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Nano-scale fabrication of mesa structureson a Bi-2201 high-Tc superconductor

Master Thesis

Thorsten Jacobs

Master ThesisStockholm UniversityFysikum - Department of Physics

Thorsten Jacobs, March 2011

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Abstract

This thesis describes the fabrication of mesas with areas of about 1µm2 and belowon a Bi-2201 (Bi2Sr2CuO6+x) high-temperature superconductor, including the ex-perimental study of their properties. The small mesa sizes were achieved using ionbeam etching with etching masks produced by electron beam induced deposition.

As expected of a cuprate with one superconducting CuO2 plane, the materialhas a considerably low critical temperature of 6.0 K. The critical field was mea-sured to be above 5 T. Intrinsic tunneling spectra of the mesas show superconduct-ing peaks around a gap, of which the temperature and magnetic field dependencesare studied. It is shown that they disappear at higher temperatures or magneticfields. However, a residual pseudogap is observed even above Tc. A strong in-crease of the mesa resistance at lower temperatures also indicate the formation ofthe pseudogap. Furthermore the effect of an extensive current applied along thec-axis is studied. Results show that it changes the mesa resistance as well as mak-ing any of the observed tunneling spectra features more pronounced.

Sammanfattning

Denna avhandling beskriver tillverkningen av mesa strukturer med en area av ca.1µm2 och mindre på Bi-2201 (Bi2Sr2CuO6+x) högtemperatursupraledare, samt denexperimentella undersökningen av deras egenskaper. Små areor uppnåddes genomanvändningen av elektronstråle inducerad deponering av etsningsmasken. Mesastrukturerna tillverkades genom jonstråle etsning.

Som förväntad för en kuprat med bara ett supraledande CuO2 lager, har materi-alet en förhållandevis liten kritisk temperatur på 6.0 K. Kritiska fältet har uppmättstill över 5 T. De intrinsiska tunnlingsspektrerna av mesa strukturerna visar supra-ledande peakar vid gapet, vars temperatur- och magnetfältberoendet undersöktes.Det visade sig att den supraledande peaken försvinner vid högre temperaturer ellermagnetfält. Ett pseudogap observerades dock även vid temperaturer över Tc. Ävenen stark tillväxt av mesa resistansen vid låga temperaturer indikerar bildandet avpseudogapet. Vidare studerades effekten av en stor ström längs c-axeln. Resultatenvisar att denna ström ändrar mesa resistansen och de observerade strukturerna itunnlingsspektrerna blir mer utpräglade.

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Contents

Introduction 6

1 Fundamentals 71.1 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Superconducting tunneling junctions . . . . . . . . . . . . . . . . 91.3 Cuprates and Bi-2201 . . . . . . . . . . . . . . . . . . . . . . . . 111.4 Micro- and nano-fabrication techniques . . . . . . . . . . . . . . 13

1.4.1 Thin film evaporation . . . . . . . . . . . . . . . . . . . . 131.4.2 Photolithography . . . . . . . . . . . . . . . . . . . . . . 151.4.3 E-beam induced deposition and focused ion beam milling 161.4.4 Ion beam etching . . . . . . . . . . . . . . . . . . . . . . 181.4.5 Plasma etching . . . . . . . . . . . . . . . . . . . . . . . 191.4.6 Wire bonding . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Experimental 212.1 Sample fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 212.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2.1 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2.2 Lock-in amplification measurements . . . . . . . . . . . . 302.2.3 Measurement setup . . . . . . . . . . . . . . . . . . . . . 31

3 Results 353.1 Temperature dependence of the resistance . . . . . . . . . . . . . 353.2 IV-characteristics and tunneling spectroscopy . . . . . . . . . . . 373.3 Magnetic field properties . . . . . . . . . . . . . . . . . . . . . . 443.4 Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

A Fabrication parameters 51

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6

Introduction

Many properties of superconductors can be determined by analyzing the electri-cal properties of tunnel junctions of the material. A superconducting tunnel junc-tion consists of two superconductors that are separated by a weak link, like aninsulating material layer or vacuum. In addition to electrons, Cooper pairs areable to surmount this potential barrier due to quantum mechanical effects andcan tunnel through the link. However, classical SIS (superconductor-insulator-superconductor) junctions are hard to fabricate, due to their extremely short co-herence length that requires a very small barrier thickness. Furthermore, the highchemical reactivity of the material surface influences the measurement reproduci-bility, for example due to an oxidation of the surface.

This can be avoided by utilizing the special bulk properties of a high-tem-perature superconductor (HTSC). The conduction electrons are localized in certainlayers of the material and its conductivity is therefore anisotropic. The transportof a charge carrier between two conducting layers is achieved by interlayer tunnel-ing through an insulating layer. The structure equals a stack of intrinsic junctionsnaturally formed by the material. But crystal defects and material heating causedby power dissipation during the measurement may lead to inaccurate results. It ispossible however to reduce these margins of error by minimizing the measured in-plane area to a small stack of material, i.e. a mesa. The amount of crystal defects isthereby reduced and the effects of heating are minimized as there is better thermalconduction corresponding to a smaller material volume.

The focus of this work is to show the fabrication of mesas on top of a HTSCcrystal whilst analyzing their properties. There were several micro- and nano-fabrication techniques used to further reduce the mesa size to an in-plane area ofapproximately 1µm2 and below. The superconductor Bi2Sr2CuO6+x was chosenfor this work, given that the material is fairly unknown in the research field.

The thesis is organized in the following order; the first chapter offers an intro-duction to the fundamental theory where the most important properties of super-conductivity are explained in brief in the chronological order of their discovery.The properties of the HTSC used and the principle of superconducting tunnelingjunctions are explained in two separate sections. In addition, all micro-fabricationtechniques applied are explained and the deployed equipment is shown as an exam-ple. Chapter two outlines complete details of the experiment conducted, includingthe sample fabrication and the measurement technique. Detailed sample fabrica-tion parameters are listed in the appendix, providing a better overview. Finally, themeasurement results are presented and discussed in the third chapter and summa-rized in the conclusions section.

Chapter 1

Fundamentals

1.1 Superconductivity

It was discovered in 1911 by H. Kamerlingh-Onnes that mercury abruptly changesits resistance down to a non-measurable value if it had been cooled down below4.2 K. At this critical temperature Tc, the material passes into a new state whichhe had given the term superconducting state [1]. In this state there is no energyexchange between the conduction electrons and the crystal lattice, allowing currentto flow persistently inside the material. The transition is reversible if the material isheated above Tc. Moreover a high enough current or external magnetic field couldsuppress the superconductivity. The respective values are denoted as the criticalcurrent Ic(T ) and the critical field Hc(T ), both being material and temperaturedependent. Currently there are numerous types of compounds and more than 20metallic elements1 that are known to be superconducting.

In 1933, W. Meissner and R. Ochsenfeld discovered that a magnetic field isrepelled from the inside of a superconductor, so they have a permeability of zeroand are highly diamagnetic [2]. The effect was quantitatively explained by F. andH. London [3]. The brothers showed that a magnetic field does penetrate the super-conductor only in a thin surface layer with penetration depth λ . A superconductingscreening current in this layer generates a magnetic field contrary to the externalone. It therefore shields the field from penetrating further into the material. Thisis called the Meissner effect and is a consequence of the minimization of energycarried by the superconducting current (supercurrent).

The above discoveries showed that the superconducting state is an independentthermodynamic state [4]. Other typical properties are a bad thermal conduction,albeit the fact that good electrical conductors are usually also good conductors of

1Also some semiconductors can be made superconducting under certain circumstances.

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8 CHAPTER 1. FUNDAMENTALS

heat. The critical temperature was found to be dependent on the isotropic mass,Tc ·√

M = const, which is called the isotope effect. Furthermore superconductorshave a temperature dependent energy gap ∆, which is further described in section1.2. An electron can only be accommodated by a superconductor if the differencebetween its energy ε and the Fermi energy is higher than ∆ [5].

A theory which accounts for all properties and explains the microscopic ef-fects is the BCS-theory, named after its founders J. Bardeen, L.N. Cooper and J.R.Schrieffer [6]. At low temperatures an attractive interaction between two electronscan lead to a formation of electron pairs, so called Cooper pairs. They overcomethe repulsive Coulomb force due to an interaction with phonons, vibrations of thecrystal lattice. The pair has a lower energy than the normal state energy and itbecomes energetically favorable to form a superconducting phase. They had foundthat the relation between the energy gap at zero Kelvin and the critical temperatureis given by

2∆0 = 3.52kBTc. (1.1)

For several decades it was believed that 30 K is the highest Tc to be theoreti-cally possible. However, in 1986 J.G. Bednorz and K.A. Müller discovered thatlanthanum barium copper oxide (a ceramic) is still superconducting up to temper-ature of 52.5 K [7]. This lead to the discovery of materials with higher criticaltemperatures, so called high temperature superconductors (HTSC). Similar to lowtemperature superconductors they demonstrate a Meissner effect if the externalfield is lower than a specific critical field H < Hc1. At high fields the magneticfield lines start to penetrate the material in the form of single vortices [8] eachcarrying a flux quanta

Φ0 =h

2e. (1.2)

This occurs if the coherence length ξ , a characteristic length in which the supercon-ductivity can change considerably within the material [9], is significantly smallerthan the London penetration depth. In this case a supercurrent flows around eachvortex and shields the rest of the material from the magnetic field. Vortices repeleach other and form a lattice structure (Abrikosov lattice) whose density increaseswith increasing magnetic field. At a certain upper critical field Hc2 the vortices startto overlap and the magnetic field will fully penetrate the material which destroysthe superconductivity. From this it follows that a HTSC has two distinct criticalfields with a mixed state or vortex state between them. The superconductor doeshave a resistance in the mixed state since vortices are moving in the material andtherefore cause an energy dissipation. Vortices pin at crystal defects or surfaceshowever, which reduces the vortex flux flow.

The exact mechanism of high-temperature superconductivity is still unclear. It

1.2. SUPERCONDUCTING TUNNELING JUNCTIONS 9

is known that the formation of Cooper pairs result in superconductivity, as for con-ventional superconductors, but in this case the Cooper pairs compose from quasi-particles (holes) instead of electrons. HTSC show an unusual isotope effect thatdisappears at a certain hole concentration2, hence the electron-phonon couplingalone does not explain the pairing of electrons [10]. There is still a lack of theo-retical or experimental proof that exists to explain the pairing mechanism in highttemperature superconductors or to describe which particles are involved.

1.2 Superconducting tunneling junctions

If two conducting materials are separated by a thin barrier in form of an insulatinglayer, electrons are still able to pass this barrier with a given probability due to thewave-particle dualism. The wave function of the electron in one of the conductorsdecays exponentially within the insulator. So at sufficiently small distances to an-other conductor there is a finite probability that the electron will occur at the otherside. This causes a tunnel current through the junction.

For superconducting junctoins, two superconductors separated by an insulator(SIS), the current from an electrode on the left to one on the right is given by

IL→R =2π

h

∫ +∞

−∞

|T |2 NL(E) fL(E)︸︷︷︸nL

NR(E+)(1− fR(E))︸︷︷︸nR

dE. (1.3)

|T |2 is the tunneling matrix element between states of equal energy, giving theprobability of tunneling, nL is the number of occupied states on the left side andnR the number of available empty states on the right side. Both values are therespective product of the density of states N(E) and the Fermi-Dirac distributionf (E), the probability that the state is occupied. A current IR→L flows back in theopposite direction and can be written in a similar matter, so that the net flow is zeroif both sides are at the same potential. At a potential difference eV between bothelectrodes, the total quasiparticle tunneling current is given by

I = IL→R−IR→L =2π

h|T |2

∫ +∞

−∞

NL(E)NR(E+eV )[ fL(E)− fR(E+eV )]dE. (1.4)

Band diagrams are helpful to understand the electrical properties of a tunneljunction. Figure 1.1 illustrates the band structure of two superconductors. At zeroKelvin the lower band is fully occupied by electrons and separated to the upperband by the energy gap 2∆. This gap is due to a Cooper pair formation at theFermi energy. All Cooper pairs in a superconductor have the same energy and form

2At optimal oxygen doping, see next section.


(a) (b)

Figure 1.1: Band structure representation of a SIS junction and respective current-voltagecharacteristics. It shows the DOS of unpaired electrons in a superconductor at 0 K (a) andat higher temperatures, where some electrons have enough thermal energy to overcome theenergy gap and occupy states in the upper band (b). The gray areas represent occupiedstates (figure modified, original taken from [4]).

a condensate at the same quantum state. This is possible since they are compositebosons, particles with integer spin for which the Pauli exclusion principle doesnot apply. Electrons have to have an energy of at least 2∆ to overcome the gap.The band structure is analog to that in a semiconductor. The bands are thereforecalled valence (lower) and conduction (upper) bands. If both superconductors areat the same potential no tunneling is possible, since the occupied states only "see"other occupied states on the other side. If a voltage eV is applied, an offset arisesbetween the energy bands. If eV = 2∆, the fully occupied valence band is onthe same energy level as the empty conduction band and electrons start to tunnelto the empty states. An abrupt current increase is visible in the current-voltagecharacteristics at that point, since the density of states is high close to the energygap. At higher voltages the IV-curve becomes linear since the DOS is constant athigher energies. For temperatures above zero Kelvin some electrons have enoughthermal energy to cross the gap and empty states exist in the valence band. In thiscase a small tunnel current can flow even at low voltages.

It was predicted by B.D. Josephson in 1962 that Cooper pairs can also tun-nel through a superconducting tunnel junction [11]. Therefore SIS junctions areas well called Josephson junctions. If both sides of the junction are at the samepotential, the arising current is given by

Is = Ic sinθ , (1.5)

where Ic is the critical current and θ the phase difference. This is called the firstJosephson relation. The effect has a contribution to the total current in the samemagnitude as the quasiparticle current and is therefore visible as a vertical line in

1.3. CUPRATES AND BI-2201 11

the IV-curve. If a voltage is applied, the tunneling supercurrent starts to oscillatewith frequency

ω j =∂θ

∂ t=

2eh

V, (1.6)

which is the second Josephson relation. So an applied DC voltage will lead toa alternating current with high frequency. But this effect is quite small and willonly appear in the current voltage characteristics when geometrical resonances orresonances with external radiation occurs.

(a) (b)

Figure 1.2: Two-part current-voltage characteristics of a superconducting tunnel junctionwith zero-voltage supercurrent (a) (taken from [11]) and an electrical model of the junction(RCSJ model) including a capacitance, the tunnel junction and a normal resistance (b).

Figure 1.2 shows the two-part current voltage characteristics of a superconduct-ing tunnel junction. If the current is increased it follows the vertical supercurrentbranch until the critical current is reached. It then switches to quasiparticle tunnel-ing and becomes ohmic at higher currents. If the current is reduced it shows a hys-teretic behavior and follows the quasiparticle branch down to lower voltages untilit re-traps and switches back to the supercurrent. The junction can be representedby an electrical model consisting of a resistor, a capacitor and the superconductorjunction (RCSJ model) and is also shown in the figure.

1.3 Cuprates and Bi-2201

The HTSC used for the experiments in this thesis is Bi2Sr2CuO6+x, a copper oxidebased superconductor or so called cuprate. It is also denoted as Bi-2201, due tothe stoichiometry of the contained elements. The zero refers to a lack of calcium,which is part of the generalized chemical formula for bismuth strontium calciumcopper oxide (BSCCO): Bi2Sr2Can-1CunO2n+4+x, with n = 1 in this case.


Figure 1.3: Crystallographic structure of Bi-2201. The single CuO2 planes are super-conducting, while the layers in between are insulating. The structure equals a stack ofsuperconducting tunneling junctions, naturally formed by the material (figure modified,original taken from [12]).

Cuprates build the largest group of superconductors and a cuprate has the high-est Tc discovered for a bulk crystal so far3. The characteristic of all high tempera-ture superconductors is their layered crystallographic structure. They have a smalland anisotropic coherence length and therefore form a sequence of superconduct-ing and non-superconducting planes. The superconducting areas are multiple or, incase of Bi-2201, single copper oxide planes. Bi-2201 with its single CuO2 planehas a much lower critical temperature (Tc ≈ 10 K and less) then cuprates with twolayers. The layers in between stabilize the structure but also act as a charge reser-voir; they supply charge carriers to the CuO2 layers which then form Cooper pairs.Figure 1.3 shows the crystallographic structure of Bi-2201.

The charge carrier concentration plays an important role for the electrical andsuperconducting properties of the material. It is possible to dope a HTSC by addingoxygen. The excessive atoms attract electrons from the superconducting planes andgenerate more charge carriers in form of holes. One way to dope the material withoxygen is by heating it up in oxygen gas. In case of Bi2Sr2CaCu2O8+x, the materialbecomes superconducting at x = 0.05 and has a Tc peak at x = 0.16 (about 90 K).But higher concentrations will overdope the material. The critical temperaturestarts to decrease until superconductivity vanishes at x = 0.27 [10]. Bi-2201 is anaturally overdoped HTSC, which in addition lowers its critical temperature [12].

Similar effects can be achieved by replacing atoms in the lattice by atoms with

3Up to 135 K for HgBa2Ca2Cu3O8+x (Hg-1223) and even higher at high pressures [13].

1.4. MICRO- AND NANO-FABRICATION TECHNIQUES 13

a different number of valence electrons. Bi-2201 can, for example, be doped by re-placing the divalent strontium with the trivalent lanthanum: Bi2(Sr2-xLax)CuO6+δ

(Bi-2201-Lax). A several times higher critical temperature can be reached in thatway at an optimal doping level4 [14, 15].

High temperature superconductors with their layered structure naturally forma stack of intrinsic tunneling (Josephson) junctions along their c-axis, the direc-tion perpendicular to the superconducting CuO2 layers. The non-superconductinglayers hereby act as insulating layers. A small single crystal with several intrinsicjunctions is called a mesa. The name mesa, meaning table in Spanish, originatesfrom the similarity in shape with natural mesas, hills with a flat top and steep sides.Apart from larger crystals which might have impurities and crystal defects withinthe layers, a smaller mesa has a quite homogeneous structure which makes it moresuitable for reproducible measurements.

1.4 Micro- and nano-fabrication techniques

The following section describes the micro- and nano-fabrication techniques thatwhere used during sample fabrication. A more detailed description can be foundin [16] or [17]. All machines are situated in the Nano-Fab Lab clean room at theAlbaNova University Center, Stockholm. The air in the clean room is filtered withhigh efficiency particulate air (HEPA) filters and special clothing is required tominimize airborne particles and particles on surfaces. This reduces the risk thata sample is spoiled by dirt particles. Furthermore all process steps involving wetchemicals are carried out at a local clean area, a laminar flow bench with extraHEPA filters that further reduce the amount of particles in the air.

1.4.1 Thin film evaporation

A common technique to deposit a thin and homogeneous layer of material on asample is by evaporating it in an ultra high vacuum (UHV) chamber, which iscalled physical vapor deposition (PVD). Different methods exist to evaporate thematerial and in this case electron beam evaporation was used. Several magneticlenses deflect the beam of an electron gun to the evaporant, which is situated in awater cooled crucible. The focused beam sweeps over the surface of the materialfor a better heat dispersion. Evaporated particles then travel to the sample holderin a straight trajectory, due to the large free mean path in vacuum. They condenseand form a thin layer at the sample surface. The purity of the deposited material

4Tc ≈ 30 K for x≈ 0.45.


depends on the pressure of residual gases in the chamber, which is why the processis conducted at UHV conditions.

The energy of the evaporated particles is very low, so that the sample is notheated substantially and the surface is not damaged. But since they travel in astraight trajectory from a small source the surface is not covered uniformly. Onlysurfaces facing towards the source are covered while the side-walls of a trench re-main uncovered. One can partly solve this by tilting the sample during deposition.

Figure 1.4: The Eurovac system for electron beam evaporation: Main vacuum chamber(1), load-lock chamber (2), sample loading arm (3), sample holder adjustment to tilt thesample (4) and operating elements for the electron beam (5).

Figure 1.4 shows the used vacuum deposition system. It consists of a mainchamber and a smaller load-lock chamber that is connected to the main chamberand can be separated with a valve. A loading arm is used to transfer the sampleholder from the load-lock to a clamp inside the main chamber. The main cham-ber is constantly kept at low pressure (about 7 · 10−8 mbar) with a turbomolecularpump. The load-lock chamber can be evacuated separately before the valve to themain chamber is opened. Furthermore, it can be flooded with nitrogen gas to openthe chamber to ambient pressure before unloading the sample. This allows a quicksample exchange and avoids a contamination of the main chamber. During de-position, the film thickness can be monitored by a thickness monitor. It uses anoscillating quartz crystal that changes its frequency if an additional mass is added.


1.4.2 Photolithography

Photolithography is a common technique to pattern thin film structures down toseveral micrometers resolution. It is used to selectively remove parts of a depositedthin film or to protect areas of a sample from being covered by a deposited material.

Figure 1.5 shows the used projection mask aligner and a laminar flow benchwith a hot plate and a spinner. The spinner is used to evenly distribute a liquidphoto resist on the sample. This is done by holding the sample with a vacuum on aplate and spinning it with several thousand rpm after a drop of resist was applied.Afterwards it is baked on the hot plate to harden the resist.

(a) (b)

Figure 1.5: Canon projection mask aligner (a): UV-light source (1), mask holder (2),objective (3), miroscope (4) and sample loading stage (5). And a laminar flow bench (b)with a spinner (1) and hot plate (2) inside.

A factory made photo mask contains the desired pattern. It is projected on thesample with an objective and focused and aligned using a microscope as help. Thesample with the photo resist is then exposed with ultraviolet light from a mercurylamp for several seconds. The resist is changing its molecular structure due to aphoto chemical reaction at the exposed areas. The areas can then be removed witha developer since the development rate is higher than for the unexposed areas. It isthen possible to etch away the parts of the thin film that are not covered by photoresist by using chemical or physical etching, explained below. In the last step thephoto resist is removed either by fully exposing and developing the sample or byusing other chemicals. All steps are shown in figure 1.6. Alternatively a negativephoto resist can be used. In this case the exposed areas of resist will remain afterdeveloping.


Figure 1.6: Photolithoragphy workflow for pattering a thin film (subtractive).

The described principle is the so called subtractive process. Another option isthe additive process. In this case a film is deposited after applying and developingthe resist. The resist and therefore the deposited material on top of it are chemicallyetched away afterwards. After this so called lift-off a pattern of deposited materialwill remain only at the surfaces that where free of resist.

The resolution is dependent on the light diffraction at the mask. It is smaller forlow wavelength, therefore ultraviolet light is used. The achievable minimal featuresize of the used projection mask aligner is in the range of a few micrometers. Alllight sources in the photolithography room are covered with a yellow UV-lightfilter, in order not to expose the photo resist unintentionally.

1.4.3 E-beam induced deposition and focused ion beam milling

Electron beam induced deposition (EBID) and focused ion beam (FIB) milling aretechniques to deposit or ablate material in a nanometer scale. Both principles and ascanning electron microscope (SEM) are combined in a dual beam system, shownin picture 1.7. Apart from imaging a sample with high magnification it can beused to bypass broken contacts by depositing material on the crack, or to eliminateshort circuits by cutting through unwanted contacts. It has two beam columnswith an angle of 52 relative to each other, hosting electron or ion sources andseveral magnetic or electrostatic lenses to focus and deflect the beam. The sampleis situated in an evacuated chamber, to allow for a large mean free path of theelectrons and ions.


Figure 1.7: Dual beam system FEI Nova-200: Sample loading door (1), electron beamcolumn (2), ion beam column (3), gas injection system for platinum deposition (4) andoperating elements (5).

SEM If accelerated electrons hit the sample surface they will either scatter back or,amongst others, produce secondary electrons. Both can be detected with adetector in the chamber. Since it is possible to focus the beam to a very smallspot and raster scan quickly over the surface, one can visualize the sampleon a computer screen with a very high magnification. Depending on thematerial and the local surface topography the amount of detected electronswill be different and lead to different contrasts in the picture.

EBID The electron beam can also be used to deposit material. A precursor gas isinjected directly to the sample surface and the beam is swept over the areawhere the material should be deposited. The produced secondary electrons5

then decompose molecules in the gas that deposit on the surface. The usedsystem is equipped with a trimethyl platinum (C9H16Pt) gas injection systemto deposit platinum, which is electrically conducting.

FIB If accelerated ions, in this case gallium ions, from the FIB hit the samplesurface they remove atoms from the sample, since ions are larger and heavierthan electrons. This property is used to mill small areas and patterns in ananometer range. Furthermore secondary electrons are produced. They canbe detected to create a picture (FIB imaging) or used in combination with theprecursor gas to deposit material (FIB deposition). Since material is alwaysremoved from the sample and gallium ions are implanted into the sample

5The primary electrons from the beam have a too high energy to break the molecule bonds.


when a ion beam is used, SEM and EBID where preferred for imaging andmaterial deposition in this case.

1.4.4 Ion beam etching

Ion beam etching or ion milling is a physical etching process (sputter etching). Theprinciple is similar to the focused ion beam; accelerated ions mill away atoms fromthe sample surface. But the beam is not focused, so the whole sample surface isetched at the same time and a less complex beam column is needed. An additionalelectron beam neutralizes the positive ions and avoids that the sample builds upa charge. The process is anisotrope and any material can be etched away with arather low etch rate. This allows for a precise control of the etch depth but alsorequires long process times in the range of several hours. Figure 1.8 shows theused system. It consists of main chamber that is evacuated with a large turbo pump(to about 4 ·10−9 mbar) and a smaller load-lock chamber that can be separated fromthe main chamber and evacuated separately. The ion gun uses argon gas which isionized and then accelerated to create the ion beam.

Figure 1.8: The "Sputnik" ion beam etching system: Main vacuum chamber (1), load-lockchamber (2), sample loading arm (3), ion gun (4) and operating elements (5).


1.4.5 Plasma etching

Plasma etching is an selective dry etching mechanism that is, depending on theparameters, either chemical, physical or a mixture of both. The sample is placedin a reactor that is evacuated and then filled with an etch gas at a few millibar.Electrodes generate a high-frequency field that create a reactive plasma. The reac-tive elements (ions, radicals) chemically react with the sample surface and createvolatile products that are pumped away with a vacuum pump. The etching prop-erties can be influenced by varying the gas type, gas flow, chamber pressure orpower. If oxygen is used as reactive gas it is possible to selectively remove pho-toresist. Plasma etching is usually isotropic, so horizontal surfaces are etched withthe same rate as vertical ones. But a physical etching component can be added bylowering the chamber pressure and placing the sample at the powered electrode.Ions start to impinge on the surface and provide energy for chemical reactions orremove material by sputtering, which makes the process anisotropic. This processis called reactive ion etching (RIE) and was used in this case. Figure 1.9 shows theused system. The system uses an inductive coupled plasma (ICP) which enablesan independent control of the ion energies and ion current density. The ion energyis dependent on the RF power and the ion current (plasma density) depends on theICP power in this case.

Figure 1.9: Reactive ion etching system OXFORD Plasmalab. The upper part is the reactorthat can be lifted up for sample loading.


1.4.6 Wire bonding

Wire bonding is a method to electrically connect an integrated circuit (IC), or inthis case the contact fingers of the sample, with a printed circuit board (PCB).The bonder uses an ultrasonic welding principle which is shown in figure 1.10.One end of an aluminum wire is pressed on top of the contact using a so calledbond wedge. The wedge then oscillates horizontally with ultrasonic frequency forsome milliseconds. This, together with the contact pressure, bonds the wire tothe surface. The process is repeated at the second contact which establishes theelectrical contact. The wire is then held by a clamp and does not follow up whenthe wedge is removed. It therefore brakes at the weakened bond and a new contactcan be bonded.

Figure 1.10: Wire bonding principle (figure modified, original taken from [18]).

Chapter 2

Experimental

2.1 Sample fabrication

Small flakes from a Bi2Sr2Cu1O6+x crystal where used to make several samples.This section describes the used process steps. Detailed process parameters arequoted in square brackets where [A. . . ] refers to the respective table in the ap-pendix. An optical microscope equipped with a CCD camera and a SEM whereused to monitor the process steps and take pictures for documentation. The picturesin this section show the sample that was analyzed in detail later on. An illustrationof all fabrication steps, together with a picture of the sample at that step is shownin figure 2.1.

Crystal preparation

First, several sapphire substrates with an edge length of about 5 mm where cleanedin an ultrasonic acetone bath. They are used as an permanent holder for the samplecrystal and as a base for gold contacts that will be made later. A drop of epoxy resinwas placed on one substrate and a small crystal flake (about 200µm edge length)was added using a toothpick. The flake sticks to the tip due to adhesive forces. Theepoxy was then hardened on a hot plate [A.1]. A second substrate with a glue dropwas then placed on top of the crystal and hardened as well. So the crystal was gluedbetween two substrates in the end. If both substrates are then separated using anscalpel, the crystal cleaves along one of its crystallographic planes and either endwill stick to one of the substrates. Cleaving the crystal is necessary to get a cleansurface that is not oxidized. By repeating it several times a crystal height of severalmicrometers can be achieved. This is done to keep the height difference betweenthe substrate and the crystal as low as possible to be able to fabricate gold contactsfingers later on. The cleaving process worked properly in about one out of three

21

22 CHAPTER 2. EXPERIMENTAL

(a)

(b)

(c)

(d)

(e)

Figure 2.1: Illustrated steps of the sample fabrication (left) and corresponding pictures ofthe sample (right): Gold deposition on cleaved surface (a), platinum etching mask depo-sition (b), mesa fabrication by ion beam etching (c), application of planarization layer (d)and gold finger fabrication to electrically contact the mesas (e).

2.1. SAMPLE FABRICATION 23

trials. Sometimes it did not cleave or the cleaved part was too small for furtherusage. When the crystal had the desired thickness a gold layer was deposited assoon as possible using e-beam evaporation [about 30 nm, A.2] to protect the freshlycleaved surface from oxidizing.

In the next step a square of photoresist was placed on a suitable position of thecrystal surface using the projection mask aligner [A.3]. The gold around the squarewas removed with a gold etch solution [50%, 20s]. Figure 2.1(a) shows the crystalafter this process step. The material around the crystal in the microscope picture isexcessive epoxy and gold remains. They where removed with a scalpel afterwards,using a 3D microscope as help. The resist on the square was completely removedwith acetone after that. The gold area was then further reduced to a singe line inthis case, using the same methods.

Mesa fabrication

The sample was treated with reactive ion etching [A.4, 10 min, high ICP] to makesure that all resist was removed and to clean the gold surface for a good electricalcontact. The used settings mainly etch the photoresist and result in a low sputteringrate, in order not to etch the gold or the crystal. Then, six rectangle platinumetching masks where deposited on the gold that will later form the tip of the mesas.Electron beam induced deposition was used for this [A.6] since the resolution ofthe optical photolithography system is too low to achieve this feature sizes. Incase the sample could not be properly grounded, the SEM/FIB picture started todrift due to a charge build-up on the sample. This makes a material depositionimpossible. In this case a 10 nm gold layer was deposited using e-beam depositionagain. The sample could be grounded to the dual beam sample holder with silverpaste afterwards. Figure 2.1(b) shows the sample after the deposition and a SEMpicture of one of the larger mesas. The deposited masks where about 40 nm high,1µm wide and the length where varied. Both outermost masks where the largestand about 2.5µm long, the next ones are 1.75µm long and the inner ones wherethe smallest with an length of about 1µm.

In the next step all gold around the platinum masks is removed using ion beametching [A.5, approx. 30 min]. The process was interrupted meanwhile to monitorthe etching progress. It was stopped as soon as all gold was removed in order notto etch the underlying crystal surface for too long and keep the amount of junctionsin a mesa low. The milling rate for gold is higher than for platinum or the crystal,so the platinum masks remain after the gold is removed. Apart from the gold somelayers of the crystal are etched away as well. Therefore small mesas with platinumtips remain in the end. They have a height of several nanometers and contain astack of intrinsic junctions, usually up to about 20. This is shown in figure 2.1(c).


The sizes of the finished mesas where measured in the SEM and are listed in table2.1. It shows that the smaller mesas have a in-plane area of less than 1µm2. Thecrystal surface around the mesas oxidizes and therefore becomes insulating.

Table 2.1: Size and area of the mesas, labeled from one to six.

Mesa 1 2 3 4 5 6

Size (µm) 2.4×1.0 1.6×0.9 1.0×0.8 1.0×0.9 1.8×0.9 2.8×0.9Area (µm2) 2.4 1.5 0.8 0.9 1.6 2.5

Fabrication of the electrical contacts

To fabricate the contacts, the height difference between the crystal and the substrateas well as the unevenness of the crystal itself had to be smoothed out first. Thiswas done to assures a complete surface coverage of the gold film that was depositedlater on. Therefore a planarization layer was added that was simply made out ofphotoresist. It furthermore avoids an unwanted electrical contact to potential goldremains on other parts of the crystal and therefore also acts as an insulation layer.After applying the resist and baking it, a circular layer around the crystal with awindow left open for the mesas was created using photolithography. This can beseen in figure 2.1(d). Due to the anisotropic developing process, the edges of thephotoresist layer will be sloped which helps to achieve a continuous gold coverage.

Afterwards the sample surface was cleaned with RIE again to remove possibleresist remains on the mesas [A.4, 10 min, low ICP]. The gold layer was then evap-orated using e-beam deposition [200 nm, A.2]. The sample was tilted two timesby 45 in both directions during the deposition to cover the sloped areas as well.Therefore the line of mesas had to be aligned parallel to the rotation axis of thesample holder. Since the deposition thickness monitor is not tilted, a factor of

√2

has to be multiplied to the displayed value during the time the sample is tilted toget the actual thickness of the film. The microscope picture in figure 2.1(d) showsthe sample with the planarization layer and the evaporated gold film.

The contact fingers where then patterned form the gold film using photolithog-raphy. The alignment of the fingers in this step was challenging due to the smallmesa size. A misaligned pattern could be removed by fully exposing and develop-ing it though. But the developer slowly creeps under the gold layer, so after severalmisalignments a sample is corrupted since the developer starts to react with the un-derlying planarization layer and forms blisters. After the pattern was aligned, thegold in between the fingers was etched away in two steps. First, most of the gold


was removed by wet etching with a gold etch [50%, 30 s]. The remaining gold wasthen removed with the less aggressive ion beam etching [A.5, 1.5 h].

Thereafter the residual gold at the edges of the substrate was removed with ascalpel to avoid shorts between the contacts. The resist on the contact fingers wasremoved in the next step by developing it. In case the resist was difficult to removewith developer, RIE was used instead [A.4, 1.5 h, low ICP]. This step also partlyremoves the planarization layer in between the fingers. But this is marginal sincethe important layer underneath the contact fingers remains.

The result is shown in figure 2.1(e). The mesas are electrically contacted fromtwo sides, which makes it possible to measure with four-terminal sensing. The partof the contact fingers around the mesa is in physical but not electrical contact withthe crystal, since the surface oxidized and formed an insulating layer. The goldcontact fingers lead from each mesa to wider bonding areas on the substrate. Theseareas are large enough to easily contact them using the wire bonder.

Measurement preparation and mending

In order to measure the sample in a cryostat it was glued to a custom made sampleholder. It consists of a printed circuit board (PCB) with contacts on the front thatare connected to two male, 10-pin plugs on the back. The cryostat sample holder isequipped with matching contacts for these plugs. After letting the glue dry for sev-eral hours the bond contacts on the substrate where connected to the PCB contactsusing wire bonding. The sample with the holder is shown in figure 2.3(a). Duringall further handling of the bonded sample holder one has to touch ground potentialto avoid corrupting the mesas by electrostatic charges.

(a) (b)

Figure 2.2: A short between two contact fingers at the edge of the crystal due to someremaining gold (a). After cutting through the gold with FIB milling (b).


The resistance between the contacts was measured using a multimeter, to checkif they where working or if shorts exist between the contacts. If a short or brokencontact is detected it can be mended to a certain extend using the dual beam. Somegold often remains between the contact fingers at the edges of the crystal, creatinga short between the fingers. Such a connection was intercepted by cutting throughit with the focused ion beam [A.7] which is shown in figure 2.2. Furthermore,it is possible to repair a broken contact by depositing a patch of platinum over asmall crack using EBID. The sample is finished if no more faults are measuredafter mending. Pictures of the finished sample are shown in figure 2.3.


(a) (b)

(c)

Figure 2.3: The finished sample: Bonded and glued to the sample holder (a). The holderis about 1.2 times 1.6 mm in size. One can see the bonding wires that connect the goldcontacts on the substrate with the PCB. The contacts lead to the crystal which is the smalldot in the middle. An optical microscope (b) and a SEM picture (c) shows the crystal witha higher magnification. The surrounding circle is the planarization layer and the crossesare alignment marks.


2.2 Measurement

A picture of the measurement equipment is shown in figure 2.4. It consists of acryostat that is connected to different measurement and controlling equipment anda measurement PC.

Figure 2.4: Measurement equipment: Cryostat (1) with cool head (2) and load-lock (3).Electronic equipment rack: Preamplifiers and electronics slots (4), PXI system (5), temper-ature controller (6), current source (7) and magnet control (8). The computer to the right isthe measurement PC, the screen and keyboard on the left belong to the PXI system.

2.2.1 Cryostat

The sample it was cooled down in a cryostat to analyze it. The used cryogen-free1

cryostat from Cryogenics can reach temperatures down to 300 mK. To measure ina magnetic field it is equipped with a superconducting magnet that can produce afield up to 5 T.

An external system compresses helium and pumps it to a cooling head at thecryostat, where it decompresses and therefore abstracts thermal energy from theinternal stages. The helium is then pumped back to the compressor, which is itselfcooled with a water cooling system. The internal design of the cryostat is illustratedin figure 2.5. Two cooling cycles contain 3He and 4He isotopes, while the 4Hesystem consists of four parts. Two cooling stages that are connected to the coolinghead of the external system, a reservoir (pot) and a pump. The pump contains

1It does not require any external cryogens like liquid nitrogen or liquid helium to operate.

2.2. MEASUREMENT 29

Figure 2.5: Screen shot of the graphical user interface of the cryostat. It schematicallyshows the internal build up of the cryostat: 3He system (blue), 4He system (purple), heatswitches (red) and superconducting magnet (green). The temperatures of all parts and thestatus of the heat switches and heaters are indicated.

activated charcoal that absorbs helium if it is cooled down to about 20 K or lower.A heat switch can thermally connect the pump to the second cooling stage in orderto cool down the pump. And a heater can warm it up to vaporize the helium. The4He pot is thermally connected to the 3He system, like shown in the picture. The3He system only contsists of a pump and a reservoir (pot). The sample is connectedto the 3He pot, so the reservoir temperature is equal to the sample temperature.

A cooldown to the base temperature works as follows. First, the 4He pump iswarmed up to evaporate the helium. It passes the two cooling stages and condensesat the second stage. The liquid helium then drops in the pot where it collects. Thethe same is done with the 3He. The pot is warmed up, causing the helium toevaporate. It condenses in the pipe, due to the thermal connection to the 4He potand collects in liquid form in the pot. This results in a temperature of about 3 Kat both pots. Thereafter, the 4He pump is cooled down by establishing a thermalconnection to the second stage with the heat switch. The evaporating helium in thepot is therefore pumped away which lowers the temperature in the the 4He and inthe 3He pot to about 1 K. A much lower temperature can not be reached using only4He. At this temperature the 3He pump is cooled down as well, which will finallycool down the 3He pot and therefore the sample to the base tmeperature of about300 mK. Since 3He has a lower boiling point than 4He a lower temperature can be


reached2. Due to the low pressure in the 3He pipe during pumping, the thermalconnection between both systems is weak and the warmer 4He pot will not effectthe 3He pot in this case. The base temperature can be kept constant up to twelvehours before all 3He is boiled off. It is possible to set a fixed sample temperatureor constantly increase it with an additional heater at the 3He pot.

The measurements are done at high vacuum conditions. Before cooling downthe cryostat it is evacuated with an external turbo pump that is connected to theload-lock. If the cryostat is then cooled down it will keep the vacuum without per-manent pumping, since the cold parts of the cryostat absorb molecules and there-fore act like a (sorption) pump. The sample is inserted through a load-lock with aremovable loading arm. The load-lock is evacuated separately before the sample isloaded to the cryostat.

2.2.2 Lock-in amplification measurements

Lock-in amplification is a common measurement technique to detect a weak signaland reject most unwanted noise even if the noise signals are much larger.

Figure 2.6: Measurement principle using an (analog) lock-in amplifier (figure modified,original taken from [20]).

The principle is explained in figure 2.6 on the basis of an analog lock-in am-plifier. It is required that the sample is excited with a fixed AC signal, which isusually done in a relatively quiet region of the noise spectrum. A (variable) re-sistor limits the current through the sample. The response signal Vs cos(ωst + φ)(with noise) from the sample is amplified and fed to a multiplier, together with thereference signal from a phase-lock loop (PLL). The PLL generates a signal at itsoutput with the same frequency fr = 2πωr and phase φ than the input signal, so it

23.2 K instead of 4.2 K at atmospheric pressure [19].

2.2. MEASUREMENT 31

is locked to the reference. To be able to measure a phase difference between thetwo signals, another 90 shifted reference signal is multiplied. The setup is thencalled dual-phase lock-in [20]. The two output signals of the multiplier are givenby

V1 =Vs cos(ωrt)cos(ωst +φ)

=12

Vs cos[(ωr +ωs)t +φ ]+12

Vs cos[(ωr−ωs)t +φ ], (2.1)

V2 =Vs sin(ωrt)cos(ωst +φ)

=12

Vs sin[(ωr +ωs)t +φ ]+12

Vs cos[(ωr−ωs)t +φ ]. (2.2)

The output signal passes a low pass filter which attenuates the sum frequency com-ponents (the first term of the equations) and lets the difference frequency compo-nents pass. Therefore all noisy parts at a different frequency than the referencewill be filtered out and two DC signals (which can be further amplified with a DCamplifier) are generated at the output. The multiplicator together with the low passfilter is also called a phase-sensitive detector (PSD) [21]. For signals in phase withthe reference, V1 will be at maximum and V2 will be zero. For non-zero phasesthe signals will be proportional to the phase difference. The phase independentamplitude is then given by

A =√

V 21 +V 2

2 (2.3)

and is proportional to the signal amplitude. And the phase difference is defined as

φ =− tan−1(

V2

V1

). (2.4)

So a lock-in amplifier acts as an extreme narrow band pass filter whose centerfrequency is matched to a reference signal. It thus lowers the signal-to-noise ratioand furthermore provides gain to a weak signal. In case of a dual-phase lock-in thephase shift, caused for example by a capacitance, can be measured as well.

2.2.3 Measurement setup

Figure 2.7 shows the measurement setup and the electrical connections. The cen-tral device is a PXI (PCI eXtensions for Instrumentation) system, an electronicinstrumentation platform with a standardized bus, which can be equipped with dif-ferent measurement and control modules [22]. In this case an analog-to-digital(A/D) converter module is used to read an analog signal with high resolution. Amulticonfiguration matrix module allows a software controlled switching between


a 20-pole cable from the sample holder in the cryostat and the measurement setup.In that way different contact configurations of the sample can be measured withoutneeding to switch cables manually. Furthermore, a multifunction module with sev-eral analog in- and outputs, connected to a field-programmable gate array (FPGA)is used. The FPGA can be programmed for individual applications by using aLabVIEW add-in that generates a hardware description language (HDL) code. Itis used due to its flexibility and its ability to simultaneously process several inputsignals with a high processing rate. A PXI controller module with an embeddedPC and LabVIEW software controls the modules in the system and is used for dataacquisition. The controller is connected to a measurement PC, also equipped withLabVIEW, where all data can be observed and saved and from where the wholemeasurement system is operated.

Figure 2.7: Scheme of the experimental setup showing the cryostat (blue), the measure-ment equipment and electronics (yellow), the measurement PC (green) and how they areconnected. Solid lines represent analog connections while the red line is the excitationsignal and the black lines the measured signals. The measured signals are split and go tothe FPGA for resistance measurements and to the A/D card for IV-curve measurements.Dotted lines are digital communication lines.

The FPGA is used for the lock-in measurement in this case. The excitationsignal is generated by the FPGA (red line) and is also used internally as referencefrequency. The outgoing signal can be adjusted by a resistor circuit, which is shownin detail in the insert in figure 2.7. It consists of a adjustable resistor for the currentrange, a potentiometer for fine adjustment and a fixed 100 Ω resistor to measure

2.2. MEASUREMENT 33

the current. The voltage response from the sample is measured using four-terminalsensing, to avoid measuring the resistance of the contacts. The sample responsesignal and the current measurement signal are pre-amplified and measured withthe analog inputs of the FPGA (black lines). The phase sensitive detection is donedigitally by the FPGA for the voltage and the current, so both are measured with alow signal-to-noise ratio. The resistance of the sample is then calculated from thesevalues. Up to eight signals can be measured at the same time with this method, e.g.to measure several mesas at one run. The gain of the pre-amplifiers is adjustedautomatically by the PXI system. Their control unit is galvanically isolated fromthe amplifying unit to keep the amplifier noise low.

To measure current-voltage characteristics the measured signals are dividedand also fed to the analog-to-digital converter, which has a higher input resolutionthan the FPGA. Due to the AC character of the signal one only needs to measurefor one period to get a full IV-curve with several thousand data points. Usuallyseveral data points are averaged to reduce the amount of data.

Further devices are a temperature controller that measures the temperature atseveral points inside the cryostat and controls the three heaters. A magnet con-troller operates the superconducting magnet. The field strength is adjusted throughthe magnet controller and not measured directly at the sample. To apply highercurrents to the sample the power output of the FPGA is not sufficient and a currentsource is connected to the sample instead. It supplies a fixed current regardless ofthe connected source by automatically adjusting the voltage. It can also supply ansinusoidal AC. All devices are digitally connected to the measurement PC to readtheir settings or control them.

Figure 2.8: Four-terminal sensing contact configuration of the sample to measure the in-plane (left) and mesa resistance (right). The squares represent a top view of the six mesasthat are electrically contacted through the crystal. The alternating current is adjusted andmeasured using the resistor configuration shown in the inset in figure 2.7.

The contact configuration of the sample is shown in figure 2.8. To analyzethe in-plane (ab-plane) properties of the crystal along the CuO2 planes, the currentwas send through the outermost mesa contacts and the voltage was measured at


two other mesa contacts. In that way the mesa resistances where not measured. Toanalyze a mesa along its c-axis,3 e.g. mesa 3, the current was send of mesa 3 andmesa 1, while the voltage was measured from the second contact finger of mesa 3and the neighboring mesa 4.

3Perpendicular to the CuO2 planes.

Chapter 3

Results

All results are from the Bi-2201 sample shown in section 2.1. Details about themeasurement are explained in section 2.2. The mesas are labeled from one to six,where the two outermost (1 and 6) are the largest ones and the two innermost (3and 4) the smallest ones. The exact sizes are listed in table 2.1.

3.1 Temperature dependence of the resistance

The resistance of the contacts and mesas was measured at room temperature usinga simple multimeter first. The bare contacts have a resistance in the range of 10Ω.The resistances of the mesas scale with their size and are roughly 250Ω for thelargest ones, 500Ω for the medium ones and 1000Ω for the small mesas. Furtherproperties where determined in the cryostat.

Figure 3.1 shows the in-plane resistance of the crystal1 and two mesas duringa cooldown from 200 K. Figure 3.2 shows a detailed view at lower temperatures.An alternating current of about 40µA at 1 Hz was used as an excitation signal. Thebulk was measured at three sections between mesa 2 and 3 (section 1), mesa 3 and4 (section 2) and mesa 4 and 5 (section 3) in this case.

The bulk crystal shows a clear superconducting transition of the in-plane re-sistance with Tcb ≈ 6.0 K in all sections, using the onset of the resistance drop ascritical temperature. Mesa 1 shows a superconducting transition at Tc1 ≈ 4.6 Kand mesa 3 at Tc3 ≈ 3.6 K. The c-axis resistance does not fully drop to zero butdecreases by 15% for mesa 1 and 8% for mesa 3. This is due to the contact resis-tance that adds to the total resistance of the mesa. The strong increase of the mesaresistance at decreasing temperatures is probably due to the opening of a second

1The preamplifier settings where not chosen ideally for the bulk measurement which caused ahigher noise and jumps in the curve due to automatic preamp adjustments.

35

36 CHAPTER 3. RESULTS

Figure 3.1: In plane and two mesa (c-axis) resistances over temperature. They all showsuperconducting transitions while a residual resistance remains for the mesas, probablydue to the contact resistance. This also explains the rather high initial resistance of themesas. The mesas show a semiconductor like low-temperature upturn which might be dueto the opening of the pseudogap.

gap besides the superconducting gap, the pseudogap. The origin of the pseudogapis not fully understood yet [23, 24]. It has been observed in c-axis direction ofseveral high-Tc superconductors and originates from a density of states decreasearound the Fermi energy. The gap causes the semiconductor like low-temperatureupturn whose intensity is dependent on the doping level [15, 25].

3.2. IV-CHARACTERISTICS AND TUNNELING SPECTROSCOPY 37

(a) (b)

Figure 3.2: In-plane resistance measured at three segments (a) and c-axis resistance oftwo mesas (b) over temperature. The in-plane critical temperature is 6.0 K in all segments,mesa 1 has a Tc of 4.6 K and the Tc of mesa 2 is 3.6 K.

3.2 IV-characteristics and tunneling spectroscopy

To measure a full current-voltage characteristics, the voltage response of the sam-ple, excited with a 1 Hz AC was measured for one second using the AD convertercard of the PXI-system. This results in about 5000 data points per IV-curve,depending on the reduction factor, the amount of measured points averaged andmerged to one.

Figure 3.3 shows the in-plane IV-characteristics of the crystal at 4.3 K. A clearvertical supercurrent is visible that switches to ohmic behavior at a critical currentof Ic = 240µA. The critical current is temperature dependent and increases at lowertemperatures. At 400 mK only the supercurrent was observed since the criticalcurrent was not exceeded yet.

Figure 3.4 shows the IV-characteristics of all six mesas. Two mesas with aboutthe same area show a similar behavior respectively. But no supercurrent is vis-ible, even though the sample is excited with a very weak current. Each tunneljunction within the mesa would usually result in one supercurrent branch in theIV-characteristics, see e.g. [26]. If the critical current of one junction is reachedit switches from superconducting into the normal state and the superconductingbranch of the next junction becomes visible. When the total current exceeded thecritical current of all junctions the characteristics becomes single valued and corre-sponds to the sum over all junctions. By counting the number of branches one candetermine the number of junctions and therefore the voltage per junction, which isnot possible in our case. The material might have a very low critical current density


Figure 3.3: In-plane IV-characteristics at 4.3 K, showing the supercurrent and the transi-tion to ohmic behavior at the critical current Ic.

that is quickly exceeded within these small mesas. Measurements on underdopedBi2201-La0.6 by A. Yurgens et al. also did not show any branches [14]. A too highcontact resistance may also preclude an observation of the critical current. Theused fabrication technique will always produce a contact resistance between themesa and the contact finger. It is influenced mainly by the time the cleaved crystalsurface is exposed to air, and therefore oxidates before the gold film is deposited.But also by the contamination of the gold surface before platinum deposition. Toreduce this factors the air exposure time is kept as short as possible and the goldsurface is cleaned using reactive ion etching before the platinum is deposited.

A small kink in the IV-curves in figure 3.4 at low voltages may be due to thesuperconducting gap. This suppression of the conductance around zero voltagecan be seen more clearly as a gap in the intrinsic tunneling spectrum, shown infigure 3.5(a) for all mesas at 400 mK. It shows the conductance over voltage andis obtained by the numerical differentiation σ(V ) = dI/dV (V ) of an IV-curve. Inthis case 49 data points where used for each calculation. This value gave a resultwith a rather low noise without smoothing out the details too much. The dI/dV -curves furthermore show a peak at each side of the gap and a dip next to it. Asimilar intrinsic tunneling spectrum and was observed by A. Yurgens for under-doped Bi2201-La0.6 [14]. Figure 3.5(b) shows that the conductance of the mesas islinearly dependent on their area. The size of the superconducting gap, determinedby the position (voltage) of the peaks, does not depend on the mesa size, which canbe seen in figure 3.5(d). That supports the assumption that it is the superconductinggap. Two groups form, indicated by the two fitted curves in the figure. This mightbe due to a different amount of junctions in the mesas, since the overall voltage is


Figure 3.4: Comparison of the IV-characteristics for all mesas at 400 mK. Mesa 1 and 6have the largest areas and therefore the smallest areas and mesa vice versa for mesa 3 and4. The inset shows a detail view of the IV-curve for mesa 1.

the sum of the voltage at each junction. The ratio between both groups is betweenapproximately 1.1 and 1.2. Assuming that this ratio corresponds to a difference ofone junction between the mesas and that the voltage drop is the same across eachjunction, the number of junctions is in the range of ten to five for these ratios. Butthis is a rather rough estimation. A difference of only one junction is a typical valueif the mesas where produced with ion beam etching, since it is a rather slow anduniform etching process.

A more detailed intrinsic tunneling spectrum is achieved by measuring it usinga DC bias voltage. The bias is slowly ramped from a negative to a positive voltagewhile a very small AC voltage is used to measure the resistivity at that point withthe lock-in amplification technique. The DC bias is then plotted over the x-axis andthe respective resistivity on the y-axis to obtain a measured dI/dV -curve. Figure3.6(a) shows the result for mesa 3 at different temperatures. One can see that thismethod is more sensitive than calculating it from the IV-characteristics. The peaksare more pronounced than in the numerically calculated version and a second setof smaller peaks becomes visible. But instead of only one second it takes severalminutes to measure one spectrum, depending on the voltage range and accuracy.

Figure 3.6(a) shows that the peaks slowly disappear with increasing tempera-ture until they totally vanish at temperatures higher than the Tc of 3.6 K. This is aclear evidence that they are closely related to superconductivity. They move fur-ther towards zero voltage at higher temperatures, meaning that the superconducting


(a) (b)

(c) (d)

Figure 3.5: Intrinsic tunneling spectra (dI/dV -curve) of all mesas at 400 mK, calculatedfrom IV-characteristics shown in figure 3.4 (a). And the same curves normalized to mesa 1(c). The peaks and the gap might be due to the superconducting gap. The conductance ofthe mesas (at 25 mV and 400 mK) is approximately linear dependent on their area, shownin figure (b). Figure (d) shows that the peak and dip positions are independent of the mesaarea. Two groups are visible, indicated by the linear fits, that might be due to a differentnumber of junctions in the mesas.


gap is closing. This can be seen better in figure 3.6(b), showing the peak and dippositions as a function of temperature. The resistance at zero voltage, extractedfrom the dI/dV -curves, is shown in figure 3.6(c). A transition at Tc is seen and thecurve looks similar to the mesa resistance over temperature measurement in figure3.2(b), as one would expect.

A larger gap remains even above Tc that could be the pseudogap. The spectrashown in figure 3.7 shows the extent of this gap. It was calculated from a current-voltage characteristics of mesa 4, measured with a higher amplitude at 6.6 K.

An asymmetry was observed during the measurements in the current-voltagecharacteristics, depending on the polarization of the current contact on the mesa.This is shown in figure 3.8 as well as the difference between both curves. Positivemeans that the mesa was connected to the plus pole of the current lead, so thecurrent was in phase with the measured voltage and flowing into the mesa. Negativemeans the minus pole was connected and the current was flowing out of the mesa.The asymmetry could be due to thermoelectric effects when the mesa heats updue to a power dissipation in the mesa during the measurement. A temperaturegradient then causes an additional voltage. This self-heating is usually quite smallfor a mesa and decreases for smaller mesa sizes due to a better thermal conduction[27]. The maximal dissipated power for the measurement shown in figure 3.8 isP = V · I = 0.2V · 800µA = 160µW. This causes an approximate temperatureincrease of ∆T = P ·Rth = 160µW · 100K/mW = 16K at the mesa. A slightlyexaggerated thermal resistance of Bi-2212 was used and it is assumed to be similarto the one for Bi-2201. This temperature difference could cause the asymmetry inthe IV-curve. Another reason might be a contact effect that arises at a transitionbetween a semiconductor-like and a metallic material at the mesa contact.


(a)

(b) (c)

Figure 3.6: Measured intrinsic tunneling spectra of mesa 3 at different temperatures (a).The peaks and dips disappear at Tc (3.6 K for mesa 3), giving an evidence for their su-perconducting origin. The average position (voltage) of the peaks and dips is plotted asa function of temperature in figure (b). Figure (c) shows the resistance at zero voltage atdifferent temperatures, extracted from the dI/dV measurements in (a). A transition at Tc isvisible.


Figure 3.7: Intrinsic tunneling spectra of mesa 4 at 6.6 K, showing the pseudogap. Itwas calculated from the IV-curve shown in the inset which was measured with at a highervoltage.

Figure 3.8: Asymmetry of the IV-characteristic for different current directions throughmesa 1 at 400 mK. Positive refers to the plus pole being connected to the mesa whilenegative refers to the minus pole. The blue curve shows the difference between both IV-curves. The asymmetry is probably due to thermoelectric effects or to a contact effect.


3.3 Magnetic field properties

The superconducting properties of a HTC are magnetic field dependent and a highfield is able to suppress superconductivity. To determine the critical field of thebulk crystal, the in-plane resistance over temperature was measured at differentfield strengths. The behavior is shown in figure 3.9. A small resistive transition isvisible even at 5 T, the highest field that can be produced in the used cryostat. Sosuperconductivity is not fully suppressed at this field and the critical field is slightlyhigher. This value is quite high considering the low critical current of the material.

Figure 3.9: In-plane resistance as a function of temperature for different magnetic fields.A small transition is still visible at 5 T, so the critical field is a little higher than 5 T.

To study the effect of a magnetic field to the c-axis properties, several intrin-sic tunneling spectra of mesa 3 where measured at different fields. Figure 3.10(a)shows the result at a temperature of 400 mK. The peaks decrease for higher fieldsand disappear completely at 1 T. This also demonstrates that they are of supercon-ducting origin. The peaks show a similar behavior than for an increasing tem-perature, like seen in figure 3.6(a). Thy move closer towards lower voltages atincreasing fields, which is seen clearly in figure 3.10(b). The resistance at zerovoltage, shown in figure 3.10(c), drops already at a very low field and increases forhigher fields.

3.3. MAGNETIC FIELD PROPERTIES 45

(a)

(b) (c)

Figure 3.10: Measured intrinsic tunneling spectra of mesa 3 (at 400 mK) for differentmagnetic fields (a). Figure (b) shows the linear decrease of the average peak and dipposition (voltage) as a function of the magnetic field. The zero point resistance (at V = 0)drops already at rather small magnetic fields and increases again for higher fields (c).


3.4 Doping

It was recently discovered that is it possible to change the superconducting proper-ties of Bi-2212 mesas along the c-axis by injecting an extensive current [28]. Andit was confirmed and further analyzed by members of the Experimental CondensedMatter Physics Group at Stockholm University [not published yet]. The effectshows a similar influence as doping with oxygen. How much the properties aretunable depends on the existing doping level of the HTSC. For an underdoped Bi-2212 sample, the current through a mesa with a few micrometer cross-section startsto influence its properties if the bias voltage exceeds ≈ 1 V. Koval et al. increasedthe critical temperature by a factor of two, the critical current was increased by oneorder of magnitude and the normal resistance was decreased. The effect was muchsmaller for an optimal doped sample though. This current doping is persistent andin addition reversible if the current direction is changed. Koval et al. assume thatthe effect is caused by trapped charges in the insulating layers, which cause a sim-ilar effect than field effect doping of semiconductors. But this assumption is notproven yet.

To see if it is possible to influence the mesa properties of Bi-2201 as well, sim-ilar measurements where carried out. If the normal resistance could be decreasedand the critical current increased it might be possible to see a critical current inthe IV-characteristics of the mesa. Mesa 4 was was chosen for this doping studiessince it is one of the smallest mesas and therefore a high voltage can be achieved atmodest currents. A current source was used for the excitation signal instead of theanalog output of the FPGA since it is not made for a high power output. The pluspole was connected to mesa 4 while the minus pole was connected to mesa 1, 2 and3 in order to spread the current and influence the other mesas as little as possible.A small 1 Hz alternating current with a DC bias was used and the bias current wasincreased stepwise. A first effect was visible at a bias voltage of about 2 V and abias current of 2.2 mA (a current density J of about 0.24 A/cm2 for this mesa). Thebias was kept constant at that point and the resistance of the mesa started to changegradually. When no further change was visible the bias was further increased. AnIV-curve was recorded after several doping states and the result is shown in figure3.11. One can see that the resistance first decreased (state 2). But after a currentinjection of 2.7 mA (J ≈0.34 A/cm2) the effect started to reverse and the resistanceincreased. This continued when the bias was increase further. The change mightbe due to a change in the c-axis resistance but also due to a changing contact resis-tance. Switching the current direction could not return the effect but increased theresistance even more.

The IV-curve of mesa 4 was measured at doping state 4 at different tempera-tures to see the influence of the doping process. This is shown in figure 3.12(a). A

3.4. DOPING 47

Figure 3.11: IV-characteristics of mesa 4 at around 4 K, showing the effect of doping byintensive current injection. The doping states are achieved after bias current/voltage of:2.5 mA, 2.38 V (state 2); 2.7 mA, 2.60 V (state 3); 4.0 mA, 2.57 V (state 4) and -4.0 mA,-1.65 V (negative doping). The resistance decreased first and increased again for highercurrents.

hump started to develop and gets more pronounced at lower temperatures. This isseen better in figure 3.12(b), where the intrinsic tunneling spectra at 400 mK beforeand after doping (state 4) are compared. The superconducting features seen beforeand especially the dip became more pronounced. The dI/dV -curve after dopinglooks quite unusual. Another possibility for the origin of the peaks and dips couldbe a supercurrent that was existent before but could not be seen more clearly dueto the large overall resistance. Therefore it does not appear as a vertical line in theIV-curve but rather tilted and is only seen as a hump. It might have changed duringdoping and therefore became better visible afterwards.

A comparison of the resistance over temperature of mesa 4 before and afterdoping (state 4) is shown in figure 3.13. The resistance increased but the criticaltemperature did not change significantly. The extend of the resistance drop duringthe transition and the curve progressions are similar, so the curve after doping isjust shifted upwards. This indicates that mostly the contact resistance changed andthe mesa resistance was probably not influenced significantly.


(a) (b)

Figure 3.12: IV-characteristics of mesa 4 after doping (state 4) at different temperatures(a). And dI/dV curve comparing the shown IV-curve at 400 mK with a curve measuredbefore doping (b). The peaks and especially the dips became much more pronounced. ThedI/dV -curve after doping looks quite uncommon for being due to the superconducting gapand might have another origin like e.g. the supercurrent.

Figure 3.13: Resistance over temperature of mesa 4 before and after doping (state 4). Theresistance increased but the critical temperature as well as the extend of the resistance dropduring the transition did not change significantly. The similar curve progressions indicatethat mostly the contact resistance changed during doping.

3.5. CONCLUSIONS 49

3.5 Conclusions

The analyzed Bi-2201 crystal has a rather low critical temperature of about 6.0 K.The upper critical field is slightly higher than 5 T, which is is uncharacteristic ofa superconductor with the observed Tc. The mesa (c-axis) resistances are increas-ing with decreasing temperature, possibly due to the formation of the pseudogap,and show a superconducting transition close to the ab-plane value. Superconduct-ing peaks are visible in the intrinsic tunneling spectra that disappear at Tc and ata magnetic field of 1 T and above. They are independent of the mesa area andmay originate from the superconducting gap, but they might also be due to a super-current which is not directly visible in the current-voltage characteristics. A highcontact resistance of the mesa or a very low critical current of the material disturba clear observation of the supercurrent. A larger gap is visible even above Tc in atunneling spectrum measured with a higher voltage, which might be the pseudo-gap. The mesa IV-characteristics show an asymmetry which is dependent on thecurrent direction during measurement. This can be attributed to a contact- or ther-moelectric effect. Furthermore, it was possible to tune the c-axis properties of thematerial by extensive current injection. The overall mesa resistance first decreasedat a bias voltage above 2 V but increased again at a higher bias. The tunneling spec-trum features where significantly more pronounced after doping, while the criticaltemperature remained nearly unchanged.

In summary, the material had shown interesting behaviors which have to befurther studied for improved understanding. A suggestion for extended researchwould be to produce a sample with larger mesas in order to lower the current den-sity within or trying a different fabrication process that will reduce the contactresistance. This could allow for observations of the supercurrent within the mesa,which might enable further conclusions.


Appendix A

Fabrication parameters

The following tables show the process parameters that where used during the sam-ple fabrication explained in section 2.1. The used apparatus is indicated in brackets.

Table A.1: Epoxy resin.

TypeMixing Hardening Hardening

ratio temperature (C) time (min)

UHU plus endfest 300 1:1 100 10

Table A.2: E-beam evaporation (Eurovac).

Chamber pressure (mbar) Deposition rate (A/min)

at least 10−7 between 1 and 2

Table A.3: Positive photoresist "S1813 G2".

Spinning Baking Exposure time Developer Developing time

1 min 1 min ≈ 25 s MF319 30 s4000 rpm 100C

51

52 APPENDIX A. FABRICATION PARAMETERS

Table A.4: Reactive ion etching (OXFORD Plasmalab RIE).

Chamber pressure Forward power Oxygen flow ICP power(mTorr) (W) (sccm) (W)

100 10 20 50 (low), 150 (high)

Table A.5: Ion beam etching ("Sputnik"). The resulting etch rate is about 1.5nm/min.

Chamber Ar gas flow Beam Beam Accelerator Dischargepressure current voltage voltage voltage(mbar) (sccm) (mA) (V) (V) (V)

at least 4 ·10−7 1.5 10 300 2.50 38.0

Table A.6: Electron beam induced deposition (FEI Nova-200 dual beam).

Accelerating voltage Beam current No. of passes Height Z(kV) (nA) (nm)

5.0 1.6 10 63

Table A.7: Focused ion beam milling (FEI Nova-200 dual beam).

Beam voltage Beam current Dwell time Height Z Width Y(kV) (nA) (µs) (µm) (µm)

30 0.5 1.0 0.3 0.3

53

Acknowledgments

I would like to thank the Experimental Condensed Matter Physics Group, es-pecially my supervisor Vladimir Krasnov for giving me the opportunity to ac-complish my degree project as a member of their team. Special thanks also goout to Holger Motzkau and Sven-Olof Katterwe for introducing me to the micro-fabrication techniques, helping me with all kind of problems and answering numer-ous questions. And to Andreas Rydth for his help with the measurement systemand advice on my measurements.

Sincere thank you to my parents who with their help have made my wish tocomplete this masters degree in Stockholm possible, not to mention their continu-ous support throughout all my academic years.

54

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