between neighboring electrons via a gate voltage. Modulating the barrier gate to increase wavefunction overlap realizes a Heisenberg exchange interaction J(t) according to Eq 1.2.

~ ~ Hs(t) = J(t)S1 S2 (1.2) ·

This leads to swapping of angular momentum between the neighboring electrons. For single qubit control, a local ferromagnet is selectively coupled to individual qubits. Given the topic of this thesis, it is interesting that the Loss and DiVincenzo paper brings up the possibility of pulsing a magnetic ﬁeld exclusively onto individual spins

2 Figure 1.1: Bloch sphere description of a qubit. An arbitrary superposition φ is represented | i by a vector along the surface of the Bloch sphere. The state vector’s conﬁnement to the surface of the sphere imposes the normalization condition on the qubit state.

Figure 1.2: Loss-DiVincenzo Proposal: (a) Schematic of two spins on neighboring localized islands, trapped in a semiconductor. (b) Spin-up and spin-down states of a single electron in the presence of a uniform magnetic ﬁeld, due to the Zeeman splitting, deﬁne qubit levels. Two qubit control is achieved by modulating a tunnel barrier between two neighboring dots. Single qubit control is achieved through selective coupling to a local ferromagnet. Spin readout is performed via spin-selective tunneling to a nearby reservoir [1].

3 (a) (b) PL1 PR1

S1 D1

IS,gS D2 S2 P

Figure 1.3: Trapping single charges in silicon. (a) Cross section of Si/SiGe heterostructures used to confine electrons in the vertical dimension. Left: Schematic of the heterostructure stack. Right: Scanning electron microscope image of a typical heterostructure. The different conduction band energies of Si and SiGe lead to the formation of a two-dimensional electron gas (2DEG) in the Si QW, if electrons are supplied by doping [2]. (b) Scanning electron micrograph image of a double quantum dots (DQD) device. The image shows the overlapping gate structure[2]. The S1,2 (source) and D1,2 (drain) gates are used to accu- mulate electrons from the separately doped region, where electrons can be injected and extracted through ohmic contacts. Gates depicted in green are barrier gates to control the flow of electrons between the quantum dots and source and drain leads. PL1,2, PR1,2, and P are plunger gates raising and lowering energy levels of the quantum dots. with a scanning-probe tip. This vision has been more or less achieved in recent Si/SiGe device experiments [3,4]. There have been promising demonstrations of scalability in recent experiments in the form of creating an array of quantum dots [5] and integrating a superconducting resonator to couple distant silicon qubits [6,7]. However there does exist an outstanding issue in building a silicon-based quantum computer. Bulk silicon has a six-fold orbital degeneracy. The strain induced by the lattice mismatch of the Si/SiGe heterostructure splits the degeneracy into four-fold and two-fold degeneracies [8]. As shown in Figure 1.4, it is the two lowest lying valleys that have posed a great challenge to silicon-based spin qubit technology. Electronic z confinement does break the two-fold degeneracy of the z valleys. However, the splitting typically ends up interfering with the desired two level system.

4 The Hamiltonian of the subsystem consisting of the z valleys on dot i can be ± written in the i, +z , i, z basis as | i | − i

0 ∆i HV,i = , (1.3)  ∗  ∆i 0     −iφi with complex valley coupling matrix element ∆i = ∆i e . The eigenstates of | | 1 iφi this system are i, = √ ( i, +z e i, z ), with eigenenergies E± = ∆i . As a | ±i 2 | i± | − i ±| | result, the valley splitting of dot i is EV S,i = E+ E− = 2 ∆i and φi is the valley-orbit − | | phase. The magnitude and phase of ∆i are physically rooted in the local properties | | of the quantum well [9]. For example, spatial variations in interface abruptness and disorder will cause ∆i to be a function of position in the plane of the quantum well, | | ∆i = ∆i (x, y), hence the term ”valley-orbit coupling.” The valley-orbit phase has | | | | no impact on the energy levels of a single quantum dot. However, it aﬀects the energy levels of a double quantum dot. For a system of two tunnel coupled quantum dots (dots i and j), in the basis of i, +z , i, z , j, +z , j, z , the Hamiltonian can | i | − i | i | − i be expressed as

0 ij/2 + EV S,i 0 tij tij

 0  0 ij/2 tij tij Hij(ij) =   (1.4)  ∗ 0∗   tij tij ij/2 + EV S,j 0   −   0∗ ∗   tij tij 0 ij/2  −    1 −iδφij 0 1 −iδφij with tij = 2 tc(1 + e ) the intra-valley coupling and tij = 2 tc(1 + e ) the intervalley coupling. This Hamiltonian results in four energy bands with two intra-valley

0 and two inter-valley anti-crossings determined by tin and tij, respectively [10]. Discovering a method to reliably engineer the z valley splitting to be large enough not to interfere with the logical qubit would be a welcome development. Yet, this has not been easy to attain due to the energy splitting’s extreme sensitivity to atomic-

5 scale interfacial details [9, 11, 12]. This leads to widely varying valley splittings among devices (25 300 µeV) [13, 14, 15, 16, 17, 18,2, 19] . Being able to collect − a large amount of valley splitting data would greatly help tackle this problem. Cy- cling through multiple devices is one way to acquire meaningful statistics, but cost and time consumption render this route unappealing. Developing a technique, while maintaining compatibility with the typical device measurement settings, to form a quantum dot at multiple locations on the same chip in a non-invasive manner would be much more preferable.

6 (a) (b) SiGe

Si 3

(nm) d 2 nm SiGe 0 0.3 0.8 I (a.u.) B4 (c) B1 B2 B3 B1 B2 B3 B4 SS P1P1 P2P2 DP3 DDSS P1P1 P2P2 DP3 4x 6x

100 Δ휙 = 0 Δ휙 = 휋/2

2x 0

EVS (μeV) E Bulk Si Strained Confine- -100 QW ment -200 -100 0 100 200-200 -100 0 100 200 휖 (μeV) 휖 (μeV)

Figure 1.4: Valley Physics in Silicon(reproduced from [13]). (a) First Brillouin zone for Silicon. The conduction band minimum in bulk Si is 6-fold degenerate. The tensile strain induced by the lattice mismatch of the Si/SiGe heterostructure separates the two z-Valleys from the in-plane valleys. Finally, the conﬁnement in the quantum well splits the remaining two valley states. (b) Atomic-resolution transmission electron microscope image of the quantum well. (c) Schematic of the cross section of a DQD with corresponding energy levels. Left: ideal quantum well, with large symmetric valley splitting and low intervalley coupling. Right: realistic quantum well with soft interfaces and steps in the QW, with smaller asymmetric valley splittings and strong intervalley coupling.

6 1.2 Scanning Probe Microscope

The prospects of being able to acquire spatially-resolved data on valley physics and potentially being able to implement the theoretical proposals outlined in Shim et al., (2019) [20] have motivated the construction of a scanning probe microscope designed to work with Si/SiGe devices. In the past, quantum dot experiments were performed with the tip of the scanning probe on GaAs and carbon nanotube devices. However, to our knowledge, it has not been done on Si/SiGe devices. We have heavily borrowed from the designs of existing microscopes [21] with modiﬁcations to work with typical Si/SiGe devices. A custom circuit board was designed to perform device physics with the microscope. The length of the scanning tube piezo was determined based on the typical topographical height variation due to dimensions of gates on Si/SiGe devices. Having to operate the microscope in a pulse tube dilution refrigerator was an extra challenge, as we had to introduce several measures to reduce the mechanical noise down to a reasonable level. We have successfully built and operated the microscope with Si/SiGe devices at 20 mK temperature. Also, we have achieved the root-mean-square noise in z of ∼ 2 nm for tip-to-device stability. In our device experiments, the voltage biased tip of the microscope has demonstrated its capability as a mobile plunger gate raising and lowering the energy levels of the quantum dot on Si/SiGe devices.

1.3 Quartz Crystal Tuning Fork and Supercon-

ducting Resonator

Quartz crystal tuning fork, a piezoelectric resonator, forms the bulk of the sensor in our newly built system. Quartz crystal tuning fork based microscope started emerging as a useful took for device characterization at low temperatures due to

7 its superior low temperature performance in the microwave regime and self sensing topography feedback doing away with the usual optical feedback requirement; for cryogenic experiments, stripline-type cantilever probes require optical feedback to achieve topography control, and the silicon based probe with built-in piezo-resistor for topography sensing does not have ideal microwave performance because the heavily doped silicon center conductor has a high loss for microwave transmission at liquid helium temperature [22]. Since the microscope is housed in a dilution refrigerator, using a quartz crystal tuning fork for sensing is intuitive. A conventional STM/AFM conductive tip, which takes on the role of a mobile plunger gate and provides spatially resolved data, opens up an avenue for interesting device experiments. To this end, we use W/PtIr wires. A conductive wire is glued to the end of the resonator and electrochemically sharpened. However, for the microscope to truly oﬀer a way to non-invasively characterize wafers and deliver high- throughput data in the microwave regime, integrating a superconducting resonator into the scanning probe tip appears to be a requirement for phase sensitive data acquisition in the single photon regime [20, 23]. Superconducting resonator has been successfully integrated in quantum dot devices in recent years and enabled microwave spectroscopy measurements to study valley physics in silicon devices [18, 13]. Geaney et al., (2019) had a superconducting resonator patterned on a silicon chip, which was glued to an oscillating prong of a commercial tuning fork. Although this does not require designing and fabricating a custom tuning fork, it does increase the complexity of the microscope; the resonator glued to the tuning fork is excited and read-out through a co-planar waveguide made from a printed circuitboard via inductive coupling. For this inductive coupling, the microscope has an additional set of piezo positioners to enable the coplanar waveguide to follow the tip of the scanning probe. We have tested the suitability of quartz as a superconducting resonator substrate and

8 etched quartz as a demonstration of feasibility of directly combining a quartz crystal tuning fork and a superconducting resonator.

1.4 Thesis Overview

In chapter 2, we document the design and assembly of the microscope with specific focus on the aspects in which this microscope is different from existing microscopes. In chapter 3, we explain the calibration and testing procedures for the microscope before the scanning probe tip preparation and cryogenic amplifier used for the frequency modulation atomic force microscope (FM-AFM) operation are discussed. We briefly touch upon the basics of the FM-AFM mode. We finish this chapter with the noise characterization of the system by analyzing data from the active damping system and by quantifying tip-to-sample junction stability. In chapter 4, we go into some device experiments performed under the microscope. We start with the most basic device design and add incremental changes. Also, we discuss how to scan a device without perturbing the device tune up in the form of Kelvin-probe imaging. In chapter 5, we fabricate and characterize hangar resonators on a z-cut quartz crystal wafer to demonstrate the compatibility of quartz with existing superconducting resonator designs. The measured data are shown to be in good agreement with expectations based on theory and simulation. In chapter 6, we look toward what needs to be done in order for the system to be capable of providing high-throughput data in a non-invasive manner.

9 Chapter 2

Microscope Design and Assembly

2.1 Design

To jump-start a scanning probe capability in the context of Si/SiGe physics, we heavily borrowed from conventional AFM/STM designs already in existence. To a large degree, the microscope is based on the time-honored Pan design [21] with several minor changes. The overall actuation mechanism for the x-, y-, and z-directions is as follows. In the original Pan-walker scheme, to move the load (microscope) in the z-direction, for example, the piezo controller sends high-voltage pulses sequentially to z-piezo stacks in order to move the piezos one at a time while other stacks hold the load in place. After the sequence of pulses is complete to displace the resting position of the load, the piezo controller slowly decreases the applied voltages to zero. However, this conﬁguration requires a pair of wires for each piezo stack. In order to simplify the wiring scheme, most modern microscopes typically assign only one pair of wires to each set of x-, y-, and z-piezo actuators. This approach leads to degraded coarse positioning performance, especially at low temperatures. Therefore, instead of assigning the same actuation voltage to all six z-piezo stacks, we grouped them into two sets. The top set of the z-piezo stacks, two of which are shown in the

10 middle red circles of Fig. 2.3 (b), and the bottom set of the z-piezo stacks, two of which are also shown in the bottom red circles of Fig. 2.3 (b), receive voltage pulses with an adjustable time delay for trouble free motion. Materials science-focused microscopes often forgo lateral positioning for the sake of mechanical stability. However, since we would always have a specific area of interest to bring our scanning probe to in order to locate engineered quantum devices, the ability to traverse the surface of a sample is important. Typically, chips are millimeters in scale, and the device area is on the order of several microns in scale. Therefore, in spite of the partial loss of mechanical stability, we adopted a walking mechanism based on xy-piezo stacks [24]. The three xy-piezo stacks (marked in red) in Fig. 2.3 (a), glued to the rectangular legs of the microscope’s main body, walk across sapphire plates on the titanium base. With the Nanonis SPM controller’s piezo motor controller (PMD4 version D) one can program an arbitrary time delay between the two sets of piezo motors. As explained in the previous paragraph, this time delay has been shown to be effective at preventing the z-piezo positioners from freezing at low temperatures. Both the xy- and z-piezo positioners are held in contact with sapphire plates using thin BeCu sheets as springs. The microscope slides across the sapphire plates for coarse positioning with respect to the area of interest on the device. For the xy piezo stacks, we used P-121.01T and for the z piezo stacks, we used PAXZ+0049 from Physik Instrumente. Since the scanning tube is the longest part of the center of the microscope, the dimensions of the scanning tube end up heavily influencing the overall shape of the microscope. Fine scanning of the sample is achieved using a piezo tube [see Fig. 2.5], which is housed inside the cylindrical body shown in Fig. 2.4(a). Generally, for mechanical stability and compactness of the microscope, the typical length of a piezo tube is around 1 inch or less. However, the total length extension linearly increases

d31VL with the length of the scanning tube as ∆L = t , where d31 is the vertical extension

11 Figure 2.1: Schematic Diagrams of Pan Walker(reproduced from [25]). (a) Top-down view of the Pan-walker design. (b) Side view along the cut denoted by the dotted line. (1) Scope body (made of titanium grade 2), (2) shear-piezo stacks (z direction), (3) sapphire contact plates, (4) prism (titanium grade 2), (5) scanning unit (AFM/STM tuning fork + tip), (6) scanning piezo-tube scanner, (7) BeCu spring plate, (8) sapphire ball bearing.

coeﬃcient, V is the voltage, L is the natural length of the tube, and t is the tube wall thickness. Given the typical vertical and horizontal dimensional proﬁle of our Si/SiGe devices, we decided to use a longer scanning tube. We chose a longer scanning tube (2 inches) in order to safely deal with 20 150 nm multilayer Al gate structure ∼ − of Si/Si0.7Ge0.3 devices [2]. In addition, the scan area available without activating coarse positioners is linearly dependent on the length of the piezo tube as ∆x = ∆y =

2 0.9d31VL , where d is the average of the inner and outer diameters of the scanning dmt m tube, and t is the thickness of the scanning tube [26]. We chose 50 mm, 6.35 mm, and 0.5 mm for the scanning tube length, outer diameter, and thickness, respectively in order to satisfy all scan dimensional requirements. When choosing the material for the piezo scanning tube, in addition to being vacuum and cryogenic compatibility, we considered the voltage dependent expansion coeﬃcient (d31 mentioned previously), which aﬀects the scan area available. From the material choices available [26], we

12 Figure 2.2: Pan Walker Actuation Mechanism (adapted from [25]). (a) Snapshot of the original Pan-walker conﬁguration of the piezo stacks during a coarse movement cycle. (Only four of the six z piezo stacks are shown.) In our setup with the Nanonis Piezo Motor Driver version D, z piezo stacks 1, 2 and 3, 4 would move in sync, respectively. (b) Voltage waveform applied to the piezo stacks as a function of time in the original Pan-walker conﬁguration. The arrow pointing at the red dashed line indicates when the snapshot is taken. Noe that z piezo 4 has not stretched back yet. chose EBL#2 for the tube material, despite the fact that in the STM community, EBL#4 is generally the preferred choice for its relative sturdiness and less temperature dependent variation of d31. In order to work with Si/SiGe devices, we designed the microscope with an accompanying printed circuit board in mind. Given the tight space inside the radiation shield of the fridge, we were forced to design a circuit board much narrower than the typical device circuit boards in the lab. Also, we decided to introduce a height elevation to the device area of the circuit board. We were inspired by our probe station where a long working distance microscope is used. The height elevation to the device area combined with the use of a long distance scope allow for rough alignment of the scanning probe tip and the device. The wedding cake like design (Fig. 2.8) of the circuit board greatly improved the ease of optical access during the rough alignment

13 of tip with respect to the device. Given the geometric constraint on the PCB, we ended up having only one Glenair connector, allowing us to have 24 as the maximum number of gates allowed on each device. We acknowledged at this point that given the mounting of the PCB under the base of the microscope and the location of the head of the scanning probe, extending the microwave measurement capability could become logistically diﬃcult[22]. Typically, MIM (microwave impedance microscopy) systems have their scanning probe pointing up in order to make it easier to route their microwave lines down to the tip of the scanning probe. We will discuss how this will be addressed in the future in chapter 6.

14 Figure 2.3: Solidworks images of the version-1 microscope are presented here (a) A frontal view of the microscope. Note the device circuit board placed under the bottom transparent piece. (b) Cross sectional view of the microscope. The red circles indicate four of the six z piezo stacks shown in the image. The red box is zoomed in for ﬁgure (c). (c) Zoom-in of the area boxed in red. The area circled in red indicates the qPlus sensor, which enables both STM and AFM measurement.

15 Figure 2.4: Coarse positioning piezo stacks are presented here. (a) The bottom of the main body of the scope is shown here. The cylindrical body holds the hexagonal piece, which houses the scanning probe sensor. The three xy-piezo stacks can be seen in this image. (b) An open view of the cylindrical body, showing two of the z piezo positioning stacks. (c) The two z piezo stacks that are not glued inside the cylindrical body are shown here. The back of the rectangular piece, made of titanium grade 2, gets pressed against the hexagonal piece housing the scanning probe sensor, in order to provide enough friction between sapphire plates and z piezo stacks. This allows the hexagonal piece to slide up and down in the vertical direction upon actuation of the z-piezo stacks. (d) A single z piezo stack before being glued with epoxy. All wires used for electrical connection are BELDEN 8083 magnet wire 34 AWG.

16 Figure 2.5: Scanning piezo tube during the assembly is shown here. It is a hollow and radially-polarized piezoelectric tube with electrodes patterned on the inner and outer surfaces. The outer surface is divided into 5 electrodes (4 quadrants and 1 ring at the top of the tube). The quadrants serve as x and y motion electrodes with deﬂection voltages of two polarities applied on the opposing sides. The inner surface is a signal electrode, which is grounded with respect to the outer electrodes. The ring electrode near the top of the tube is to provide a dithering motion to the qPlus sensor for the mechanical actuation. The metalic piece glued at the other end of the scanning piezo tube is the base. The two wires coming out of the hole are both glued to the inner electrode of the tube for grounding purposes. Two wires are used for some redundancy, in case one comes oﬀ later on.

Figure 2.6: Scanning piezo tube after the assembly is shown here. (1) AFM/STM qPlus sensor holder (2) and (3) sapphire plate z piezo stacks move across (4) opening to route scanning tube electrode wires out.

17 2.2 Assembly

In the scope assembly, we had to be mindful of several aspects. One was the Curie temperatures of piezo electric materials we chose for the scanning tube and coarse positioners. The Curie temperature for the scanning tube (EBL #2) is rated at around 660 ◦F. Since the Curie temperature of the positioners is rated at 300 ◦F, we set the oven temperature to 300 ◦F for all curing steps. When it came to gluing xy piezo stacks to the legs of the cylindrical body, it was important to ensure that the cured positions of the stacks were such that the bottom surfaces of the stacks are coplanar. The same principle applied to the curing of the sapphire plates, which the corresponding piezo surfaces move across. Therefore, all xy piezo stacks and their matching sapphire plates were cured simultaneously while the cylindrical body was put in the usual operating position. Once the curing of epoxy and assembly were complete, the electrical wires were soldered onto the inner ends of the bare copper segments. These segments were threaded through holes in ceramic bars mounted along the three pillars of the scope. In total, 27 wires are required. However, a lot of them can be merged together and only 10 unique signals are required (x,y,z(t), z(t+δt) coarse positioning, 1 dither and 4 quadrants of scanner and GND). The fully assembled microscope is shown in Fig. 2.7 (d).

18 Figure 2.7: Scanning probe microscope intermediate assembly images: (a) Image of the main body of the scope before curing the epoxy on the xy piezo stacks with a ruby ball sitting on top. (b) Close-up of the xy piezo stacks. The electrodes on the right are GND and the top and bottom pairs on the left are x and y electrodes, respectively. (c) The main body of the scope positioned upside down, showing the bottom surfaces of the x, y positioners. Each stack gets 3 wires, x, y and ground get one wire each. The curing of epoxy occurred in an oven at 300◦F. (d) Image of the microscope after fully assembled. Note the butterﬂy- shaped BeCu spring pressing against the ruby ball, which in turn pushes the scope body down to ensure adequate contact between xy piezo stack surfaces and opposing sapphire plates. 19 Figure 2.8: Printed Circuit Board Design: In order to improve the visibility of the device structure during rough alignment, we introduced a pedestal on our circuit board. With the 5 mm elevation in height, the surface of the chip is now on level with the top surface of the base of the microscope. This greatly enhances the visibility of the device under the optical microscope, as shown in Fig. 2.10.

Figure 2.9: Printed Circuit Board in Action: The printed circuit board with a dose test chip before an AFM imaging test is mounted on the accompanying wire bonder mount. The wings shown on either side of the circuit board are for mounting the PCB during bonding wires.

20 Figure 2.10: Rough alignment of tip with device: A typical view of the scanning probe’s tip roughly aligned with the device before closing the Bluefors fridge. Using a long working distance microscope, we achieve a coarse alignment in order to minimize the amount of time spent searching for the target area of the device.

21 Chapter 3

Setup and Operation

3.1 Initial Testing and Adjustment

One of the challenges in cryogenic microscopy is dealing with the freezing of the coarse piezoelectric positioners. We note that if the pressure on the z-piezo motors is excessive, the z-direction actuation tends to freeze at low temperatures. For optimal operation, the spring tension is adjusted at room temperature such that the ratio between the number of steps we need to take up and down to walk the same z distance is roughly 1.38 (here, a step means one voltage pulse sent to the z-piezos). When building a scanning probe microscope with STM/AFM capability, the initial troubleshooting steps are taken in the STM mode, as the AFM module introduces an additional layer of complexities in the form of phased locked loop, quartz crystal tuning fork, and a cryogenic ampliﬁer. For us, this was primarily to test and ensure that the coarse positioners and scanning tube were working as intended. We performed some STM measurements on a highly oriented pyrolytic graphite (HOPG) sample. The dimensions shown here are prior to piezo calibration at 4 Kelvin. There- fore, the numbers are nominal and must be divided roughly by a factor of 6. We tracked the feature marked in a red dashed circle shown in Fig. 3.1. Given the use of

22 thermal braids for thermalization of the microscope, rather than having a rigid mount on the mixing chamber plate, we wanted to characterize the additional time needed to achieve proper thermalization of the microscope with the mixing chamber plate. We characterized the thermal drift during the thermalization by tracking the feature shown in Fig. 3.1, as the temperature reading went from 4.16 Kelvin down to 3.96 Kelvin. In this measurement run, we did not circulate the He mix and only cooled down with the pulse tube. The x thermal drift was signiﬁcantly greater than the y thermal drift. Also, the x thermal drift was monotonic whereas the y drift was not, as the cumulative drift went down. After about 50 hrs, no noticeable drift was observed. With a proper thermal scaling of the scanning piezo tube, the drift was determined to be well below 3 nm. Given the typical size of gate structures on our devices, we determined that the thermal drift was negligible to the extent that we could start tuning our quantum dot devices without having to wait for the full thermalization of the entire body of the microscope. We expect that given the connections to the wire bond pads, the device would thermalize faster than the body of the microscope. With the STM measurement, we were able to have an order-of-magnitude feel for the mechanical oscillation between the tip and the graphite sample. When going from room temperature to 4 Kelvin, in order to prevent the tip from crashing into the surface, we had to lower the setpoint current from 500 pA to 50 pA, lowering the setpoint by an order of magnitude. Having a higher setpoint current means the tip is brought closer to the surface. Given the pulse tube induced noise, we were unable to ﬁnd the PI loop settings to prevent the loss of the tip without lowering the setpoint current. Setting the setpoint current to 50 pA resulted in an order of magnitude oscillation of the tunneling current but given the tip’s average position being farther away from the surface, we were able to acquire topographic scans of the same area continuously without a complete loss of the tip at the 50 pA setpoint.

23 Element Al Au Cu Ir Ni Pt Si W Φ(eV ) 4.1 5.4 4.6 5.6 5.2 5.7 4.8 4.8 κ(A˚−1) 1.03 1.19 1.09 1.21 1.16 1.22 1.12 1.12

Table 3.1: Work functions and decay constants for selected materials

The electron tunneling probability can be obtained by matching of the wave functions and their derivatives ∂ψ/dz at the two interfaces, sample–barrier and barrier–tip. The tunneling probability comes out as follows:

18κ2k2 T e−2κs, (3.1) ∝ (k2 + κ2)2 ·

√2m(E−|U| ) In Eq 3.1, κ denotes the work function dependent decay constant, k = ~ denotes the wave vector of the tunneling electron, and s denotes the distance between the tip and the sample [27]. Given the exponential dependence on the tip-to-sample distance, for the typical values of the work function (5 eV), the current decays by one order of magnitude per 1 A˚. From this, we came to believe that the rough oscillation of the tip, with the PI feedback loop on, was on the scale of one Angstrom. Several cooldown sessions were performed in the STM mode for BeCu spring adjustment to optimize the tension on the x, y, z piezo positioners in order to prevent the freezing of coarse positioning motion, the steps of which were outlined in Chapter 2.

24 Figure 3.1: Thermalization and Drift: At 4.16 Kelvin (mixing chamber plate), we found step edge with a discernible feature on the graphite surface. We tracked this feature over time to characterize the true thermalization and thermal drift of the microscope. Note the diagonal and occasional horizontal streaks in the image. The diagonal ones are mechanical in nature. The horizontal ones are tip changes due to tip-to-sample instability.

25 Figure 3.2: Thermal Drift Tracking: We scanned the same area starting at 4.16 Kelvin down to 3.96 Kelvin over a 50 hour span. After roughly about 50 hrs, no thermal drift was measured. Similar to Fig. 3.1, the dimensions shown here are prior to proper temperature dependent piezo calibration.

26 3.2 AFM Operation

Ultimately, our experiments would not involve the tunneling of electrons between the scanning probe’s tip and the sample surface. The AFM (atomic force microscope) mode is more relevant to the experiments that the system is designed for.

3.2.1 qPlus Sensor and Tip Preparation

A fair amount of time was spent on figuring out how to electrochemically etch a 0.001 inch thick tungsten wire to produce sharp tips on a consistent basis. A double lamellae dropoff etching procedure was adopted to that end[28]. In the double lamellae drop off, we lower a positively biased rod into the beaker containing the etchant (KOH), and the tungsten wire to be etched gets lowered through the etchant bubble (negatively biased) into the same beaker as the rod. Once everything is in position, we turn on the voltage source, which starts the etching process. In this scheme, gravity pulls on the segment of the wire to be dropped off into the beaker, cutting off the etching when the tip is sharp. This also pulls on the side of the wire that ends up becoming the tip of the scanning probe, leading to a desirable aspect ratio of the tip. The positively biased stainless steel rod needs to remain immersed in the solution held in the beaker. Also, the end of the wire to be etched needs to remain immersed in the solution held in the beaker to close the circuit. Etching is done by the thin bubble of etchant formed inside the ring. To create a membrane, which is what etches the tungsten wire and create a tip, the ring was slowly dipped in and pulled out of the etchant. Once etching is done, the portion of the wire below the ring is going to fall off. For the etching, we used 5 V bias and 4.5g of KOH in 40mL of DI water. Fig. 3.4 shows the typical tungsten tips we achieve with the recipe outlined here. Given the sharpness and the aspect ratio of the tip, we concluded that we would have

27 Figure 3.3: Electro Chemical Etching: (a) Image showing how to align a bare tungsten wire onto the end surface of the prong of the qPlus sensor. Using conductive epoxy, the bare tungsten wire is glued. (b) Image showing the electrochemical etch setup used in producing qPlus sensor probe tip. enough resolution in the AFM mode to be able to resolve typical gate structures on our devices.

28 Figure 3.4: Electrochemically Etched Tip: (a) Image showing a typical result of electrochemically etching a tungsten wire following the recipe outlined above (b) A zoom-in of the tip shown in image (a).

29 The mechanical resonator one uses is the crux of the microscope. In our setup, we have chosen to employ a qPlus resonator. As opposed to the quartz crystal resonator where two prongs oscillate opposite to each other, the qPlus conﬁguration has only one free-to-oscillate prong with the other prong ﬁrmly glued to the resonator’s mount. We purchased custom designed resonators that only have a single oscillating beam from the start (Nanosurf S 1.0B). The sensor’s resonance frequency changes in its interaction with the sample. Therefore, it is important to characterize the natural eigenfrequency. For a rectangular beam with width w, thickness th, and length L, the spring constant k is given by Eq 3.2.

3 Eγ w th k = · · , (3.2) 4L3

where Eγ is Young’s modulus. Additionally, the eigenfrequency of a harmonic

∗ ∗ oscillator is given by f0 = k/m , where m is the eﬀective mass. For a beam with length L, width w, heightp th, a constant cross section, and constant mass density ρ, the eﬀective mass is given by m∗ = 0.243m = 0.243 ρ w th L. As a result, the · · · · fundamental eigenfrequency comes out to be Eq 3.3.

th f0 = 0.162 υs, (3.3) · L2 ·

where υs is the speed of sound in quartz given by υ = Eγ/ρ.

Type L(µm) Le(µm) th(µm) w(µm) k(N/m)p f0(Hz) electrodes qPlus S1.0B 2360 1600 214 127 1800 32768 4

Table 3.2: Geometrical parameters (L: length of beam, Le: length of electrode, th: thickness theory of prong, w: width of prong), stiﬀness k, eigenfrequency f0, charge per deﬂection Sq .

Broadly speaking, AFM imaging is available in two different modes: Amplitude Modulation (AM) and Frequency Modulation (FM) mode. In the AM mode, the resonator (generally either a cantilever or a quartz crystal tuning fork) is driven to oscillate at a fixed frequency slightly above the natural resonance frequency. The 30 Figure 3.5: AFM Sensor Preparartion: (a) After gluing a bare tungsten wire onto the end surface of the free oscillating prong of the qPlus sensor, we install it on the test setup to sweep the sensor frequency and confirm the existence of a mechanical resonance. (b) Once the bare tungsten wire glued on the prong is etched, the qPlus sensor head preparation is complete. There are three wires bonded to the electrodes on both the qPlus sensor and the base. The Hesse GmbH wirebonder, typically used for device bonding, is used to connect qPlus and base electrodes. interaction between the tip and the sample changes the oscillation amplitude, from which information is extracted. However, this method is more popular in ambient conditions, as operating an AFM with a reasonably high quality factor in the AM mode under vacuum makes the scanning period impossibly long. Also, operating in the FM mode is less damaging to the scanning probe’s tip. In the FM mode, the excitation frequency tracks the resonance frequency, which changes in response to the tip’s interaction with the sample. The phase locked loop uses the fact that the input and output signals have a phase difference of π/2. By zeroing the phase shift, the feedback loop can track the resonance frequency. The schematic of the FM mode operation is shown in Fig. 3.8

31 Figure 3.6: qPlus Sensor Anatomy (reproduced from[29]): (a) qPlus sensor (Nanosurf Type S1.0B). The top/bottom electrodes (A) and the side electrodes (B) serve for a differential deflection detection, the center electrode (C) on the front provides electrical contact to the tip. There are differential deflection detection reading electrodes (connected to A and B) on the flip side as well. (b) (left) Cross section of the free-to-oscillate beam and the typical placement of the electrodes. The top and bottom electrodes (red) are connected, as are the side electrodes (blue). (right) Distribution of the electric field when the beam is deflected.

32 Figure 3.7: Working points in amplitude modulation mode (red dots) and in frequency modulation mode (green dots). The frequency modulation mode traces the resonance frequency of the oscillating lever.

Figure 3.8: Schematic of the Frequency Modulation(FM) Mode Operation: At the resonance frequency, the phase shift between input and output signal is π/2. This fact is used in the FM mode to control the excitation frequency. An extra proportional integral control loop is operated to keep the excitation on resonance. The input value for this loop is the phase between excitation and oscillation signal as it is calculated by the internal lock-in ampliﬁer, the output value is the excitation frequency or simpler the shift in excitation frequency ∆f. This control loop is called phase loop. The frequency shift ∆f is directly proportional to the force gradient that is aﬀecting the lever oscillation. The output of the phase loop will be used as an input to control the distance between the probe tip and the sample, keeping the frequency shift and thus the force on the tip constant.

33 3.2.2 Cryogenic Ampliﬁer for AFM Readout

The qPlus sensor (quartz crystal oscillator) readout signal is important, as it plays a crucial role in maintaining the tip-to-sample junction stability. Electrical noise from the amplification stage is hard to distinguish from the readout signal of the tuning fork and, in turn, the feedback circuit reads it as part of the frequency shift. Since a longer coaxial cable introduces greater parasitic capacitance, having an amplification stage as close to the source of the signal is generally advised. However, because most transistors’ charge carrier freezes at a cryogenic temperatures, it is a challenge to find an amplifier that works inside dilution refrigerators. High-electron mobility transistors (HEMTs), often made of GaAs, are well known for having a finite transconductance even at low temperatures. We decided to take an existing HEMT amplifier in our lab but replace some surface mount component values to adjust the bandwidth to the kHz range in order to achieve a reasonable gain around the qPlus sensor operating frequency (between 25 and 35 kHz). Looking at the circuit schematic, we determined that by increasing the value of the capacitor (indicated with the red arrow in Fig. 3.9), we could achieve the desired bandwidth. With the capacitance value set to 282 ad 470 nF, the gain of the amplifier was simulated in LT Spice. The result of the simulation was compared to the measured gain of the amplifier to show a good agreement. However, the plot of the measured gain was acquired after the calibration data (roughly -13 dB across the given frequency range) were subtracted from the raw data (calibration data are acquired to determine the loss of the bare circuit without the device under test). Given that when operating the microscope, the calibration data would be included in the raw data to be used in the feedback loop, we had to modify the circuit so that the loss was moderate. We changed the capacitance value (indicated with the blue arrow in Fig. 3.9) to 10 uF, which resulted in a much higher raw transmission data. This ended up becoming our amplifier circuit in the eventual AFM setup. After seeing a satisfactory gain, we identified the 3 dB point as part of

34 Figure 3.9: Cryogenic AFM Signal Amplifier Testing: The amplifier should provide a max- imal gain while keeping its own electrical noise to the measurement to a minimum. The cryogenic amplifier that the lab has used over the years for sensor dot readout in Si/SiGe devices was repurposed for qPlus sensor readout. The value of the capacitor (indicated with the red arrow) was adjusted in order to move the bandwidth such that it includes the typical qPlus sensor resonance (25-35 KHz) (Instead of ATF 38143, the actual circuit has ATF 34143). For the simulation and measurement shown in Figs. 3.10 (a) and (b), 11 nF was used (indicated with the blue arrow in Fig. 3.9). For the fit shown in Fig. 3.12 and eventual operation of the amplifier, 10 uF was used. the bandwidth characterization. Since we were interested in the effect of the capacitor (indicated with the blue arrow) on the transmission of the input signal, we fit Eq 3.5 to the data after subtracting the calibration data. The fit shown in Fig. 3.12 shows 3 dB around 15 kHz. This confirmed that the setup would work well with the typical qPlus sensor resonance values.

Vout S21 = 20log( ggain), (3.4) Vin

V ωRC out = , (3.5) Vin √1 + ω2R2C2

35 Figure 3.10: HEMT Amplifier Simulation and Measurement Data Comparison. (a) HEMT amplifier simulated gain plots. The black trace is the simulated gain plot in the intial configuration (15 nF). The red trace corresponds to 282 nF. The blue trace corresponds to 470 nF. (b) HEMT amplifier measured gain plots. Note the qualitative similarities with the simulated gain plots.

Figure 3.11: HEMT Gain Characterization: With the capacitor value set to 10 uF (indicated with the blue arrow in Fig. 3.9), the S21 was measured again. (a) Raw data. (b) Calibration data (transmission without the ampliﬁer) shown here were subtracted from the raw data and used for curve ﬁtting in Fig. 3.12.

3.3 Noise Isolation and Characterization

Several measures were implemented both outside the vacuum chamber and inside the vacuum chamber of the Bluefors fridge in order to minimize the mechanical noise transferred to the tip-to-sample junction. The XLD fridge was conﬁgured with some

36 Figure 3.12: Bandwidth Characterization: Fitting was done to determine the 3 dB point. noise isolation features incorporated. It had isolation bellows installed around the T piece in order to decouple the mechanical noise of the gas handling system and the wall of the shielded room from the inside of the fridge chamber, as shown in Fig. 3.14. Also, we took up the remote option for the pulse tube motor so that it does not sit mounted to the top of the fridge directly. An active damping unit (AVI-400/LP for high frequency and LFS-3 for low frequency) was installed to not only decouple the pulse tube noise of the fridge from the microscope, but also partially decouple the mechanical noise of the surrounding area. Inside the vacuum chamber of the fridge, instead of having a rigid mount for the Si/SiGe device and the microscope, we used 3 linear springs made of beryllium copper for mechanical decoupling of the microscope from the mixing chamber plate. The length of the springs is adjusted to so that the device is roughly 30 cm below the mixing chamber plate. In the initial testing of the microscope in the STM mode, we realized the need to add a damping mechanism to the oscillation of the microscope on the BeCu springs. As a quick fix, we added a disk made of titanium above the 37 Figure 3.13: Operation of the microscope in AFM mode. (a) Typical amplitude A and phase φ of the qPlus sensor signal at 20 mK as a function of frequency offset ∆f. The center frequency is 27.499 kHz and the quality factor Q 17,600. (b) z-spectroscopy is used to ∼ determine the frequency shift-to-distance conversion factor ( 6.433 107 Hz/m) − × around the setpoint frequency ∆f = 3.625 Hz. This conversion factor becomes useful in noise characterization (c) AFM image of a three-layer aluminum gate stack fabricated on a silicon surface. (d) A line-cut through the data in (c), showing the heights of the different gates. butterfly BeCu spring to mount an open copper box above the microscope. A block with samarium-cobalt magnets is installed on a ladderlike bar to provide magnetic damping to the microscope’s oscillation. Each inner side of the open copper box interacts with a magnetic disk, leading to the desired damping effect. The magnetic damper is shown in Fig. 3.15. After implementing all the noise isolation and damping measures, we did two quantitative analyses of the noise reduction. Due to time constraint, we only con- ducted analyses of the active damper’s noise isolation effect. First, we routed the the

38 Figure 3.14: Mechanical Noise Isolation Outside Vacuum Chamber: Three measures were implemented to reduce the mechanical noise transfer to the inside of the Bluefors XLD fridge where the microscope is housed. First, the mechanical decoupling implemented in the form of isolator bellows (left dashed box). This was implemented to mostly minimize the noise transfer from the fridge’s gas handling system. Second, we implemented the remote option for the motor design with the rotary valve/motor assembly separated from the pulse tube expander (left dashed box). Third, we installed spring stages, actuated by AVI-400/LP and LFS-3 between the cryostat support frame and the aluminum slabs on which the fridge rests.

signals of the accelerometers inside the spring stages of the active damping unit. The signal output is the power spectral density (PSD) in units of V/√Hz. We integrate the power spectral density to acquire the RMS vibration noise, de- ﬁned as Eq 4.1. In the case of accelerometer PSD, the integrated noise is in the units of V.

f 0 2 0 IZ[1, f] = [S(f )] df . (3.6) s 1 Z Each of the two spring stages operated by the AVI-400L/P and LFS-3 sensors have 8 accelerometers, with 4 in the vertical direction and the rest in the horizontal direction. In Figs. 3.16 and 3.17, we show some of the sample PSD and their integrated noise plots. The spring stages are actively actuated by the two sensors: AVI-400L/P and LFS-3. The AVI-400L/P is designed to actively cancel mechanical noise from 1 to 39 Figure 3.15: Mechanical Noise Isolation Inside Vacuum Chamber: Two measures were implemented to reduce the mechanical noise transfer from the last temperature stage (mixing chamber plate) to the microscope. First, the microscope is hanging by three linear springs made of beryllium copper. Second, we installed a simple Eddy current damper in the form of an open copper box mounted on the top of the scope with the magnet holding titanium bar mounted under the mixing chamber plate. In addition, all wires that come in contact with the microscope were kept ﬂexible, and the copper braids used for thermalization were annealed to minimize the mechanical noise transfer. Image (a) shows the closed side of the Eddy damper copper box. The white Macor piece is introduced to provide an angular degree of freedom to align the samarium-cobalt magnets with inner surfaces of the box. Image (b) shows the inside of the copper box with three of the four magnets shown. Each of all four inner sides of the copper box has a dedicated damping magnet.

200 Hz and passively thereafter. However, it is known to be rather ineﬀective in the frequency range where pulse tube noise exists (around 1.4 Hz), and LFS-3 sensor was designed to improve the noise suppression at the range of 0.2 to 2 Hz. Unfortunately, the data presented in Figs. 3.16 and 3.17 say otherwise. The LFS-3 sensor appears unable to correct for rotational vibration, which is what happens at the pulse tube. The main pressure pulse at 1.4 Hz interval causes the pulse tube cold head to expand and twist, and the impulse has a square-wave character and therefore has all the har- monics of 1.4 Hz. Rather, having the LFS-3 turned on appears to increase the overall

40 noise level. When the noise level only with AVI-400L/P turned on is compared to the noise level without any of the sensors turned on, the integrated noise does appear to decrease. However, the PT noise of 1.4 Hz does appear to be consistently worse at least in the vertical direction. Ultimately, we were most interested in the tip-to-sample junction stability, as this dictates a lot of the measurement noinse. Therefore, we quantitatively analyzed the microscope’s noise characteristics by measuring the power spectral density of the tuning fork resonance frequency. As discussed in the previous section, the phase locked loop in the microscope controller unit tracks the shift in the resonance frequency of the qPlus sensor (tuning fork). We measured the power spectral density of the shift in the resonance frequency of the qPlus sensor, which is in the units of Hz/√Hz. Integrating this power spectral density was enough to allow us to conclude that the tip-to-sample junction stability indeed improved with the AVI-400L/P sensor on, we wanted to confirm this in the unit of distance. Therefore, we acquired the frequency-to-distance conversion factor by performing the z-spectroscopy, shown in Figure 3.13(b). The steps taken to acquire the plot shown in Fig. 3.13(b) are as follows: i.) Choose a setpoint frequency (3.68 Hz, in this specific case) where the scanning piezo tube stabilizes. ii.) Note how much the scanning tube piezo had to expand in order to reach the setpoint frequency and choose the z-sweep range appropriately, so that the frequency shift includes the setpoint while the tip does not crash into the sample surface for the entire sweep range. iii.) Perform multiple sweeps over the selected z-range while measuring the shift of the tuning fork resonance frequency and signal average. Fig. 3.13(b) shows the raw data acquired from z-spectroscopy. We extract the frequency-to-distance conversion factor in Hz/nm from the linear fit around the frequency setpoint (shown in Fig. 3.13(b). This conversion factor is required to convert the frequency noise power spectral density (units of Hz/√Hz) to tip-to-sample noise power spectral density in (units of nm/√Hz).

41 Since the frequency-to-distance conversion factor from the z-spectroscopy performed in the previous section is acquired from the linear fit around the frequency of 3.68 Hz, the frequency power spectral density is measured at the setpoint of 3.68 Hz in order to be able to accurately convert the frequency fluctuation to the distance fluctuation equivalent. The resulting tip-to-surface power spectral density is shown in Fig. 3.18(a). In order to test the effectiveness of the active vibration damper, we measure the tip-to-surface power spectral density with the AVI-400L/P on and off. The integrated noise plotted in Fig. 3.18(b) shows that the main contributions to the noise occur at around 120, 140 and 300 Hz. Overall, the damping system reduces the noise by 16%. We find the noise level of our system to be comparable to other setups [30, 31, 23], which have reported 2.1 nm or more for the tip-to-sample vibration.

42 Figure 3.16: Power Spectral Density and Integrated Noise (vertical): Since the pulse tube noise is at around 1.4 Hz, we focused on the eﬀect of the active damping unit in the low frequency range. The PSDs in (a) and (b) are plotted on the log-log scale. The integrated noise plots are on the linear scale. In all plots, the red arrows indicate the 1.4 Hz PT noise contribution. Interestingly, the low frequency sensor LSF-3 seems to, rather than dampen the noise, slightly increase the total noise level. In addition, although the overall noise seems to be quieter with the AVI-400L/P turned on, the 1.4 Hz PT noise seems to get ampliﬁed with the active damper on.

43 Figure 3.17: Power Spectral Density and Integrated Noise (horizontal): Observations similar to those of Fig. 3.16 are made. Although the worsening of the 1.4 Hz PT noise does exist in the horizontal direction, the extent of the worsening is shown to be less.

44 (a)

(nm/√Hz)

z S 0.1 Active Damping Off Active Damping On (b)

(nm) ] ]

f 1 [1 [1 Hz,

z Active Damping Off I Active Damping On

1 10 102 103 f (Hz)

Figure 3.18: Noise analysis. (a) z-position noise power spectral density SZ acquired with the active damping system (AVI-400/LP) turned oﬀ and on. (b) Integrated noise IZ over a frequency range of 1 to 1000 Hz with active damping turned oﬀ and on.

45 Chapter 4

Device Imaging

The Petta lab has produced some stunning devices over the years with the advent of the overlapping gate architecture[2], culminating in a 9 dot device capable of shuttling electrons from one end to the other[5]. In addition, the lab has successfully integrated a superconducting resonator on Si/SiGe quantum devices[32], demonstrating impres- sive technological advances of spin-photon coupling[33, 34] and probing valley degrees of freedom[18], which are often detrimental to the integrity of spin qubits. Given the complexity of these devices and our desire to have a better spatial understanding of our devices, especially in the context of valley splitting, we began to think about adding a new tunable knob in the form of introducing a movable gate. Prior to our eﬀort, applying scanning probe microscopy techniques to devices physics has been demonstrated on carbon nanotube[35] and Ga/GaAs devices[36]. However, it was never done on Si/SiGe devices. This chapter recounts the journey of exploring the few unknowns of Si/SiGe devices in the context of scanning probe microscopy.

4.1 Physics Overview

In this section, we will brieﬂy go over the physics needed to understand the data to be presented later on. In a rather simple description called ”the constant interaction 46 model,” where the Coulomb interactions are parametrized by a single, constant capacitance C, which is the sum of all capacitive contributions from source, drain, and gates, and the single-particle energy-level spectrum is independent of the number of electrons, the total energy U(N) of a dot with N electrons in the ground state is given by

2 N [ eN + CSVS + CDVD + CGVG] U(N) = − + En, (4.1) 2C n=1 X N where the last term, n=1 En, is the sum over the occupied single-particle energy

levels En, which dependsP on the characteristics of the conﬁnement potential. Next comes the quantity called ’electrochemical potential,’ denoted as µ(N). This is the energy required to add the Nth electron to the dot, deﬁned as

1 Ec µ(N) U(N) U(N 1) = (N )EC (CsVs + CDVD + CGVG) + EN , (4.2) ≡ − − − 2 − e

e2 where EC = C is the charging energy. Here, µ(N) denotes the transition between the N-electron ground state and the (N 1)-electron ground state. Unlike the energy − of the dot, the chemical potential of each state in the dot shifts linearly with respect to gate voltage. In the low bias regime, as shown in ﬁgures 4.1 (b) and (c), one can adjust the gate voltage such that only µ(N) sits in the bias window. When the chemical potential is not positioned inside the bias window, no electron is allowed to tunnel from source to drain via the dot. This arrangement is called the Coulomb blockade. When the gate voltage is properly adjusted to have the chemical potential inside this bias window, the Coulomb blockade is lifted, and an electron can jump from source to dot to drain sequentially. This cycle is known as single-electron tunneling. The magnitude of the current registered depends on the tunneling rate between the dot, source, and

47 drain. In the single-electron tunneling regime, if the plunger gate voltage is swept while measuring the current, one could observe a trace similar to ﬁgure 4.1 (d). The spacing between µ(N) and µ(N 1) is called addition energy, deﬁned as −

Eadd(N) = µ(N + 1) µ(N) = EC + ∆E, (4.3) −

where ∆E is the energy spacing between two discrete quantum levels, which can be zero if two electrons are added to the same spin-degenerate level. Although our double quantum dot experimental results are not shown in the thesis, in anticipation of DQD experiments in the near future, we will brieﬂy go over DQD physics here as well. Similar to the single dot case, we will start with the equation for the total energy. Using the terms shown in 4.2,

1 2 1 2 1 U(N1,N2) = N EC1 + N EC2 + N1N2ECm Cg1VL(N1EC1 + N2ECm) 2 1 2 2 − e 1 1 1 2 2 1 2 2 Cg2VR(N1ECm + N2EC2) + ( C V EC1 + C V EC2) + Cg1VLCg2VRECm, −e e2 2 g1 L 2 g2 R (4.4)

where EC1(2) is the charging energy of the individual dot 1(2), ECm is the electro-

static coupling energy, and -e is the electron charge. ECm is the change in the energy of one dot when an electron is added to the other dot [37].

When Cm = 0, Eq. 4.4 reduces to

2 2 ( N1 e + Cg1VL) ( N2 e + Cg2VR) U(N1,N2) = − | | + − | | , (4.5) 2C1 2C2

which is the sum of the energies of two independent dots.

In the limit of Cm/C1(2) 1, Eq. 4.4 reduces to →

[ (N + N e ) + C V + C V ]2 U(N ,N ) = 1 2 g1 L g2 R . (4.6) 1 2 − | | ˜ ˜ 2(C1 + C2)

48 Figure 4.1: Single quantum dot (reproduced from [38]). (a) Schematic representation of a single quantum dot deﬁned with source and drain contacts and a plunger gate. (b), (c) Schematic diagrams of the electrochemical potential levels of a quantum dot in the low-bias regime. In (b), no energy level falls in the bias window. In (c), The µ(N) level is in the bias window, leading to a single electron tunneling current, the magnitude of which depends on the tunneling rate between the dot and the reservoir both on the left and right. (d) Plot of the tunneling current through the dot as a function of plunger gate voltage.

This is the energy of a single dot with a charge N1 + N2 and a capacitance of ˜ ˜ ˜ C1 +C2, where C1(2) = C1(2) Cm is the capacitance of dot 1(2) to the outside world. − Eﬀectively, the double quantum dot has reduced to a large single dot.

One interesting case is when Cm is in between the limits shown in 4.3(a) and (c). For double dots coupled in series, a conductance resonance is found when electrons can tunnel through both dots. This condition is met when three charge states,

(N1,N2), (N1 + 1,N2), and (N1,N2 + 1), become degenerate. There are two kinds of such arrangements, as shown in 4.3 (d). (N + 1,M) (N,M + 1) (N,M) − → → corresponds to the sequential tunneling of an electron from the left lead to the right lead. (N + 1,M) (N,M + 1) (N + 1,M + 1) corresponds to the sequential − → → tunneling of a hole in the direction opposite to the electron.

49 Figure 4.2: Double quantum dot schematic (reproduced from [37]). Double quantum dot schematically represented as a network of resistors, capacitors, and reservoirs.

Figure 4.3: Stability diagram of DQD (reproduced from [39]). Stability diagram for the limit of zero mutual capacitance (a), intermediate capacitance (b), and large mutual capacitance (c). (d) Zoom-in on an edge consisting of two adjacent triple points where three diﬀerent charge states are degenerate in energy and electrons can pass through the device.

50 4.2 Design

Given the device fabrication expertise that has matured over the years in the Petta lab, it was a logical decision to retain as much commonality with the existing designs as possible. The main concern we had at the initial stage was overlapping gates’ screening of electric ﬁelds, which may hinder the scaning probe’s ability to modify the 2 dimensional electron gas and form a quantum dot. Therefore, in our COMSOL simulation, we tried a very simple design, focusing on the feasibility of the dot formation on Si/SiGe devices by just introducing a pair of ohmic and a pair of barrier gates only, as shown in Fig. 4.4 (a). In the simulation, the tip height is assumed to be 1 nm away from the surface of the device and, to keep the simulation geometry simple, we did not introduce the impact that the aspect ratio of the probe’s tip has on the 2DEG; the tip is modeled as 50 nm in diameter. The simulation showed the feasibility of the dot formation. We proceeded to iterate device design, fabrication, and measurement under the microscope. We will provide a quick overview of the device designs here before presenting the data acquired from each design in the next section. The design shown in Fig. 4.5 (a) is originally intended to be a quantum point contact (QPC). However, in our measurement, instead of working as a QPC, it showed the formation of a quantum dot. The design shown in Fig. 4.5 (b) is the ﬁrst multi-layer device where ohmic gates and barrier gates are laid down in two separate aluminum deposition layers. In this measurement run, the scanning probe’s ability to act as a plunger gate was fully demonstrated with columob peaks. In addition, we demonstrated the scanning probe’s ability to acquire topographic information of samples in what is called “Kelvin Probe” method[40].

51 Figure 4.4: Early device design simulation. (a) The geometry of the device in the COMSOL simulation is shown here. The width of the barrier gates is chosen to be on the same order of magnitude as typical barrier width of other devices. However, the gap between the barriers is much wider. The purpose of the simulation was purely to see if it would be feasible to form a quantum dot with the tip of the scanning probe, given the depth of the 2DEG in Si/SiGe devices (80 nm). (b) COMSOL simulation of the electron density in the QW with the left ohmic, right ohmic, left barrier, right barrier, and tip set to 0.7, 1, 0, 0.65, and 1.7 Volts, respectively.

4.3 Operation and Data

Consistent with the way we typically operate other Petta lab devices, we cooled the Bluefors XLD fridge down to 4 Kelvin and formed the 2DEG in our device. After the base temperature of 20 mK was reached, we moved the scanning probe’s tip near the surface of the device in the AFM mode (the operation of the microscope in the

52 Figure 4.5: Early device designs that were fabricated and measured shown in KLayout. (a) The geometry of the quantum-point-contact like device is shown here. The dimensions are 30, 60, 230 nm, in the numerical order of the labels. The device was originally intended to be a quantum point contract (QPC) but was shown to form a quantum dot. The device’s gates are all formed in one layer of aluminum deposition (b) The geometry of the device consisting only of ohmic gates and barrier gates. The dimensions are 35, 77, 260 nm, in the numerical order of the labels. The barrier and ohmic gates are formed in two separate layers of aluminum deposition.

AFM mode is described in the AFM section above). Once the tip was brought near the surface, we scanned a few topographic images in the AFM mode (near but not directly over the device) and oriented ourselves with respect to the target device with the help of a multitude of positional markers patterned across the device surface. Given the design of the device as a QPC, the pinch-off voltage was first identified, as shown in Fig. 4.6 (b). We then scanned the device under test in the AFM mode to locate the side gates and ohmic gates, as shown in Fig 4.6 (c). With the voltage bias of the scanning probe’s tip set to 0 V, side gates set to 85 mV (pinch-off voltage) and

VSD = 50 µV, we positioned the tip around 100 nm above the device and mapped the current as a function of spatial coordinates, as shown in Fig. 4.6 (d). Due to the difference in the work functions of different materials, the probe tip, despite being set to 0 V, still influenced the energy level of the confinement, which is shown as closed concentric curves around the device. The device intended to be a QPC actually

53 formed a quantum dot. We proceeded to produce a stability diagram as a function of

Vtip and VG, as shown in Fig 4.7. From this data set, two line cuts were performed to examine Coulomb peaks and identify how strong the scanning probe tip’s lever arm is, in comparison to that of VG. As opposed to the densely packed peaks in Fig. 4.7 (b), the scarcity of the peaks over a larger voltage sweep range is noticeable. From this, we concluded that the lever arm (capacitive coupling to the quantum dot) of the probe’s tip is roughly 100 times less than that of the side gates. In the context of the weak lever arm of the scanning probe’s tip and the fact that the quantum dot of the device tested was prepopulated with the side gates, the question became whether it was possible to load single electrons purely by the scanning probe tip’s voltage adjustment. In the experimental run of the QPC device, we learned that scanning the topography of the device in the AFM mode, even with the tip voltage set to 0 V, often leads to switching of the device, which means the device operation characteristics, such as dot shape and pinch-off voltage, look different. This is because, with the tip coming so close to the device, the device can suffer from an electrical shock due to the different metals’ work function. Also, there is potential danger of the device getting outright destroyed[41]. Therefore, we only performed AFM scans of the markers surrounding the device in order to locate the target. Then, we withdrew the tip (tip moved away from the surface of the device, corresponding roughly to 470 nm) and positioned the tip above where the device was. Then, we incrementally brought the tip closer to the surface of the device manually until the distance roughly corresponded to 100 nm. With O1=B1, O2=B2, and probe’s tip set to around 245, 268, and 380 mV, current was measured as a function of the tip position, as shown in Fig. 4.8 (b). This data set shows closed concentric curves, similar to Fig. 4.7 (b). After tracing out the energy levels of the quantum dot, we tested the probe tip’s ability to induce a dot without the help of on-chip gates. We withdrew the probe tip

54 Figure 4.6: Demonstration of scanning gate microscopy on a Si/Si0.7Ge0.3 quantum device (QPC design). (a) Schematic of the local potential induced by the tip with a negative voltage bias. In order to create a quantum well, one would apply positive voltage (positive in a relative sense). (b) Current I through the device (see inset) as a function of the voltage VG on the splitgates. The dotted line marks the value of VG chosen for the scanning gate measurements. The pinch-off voltage of the device shown in the inset is identified as VG = 85 mV with VSD = 50µV. Also note that close to the pinch-off (VG = 60 mV), we observed few sharp Coulomb peaks indicating that the QD was starting to form somewhere in the conducting channel. (c) AFM topographic image of the scanned area around the device. (d) I as a function of the tip position with the tip voltage Vtip = 0. The tip is parked roughly 100 nm above the surface of the wafer. Note that the center of the quantum dot is slightly off the center of the device. No filtering or data smoothing is used. about 470 nm away from the device surface (the maximum distance the microscope controller settings allowed) and measured current as a function of barrier gates 1 and 2. We did not observe any current through the ohmic gates, as can be seen in Fig. 4.9 (a). However, when the tip was brought closer to the distance of 100 nm, we were able to observe a stability diagram, typical of a single quantum dot, as shown in Fig. 4.9

55 Figure 4.7: Stability diagram: tip voltage versus side gates. Dashed lines deﬁne the linecuts. (a) Current I is measured as VG and Vtip = 0 are swept from 280 to 320 mV and -200 to 200 mV, respectively. Horizontal and vertical dashed lines deﬁne the line cuts for Coulomb peaks as functions of side gates and tip voltage values, respectively (b) Coulomb peaks as a function of VG. (c) Coulomb peaks as a function of the tip voltage.

(b). The data show that the dot was relatively well coupled to both barriers. Based on this observation, we proceeded to measure the tunneling current as a function of Vtip to produce Fig. 4.10. From this, we concluded that the probe tip is indeed capable of playing the role of a stand-alone movable plunger gate. In addition to the confirmation that the voltage biased tip of the probe is capable of forming a dot and loading electrons in lieu of an on-chip plunger gate, we confirmed the scanning probe’s ability to provide qualitative scanned images of devices in the Kelvin probe mode. In our scanning probe setup, the phased locked loop of the controller tracks the shift of the mechanical resonator’s oscillation frequency, which rises from the force interaction with the surface[42]. More specifically, the frequency 56 Figure 4.8: Demonstration of scanning gate microscopy on a Si/Si0.7Ge0.3 quantum device (double Al layer device with barrier gates). (a) An SEM image of a dose test device with similar structures as the eventual real device. (b) I as a function of the tip position with the tip voltage Vtip = 380 mV. No filtering or data smoothing is used. All data are acquired at the base temperature of 20 mK. shift of the mechanical resonator reflects the force gradient following Eq. 4.7 (ts in the subscript refers to tip to sample).

dF 0 ∆f ts =: F . (4.7) ∝ dz ts

Additionally, a metallic system is expected to have a parabolic voltage dependence of the force gradient, and the curvature of the parabola is determined by the capacitive coupling between tip and sample. These relations are shown in Eq. 4.8.

2 0 1 d C(z, U) 2 F = (U UCPD) . (4.8) ts 2 dz2 −

where UCPD is the electrostatic potential diﬀerence between two metals that are in contact and in thermodynamic equilibrium, and C(z, U) is the tip-sample capacitance. Given z (distance between tip and sample) and U dependence of the force gradient, it was expected that height and material change across the surface of the device would be reﬂected in the frequency shift of the qPlus sensor.

57 Figure 4.9: Demonstration of loading of electrons on a Si/Si0.7Ge0.3 quantum device (double Al layer device with barrier gates). (a) Current I is measured as a function of B1 and B2 gate voltage values with the probe tip biased at 386 mV and parked as far away from the device as the setup allowed (roughly 470 nm from the surface). Note the total absence of current through the ohmics. (b) Same measurement as (a) with the probe tip brought closer (100 nm away from the surface). The stability diagram shows what is typically observed in a single quantum dot. Note the similarities between ﬁgure (b) and Fig 4.3 (d).

We were able to test the eﬀects of height, material dependent capacitive coupling, and the voltage bias of the probe tip. First, we scanned a gate structure far from the active device area in the FM-AFM mode, as shown in Fig. 4.11 (a). Then, over the exact same scan area, we plotted the frequency shift of the qPlus sensor of the scanning probe as a function of x,y coordinates under varying z position and voltage bias of the tip. We tried 60 and 134 nm above the surface of the device for z positions and 0 and 10 Volts for the bias of the tip. The results are presented in 4.11 (a) through (d). From this, we concluded that we can, in fact, directly scan the surface of the active area of the quantum dot device without risking damaging the gate structures by crashing the tip in the AFM mode while staying minimally invasive to the 2DEG underneath.

58 Figure 4.10: Coulomb peaks measured as a function of Vtip are a clear sign that electrons are getting loaded by the probe tip. The scanning probe’s tip was parked at 100 nm above the surface of the device.

59 Figure 4.11: AFM Reference Image for Kelvin Probe Method: (a) A gate structure far from the device was scanned in the AFM mode to be used as a reference image for the Kelvin probe imaging. (b) A line cut is plotted along the vertical red line to show the height of the gate.

60 Figure 4.12: Kelvin probe imaging demonstration: For all four images, the same area as Fig. 4.11 (a) was scanned, in the Kelvin probe imaging mode. For images (a) and (b), the tip was parked 134 nm above the surface of the device. For images (c) and (d), the tip was parked 60 nm above the surface of the device. For images (a) and (c), the tip was biased at 10 V. For images (b) and (d), the tip was biased at 0 V. It is clear that one achieves higher resolution when the probe tip is closer and the voltage bias is higher.

61 Chapter 5

Quartz Tuning Fork Design and Fabrication

5.1 Design, Simulation, and Preliminary Test of

Resonator on Quartz

As the experiments that we have in mind require the scanning probe’s microwave resonator to be operated in the single photon regime, a high quality factor microwave superconducting resonator takes the place of a chemically etched sharp metalic tip, used in the standard microwave impedance microscopy setup. Since a superconducting resonator is intended to be integrated into the scanning probe’s quartz tuning fork, it is beneﬁcial to study resonator design’s compatibility with quartz when the material is used as a substrate. Due to the simplicity of the design and ease of fabrication, hanger resonators are often patterned, and scattering parameters are measured when testing a new wafer. For the purpose of testing the suitability of quartz as a substrate, hanger resonators of various quality factors and resonance frequencies are designed, fabricated, and characterized.

62 5.1.1 Resonator Design

Design characteristics of hanger resonators are well understood, as they have been patterned and measured many times on silicon [43]. In general, it is desirable to select dimensions of resonators in order to have the impedance matched. Most RF instruments have 50 Ω termination, and so resonator dimensions are chosen to give 50 Ω characteristic impedance. The dimensions shown in Fig. 5.1 are chosen to give a characteristic impedance of 50 Ω for silicon substrates. Often, it is desirable to intentionally design a high impedance resonator, as higher impedance leads to a larger amplitude for the electric field; one example of this being desirable is when a resonator is coupled to a quantum dot. For this reason, the same dimensions are used for resonators on quartz. However, the length of the coupling region for the hanger resonators is modified in order to achieve different capacitive coupling strength. The longer the coupling region between the transmission line and the bracket of the hanger resonator, the stronger the capacitive coupling. Higher capacitive coupling means more energy is leaked, and therefore the quality factor of the resonator is designed to be lower. In the S21 parameter measurement, energy transmission is measured between the two ports of the center line, shown in Fig. 5.1. Near the center line, there are 6 hanger resonators with slightly different lengths. Those 6 resonators show up in the S21 spectrum measurement as 6 dips as energy is leaked into the resonators at their resonance frequencies. The characteristic impedance of a resonator is a function of relative dielectric constant, r, track width, gap width, and dielectric thickness. Under the assumption that r = 3.78 (the most often cited number for quartz), with the given dimensions and a 500 mm thick quartz substrate, the characteristic impedance comes out to be

Z0 = 83.69 Ω [44].

63 Figure 5.1: AutoCAD drawing of hanger resonators (dimensions indicated in µm). (a) Overall CAD design and (b) Zoom-in of the coupling area

Figure 5.2: AutoCAD drawing of hanger resonators (dimensions indicated in µm)

64 Figure 5.3: Capacitive junction set up in (a) Maxwell and (b) Sonnet. The capacitive coupling segment is set as a variable.

65 Figure 5.4: Schematic representation of capacitive junction.

With all the dimensions of the resonator and characteristic impedance determined, the only parameter missing to calculate the design quality factors and resonance frequencies is the capacitance between the hanger resonators and the center line. We use two methods to simulate the capacitance value of the junction between the center line and the hanger resonator. The ﬁrst method is to use “ANSYS Maxwell” to directly simulate the capacitive coupling. The direct simulation gave 2.1074 and 0.53687 fF for low Q and high Q resonators respectively. The second method is to simulate the S21 parameter with Sonnet and then compare it to the corresponding value from the ABCD matrix for transmission Based on the schematic representation shown in Fig. 5.4, one can write down the corresponding ABCD matrix as follows:

AB 1 1 1 0 = iωC (5.1)      1  CD 0 1 Z 1      0        Then, given that the S21 parameter is given as

66 Figure 5.5: (a) Typical S21 spectrum from the ABCD matrix. (b) Zoom-in on 1st resonance dip.

2 2 S = (5.2) 21 A + B/R + CR + D L L

One has a transmission spectrum as a function capacitive coupling [45]. By ﬁtting this to the earlier Sonnet simulation, one can obtain the capacitance. From this, the obtained capacitance values are 1.28 and 0.38 fF for low Q and high Q resonators respectively. Since the Sonnet results and Maxwell results are oﬀ by less than a factor of 2, we conclude that both methods do result in reasonable capacitance values. For future calculations, we proceed with the Maxwell results.

Design frequencies and quality factors are often obtained from the full the S21 spectrum from the ABCD matrix, from such a plot as shown in Fig. 5.5; the position of the dip corresponds to the resonance frequency, and the frequency divided by the full width at half maximum corresponds to the quality factor. However, we wanted to have another way to obtain those values. To that end, we were able to obtain design frequencies and quality factors from the analytical expressions from [43]. The following equations are used.

67 2 2Z0ω1/4ω0C 2Z0ω1/4C ω0 ω1/4 = − − , (5.3) − π ≈ π

ω0 ω1/4 2 − , (5.4) ω ≈ − πQ 1/4 r c where ω1/4 is the angular frequency when the quarter wave condition is met, and ω0 is the “loaded” resonance frequency that depends on the coupling capacitor C, which is explained earlier. Below are the lengths of the low Q and high Q resonators.

low Q resonator lengths Length(mm) High Q resonator lengths Length(mm) 1 4.5756 1 4.3556 2 4.4503 2 4.2626 3 4.3606 3 4.2316 4 4.3586 4 4.1376 5 4.3366 5 4.1146 6 4.2306 6 4.0056

Table 5.1: Lengths of low and high Q resonators.

Using the equation for the ω1/4 condition,

c 2π ω1/4 = (5.5) √r 4l where l is the length of a resonator. From the ABCD matrix method and analytical expressions, resonance frequencies and quality factors are obtained and compared.

Low Q resonator Low Q resonator Designed ω (GHz) Designed ω (GHz) (Analytical) 0 (ABCD) 0 1 10.4952 1 10.49 2 10.7884 2 10.79 3 11.0086 3 11.00 4 11.0136 4 11.01 5 11.0691 5 11.07 6 11.3442 6 11.34

Table 5.2: Low Q resonator design frequency comparison.

68 High Q resonator High Q resonator Designed ω (GHz) Designed ω (GHz) (Analytical) 0 (ABCD) 0 1 11.0853 1 11.09 2 11.3267 2 11.33 3 11.4095 3 11.41 4 11.6682 4 11.67 5 11.7333 5 11.73 6 12.0519 6 12.05

Table 5.3: High Q resonator design frequency comparison.

Low Q resonator Low Q resonator Design Q Design Q (Analytical) (ABCD) 1 11,686 1 11,597 2 11,055 2 10,972 3 10,614 3 10,447 4 10,604 4 10,630 5 10,498 5 10,442 6 9,991 6 9,944

Table 5.4: Low Q design Q comparison.

One can notice that for both resonance frequencies and quality factors, the two methods are in good agreement. After getting results in good agreement from both methods, we proceed to fabrication.

5.1.2 Resonator Fabrication and Data Acquisition

Here, a brief description of the resonator fabrication recipe is provided. A 0.5 mm thick quartz wafer was diced into 10 mm by 10 mm chips with the ADT dicing saw

High Q resonator High Q resonator Design Q Design Q (Analytical) (ABCD) 1 163,171 1 160,374 2 156,277 2 153,578 3 154,012 3 151,316 4 147,246 4 145,123 5 145,613 5 143,015 6 138,001 6 135,657

Table 5.5: High Q design Q comparison.

69 Figure 5.6: Image of high Q resonator after wire bonding. available in the QDNL. Prior to depositing a 50 nm thick layer of niobium acetone, IPA sonication, and 5 minute long oxygen plasma stripping were done on the wafer to clean the surface. After Nb deposition with the AJA deposition system, S1818 photoresist was spun and resonators were patterned with Heidelberg DWL66. 2 low Q and 1 high Q chips were patterned on the same 10 mm by 10 mm chip. After development in MF319 to expose the parts of the Nb that need to be removed, the South Bay reactive ion etcher was used to etch Nb. The remaining photoresist was washed oﬀ, and a new layer of photoresist was spun. It was taken back to the ADT dicing saw and diced into 2 low Q and 1 high Q resonator chips. The chips were bonded to a PCB to be tested in the CIA 2 dunker setup.

Fig. 5.8 shows S21 spectra of low Q and high Q resonators measured. Note that the second dip present in the ﬁrst S21 spectrum of low Q is missing in the secondS21 spectrum. Fig. 5.10 shows plots of design and measured resonance frequencies. With the S21 spectra of the chips acquired, we move on to analyze the data.

5.1.3 Data Analysis

S21 spectra in Fig. 5.8 and plots of design and measured resonance frequencies in Fig. 5.10 show several features that warrant closer inspection. First, the middle 70 Figure 5.7: Schematics of the CIA2 dunker setup. plot in Fig. 5.8 has the second dip missing. Second, Fig. 5.10 shows a systematic offset of about 1.2 GHz between design resonance frequencies and measured resonance frequencies of both high and low Q resonators. Last, the third S21 spectrum plot in Fig. 5.8 has the baseline about 25 dB higher than other plots. The missing dip is explained by the fact that the corresponding resonator on the second chip was shorted in the fabrication process, as shown in Fig. 5.9. A systematic shift between design resonance frequencies and measured resonance frequencies sug- gests that r = 3.78 used for capacitance simulation is different from the true value of the quartz wafer. Given that r is dependent on crystal direction and various factors, such as heating, it is reasonable to believe that r for the wafer could be greatly different; r could go as high as 5.4 for Z cut [46]. When capacitive coupling at the coupling junction is simulated again with r = 5.2, it resulted in 2.71 and 0.70 fF for low Q and high Q resonators respectively. The new capacitive coupling strengths do lead to design frequencies much closer to measured frequencies, as can be seen in 5.11.

71 Figure 5.8: S21 spectra of low Q and high Q resonators (2nd dip missing in middle plot).

Figure 5.9: Shorted hanger resonator in second chip.

72 Figure 5.10: Plots of design(green) and measured(blue) resonance frequencies (note the systematic oﬀset of around 1.2 GHz). 73 Figure 5.11: Plots of design(green) and measured(blue) resonance frequencies with new C (note greater agreement between design and measured frequencies). 74 The third seeming anomaly, that the third spectrum has a higher baseline by 25 dB, can be explained in terms of the diﬀerent losses that the resonator chips experience due to the PCB. It is an intrinsic feature of the PCB used for the measurements. Fig. 5.12 shows where the two low Q and one high Q chips are placed on the PCB. The high Q resonator chip is placed where less loss is experienced.

Figure 5.12: Front view of sample box which PCB sits on (red dots indicate lossy channels).

Figure 5.13: S21 spectra through diﬀerent ports with background subtracted (note higher baseline in red).

75 5.1.4 Preliminary Quartz Etching Attempt

After having conﬁrmed that the standard superconducting resonator recipe in Petta lab is compatible with quartz crystal as its substrate, we tried etching a quartz crystal wafer in the shape of a tuning fork. As mentioned in Section3, dimensions of the prong inﬂuence the natural frequency of the tuning fork. Therefore, our design dimensions of the tuning fork, except for the thickness, are roughly chosen in accordance with the dimensions of the AB38T commercial tuning fork [47]. A 10 x 10 x 0.1 mm quartz chip was used, consistent with the thickness of the quartz wafers mentioned in literature[48]. The etching recipe used is roughly consistent with what is outlined in Hida et al., (2009)[48]. However, to accelerate the speed of etching, we did perform

◦ ◦ the etch in NH4HF2at 90 C, instead of 80 C[49] (The details of the recipe used in the etch are provided in ??.). A z-cut wafer was used for its piezoelectric property and the crystal direction dependent anisotropic etching characteristic. The etching rate of the z-axis is about a hundred times greater than those of the parallel crystal planes to z-axis. Also, the etch rate along the x and y direction are known to be equal. Based on this, we could disregard the orientation of the etch mask with respect to the plane perpendicular to the z axis. We wrote the etch mask in the usual photolithographic technique and deposited chromium and gold to define the etch mask. The etch mask had to be written on both front and back sides of the quartz chip. Ideally, both masks would ideally overlap each other. We use the bracket below the tuning fork shown in Fig. 5.14 (a) as an alignment mark. We pattern the tuning fork and bracket shaped masks on the front surface of the quartz chip. Once the tuning fork and bracket masks are fully defined after gold deposition on the front surface, we flip the chip over and pattern the same tuning fork without the bracket on the back side. We use the corners of the bracket as reference points to align the back surface mask with the front mask. We went through the same deposition process for the back surface.

After removing the photoresist, the chip was placed in NH4HF2 etchant (7 grams of 76 NH4HF2 crystal in 11 mL of DI water). The chip was monitored till it was visually confirmed that the z direction etch went through to define the prongs. Several SEM images were taken to inspect the surface quality of the result. The sidewalls resulting from the etch along the z axis appear smooth, which is consistent with the reports shown in Hida et al., (2009) [48]. The etching does appear to contaminate the gold surface, which was directly exposed to the etchant. However, this preliminary etch attempt, despite less than ideal mask alignment method and relatively simple etch mask design, showed that one could etch a quartz crystal chip into the shape of a tuning fork with relative ease. Figure 5.16 (a) shows the typical electrode pattern for commercial quartz crystal tuning forks and (b) shows the electrode pattern one could create when oblique angle deposition is done away with. When both prongs of the tuning fork are free to oscillate, the fundamental resonance excites the prongs out of phase, which, in theory, should allow for the tuning fork signal readout even without electrodes on the side walls. Although no readout signal characterization was shown in Lee et al., [50] the authors do claim that quartz crystal tuning forks were mass produced without defining electrodes on side walls. All in all, preliminary optical inspection of the piece that we were able to achieve following the recipe outlined in Hida et al., (2009)[48] appears to be consistent with what has been reported in literature. The next step forward would be to figure out a way to define electrodes either by creating electrical separations between top and bottom surfaces of the two prongs or etch away the existing Au/Cr etch mask and perform a new round of Au/Cr deposition. Ultimately, we would like to incorporate a superconducting resonator into our quartz resonator. Bennett et al., [51]proposes the idea of embedding electrodes between two separate layers of z-axis cut quartz crystal wafers by patterning electrodes on the top side of a layer and gluing the two layers together. Their reason for wanting to have the electrodes defined on the inside of the tuning fork is to isolate the effect of

77 Figure 5.14: Etch mask (a) is written in photolithography on a 10 x 10 x 0.1 mm z cut quartz crystal chip. The mask was defined via 250 nm gold deposition after 45 nm chromium deposition. (b) shows the surface covered in gold. (c) shows the body that splits into two prongs. The area circled in red in (d) is magnified in Fig. 5.15 (b). immersing the quartz resonator into a fluid on the electrical readout when measuring physical properties of the said fluid. However, in our case, we would benefit from having the microwave resonator well protected from potential contamination during handling and having more real estate available for patterning electrodes for tuning fork signal readout.

78 Figure 5.15: High magnification SEM images showing surface quality of etching. The area circled in blue in (a) is magnified in fig (c). (b) shows the right corner of the area where the right prong begins. The area circled in yellow is magnified in fig (d).

Figure 5.16: Tuning Fork Electrode Patterns: (a) Typical electrode pattern found on commercial tuning forks. (b) Proposed electrode pattern in order to bypass the need for oblique angle deposition.

79 Chapter 6

Conclusion and Outlook

Silicon quantum computing is in need of a measurement tool capable of providing spatially-resolved, high throughput valley splitting data. Spatial resolution means scanning probe spectroscopy, and high throughput data acquisition would most likely mean less or no dependence on on-chip gate patterning. The scanning probe microscope we have built is the first step toward building such a system. The work described in this thesis has demonstrated for the first time that scanning gate microscopy experiments can indeed be performed on Si/SiGe devices with overlapping gate architecture, as we have successfully formed a dot with the tip of the scanning probe replacing an on-chip plunger gate for both single and double quantum dots. However, in the presence of the overlapping gates, especially when screening gates were patterned, the lever arm of the tip was so low that we ended up having to use a use a voltage amplifier and sweep a large range of bias values (-6 to 10 V, for example, as opposed to 330 to 420 mV for the on-chip plunger gate) to plot a reasonable stability diagram for a double quantum dot device. Although we may still be able to perform detuning axis pulse spectroscopy [14], the extremely weak lever arm will greatly limit its pulsing capability in spectroscopy experiments. In order to overcome the weak lever arm, one could pattern a series of metalized islands across the device,

80 and with the tip making contact with one island at a time, form dots at individual sites selectively. However, patterning localized islands means dependence on patterning on-chip gates and introduces another variable in the non-uniformity of patterned gates (However, it must be acknowledged that the interfacial non-uniformity is much more relevant at the interface between Si and SiGe). All this points to the conclusion that in order for the system to reach its full potential, regarding the acquisition of spatially-resolved, high throughput valley splitting data, integrating a superconducting resonator into the overall quartz crystal tuning fork is paramount. Geaney et al., (2019) has built a system to this end [23]. However their approach was to bypass the need to modify the quartz crystal tuning fork, which ended up increasing the complexity of the microscope and the microwave circuitry. Our approach intends to modify the tuning fork, such that we can adopt the well established, relatively easier microwave measurement techniques. Some preliminary work has been shown in this thesis to justify our current approach. Ultimately, a resonator simiar to the renderings shown in 6.1 or embedding a microwave resonator sandwiched between initially independent quartz layers [51] appear to be a reasonable step going forward. A microscope equipped with such a tuning fork would truly become a measurement tool capable of providing spatially-resolved, high throughput valley splitting data [20]. Single quantum dot induce by the DC voltage bias of the microwave resonator experiments proposed in Shim et al., (2019) would require an external magnetic ﬁeld. Also, sending a microwave line down to the scanning probe tip will be important. Having a vector magnet meant the use of springs to suspend the microscope for partial noise isolation was no longer an option; the microscope had to be rigidly mounted. Also, the existing system’s orientation of the tip and device placement are not ideal for routing the microwave signal. With these requirements in mind, we have adopted a non-linear damping stage designed by Prof. Barnard and ﬁnished designing

81 Figure 6.1: Potential resonator layouts: A λ/4 resonator capacitively coupled to a readout/excitation port(s). Design (b) is akin to the hangar resonator tested earlier5.

Figure 6.2: Microscope design iteration: (a) The red arrow points at the non-linear vibration stage the design of which was provided by Prof. Barnard. The blue arrow points at the next microscope. (b) A close-up of the device circuitboard and scanning probe area. In contrast to the existing scope design, the device and tip are inverted in the new design. 82 a new microscope, where the scanning probe tip points up and sits close to the top of the scope, rather than near the bottom. We predict that the next main focus of this project will be on designing and fabricating a quartz crystal tuning fork with a built-in microwave superconducting resonator.

83 Appendix A

Cryogen-free scanning gate microscope for the characterization of Si/Si0.7Ge0.3 quantum devices at milli-Kelvin temperatures (Submitted to Review of Scientiﬁc Instruments)

84 Cryogen-free scanning gate microscope for the characterization of Si/Si0.7Ge0.3 quantum devices at milli-Kelvin temperatures Seong Woo Oh,1 Artem O. Denisov,1 Pengcheng Chen,2 and Jason R. Petta1, a) 1)Department of Physics, Princeton University, Princeton, New Jersey 08544, USA 2)Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA (Dated: 11 August 2021) Silicon can be isotopically enriched, allowing for the fabrication of highly coherent semiconductor spin qubits. How- ever, the conduction band of bulk Si exhibits a six-fold valley degeneracy, which may adversely impact the performance of silicon quantum devices. To date, the spatial characterization of valley states in Si remains limited. Moreover, techniques for probing valley states in functional electronic devices are needed. We describe here a cryogen-free scanning gate microscope for the characterization of Si/Si0.7Ge0.3 quantum devices at mK temperatures. The newly built instrument is the ﬁrst cryogen-free scanning gate microscope capable of forming and measuring a quantum dot on a Si/SiGe device with an overlapping gate structure without compromising the ability to host multiple DC and microwave lines for quantum control experiments. The microscope is based on the Pan-walker design, with coarse positioning piezo stacks and a ﬁne scanning piezo tube. A tungsten microscope tip is attached to a tuning fork for active control of the tip-to-sample distance. To reduce vibration noise from the pulse tube cooler, we utilize both active and passive vibration isolation mechanisms, and achieve a root-mean-square noise in z of 2 nm. Our microscope is designed to character- ∼ ize fully functioning Si/Si0.7Ge0.3 quantum devices. As a proof of concept, we use the microscope to manipulate the charge occupation of a Si quantum dot, opening up a range of possibilities for the exploration of quantum devices and materials.

I. INTRODUCTION large valley splitting would accelerate the development of a silicon-based quantum processor15,29,30. Silicon spin qubits have rapidly evolved over the past Looking beyond the materials challenges, progress has decade and are now a legitimate contender in the race to been impeded by a lack of a high throughput measurement build a scalable quantum computer1–6. The device fab- of valley splitting. Valley splittings obtained from simple rication process has matured, allowing for high yield and quantum Hall measurements are often much larger than those scale-up of modest one-dimensional Si quantum dot ar- obtained from measurements on quantum dots31, calling into rays7–10. Recent experiments have demonstrated the suitabil- question the utility of quantum Hall characterization. Quan- ity of Si/Si0.7Ge0.3 heterostructures as a platform for highly tum dot valley splittings are often extracted using magne- controllable Si spin qubits4,11–13. Silicon’s small intrinsic tospectroscopy or are inferred from measurements of a spin- spin-orbit coupling and long spin coherence times, accompa- relaxation hot-spot that occurs when the Zeeman energy is nied with well-established industrial fabrication process, have comparable to the valley splitting32. Recently, new val- made Si/Si0.7Ge0.3 a promising platform for scalable quantum ley splitting measurements have been developed that utilize computing. single-shot singlet-triplet readout33, pulsed detuning spec- While Si has many favorable properties for the fabrication troscopy27, or microwave spectroscopy in the circuit quantum of semiconductor quantum devices, the bandstructure of bulk electrodynamics architecture23,28. All of these approaches re- Si exhibits a six-fold “valley degeneracy,” which may intro- quire the time-consuming cycling through multiple devices duce an uncontrolled orbital degree of freedom14,15. The ten- to acquire meaningful statistics. Developing a scanning- sile strain of the Si quantum well induced by the larger lattice probe measurement approach with spatial resolution and the constant of Ge in Si/Si0.7Ge0.3 heterostructures partially lifts ability to form a quantum dot at multiple locations on the the six-fold valley degeneracy by raising the in-plane valleys same chip in a non-invasive manner would accelerate sample in energy relative to the z valleys14. It is the two lowest characterization.34 ± − lying valleys that have posed one of the great challenges to In conjunction with improvements in quantum device fabri- 16,17 silicon-based spin qubit technology . Abrupt Si/Si0.7Ge0.3 cation, the range of scanning probe microscopy techniques has interfaces can lift the two-fold degeneracy of the z-valleys, broadened considerably over the years. Conventional trans- 18–21 but in reality interfaces are not perfectly sharp . Com- port measurements, when combined with different scanning bined with atomic-scale disorder and step-edges, these ef- probe techniques, have opened up a range of capabilities in- fects lead to a large spread 25 300 µeV in reported valley cluding spatial mapping of branched electron ﬂow35,36 and the 8,22–28 − splittings . Discovering a method to reliably engineer a visualization of electron-hole puddles in graphene37. Appli- cations of these capabilities in mesoscopic physics are abun- dant and include shot noise measurements of carrier charge38 and the energy distribution function39,40, as well as imaging a)Author to whom correspondence should be addressed; electronic mail: of temperature gradients41 and local magnetic ﬁelds42–44. We [email protected]. envision the combination of scanning gate techniques with 2

(a) (b) 20 mm (c) 10 mm

(d) 10 mm

(e) 0.5 mm

2 μm

FIG. 1. Instrument overview. (a) The scanning gate microscope is installed beneath the mixing chamber plate of a BlueFors XLD dilution refrigerator. Active vibration dampers (circled in red) decouple the cryostat from the structural support stand. (b) Cross-section through the microscope, which consists of coarse x- and y-positioners, a fine scanning tube, and a custom machined base plate that can accommodate a circuit board and quantum device. Sitting above the microscope is an open copper box with a block holding SmCo magnets for eddy current damping (top red circle). Circled in red below are four of the six coarse z-positioners. (c) Microscope body and coarse xy-positioners. (d) Fine scanning tube. (e) Optical image showing the tungsten scanning probe tip positioned above a Si/Si0.7Ge0.3 quantum device. The tungsten tip is attached to a Nanosurf S1.0 qPlus sensor and the sensor is glued to a rectangular chip that is pre-patterned with gold electrodes. A wire bonder is used to bond up the sensor lines. Inset: Scanning electron microscope (SEM) image of a tungsten tip that has been electrochemically etched for sensing purposes. dispersive readout on-tip34 to allow spatial mapping of the inside and outside the fridge are detailed. We describe the valley splitting in Si/Si0.7Ge0.3 heterostructures. Pan walker design principle, which enables the microscope to Here we describe the construction of a cryogen-free scan- achieve coarse positioning. Then, we explain how the area ning gate microscope that is compatible with Si/Si0.7Ge0.3 of interest is located for imaging and device measurements. quantum dot devices and operates at mK temperatures. The The scanning head design and assembly are outlined, as well dimensions of the microscope parts, such as the scanning tube, as the printed circuit board (PCB) that enables transport mea- sample holder printed circuit board, and microscope base, are surements while the scanning gate is rastered above the de- chosen to be compatible with the dimensions of a BlueFors vice. We also explain how the microscope tip approaches the XLD dilution refrigerator. Where possible, we have heavily sample in frequency modulated AFM (FM AFM) mode. borrowed from existing STM/AFM designs45. Several noise mitigating measures have been taken to reduce low frequency vibrations from the pulse tube. The article is divided into four A. Vibration Isolation technical sections. In Sec. II we give an overview of the microscope design parameters and mode of operation. The cal- As opposed to high-end microscopy setups designed for ex- ibration of the microscope’s scanning piezo tube is described periments that require ultra-high vacuum and a high degree of in Sec. III. In Sec. IV, we measure the noise in the micro- noise suppression for subpicometer stability46, the setup de- scope and make comparisons with existing cryogen-free sys- scribed here is designed for versatile operation under rather tems. In Sec. V we demonstrate scanning gate microscopy of harsh conditions. Our microscope is designed to be fully com- a Si/Si0.7Ge0.3 device, specifically using the microscope tip to patible with a BlueFors XLD cryogen-free dilution refriger- control the charge occupation of a quantum dot. ator. Several adjustments have been made to the standard BlueFors fridge installation configuration for the purpose of mitigating the mechanical noise from the pulse tube. The re- II. INSTRUMENTATION DESIGN AND OPERATION mote option is used to decouple the pulse tube motors from the pulse tubes (Cryomech PT-415), and has been shown to In this section several aspects of the microscope design suppress to a large degree the vibrations that would otherwise are presented. Vibration isolation methods employed both transfer to the mixing chamber plate of the fridge47. In ad- 3 dition, heavy aluminum slabs on the top of the fridge frame sion D) one can program an arbitrary time delay between the provide additional stability. An AVI-400/LP active damper two sets of piezo motors. As explained in the previous para- [see Fig. 1(a)] is employed between the cryostat support frame graph, this time delay has been shown to be effective at pre- and the aluminum slabs on which the fridge rests as a cost- venting the z-piezo positioners from freezing at low tempera- effective alternative to more intricate vibration damping sys- tures. Both the xy- and z-piezo positioners are held in contact tems employed in other setups. The BlueFors cryostat is with sapphire plates using thin BeCu sheets as springs [BeCu housed in a shielded room with walls lined with extruded sheet sitting above the red ruby ball in Fig. 1(b)]. The micro- melamine foam to reduce ambient acoustic noise. scope slides across the sapphire plates for coarse positioning Additional vibration mitigation measures are taken below with respect to the area of interest on the device. Additionally, the mixing chamber plate of the dilution refrigerator. Linear we note that if the pressure on the z-piezo motors is excessive, BeCu suspension springs mechanically decouple the micro- the z-direction actuation tends to freeze at low temperatures. scope from the mixing chamber plate of the cryostat. An eddy For optimal operation, the spring tension is adjusted at room current damper provides additional stability and is constructed temperature such that the ratio between the number of steps by rigidly attaching a rectangular titanium piece to the bottom we need to take up and down to walk the same z distance is of the mixing chamber plate. The lower end of the Ti piece roughly 1.38 (here, a step means one voltage pulse sent to the has samarium-cobalt magnets attached to each side [top red z-piezos). circle in Fig. 1(b)]. These magnets face the inner walls of a Cu box that is mounted to the top of the microscope to create the magnetic damping effect. An annealed copper braid is C. Scanning used to thermally link the microscope to the mixing chamber plate. Fine scanning of the sample is achieved using a piezo tube [see Fig. 1(d)], which is housed inside the cylindrical body shown in Fig. 1(c). Generally, for mechanical stability and B. Coarse Positioning compactness of the microscope, the typical length of a piezo tube is around 25 mm or less. The total length extension To a large extent, the microscope is based on the well- linearly increases with the length of the scanning tube as d31VL known Pan design45 with a slight modification. The overall ∆L = t , where d31 is the vertical extension coefficient, actuation mechanism for the x-, y-, and z-directions is as fol- V is the voltage, L is the natural length of the tube, and t is lows. In the original Pan-walker scheme, to move the load the tube wall thickness. We choose a longer scanning tube x (50 mm) in order to safely deal with 20 150 nm mul- (microscope) in the -direction, for example, the piezo con- ∼ − 8 troller sends high-voltage pulses sequentially to x-piezo stacks tilayer Al gate structure of Si/Si0.7Ge0.3 devices . In addi- in order to move the piezos one at a time while other stacks tion, the scan area available without activating coarse positioners is linearly dependent on the length of the piezo tube as hold the load in place. After the sequence of pulses is com- 2 ∆x = ∆y = 0.9d31VL , where d is the average of the inner and plete to displace the resting position of the load, the piezo dmt m controller slowly decreases the applied voltages to zero. How- outer diameters of the scanning tube, and t is the thickness of ever, this configuration requires a pair of wires for each piezo the scanning tube49. We chose 50 mm, 6.35 mm, and 0.5 mm stack. In order to simplify the wiring scheme, most modern for the scanning tube length, outer diameter, and thickness, microscopes typically assign only one pair of wires to each respectively. When operated in the AFM mode, the qPlus sen- set of x-, y-, and z-piezo stacks. This approach leads to de- sor, used for surface approach and scanning, is read out and graded coarse positioning performance, especially at low tem- amplified with a cryogenic amplifier mounted to the cold plate peratures. Therefore, instead of assigning the same actuation of the BlueFors dilution refrigerator. When operated in STM voltage to all six z-piezo stacks, we group them into two sets. mode, the tunneling current, used for surface approach and The top set of the z-piezo stacks, two of which are shown in scanning, is converted to a voltage signal via a room tempera- the middle red circles of Fig. 1(b), and the bottom set of the z- ture I/V converter (FEMTO LCA-4K-1G). However, the data piezo stacks, two of which are shown in the bottom red circles presented in this paper are not acquired in STM mode. of Fig. 1(b), receive voltage pulses with an adjustable time delay for trouble free motion. Materials science-focused microscopes often forgo lateral D. Scanning Head (qPlus sensor and Tip) positioning for the sake of mechanical stability. However, for our application to quantum devices, the ability to traverse the A sensor in our typical configuration is shown in Fig. 1(e). surface of a sample is important since our chips are millime- We use the S1.0 Nanosurf qPlus sensor as our mechanical ters in scale, and the device area is on the order of several resonator50. As opposed to a quartz tuning fork with two microns in scale. Therefore, in spite of the partial loss of me- oscillating prongs, a qPlus sensor has only one freely oscil- chanical stability, we adopt a walking mechanism based on xy- lating prong. qPlus sensors exhibit cantilever-like dynamics 48 piezo stacks . As shown in Fig. 1(c), three xy-piezo stacks, and a lower effective elastic constant keff. However tuning glued to the rectangular legs of the microscope’s main body, fork sensors can have a much higher quality factor Q and pro- walk across sapphire plates on the titanium base. With the duce at least twice the piezoelectric voltage of a qPlus sensor Nanonis SPM controller’s piezo motor controller (PMD4 ver- for a given tip oscillation amplitude51. Our decision to use 4 the Nanosurf qPlus sensor is mostly due to the convenience F. Tip-Sample Approach of having a dedicated electrical lead on the resonator for the scanning probe tip. The PCB sample holder is designed to accomodate chips of To prepare a scanning head, we first glue a qPlus sensor size 6 6 mm. Each chip typically has four devices on it, with onto a square quartz chip with non-conductive epoxy. The the electrically× active 5 5 µm area located in the center quartz chip has been pre-patterned with Ti/Au electrodes and of each device. Given∼ the absence× of a viewport in the Blue- the far ends of the Ti/Au electrodes are connected to enameled Fors XLD fridge, we use a long working distance microscope copper wires. Two of the wires are used to read out the qPlus to achieve rough alignment of the scanning probe to the active resonator oscillation signal, and the remaining wire is used to area of the device. A long working distance microscope is apply voltage to the probe tip. Once the epoxy is cured in an attached to the frame of the BlueFors fridge for this purpose. oven at 375 ◦F for 20 min., we use a wirebonder to make elec- With a qPlus sensor packaged with a sharp metallic tip and in- trical connections between the electrodes on the quartz chip serted in the sensor housing, and a device mounted underneath and the qPlus sensor. We then glue a 25 µm diameter tung- the base of the microscope, we perform a rough alignment sten wire with conductive epoxy to the free prong of the qPlus between the tip and the device by actuating the coarse xyz- sensor, while ensuring that the wire is in electrical contact piezo positioners. The result of such a procedure is shown in with the qPlus sensor’s probe electrical lead. The tungsten Fig. 1(e). When the rough alignment is complete, the bottom tip is electrochemically etched following a commonly used loading cryostat is closed and pumped down. Once the vac- recipe52. uum level reaches a reasonable level (below 1 10 2 mBar), × − Although the declared resonance frequency of the tuning the qPlus sensor can start approaching the device at room tem- fork is 32,768 Hz, with a metallic tip glued to the free-standing perature. prong of the resonator, the actual resonance frequency is be- We approach the device in FM AFM mode. In this mode low 30 kHz. The base of the quartz chip, which has the qPlus of operation, the phase locked loop (PLL) of the microscope sensor glued on it, is next glued to a ceramic plate. The ce- controller tracks the resonance frequency of the qPlus sen- ramic plate has BeCu springs attached to it. The two enameled sor. When the tip gets close to the device, the mechanical wires on the quartz chip for the qPlus oscillation voltage read- resonance frequency shifts due to the force interaction with out are glued to the BeCu springs. Then, the packaged sensor the surface. Once the resonance frequency shift reaches the is plugged into the sensor housing located on the end of the setpoint, the touchdown is complete. Then, a few AFM to- scanning tube as shown in Fig. 1(d). The BeCu springs offer pographic images are taken at the room temperature for the mechanical stability inside the sensor housing and also make purpose of locating the center of the device. After each scan, electrical contact with a pair of stainless steel wires in order the xy-coarse piezo positioners are actuated to position the tip to provide the means for the qPlus sensor signal readout. The of the sensor closer to the center of the device. After the itera- electrical wires are threaded out of the sensor housing to a tive positioning process, the device is found, and the cryostat cryogenic amplifier that is mounted on the cold plate (around is ready to be cooled down to base temperature ( 20 mK). ∼ 750 mK) of the pulse tube dilution refrigerator. A dedicated We optimize the PLL and proportional-integral (PI) settings microwave line is installed in the system and connected to the of the AFM controller once we reach base temperature. How- tip via a bias-tee to enable future microwave experiments. ever, we compensate for the lateral thermal drift of the microscope during the cooldown to mK temperatures by repeating a topographic scan and adjusting the lateral position of the microscope at 4 K. E. Sample Holder

A custom-made PCB is used as a sample holder. The PCB III. INSTRUMENTATION CALIBRATION has one Glenair connector with 25 pins, 24 of which are used to electrically bias gate electrodes and apply signals to ohmic In order to scan a sample and characterize the noise in the contacts on the device. The circuit board allows a level of tip-to-sample separation (detailed description in the next sec- multi-gate control not seen in existing scanning gate micro- tion), one must first choose a mechanical resonance frequency scope systems. Standard wedgebonding is used to make con- to track. We first identify the mechanical resonances of the nections between bond pads on the chip and the conductive tuning fork by measuring the voltage and phase across the traces on the PCB. In addition to the usual design considera- tuning fork as a function of drive frequency f as shown in tions for Si/Si0.7Ge0.3 device circuit boards, there are two ex- Fig. 2(a). A tuning fork has multiple resonances with varying tra dimensional requirements. First, the width of the PCB has quality factors Q. For a scanning probe system with a pulse to be narrow enough to fit under the base of the microscope tube cooler, it is important to optimize the PI loop parameters without interfering with the bore of the vector magnet. Sec- to deal with external mechanical noise, especially when sam- ond, the device sits on a pedestal relative to the other surfaces ple features are on the order of tens of nm or more. High Q of the PCB, allowing for optical access and rough alignment resonances tend to react more drastically to external noise and of the tip to the active area of the device. The result is a wed- height variations during scans, which lead to a higher chance ding cake PCB design with the motherboard (1 mm thick) and of damaging the tip. Therefore, we went about identifying op- pedestal (1.7 mm thick) consisting of two copper layers each. timal PI loop parameters. In our findings, the optimal P range 5

(a)

1 (nm/√Hz) z S 0.1 Active damping off Active damping on (b) 2 ] (nm) f 1 [1 Hz,

z Active damping off I Active damping on

1 10 100 1000 f (Hz)

FIG. 2. Operation of the microscope in AFM mode. (a) Typical am- FIG. 3. Noise analysis. (a) z-position noise power power spectral plitude A and phase φ of the qPlus sensor signal at 20 mK as a func- density SZ acquired with the active damping system (AVI-400/LP) tion of frequency offset ∆ f . The center frequency is 27.499 kHz and turned off and on. (b) Integrated noise IZ over a frequency range of the quality factor Q 17,600. (b) z-spectroscopy is used to deter- 1 to 1000 Hz with active damping turned off and on. mine the frequency shift-to-distance∼ conversion factor ( 6.433 107 Hz/m) around the setpoint frequency ∆ f = 3.625 Hz. (c)− AFM image× of a three-layer aluminum gate stack fabricated on a silicon surface. frequency and choose the z-sweep range appropriately, so that (d) A line-cut through the data in (c), showing the heights of the dif- the frequency shift includes the setpoint while the tip does not ferent gates. crash into the sample surface for the entire sweep range. iii.) Perform multiple sweeps over the selected z-range while measuring the shift of the tuning fork resonance frequency and is on the order of nm/Hz, and the optimal I range tends to signal average. Figure 2(b) shows the raw data acquired from be around hundreds of nm/Hz/sec. These settings allow for z-spectroscopy. We extract the frequency-to-distance conver- reliable imaging with a high Q 15,000 resonance. sion factor in Hz/nm from the linear fit around the frequency ∼ After finding the main resonance of the tuning fork, we setpoint [see dashed lines in Fig. 2(b)]. This conversion factor scan the gates of the device in order to acquire the room is required to convert the frequency noise power spectral den- temperature-to-mK scaling factor for the scanning piezo tube. sity (units of Hz/√Hz) to tip-to-sample noise power spectral The expansion coefficient of the scanning tube piezo varies as density in (units of nm/√Hz). a function of temperature, such that the scanning tube piezo We do not presently understand the reason for the positive requires a higher voltage for the same amount of expansion sign of the frequency shift, as it would imply that the force at low temperatures49. Figure 2(c) shows an image of four between the surface of the sample and the tip is repulsive for metallic gates. The kinks visible in the lower left corner of the entire range of the z-sweep. However, given the agreement this image are intentional and the overall data acquisition time between both forward and backward sweeps, and since the for this scan was 12 hrs. Knowing the heights of the gates, we absolute value of the slope of the z-spectroscopy is used to determined that the room temperature-to-mK scaling factor estimate the mechanical noise of the microscope, the sign of is roughly 7.46 in the z-direction. During imaging, the mi- the force does not affect the noise analysis presented in the croscope control software adjusts the voltage applied to the next section. scanning tube piezo in order to track the height variation of the surface. The applied voltage is then converted to meters based on the distance to input voltage conversion factor. The IV. PERFORMANCE EVALUATION scaling factor that we found above is used to adjust this conversion factor appropriately. From this point on, the measured We quantitatively analyze the microscope’s noise charac- z-position is now scaled according to the temperature depen- teristics by measuring the power spectral density of the tun- dence of the scanning piezo tube. ing fork resonance frequency. Since the frequency-to-distance To characterize the vibrations in the tip-sample distance in conversion factor from the z-spectroscopy performed in the the absence of a feedback loop we measure the shift in the previous section is acquired from the linear fit around the fre- tuning fork resonance frequency as a function of tip-sample z- quency of 3.68 Hz, the frequency power spectral density is separation, also known as z-spectroscopy. The steps taken to measured at the setpoint of 3.68 Hz in order to be able to ac- acquire the plot shown in Fig. 2(b) are as follows: i.) Choose curately convert the frequency fluctuation to the distance fluc- a setpoint frequency (3.68 Hz, in this specific case) where the tuation equivalent. The resulting tip-to-surface power spectral scanning piezo tube stabilizes. ii.) Note how much the scan- density is shown in Fig. 3(a). In order to test the effective- ning tube piezo had to expand in order to reach the setpoint ness of the active vibration damper, we measure the tip-to- 6 surface power spectral density with the damper on and off. (a) (b) For easier comparison, we integrate the noise spectra to ac- Vtip quire the root-mean-square (rms) vibration noise, defined as f 0 2 0 x IZ[1, f ] = 1 [S( f )] d f . The integrated noise plotted in � p poten � al Fig. 3(b) showsqR that the main contributions to the noise occur at around 120, 140 and 300 Hz. Overall, the damping system reduces the noise by 16%. We find the noise level of our 200 nm system to be comparable to other setups47,53,54, which have y reported 2.1 nm or more for the tip-to-sample vibration. I (nA) 0.6 (c) (d) 0.8

I (nA) 0.4 V. SCANNING GATE MICROSCOPY

5001 μnmm 0 0 We now demonstrate full operation of the microscope by 3.6 4.0 4.4 V (V) imaging an electrically active Si/Si0.7Ge0.3 quantum device at tip mK temperatures. A scanning gate microscopy experiment is performed by scanning the tungsten tip, which is dc-biased at FIG. 4. Demonstration of scanning gate microscopy on a Si/Si0.7Ge0.3 quantum device. (a) Schematic of the local potential a potential Vtip relative to the substrate, above the active area of 55–57 induced by the tip with a negative voltage bias. (b) SEM image of the device . The sample consists of a 11 nm thick Si quan- the double-layer device. (c) Coulomb peaks as a function of the tip tum well that is buried by a 20 nm thick layer of Si0.7Ge0.3 and voltage measured at constant gate voltages. The tip is parked roughly 58 capped by 2 nm of Si . Figure 4(a) illustrates the potential 100 nm above the surface of the wafer near the center of the device. induced by the negatively biased tip in the buried Si quantum (d) Scanning gate microsocopy. Measured currrent as a function of well. The tip induced potential can be changed by adjusting the tip position with the tip voltage Vtip = 0.5 V. Notice that device Vtip or the tip-device distance. Changing the xy-position of tuning is now different from (c). No filtering or data smoothing is the tip around a gate-defined quantum dot (QD) affects the used. All data are acquired with a 20 mK lattice temperature. QD confinement potential and shifts the QD energy levels59. Scanning-gate microscopy is the mapping of the current or conductance through the QD as a function the tip position.

The SEM image of the device made on the Si/Si0.7Ge0.3 VI. CONCLUSIONS heterostructure8 is shown in the inset of Fig. 4(b). By applying a voltage VG to two Al barrier gates we can form a QD between the pair of accumulation gates. We intentionally re- We have designed, constructed, and evaluated the perfor- moved a plunger gate from the device to demonstrate that we mance of a cryogen-free scanning gate microscope capable can use the tip instead to change the electron occupation of the of operation at mK temperatures. Active vibration isolation QD. To that end, we fix the tip approximately 100 nm above is achieved at room temperature and pulse tube noise is fur- the wafer surface near the center of the device and turn off ther supressed at mK temperatures using passive vibration the dither excitation and the feedback loop. In Fig. 4(c) single isolation. The scanning probe consists of a dc-biased tung- electron transport is evident from the Coulumb peaks in the sten tip that is attached to a commercial qPlus tuning fork. measured dc current I which is plotted as a function of V . tip Imaging over large areas is made possible using coarse xyz- The other gate voltages are held fixed during this measure- piezo positioners. Fine scanning in the active area of the de- ment and we apply a source - drain bias V 150 µV across sd vice is achieved using a scanning tube in a Pan microscope the device. ∼ configuration45. Measurements of the noise power spectral The scanning gate image of the QD is shown in Fig. 4(d). density indicate a rms noise in the z tip-sample separation of We adjusted the barrier gate voltage V to reach few electron 2 nm, comparable to other cryogen free microscopes. This G ∼ occupancy of the QD with the tip close and Vtip = 0.5 V. The level of noise demonstrates that scanning gate microscopy ex- image is acquired as the tip is scanned in the plane around periments can be performed on complicated electronic devices 100 nm above the device with zero dither excitation and a requiring >20 connections without sacrificing performance. constant tip voltage. As expected55,56,60, the concentric rings Our system is designed to be compatible with fully functional observed in the scanning gate image correspond to Coulomb quantum devices. As an example, we use the constructed mi- blockade peaks in the measured current. Each ring corre- croscope to perform a scanning gate experiment on a quantum sponds to an equipotential line. Moving in the radial direc- dot defined in a Si/Si0.7Ge0.3 heterostructure. Future efforts tion towards the center of the dot, the crossing of each ring will be directed at measuring the spatial variation of the val- corresponds to the addition of an electron to the dot. ley splitting in Si/Si0.7Ge0.3 quantum dots. 7

VII. DATA AVAILABILITY 14F. Schäffler, “High-mobility Si and Ge structures,” Semicond. Sci. Technol. 12, 1515 (1997). 15F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. The data that support the findings of this study are available Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, from the corresponding author upon reasonable request. “Silicon quantum electronics,” Rev. Mod. Phys. 85, 961 (2013). 16M. Friesen, M. A. Eriksson, and S. N. Coppersmith, “Magnetic field dependence of valley splitting in realistic Si/SiGe quantum wells,” Appl. Phys. Lett. , 202106 (2006). VIII. ACKNOWLEDGEMENTS 89 17M. Friesen and S. N. Coppersmith, “Theory of valley-orbit coupling in a Si/SiGe quantum dot,” Phys. Rev. B 81, 115324 (2010). 18 We thank Arthur Barnard, David Goldhaber-Gordon, B. Tariq and X. Hu, “Effects of interface steps on the valley-orbit coupling in a Si/SiGe quantum dot,” Phys. Rev. B 100, 125309 (2019). 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Preliminary Quartz Tuning Fork Etch Recipe

Here, we present the preliminary etch recipe primarily adapted from Hida et al., (2009) [48]. Tha main goal of the etch attempt was simply to test the feasibility of etching a quartz crystal wafer into the shape of a generic tuning fork. The result of the etch attempt and SEM images are presented in Sec. 5.1.4.

93 Quartz TF first attempt recipe (0.1mm thick)

Pre oxide strip clean • AC dip + New Ac 3 min US + new IPA 3 min US + N2 blow • Tepla 5 min strip • Ac dip + IPA dip + N2 Photoresist to define TF mask front

• (Spin on S1818 4500rpm 60s, bake 2mins)

Lithography on mask front • Heidelberg 10% filter, 30% int, focus: TBA -> 60% int Development of TF masks on mask front • Develop: 100s MF319, stop in DI 1min, N2 blow dry Chromium/Gold deposition via Sharon • 45 nm (Cr) 250 nm (Au) Metallization • N2 blow to get rid of dust • AJA: Nb 50 nm longstrikedelay recipe Wash-off resist • 30 mins in PG remover @80C • 5 mins in new PG remover • IPA spray • Put in new IPA (US if structures permit – should be fine for all resonators) • If really paranoid: another IPA • N2 blow. Once the sample is dry you cannot get rid of residues! Photoresist to protect TF mask front • (Spin on S1818 4500rpm 60s, bake 2mins) (Mask front done) Photoresist to define TF mask back • (Spin on S1818 4500rpm 60s, bake 2mins) Lithography on mask back • Heidelberg 10% filter, 30% int, focus: TBA -> 60% int Development of TF masks on mask back • Develop: 100s MF319, stop in DI 1min, N2 blow dry Chromium/Gold deposition via Sharon • 45 nm (Cr) 250 nm (Au) Wash-off resist • 30 mins in PG remover @80C • 5 mins in new PG remover • IPA spray • Put in new IPA (US if structures permit – should be fine for all resonators) • If really paranoid: another IPA • N2 blow. Once the sample is dry you cannot get rid of residues! Etching quartz with NH4HF2 • (NH4HF2 (7g : 11mL DI water ) at @90C. + stop in DI for 10 min + N2 blow

Appendix C

Tuning Fork-Based Mobile Microwave Cavity Spectroscopy (poster)

96 Tuning Fork-Based Mobile Microwave Cavity Spectroscopy Seong Woo Oh1, Pengcheng Chen2 , and Jason R. Petta1 1. Department of Physics, Princeton University 2. Princeton Institute for Science and Technology of Materials, Princeton University

Motivation Tuning Fork and Cavity Fabrication

• Recent experiments have demonstrated ability to couple superconducting cavities to two- Cavity on Quartz level systems in the single photon regime. • AFM technique has matured, Microwave Impedance Microscopy has been demonstrated, • To check the existing and the need to better understand TLS noise has intensified. resonator designs’ • We seem to have all the tools needed to build a mobile superconducting cavity. compatibility with quartz substrates, hanger resonators are patterned and measured f and Q are compared with designed f and Q. • The length of the coupler is varied for different capacitive strength for testing purposes.

Xiao et al., Nature (2018) Y.-T. Cui et al., Rev. Sci. Instrum. (2016) S. E. de Graaf et al., Rev. Sci. Instrum. (2013) Fabricating Tuning Fork via Etching Basis of Cavity Scope • To have a built-in resonator patterned onto a surface of a tuning fork, it is • The basis of microscope is “Pan-type” walker, necessary to fabricate a tuning fork out of commonly used in the STM community. a quartz wafer with a resonator already • The symmetric design makes the scope patterned. highly robust to thermal drift. • Sharpening, if solely done with the FIB (Focused Ion Beam), could be prohibitively expensive. • Hence, etching a sharp tip-equipped tuning fork is desirable.

H. Hida et al., IEEE Intl. Symp. on Micro-NanoMechatronics and Human Sci. (2005)

Final Design and Operation

• The tuning fork is • The scope head, (quartz crystal tuning fork in mechanically driven by a the picture) is designed to be removable with dither piezo. Hence, one ease, enabling fast scope head exchange. prong can be free of electrodes. • Electrodes on the other

S. H. Pan et al., Rev. Sci. Instrum. (1999) (Hz) 1

prong are used to measure Γ the voltage signal of the Evolution of Scope Head tuning fork: mechanical resonance frequency tracking. • A λ/4 resonator patterned on the tuning fork is used for MW signal measurements.

Conclusion and Outlook

X. Wu et al., Rev. Sci. Instrum. (2018) S. Geaney et al., arxiv:1902.08066v2 (2019)

• λ/4 hanger resonators with high and low designed Qs are patterned on • The scope head is formed by gluing a • A Nb superconducting resonator is patterned on a quartz crystal z-cut wafer and studied for compatibility test. sharp etched Pt/Ir wire to a tuning fork. a silicon substrate and glued to a tuning fork. • Given the versatility and modular scope head design, the scope can be • It is demonstrated to be a useful tool for • Single photon regime topographic easily switched between the more conventional Microwave Impedance measurements of nanoscale permittivity measurement capability has been Microscopy configuration and the single photon regime Near-Field and conductivity. demonstrated. Scanning Microwave Microscopy configuration. • Integrating a λ/4 resonator and a tuning fork seamlessly in fabrication • Manually gluing a sharp tip or a superconducting resonator to a tuning fork introduces an remains a challenge. element of irreproducibility. Bibliography

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