Towards oxide-based spintronic
devices
THESIS
submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in
PHYSICS
Author : Dani¨el Opdam
Student ID : 1256055
Supervisor : Prof.dr. J. Aarts
Daily supervisor : N. Lebedev, Msc.
2ndcorrector : Dr. M.P. Allan
Towards oxide-based spintronic
devices
Dani¨el Opdam
Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands
January 9, 2019
Abstract
In this thesis, we have worked on devices for two oxide systems, with which spin-polarized currents could in future be controlled. Firstly, we
have worked on the optimization of growth parameters for the depositions of La0.7Sr0.3MnO3thin-films in off-axis sputtering. We have
characterized the grown films using Atomic Force Microscopy, X-Ray Diffraction and resistance measurements. La0.7Sr0.3MnO3is a ferromagnetic oxide, which we believe could be used in conjunction with
the oxide superconductor Sr2RuO4to induce polarized supercurrents. Further, we illustrate a lithography procedure which allows for the
patterning of LSMO films into Hall bar structures. Next, we have designed a side-gated Hall bar pattern for LaAlO3/EuTiO3/SrTiO3 devices. This system has been shown to give rise to a spin-polarized two dimensional electron gas [1]. Our structure is designed to allow for local
Contents
1 Introduction 7
2 Long-range proximity effect 9
2.1 Pairing symmetry 9
2.2 Proximity effect 10
2.2.1 Proximity effect inside the ferromagnet 12 2.2.2 Proximity effect inside the superconductor 13
2.3 Long-range proximity effect 14
2.3.1 Singlet superconductor 14
2.3.2 Triplet superconductor 15
2.4 Half-metal/triplet superconductor heterostructure 17
3 Spin-polarized 2DEG 21
3.1 Two-dimensional electron gas 21
3.2 Europium titanate delta-doping 23
3.3 Side-gating 24 4 Methods 27 4.1 Substrate termination 27 4.2 Lithography 28 4.2.1 Optical lithography 28 4.2.2 E-beam lithography 30 4.3 Sputtering 32
4.3.1 On-axis sputtering on resist 32
4.3.2 Off-axis sputtering 33
4.4 X-ray diffraction and reflectometry 34
6 CONTENTS 5 Results 37 5.1 LSMO 37 5.1.1 Growth parameters 37 5.1.2 Optical lithography 40 5.1.3 Argon etching 41
5.2 Side-gated Hall bars 44
5.2.1 Main channel constriction 45
5.2.2 Structure optimization 47
5.2.3 Oxygen plasma cleaning 53
6 Conclusion 57
6
Chapter
1
Introduction
Transition metal oxides are an interesting class of materials which show a wide variety of electronic states, such as superconductors (Sr2RuO4), in-sulators (LaAlO3), dielectric materials (SrTiO3) and ferromagnets
(La0.7Sr0.3MnO3) [2]. However, despite their promising properties, oxides are quite difficult to work with and have not been applied in many fields yet. In this thesis, we focus on device fabrication for two oxide materials which have properties of are of particular interest for spintronic applica-tions.
Spintronic devices have been predicted to replace many conventional semiconductor-based devices in the future [3]. In spintronic devices, in-formation is not just encoded in the charge of carriers but also in the spin. Spin-polarized materials play a role in many such devices as a source of spin-polarized currents. In this thesis we work on devices for two oxide systems: La0.7Sr0.3MnO3, a fully spin polarized material and
LaAlO3/EuTiO3/SrTiO3, an oxide heterostructure which gives rise to an electric field tunable spin-polarization.
Firstly, we work on the growth of La0.7Sr0.3MnO3 by off-axis sputter-ing. We propose a scheme by which a fully spin-polarized supercurrent could be induced in La0.7Sr0.3MnO3. Devices which allow for the penetra-tion of superconducting currents into a ferromagnet have been created be-fore [4]. However, these devices do not retain spin-information across the interface of the ferromagnet and are thus hard to use in spintronic appli-cation. Recently it was shown that this difficulty could be overcome using the oxide superconductor Sr2RuO4[5], allowing for the direct application of superconductors in spintronic devices. We believe La0.7Sr0.3MnO3,
be-8 Introduction
ing a fully spin-polarized material, is especially promising in this area. Next, we work on a structure for a EuTiO3 doped LaAlO3/SrTiO3 de-vice. LaAlO3 and SrTiO3 are two insulating materials which have been known to give rise to a highly conducting two dimensional electron gas at their interface. Recently it was discovered [1] that an electric field tunable spin-polarization could be induced in the electron gas, by doping with EuTiO3 in the interface. In this thesis we design a structure which could be used to locally tune the polarization of this doped LaAlO3/SrTiO3 in-terface.
In chapter 2 we discuss the long-range proximity effect, a supercon-ducting phenomena that occurs in certain ferromagnet/superconsupercon-ducting heterostructures. We describe the properties of the materials La0.7Sr0.3MnO3 and Sr2RuO4 which allow for the creation of a spin-polarized long-range proximity effect. In chapter 3 we describe the properties of the
LaAlO3/EuTiO3/SrTiO3 system. We describe how recent advances allow for the creation of an electric field tunable spin-polarization. In chapter 4 we describe the experimental techniques used in this project, as well as the patterning processes used to create structures. In chapter 5 we discuss the results, mainly focusing on characterization of the structures created.
8
Chapter
2
Long-range proximity effect
In this chapter we will discuss the proximity effect in a ferromagnet. Elec-trons in a superconductor are conventionally in a singlet-state with anti-parallel spins while spins in a ferromagnet are aligned. This makes these two phenomena naturally quite combative, it will be shown however that, using certain schemes, ferromagnetism and superconductivity can occur simultaneously. We propose such a scheme using the materials strontium ruthenate and lanthanum strontium manganate.
2.1
Pairing symmetry
Electrons in a superconductor pair up to create bosonic particles known as Cooper pairs. As electrons themselves are fermions, the total wavefunc-tion of the Cooper pair must be odd to obey the Pauli exclusion principle. The wavefunction can be divided into three parts, where each part allows for even or odd symmetry. Firstly a spin part, which can either be a sin-glet (odd) or a triplet (even) state. In a sinsin-glet state the spin-projection of the pair (m) is necessarily 0 while for a triplet state it can be either 0 or±1. Next, the momentum part is characterized by the orbital angular momentum quantum number L. L=0 (s-wave) and L=2 (d-wave) are even functions, while L=1 (p-wave) and (f-wave) are odd functions. Lastly the wavefunction has a time dependent part, which can also be even or odd. All allowed combinations are summarized in table 2.1:
10 Long-range proximity effect
Table 2.1:Allowed pairing symmetries for fermion pairs.
Spin Momentum Frequency
singlet(odd) s-wave/d-wave(even) even singlet(odd) p-wave/f-wave(odd) odd triplet(even) s-wave/d-wave(even) odd triplet(even) p-wave/f-wave(odd) even
Figure 2.1: Proximity effect in superconductor/normal metal heterostructure. Figure adapted from [6].
2.2
Proximity effect
When a superconductor is interfaced with a normal metal, Cooper pairs may cross the interface between the materials and enter into the normal metal. This induces a superconducting state in the normal metal while lowering the superconducting order parameter in the superconductor, thus changing the properties of both materials. Such effects are referred to as the proximity effect. The lengthscale over which the proximity effect oc-curs is given by the coherence length in the material ξ (figure 2.1). The coherence length in a normal metal is determined by disorder in the metal and thermal fluctuations of the electrons:
ξN = s
¯hD
kBT (2.1)
where D is the diffusion coefficient, ¯h is the reduced Planck constant and kBT is the thermal energy.
The proximity effect will also occur in a superconductor/ferromagnet junction. However in a ferromagnet the energy bands of spin-up and 10
2.2 Proximity effect 11
Figure 2.2: Band diagram showing the energy shift of spin bands in a ferromag-net. Momenta at the Fermi energy are shown with the red and blue arrows. Adapted from [7].
spin-down electrons are shifted by the exchange energy 2Ex (figure 2.2) making it energetically favorable for electrons to be parallel. As the elec-trons that make up Cooper pairs in a conventional superconductor are in a singlet state, they are necessarily anti-parallel. The exchange force po-larizing electrons will thus also lead to Cooper pairs breaking up. The coherence length in a ferromagnet is therefore governed by the exchange energy rather than by thermal fluctuation:
ξF = s
¯hD
Ex (2.2)
For a strong ferromagnet ξF can be smaller than a unit cell of the crystal lattice. For half-metals, where one spin band of the ferromagnet is metal-lic and one is fully insulating (figure 2.3), the singlet Cooper pairs can not enter the material at all.
12 Long-range proximity effect
Figure 2.3: a). An illustration of the band diagram of Nickel, a conventional ferromagnet. The spin-up and spin-down bands in the diagram have been shifted by the exchange force. The green area denotes the Fermi energy, as both bands are intersected by the Fermi energy both would be occupied. b). An illustration of La0.7Sr0.3MnO3 (LSMO), a half-metal. In a half-metal the exchange force lifts
one spin band completely above the Fermi energy, leaving it unoccupied. This leaves a half-metal fully spin polarized. Adapted from [8].
2.2.1
Proximity effect inside the ferromagnet
The electrons that make up these Cooper pair are located around the Fermi energy with opposite momenta. When a Cooper pair enters the ferromag-net, the spin-up and spin-down bands are shifted (figure 2.2) and thus the k-vectors of the electron shift along with them [9]: kf↑ = kf +Q/2 and kf↓ = kf −Q/2. Here Q/2 = ¯hvExf where vf is the Fermi velocity. This leaves the Cooper pair with a non-zero center of mass momentum of
Q. This non-zero center of mass momentum of the Cooper pair leads to a spacial modulation of the order parameter. For a pair of electrons this modulation follows:
| ↑↓i| ↓↑i⇒ | ↑↓iei(kf ↑−kf ↓)R| ↓↑iei(kf ↓−kf ↑)R (2.3)
Where R is distance. This modifies the singlet state according to:
| ↑↓ − ↓↑i ⇒ | ↑↓ieiQR− | ↓↑ie−iQR
= | ↑↓ − ↓↑icos(Q·R) + | ↑↓ + ↓↑isin(Q·R) (2.4) The first term on the right hand side is an oscillation of a singlet state and the second term is an oscillation of a opposite spin (m = 0) triplet 12
2.2 Proximity effect 13
Figure 2.4:Proximity effect in a superconductor/ferromagnet heterostructure. A short-range oscillation of both singlet and triplet components of the supercon-ducting order parameter can be observed in the ferromagnet. Scattering of the ferromagnetic interface creates a triplet state inside the superconductor. Figure adapted from [7].
state. This result is illustrated in the right side of the middle panel of figure 2.4, one can see a oscillation of both a singlet and triplet order parameter, which rapidly drop of due to the exchange force breaking up the opposite spin Cooper pairs in the ferromagnet.
2.2.2
Proximity effect inside the superconductor
While some Cooper pairs enter the ferromagnet, some may also scatter of the interface with the ferromagnet. For a half-metal all Cooper pairs will scatter of the interface, as no compatible states are available inside the half-metal (figure 2.3). The electrons which scatter of the magnetic interface will be affected by the exchange force, leading to a phase shift dependent on their spin. TakingΘ as the difference in phase between a spin-up and a spin-down electron, it follows that a scattered singlet Cooper pair obtains a phase according to:
| ↑↓ − ↓↑i ⇒ | ↑↓ieiΘ− | ↓↑ie−iΘ
= | ↑↓ − ↓↑icos(Θ) + | ↑↓ + ↓↑isin(Θ) (2.5) Again the first term on the right hand side is an oscillation a singlet state and the second term is an oscillation of opposite spin (m=0) triplet state. This result is illustrated in the left side of the middle panel of figure 2.4. The amplitude of the spin triplet order parameter inside the superconduc-tor is dependent on the size of the phase shift and thus on the exchange
14 Long-range proximity effect
force in the ferromagnet. For ferromagnets with a strong exchange force (half-metals) the triplet correlations will be strongest.
2.3
Long-range proximity effect
While an opposite spin cooper pair will break up inside a ferromagnet due to the exchange force, for an equal spin (m = ±1) triplet Cooper pair the exchange force acts equally on both electrons. Therefore, the coherence length of equal spin triplet Cooper pairs is not limited by the exchange energy, allowing them to penetrate for much further than ξF. This effect is known as the long-range proximity effect.
2.3.1
Singlet superconductor
A theoretical scheme was developed to induce a triplet supercurrent in a ferromagnet by Bergeret et al. [10] [11]. The scheme revolves around the (m=0) triplet state which emerges in the superconductor at the inter-face with a ferromagnet (section 2.2.2). This state, unlike the conventional singlet superconducting state, is not rotationally invariant. This can be ex-ploited using a second magnetic layer with a polarization perpendicular to the bulk magnetization. The (m=0) triplet state is quantized along the polarization axis of the interface. The rotation of the magnetization go-ing from the interface to the bulk can be seen as a rotation of the frame of reference for the Cooper pairs. This rotation changes the (m=0) triplet state into an equal spin (m=±1) triplet state (figure 2.5). As the amplitude of triplet correlations inside the superconductor depends on the exchange force of the ferromagnet, half-metals are most suited for application of this scheme.
The wavefunction describing the triplet Cooper pairs must be odd to obey Pauli’s exclusion principle, however the orbital s-wave state as well as the spin triplet state are even functions under exchange of the two elec-trons. Bergeret et al. show in their papers that the induced triplet super-conductivity is an odd-frequency state, a state where the time part of the wavefunction is odd under exchange of the electrons, which thus obeys Pauli’s exclusion principle. The odd-frequency pairing of triplets was first theorized by Berezinksii [12] however it had not been observed in any ma-terial and would thus be a novel electronic state. This theoretical scheme was successfully applied by Keizer et al. in 2006 using superconducting 14
2.3 Long-range proximity effect 15
Figure 2.5: Illustration showing the influence of an extra magnetic layer at the interface of an superconductor-half metal structure. a, The effect of an interface where the magnetization is aligned to the bulk magnetization. The ferromagnetic interface induce (m=0) triplet Cooper pairs in the superconductor but due to the exchange energy, no opposite spin Cooper pairs are present in the half-metal (fig-ure 2.2). b, The effect of an interface where the magnetization is perpendicular to the bulk magnetization. The (m=0) triplets present in the superconductor are quantized with respect to the magnetization axis of the interface. Due to the ro-tational invariance of the (m=0) triplet state, these triplets are equal spin triplets with respect to the bulk magnetization, and may propagate into the half-metal. Adapted from [7].
NbTiN contacts on a film of half-metallic CrO2[4], this was the first exper-imental realization of a long-range proximity effect in a ferromagnet.
2.3.2
Triplet superconductor
A different way to introduce spin-triplet superconductivity in a ferromag-net is, to use a triplet superconductor instead of using a conventional sin-glet superconductor. As the Cooper pairs would already be in a triplet state it would allow them to directly enter and propagate in the ferromag-net, without the need for an extra magnetic layer. This would give some direct advantages in the field of spintronics, as it allows spins carrying information to cross the interface without disruption. This method of in-ducing a long-range proximity effect was first realized by Anwar et al. [5] using a heterostructure of the superconductor Sr2RuO4(SRO214) and the ferromagnet SrRuO3.
16 Long-range proximity effect
Figure 2.6:Crystal structure of Sr2RuO4. Adapted from [7]
SRO214 is a perovskite material with a tetragonal unit cell of lattice constants a=b=0.3871 nm and c = 1.2722 nm [13]. SRO214 is a well behaved Fermi liquid showing a T2dependence of its resistance down to 1.5 K [14] where it undergoes a superconducting transition. Measurements of the spin susceptibility by NMR Knight shift [15] and Polarized Neutron Scat-tering [16] have shown that the Cooper pairs SRO214 are in a spin triplet state. These triplets are quantized in the ruthenate ab-planes of the ma-terial, as the pairs are randomly orientated the material shows no net po-larization. Unlike the odd-frequency triplet state that can be induced in a singlet superconductor-ferromagnet junction, the Cooper pairs in SRO214 are in a orbital p-wave even frequency state. Using Muon spin rotation it was found that the superconducting state of SRO214 broke time rever-sal symmetry [17], with this the d-vector describing the superconducting order parameter in SRO214 could be determined: d(k) = (kx±i·ky)ˆz. The superconductivity of SRO214 is high 2-dimensional with coherence lengths of ξab= 66 nm in the ab-plane, and of ξc = 3.3 nm along the c-axis. 16
2.4 Half-metal/triplet superconductor heterostructure 17
Figure 2.7:Crystal structure of LSMO. Adapted from [8]
2.4
Half-metal/triplet superconductor
heterostruc-ture
In this thesis we will aim to create a heterostructure of Sr2RuO4, a triplet superconductor and La0.7Sr0.3MnO3(LSMO), a half-metal. As in the work of Anwar et al. we expect the triplet Cooper pairs of the Sr2RuO4to directly penetrate into the LSMO. As LSMO is a half-metal this would allow one to work with a fully polarized supercurrent. Also, as no spin-flip scattering occurs in half-metals, the supercurrent in this material is only limited by diffusion and thermal excitations as in a normal metal.
LSMO is a perovskite material with a rhombohedral crystal structure and lattice constants of a=b=c=0.3873 nm [8]. LSMO is made of parent ma-terial LaMnO3which has been p-doped with Sr-atoms (figure 2.7). LSMO shows a rich phase diagram, illustrated in figure 2.8. With the Sr doping concentration Mn3+ions are transformed to Mn4+, for a doping concentra-tion of around 0.3 the ratio Mn4+ is about 50%. For this doping concen-tration LSMO is a half-metal, which is due to a strong double-exchange interaction between the Mn3+and Mn4+. The Curie temperature of LSMO at this doping concentration is 360 K [8].
The d-shell of the Mn3+ ions contain 4 electrons, the first 3 occupy the t2g level in a parallel configuration. The last electron occupies the eg level and can hop over the oxygen atom to Mn4+ ions where the eg level is empty (figure 2.9). However due to Hund’s energy the hopping proba-bility is largest when t2g electrons are aligned with the electron. Because a configuration that allows for hopping is energetically favorable the
neigh-18 Long-range proximity effect
Figure 2.8: Phase diagram of LSMO. For a Sr doping concentration of 0.3 LSMO is a ferromagnetic metal below the Curie temperature and an anti-ferromagnetic insulator above the Curie temperature. For a too low or too high Sr doping con-centration, LSMO becomes insulating at low temperatures. Adapted from [18]
18
2.4 Half-metal/triplet superconductor heterostructure 19
boring atoms will align themselves [19].
This double-exchange mechanism is not only responsible for the ferro-magnetism of the material but also provides the main means of electrical transport [8]. Because of this LSMO undergoes a metal-insulator transi-tion at the Curie temperature, when the double-exchange mechanism is suppressed. When the Sr-doping concentration in LSMO is too high/low the Curie decreases, followed by the metal-insulator transition. Above the Curie temperature the Mn-ions in LSMO can still be aligned by an external magnetic field. This will induce the double-exchange interaction causing the electrical resistance to drop significantly, resulting in a negative colos-sal magnetoresistance (CMR).
Firstly in this thesis, we will need to find a suitable growth process for LSMO-films. The metal-insulator transition of LSMO and the associated CMR effect can be used to test for the stoichiometry of the film. For the desired Sr-doping concentration of 0.3, the metal insulator transition oc-curs around 360 K, and a strong negative CMR should be observed above this temperature. To accurately measure the resistance and CMR effect in LSMO films we aim to pattern the LSMO into a Hall bar structure (section 4.2.1).
Figure 2.9: Illustration of the double exchange mechanism in LSMO. On the left the 4 electrons which fill the d-shell in a Mn3+ion, the electron in the e
glevel can
hop across the neighboring oxygen atom onto a Mn4+ ion. For this hopping to occur the electrons in the t2glevels of the 2 ions must be aligned to minimize the
Chapter
3
Spin-polarized 2DEG
In this chapter we will discuss the conducting interface between LaAlO3 and SrTiO3. We will discuss recent discoveries which would allow one to create and manipulate a spin-polarization of this interface. Lastly we discuss how one can design a device to achieve this purpose.
3.1
Two-dimensional electron gas
LaAlO3 (LAO) and SrTiO3(STO) are two perovskite materials, which fol-low a general structure formula ABO3. The crystal structure of a per-ovskite can be described as alternating (001) planes of AO and BO2. While LAO and STO are both band-insulators, it was discovered [20] that the interface of the two materials could give rise to a highly conducting two-dimensional electron gas (2DEG). The conducting interface of LAO-STO heterostructures gives rise to a host of interesting phenomena such as tun-able superconductivity [21], traces of magnetism [22] and a metal-insulator transition can also be induced by gating [23]. These properties make LAO/STO interfaces a particularly interesting material for spintronic application.
Several theories exist explaining the origin of this 2DEG in (001) orien-tated LAO/STO interfaces. One popular interpretation is the polar catas-trophe model. This model notes that while the SrO and TiO2planes of STO are both uncharged, the LaO and AlO2planes of LAO have charge +1 and -1 respectively. The abrupt change from neutral layers to charged layers is what leads to the polar catastrophe (illustrated in figure 3.1). For a film starting with a layer of LaO, each new plane will make the structure ei-ther positive or neutrally charged, this causes the potential describing the
22 Spin-polarized 2DEG
Figure 3.1:Illustration of the polar catastrophe model. a, In film starting with an LaO plane the electric field of the film oscillates around a positive value, leading to a positively diverging potential. b, the opposite occurs when a LAO film starts with an AlO2 plane. c, in order to prevent the diverging potential, half an
elec-tron per unit cell may leave the LaO plane to occupy the TiO2layer, leading to a
conducting interface layer. d, When a LAO film starts with an AlO2plane, half an
electron per unit cell may leave the AlO2 layer to prevent the polar catastrophe.
In practice this is not observed in AlO2/SrO interface. Adapted from [24]
electric field to diverge with thickness. To avoid this divergence of the po-tential half an electron per unit cell of the LaO plane can occupy the TiO2 plane, changing some Ti4+-ions to Ti3+-ions, leading to a conducting inter-face. A similar argument can be made for an AlO2/SrO interface, how-ever experiments have found that the polar catastrophe in the AlO2/SrO interface is consequently solved by other mechanisms [24]. A conducting interface is thus only possible, when LAO is deposited on a TiO2 termi-nated STO substrate [20].
The extra electrons in the TiO2 plane would occupy the previously empty t2gd-shells of the titanium. At 80 K the STO undergoes a transition from a cubic crystal symmetry to a tetragonal one [25]. This symmetry break gives dxystates a higher energy than the dyzand the dxzstates. The presence of the LAO interface reverses the bands, making dxy the lowest energy state [25]. The dxy states are localized close to the interface (fig-ure 3.2), contributing to the 2-dimensional behavior of the conductance. When the carrier concentration is raised the dyz and the dxz can also be filled, changing the system from 1-band to 2-band [26].
22
3.2 Europium titanate delta-doping 23
Figure 3.2: Illustration of the band structure of STO and LAO. One can see the Dxy band closest to the interface as well as the dyzand the dxz bands extending
deeper into the STO. Adapted from [27]
3.2
Europium titanate delta-doping
Interestingly, Stornaiuolo et. al. [1] found that delta-doping ETO in an LAO/STO interface leads to a polarization of the 2DEG. Delta-doping refers to doping only a few unit-cells in between the two materials. EuTiO3
(ETO) in bulk state is a cubic perovskite with a lattice constant of a=0.3905 nm [28]. It was found that the polarization in the LAO/ETO/STO system could be
easily tuned with an electric field. This is the first realization of an elec-tric field tunable spin-polarized 2DEG in an oxide, an important result for the possibility of oxide-spintronics. The polarization of the 2DEG can be monitored using the anomalous Hall effect, an enhanced version of the conventional Hall effect which occurs in spin-polarized materials.
The origin of this ferromagnetic ordering is still unclear. Bulk ETO is a band-insulator and is both anti-ferromagnetic (AFM) and paraelectric (PE). Lanthanum doping of ETO into the ferromagnetic ELTO could be possible, however a second explanation exists. A theoretical model pre-dicted [29] that certain AFM PE insulators could have an excited
multifer-24 Spin-polarized 2DEG
oic state, which could be reached using spin-lattice coupling. A multifer-oic being a material which shows multiple simultaneous ferrmultifer-oic orderings such as ferroelectricity (FE) and ferromagnetism (FM). Multiferoics of this kind are of great interest in spintronics, as the coupling between FE and FM allows one to drive the magnetic polarization using an electric field.
The transition to a multiferoic state would require a coupling between a polar-distortion of the cubic unit-cell, necessary for FE, and magnetic or-dering of the spins. This transition would be characterized by an infrared-active (ir) soft polar phonon with the following properties:
• The phonon must be coupled strongly to strain.
• The phonon must be coupled strongly to magnetic ordering.
• It should be possible to polarize the AFM spins in the material with a sufficient magnetic field, this should decrease the phonon frequency. ETO matches all these properties and is thus a prime candidate for this model. Using density functional theory (DFT) it was determined [29] that the phonon found in ETO was indeed the sought after soft polar phonon. By placing ETO under strain the phonon frequency of this soft mode de-creases. Vanishing of this phonon frequency is linked to the phase transi-tion from PE AFM to FE FM. Using DFT it was predicted that the phonon frequency disappears for a compressive strain of 1.2% assuming AFM or-dering and 0.9% assuming FM oror-dering [29], the frequency also vanishes at a tensile strain of 0.75% [28]. The region in between 0.9% and 1.2% com-pressive strain is of particular interest, as it was predicted that the strong coupling between electric and magnetic order allows one to tune the mag-netic polarization using an electric field and vice versa. The electric field tunable magnetic polarization was experimentally confirmed by Ryan et. al. [30].
3.3
Side-gating
The electronic phase of the LAO/STO interface can be tuned using gating (examples given in section 3.1). Due to the high electric permittivity of STO at low temperatures, back-gating can easily be achieved by applying silverpaste on the back of the substrate. Such a back-gate acts as as a paral-lel plate capacitor: as a positive voltage is applied, more negative charge is 24
3.3 Side-gating 25
attracted to the interface and the carrier concentration of the interface is in-creased [31] [32]. Back-gating can also be used to drive the system through a Lifshitz transition: when a certain critical carrier density is reached in the interface, the dyzand dxz bands start filling, changing the system from 1-band to 2-band [26]. Recently, two groups [33] [34] successfully imple-mented side-gates in an LAO/STO interface. These side-gates were found to have the same effect on LAO/STO interfaces as a back-gate. However, the side-gates only affect a small part of the interface; This allows one to tune or even deplete a small part of the interface, while contacts further away from the side-gates remain completely metallic.
By using side-gating in an LAO/ETO/STO heterostructure one could locally control the spin-polarization of the 2DEG. A back-gate can be used to fully spin-polarize the 2DEG, which the side-gate can locally reverse this polarization. This allows for the creation of a device in close analogue to a Datta-Das spin transistor [35]. A Datta-Das spin transistor consists of a semiconductor channel with two ferromagnetic contacts, acting as a source and drain. A spin-polarized current comes from the source through the channel. If spins at the end of the channel are aligned with the magne-tization of the drain, the resistance is low. In this scheme, an electric field may be applied to alter the spin-polarization in the channel.
In this thesis we aim to create a side-gated Hall bar which could serve this purpose. Hall bar contacts will allow for measurements of the polar-ization of the 2DEG by means of anomalous Hall effect. The side gates al-low for control of the polarization of the main channel, without depleting the contacts of the channel. We aim to create the pattern on an aluminum oxide (AlOx) mask. When LAO is deposited on this mask, the conduct-ing LAO/STO interface is only created inside the desired pattern, LAO deposited on the AlOx will be amorphous and insulating.
Chapter
4
Methods
In this chapter will we describe the experimental methods used in this thesis. Notably we give a full description of the lithography processes used to create various structures created. Further, we explain the influence of some important parameters in the growth process of LSMO.
4.1
Substrate termination
In this thesis we work with TiO2-terminated STO substrates. This is im-portant both to create a conducting interface in LAO/STO films as well for growing epitaxial LSMO films. 5x5x0.5 mm STO substrates are bought from the company CrysTec GmbH, containing an even amount of SrO and TiO2domains. A TiO2-termination is created following the general proce-dure described by Koster et. al. [36].
Substrates are first sonicated in acetone and ethanol for 5 minutes each, this leaves the surface clean of most dirt. The terminations of the sub-strates is based off the hydroxylation of the surface SrO. The substrate is sonicated in water for 30 minutes; Strontium hydroxides easily form this way, while the chemically stable TiO2layer is left mostly unaffected. The substrate is submerged in buffered hydrofluoric acid for 30 seconds which removes all strontium hydroxides and leaves nearly perfect TiO2plateaus (figure 4.1).
28 Methods
Figure 4.1: AFM height scan of a TiO2-terminated STO substrate used in this
project. This sTO substrate was treated using the method described in section 4.1.
4.2
Lithography
To create the structures used in this thesis we apply two different lithog-raphy techniques: E-beam lithoglithog-raphy and optical lithoglithog-raphy. In both these lithography techniques the sample is coated in a layer of positive (negative) resist. Parts of the sample are subsequently exposed to radia-tion. This radiation will cause molecules in the resist to break up (bond together) making the rest more (less) soluble. The resist is then exposed to a developer in which the (un)exposed parts will dissolve, leaving behind the desired pattern.
4.2.1
Optical lithography
For accurate measurements of the magnetoresistance of LSMO we will pattern our LSMO films into a Hall bar. Initial plans were to pattern LSMO using an AlOxmask as described in section 4.2.2. However, as amorphous LSMO is not an insulator a very thick layer of AlOx would be required to prevent conductance over the mask. This would require a long sput-tering time which would make subsequent lift-off impossible. Instead we 28
4.2 Lithography 29
Figure 4.2: Lithography process used to create a Hall bar pattern on LSMO thin films. Adapted from [37]
decided to create a pattern using a two step optical lithography process as described in figure 4.2, using etching rather than lift-off.
In optical lithography the sample is covered in a patterned chromium hard mask. The sample is exposed to UV radiation, transcribing the pat-tern from the hard mask onto the sample. We use the positive optical resist OIR 917.12 and the developer OPD 4262.
1. First an LSMO thin film of around 20 nm thickness is deposited as described in section 4.3.
2. The film is covered in a layer of photoresist, the resist is baked at 80 C◦ for 1 minute.
3. For the first lithography step only the contact pads of the Hall bar are exposed to UV-light. The sample is submerged in the developer for 1 minute, this removes the exposed resist.
4. Roughly 30 nm of gold is sputtered on the resist mask.
5. Lift-off of the resist leaves the gold contact pads on top of an LSMO film.
6. A new layer of photoresist is applied.
7. This time a Hall bar pattern is used on the hard mask while the re-maining resist is exposed to the UV-light. The mask must be aligned
30 Methods
Figure 4.3:Schematic of an E-beam setup. Adapted from [38]
exactly with the earlier deposited gold contacts. Development leaves behind the desired Hall bar pattern.
8. Argon ion-beam etching (IBE) is preformed to remove all exposed parts of the LSMO film. As the LSMO film is only 20 nm thick while the photoresist is roughly a micron thick, the LSMO under the resist is fully protected during the etching process. The remaining resist can be removed using acetone.
4.2.2
E-beam lithography
In E-beam lithography a sample is loaded in a high-vacuum chamber and exposed to an electron beam. The beam is generated in an electron gun and send through a series to coils which control the width of the beam (figure 4.3). Using a narrow beam focus and precise stage control, E-beam lithography allows one to write any desired pattern. This allows one to easily iterate on a design. An E-beam design is divided into polygons which are traced one by one by the electron beam. As the electrons cross the resist some scatter of the substrate and cross the resist a second time. These secondary electrons cause an exposure of resist outside of the pat-tern, creating a discrepancy between the design and resulting structure.
30
4.2 Lithography 31
Figure 4.4: Lithography process used to create AlOx masks on STO substrates.
Adapted from [34]
In this thesis we will use E-beam lithography to create AlOxside-gated Hall bar patterns. In order to create a conducting interface between the STO substrate and the deposited LAO film it is crucial that no resist re-mains on the STO substrate after the lithography procedure. We will fol-low the basic procedure of Monteiro et al. [34] which was also adopted by a previous master student, Jessika Pineiros [39], who successfully created patterns on STO substrates. The procedure is illustrated in figure 4.4, we first use a positive resist and write the negative of the desired pattern.
We tried three different combinations of resist to find what worked best for our pattern: a single layer of PMMA 950K, a double layer of PMMA 200K covered with PMMA 950K and a double layer of PMMA 600K cov-ered with PMMA 950K. The use of a double layer creates an undercut which will make lift-off easier. We found that lift-off of the AlOxwas most successful using the double layer of PMMA 950K and PMMA 600K. We bake each layer of PMMA for 60 seconds at 180 C◦after application. After this the sample is coated in a layer of Electra 92, a conducting polymer. As STO itself is insulating the conducting layer is necessary to prevent charg-ing of the substrate durcharg-ing writcharg-ing, which would make writcharg-ing a pattern impossible. We bake this layer for 120 seconds at 90 C◦.
After the writing process firstly the sample is submerged in Milli-Q water for 60 seconds, this will dissolve the layer of Electra 92. The sample is developed in a 3:1 mixture of MIBK and IPA for 30 seconds and then submerged in pure IPA for 30 seconds in order to stop the development. After the development process, we sputter a layer of AlOxon the sample, as described in section 4.3. Lift-off is done by sonicating the sample in 35 C◦ acetone for 45 minutes, this leaves the desired AlOx mask on the STO substrate. Lastly the sample is exposed to an O2 plasma for 90 sec-onds, which will remove most remaining resist off the sample.
32 Methods
4.3
Sputtering
To grow thin-films of desired materials we employ a deposition technique called sputtering. In a sputter set-up a target made of the material of inter-est is placed in a vacuum chamber with a small inflow of gas, often argon gas is used for its inert properties. A current is applied to the target, ion-izing gas particles around the target and creating a plasma. Many oxide targets are insulating, when an DC-current is applied to such a target they will charge until the DC-power is canceled out. To prevent this, commonly an radio-frequency (RF) AC-current is applied instead. Ions are released from the target due to the bombardment by the plasma. A substrate is placed on a grounded part of the the vacuum chamber, conventionally op-posed to the target. Ions leaving the target will be accelerated towards the substrate by the bias difference, building up a film of the material of inter-est.
4.3.1
On-axis sputtering on resist
We apply a conventional on-axis RF sputtering set-up to deposit both AlOx for LAO/STO structures and gold for LSMO resistance-measurements. In both cases the material is deposited on a resist mask which is subsequently removed in lift-off. During sputtering, the exposure to a plasma causes the substrate and resist to heat. If the temperature of the resist is increased too much or for too long the resist will harden, which will make lift-off impos-sible. In the case of gold this is not a big problem since the sputtering rate is rather high, for AlOxhowever special measures must be taken to ensure lift-off remains possible. Firstly, we sputter in 30 second sessions, leaving the substrate to cool 30 seconds between each sputter session. The back of the substrate is coated in silverpaste during the sputtering, which ensures a good thermal conduction between the substrate and the set up. The sil-verpaste is removed after sputtering using a cotton swab and acetone. We sputter AlOx at 750 W with a grow rate of 0.96 nm/min [39].
32
4.3 Sputtering 33
Figure 4.5: Diagram showing the off-axis sputter system used in this project. Reprinted with permission from C. Yin MSc
4.3.2
Off-axis sputtering
To deposit LSMO films we use off-axis sputtering. In an off-axis sput-tering setup the target is rotated 90◦ with respect to the substrate (fig-ure 4.5). Off-axis sputtering can be used for smooth epitaxial growth of perovskite oxides, so has it been used before to grow perovskite superlat-tices [40] [41]. Several differences allow for the better growth of perovskite oxides. Firstly, the change in geometry along with the large distance be-tween the substrate and the target decrease the rate at which particles land on the substrate. The slow growth rate is crucial for growing crystalline oxide films. The system uses a mixture of argon and oxygen as sputter gas, at a relatively high pressure (≈0.1 mbar). Due to the high pressure, parti-cles from the substrate undergo an increased number of scattering events before reaching the substrate, hence losing their energy along the way. We grow at high temperatures (600-850 C◦), which gives atoms enough en-ergy to move to an energetically favorable position on the substrate. The oxygen and argon pressure as well as the temperature of the substrate are all crucial parameters for crystalline growth. An optimal value for these parameters will have to be determined for the growth of LSMO.
34 Methods
4.4
X-ray diffraction and reflectometry
X-Ray Diffraction (XRD) is a technique that can be used to determine the crystalline properties of the grown thin films of LSMO. In XRD, a sample is exposed to X-ray radiation. Atoms in the sample absorb and re-emit the X-rays, acting as elastic scattering points. Interference occurs between the scattered radiation leading to an interference pattern. Positive interference occurs when the angle of incidence meets the Laue condition:
~kin−~kout = ~G (4.1)
where~kin(out) is the momenta of the incoming (scattered) X-ray radiation
and G is a reciprocal space vector of the crystal. From this equation one~ can link the location of positive interference to the lattice constants of the crystal.
Figure 4.6: Figure illustrating an x-ray diffraction measurement of the out-of-plane lattice constant of a crystal.
A special case of equation 4.1 is Bragg’s law which describes positive interference between (001) planes (figure 4.6). Bragg’s law can be written as:
nλ=2d sin θ (4.2)
where n is an integer, λ is the wavelength of the x-rays radiation, d is the distance between (001) planes and θ is the angle of incidence of the x-rays. X-Ray Reflectometry (XRR) is a technique similar to XRD that can be used to determine the thickness, density and roughness of a film. In XRR, X-ray radiation is applied to a sample under a small angle of incidence 34
4.5 Atomic Force Microscopy 35
(figure 4.7). The surface of the film and the interface between the film and the substrate will reflect part of the radiation. Interference between these two reflected radiation fronts leads to an interference pattern according to:
~kin−~kout = 2πm
d (4.3)
where m is an integer and d is the film thickness. The intensity of the reflected radiation compared to the incoming radiation is a measure of the roughness of the film.
Figure 4.7: Illustration of x-ray reflectometry. X-ray radiation is reflected of the surface of the film and the substrate, interference between these reflections can be used to determine the thickness of the film. Adapted from [42].
4.5
Atomic Force Microscopy
Atomic Force Microscopy (AFM) has been deployed to characterize the surface of films and substrates, as well as the quality of patterns created with lithography (section 4.2). AFM is an imaging technique based detect-ing the surface atoms on a sample usdetect-ing an ultra-sensitive cantilever. AFM produces a 3D height profile of the surface of a sample.
AFM images are taken in tapping mode, in this mode the tip is sus-pended between 10 and 100 nm above the sample and left the oscillate at its resonance frequency. Long-range forces act between the sample and the tip, such as magnetic, electric and Van der Waals force, affecting the oscil-lation of the cantilever. The vertical movement of the cantilever is detected via an optical interferometer.
Chapter
5
Results
In this chapter we present the results reached in this project. First we char-acterize the LSMO films grown in this thesis, than we give an overview of a patterning process which can be used to create an LSMO Hall bar. Next we illustrate the design process of the side-gated Hall bar structures developed for LAO/ETO/STO devices.
5.1
LSMO
Firstly we aim to find a set of parameters for off-axis sputtering which allow for crystalline growth of LSMO. Several films were grown using dif-ferent parameters and characterized using AFM, XRD and resistance mea-surements. After repeated use the LSMO target began to produce particles during sputtering. Due to this the target could no longer be used and the optimization of the growth process could not be completed.
5.1.1
Growth parameters
After initially having technical problems with the LSMO target, we decide to focus on the substrate temperature during growth, as we know this to be an especially influential parameter. We begin this characterization with an LSMO film grown at 800 C◦. The chamber pressure was 0.18 mbar, us-ing a 2:3 oxygen/argon mixture. The film was sputtered with an RF-power of 100 W. Figure 5.1 shows an AFM image of this film; The surface of the film is clearly very rough, showing the growth parameters were incorrect. The film is determined to be roughly 38 nm thick using XRR, the growrate
38 Results
Figure 5.1: AFM height scan of an LSMO film. The film was grown at 800 C◦, 0.18 mbar chamber pressure and a 2:3 oxygen/argon ratio. The film was roughly 38 nm thick. The surface of the film is very rough, without any clear pattern.
is adjusted in subsequent films.
The temperature for growth is lowered to 700 C◦, other parameters are kept constant. Figure 5.2 shows an AFM image of this film; The surface is much flatter, however many holes have appeared. The holes are mostly likely formed by gas escaping from the film during growth. The step pat-tern of the STO substrate is also visible in the film, showing growth has become more smooth.
Figure 5.2: AFM height scan of an LSMO film. The film was grown at 700 C◦, 0.18 mbar chamber pressure and a 2:3 oxygen/argon ratio. The film was roughly 16.5 nm thick. The surface of the film mostly flat but has many holes in it. The step pattern of the STO substrate is also visible in the LSMO film.
38
5.1 LSMO 39
The most successful LSMO film was grown at 650 C◦, other parameters are kept the same as in the previous two films. Figure 5.3 shows an AFM image of this film. The step-pattern of the STO-substrate has been pre-served after the LSMO growth, showing the LSMO has grown smoothly and the surface is only slightly rough. The film was determined to be roughly 20 nm thick.
(a) (b)
Figure 5.3: AFM height scan of an LSMO film. The film was grown at 650 C◦, 0.18 mbar chamber pressure and a 2:3 oxygen/argon ratio. The film was roughly 20 nm thick. The film clearly shows the step pattern of the STO-substrate, and the surface is only slightly rough.
With the growth appearing more smooth under AFM we use XRD to determine the out of plane lattice constant of the LSMO film. A clear peak is observed in the XRD-scan, showing the film is indeed crystalline. The peak is located at 47.18 ±0.03◦, using Bragg’s law (equation 4.2) the lat-tice constant is found to be 0.385± 0.001 nm, which is quite close to the literature value of 0.3873 nm [8].
Gold is deposited on the corners of the sample in order to contact the film using aluminum wirebonds. Directly placing wirebonds on the LSMO will cause the aluminum to oxidize as the temperature reaches 400 K. Figure 5.5 shows a two-probe resistance measurement carried out on a sample grown under the best found conditions. Characteristic be-havior for LSMO would be a decrease in resistance below 360 K, as the metal-insulator transition of the material is crossed. The resistance of the film can be seen to increase slightly below 360 K and strongly below 60 K.
40 Results
Figure 5.4:XRD 2θ-scan of an LSMO film grown at 650 C◦. The maximum of the peak is located at 47.18±0.03◦.
This clearly indicates that the growth of LSMO is not yet successful. One possible explanation for the low temperature resistance would be an incor-rect stoichiometry of the LSMO film. In figure 2.8 we see that with a too low or high Sr doping concentration LSMO is expected to be insulating at low temperatures.
5.1.2
Optical lithography
To measure the CMR effect in LSMO we aim to pattern LSMO films into a Hall bar with gold contacts. As the LSMO growth could not be com-pleted, no measurements were done using these structures. Figure 5.6 shows patterning process applied on a bare STO substrate. Firstly a layer of resist is applied to substrate. Contacts are exposed during the lithogra-phy process and developed away (figure 5.6a). Some dirt can be observed on the sample, this is due to the use of demi-water, which contains much organic dirt, to stop the development. Milli-Q water should be used in-stead, which would yield much cleaner samples. Next a roughly 30 nm thick layer of gold is sputtered onto the sample (figure 5.6b). The sam-ple is left overnight in acetone to lift-off and placed in the sonicator for 2 seconds to remove the lifted-off gold from the surface (figure 5.6c). A sec-40
5.1 LSMO 41
Figure 5.5:Two-probe resistance measurement of an LSMO film grown under the best found parameters. We see two increases in resistance below 360 K and 60 K which is uncharacteristic of crystalline LSMO.
ond lithography step is preformed, now to create a Hall bar pattern (figure 5.6d); The width of the created Hall bar is 7 μm.
5.1.3
Argon etching
To transcribe the Hall bar pattern onto the LSMO we apply argon-ion etch-ing. A resist Hall bar as in figure 5.6 was created on a non-conducting LSMO film. As the film was of poor quality, no attempt at making con-tacts was done. Argon-ion etching was applied to remove all LSMO not covered by the resist Hall bar. After etching the remaining resist is re-moved using acetone. Figure 5.7 Shows the resulting LSMO Hall bar. The film was not fully etched away, allowing us to determine the etch-rate us-ing AFM. The etch-rate was found to be 4.33 nm/min, but as the LSMO was of poor quality this might not be a reproducible figure.
One issue with the argon etching is the effect it has on STO substrates. When the LSMO is etched away, inevitably, some STO will also be etched. The etching creates oxygen vacancies in the STO, causing the substrate to become conducting. We propose two possible solutions for this problem:
42 Results
(a) (b)
(c) (d)
Figure 5.6: Illustration of the patterning process planned for LSMO, used on an STO substrate. a. Image of the resist mask used to create contact pads. Most of the sample is covered in a layer of resist, while an outline of the contact pads is exposed. b. 30 nm of gold has been deposited on the resist mask, the resist can still be seen under the layer of gold. c. The resist is lifted-off by leaving the sample is acetone over night. Gold contacts remain on the sample. d. A second lithography step is used to create a resist Hall bar. This time most of the sample is left exposed while only the desired pattern is covered in resist.
42
5.1 LSMO 43
Figure 5.7: Image showing an LSMO Hall bar created using argon-ion etching. The structure is 1500 μm long and the main channel is 7 μm wide.
• Firstly, one could simply anneal the substrate and patterned film in oxygen. This would return the substrate back to its insulating state, however it might have unforeseen effects on the quality of the LSMO film.
• A second solutions comes from Beekman et al. [43] who success-fully restored STO using an oxygen plasma. The authors do note that this method only works when the STO is only very slightly etched, which would require a very precisely determination of the etch-rate of LSMO. If possible this would be the preferred method.
44 Results
(a) (b)
Figure 5.8: Initial E-beam design used to create side-gated Hall bars. The green figures are exposed by the electron beam; development leaves the white structure behind. a. Full structure including the contacts. b. Central 25 μm2of the structure. The source (S), drain (D), voltage leads (VL) and side-gates (SG) are marked. The constriction in the center of this design is 300 nm wide, the voltage leads are 100 nm wide and the Side-gates are 600 away from the main channel.
5.2
Side-gated Hall bars
We design a gated Hall bar for LAO/ETO/STO structures. The side-gates allow for tuning of the polarization and carrier concentration of the central channel. The voltage leads allow for measurements of the anoma-lous Hall effect, indicative of spin-polarization. Our initial side-gated Hall bar design is shown in figure 5.8; the design is based on the general shape of the design by Monteiro et. al. [34]. In this design the voltage-leads used for Hall effect measurements are not perpendicular to the main channel but rather tilted away from the side-gates. This will ensure that when a gate voltage is applied, the main channel will be affected much stronger than the voltage leads. Rather than a straight central channel, this design has a narrow constriction in the center. This allows for easy lift-off of this otherwise small channel.
Geometrical errors can occur when the shape of a Hall bar deviates from the ideal[44]. To avoid these errors some general rules must be fol-lowed:
44
5.2 Side-gated Hall bars 45
• The width of the bar must be one third of the length or smaller. • The width of the voltage leads must be one third of the width of the
main bar or smaller.
Taking into account the time constraints and available equipment we deem 100 nm the smallest achievable size for our design. The Hall bar will thus have the following dimensions: the width of the voltage leads will be 100 nm, the width of the main channel (W) will be 300 nm and the length (L) 3000 nm and the side-gates will be 600 nm away from the main channel. This will ensure geometrical errors are kept to a minimum while simultaneously making the bar as small as possible.
5.2.1
Main channel constriction
The main channel of the Hall bar is defined using two circles or radius r, a distance 2r+W separated from each other, given by
C1 : (x−r)2+y2 =r2 (5.1)
C2 : (x+r+w)2+y2 =r2 (5.2)
The length of the bar, L, is defined as the distance between two 45 degree tilted lines tangent to the circle, as illustrated in figure 5.9. The green lines are given by:
y= x+ L 2 + W 2 (5.3) y= −x− L 2 − W 2 (5.4)
and the blue ones by:
y= x+ L 2 − W 2 (5.5) y= −x− L 2 + W 2 (5.6)
The radius of the circle can be defined in terms of the desired with and length of the bar by inserting equation 5.3 into equation 5.1:
2x2+ (W+L−2r)x+ (L
2 + W
2 )
46 Results
Figure 5.9: Graph illustrating how the main channel of the Hall bar is defined. Two circles form a constriction in the center of the figure, this forms the main channel of the Hall bar. Four 45 degree lines are drawn, tangent to the circle. The distance between the intersects of the top and bottom pairs of lines is defined as the length of the Hall bar L, the width W is defined by the distance between the 2 circles. After the main channel has been defined in this manner, contacts to the bar are drawn. Firstly two contacts above and below the Hall bar provide a current through the main channel. Four voltage leads for measuring the Hall voltage are drawn along the four lines in the figure. Lastly two side gates are drawn inside the circles either side of the main channel, these side gates make no contact with any other part of the structure.
This can be solved as x = 2r−W−L±
p
−W2−L2+4r2−2W L−4r(W+L)
4 (5.8)
The optimal radius corresponds to the line being tangent to the circle, where there is thus only 1 solution. This will occur when the root in equa-tion 5.8 is equal to 0. 0=4r2−4r(L+W) −W2−L2−2W L (5.9) r= √ 2+1 2 (L+W) (5.10)
5.9 also has an irrelevant smaller r solution.
46
5.2 Side-gated Hall bars 47
5.2.2
Structure optimization
To optimize the design of the structure, a series of tests samples were cre-ated. Each test contains the central 25 μm of the structure (figure 5.8), exposed to several area doses. The initial design for the Hall bar had a 300 nm constricted middle and long, 100 nm wide voltage leads, as de-scribed in section 5.2.1. Figure 5.10 shows a Scanning Electron Microscope (SEM) image of the AlOx mask after lift-off. The best area dose for this sample was 150 μC/cm2. While the central channel is clearly visible, the voltage leads for all doses are closed. The size of the voltage leads was in-creased to 300 nm, yet still all voltage leads remained closed (figure 5.11). The width of the central channel in this design was 900 nm, however, for the optimally dosed sample we observe only 500 nm in the SEM image. We conclude that, for the optimal dose, sizes of the AlOxmask are 200 nm wider than the designed structure and we account for this in the next de-sign. The constriction in the center of the Hall bar again was open for var-ious area doses, however all voltage leads were still closed. This suggests that replacing the narrow channels of the voltage leads by a constriction might allow for easier lift-off.
(a)
Figure 5.10: a.SEM image showing the first attempt at making a side-gated Hall bar. The structure was exposed to an area dose of 150 μC/cm2. Long, 100 nm
thick voltage leads were used in the design. Lift-off of these voltage leads failed, leaving the aluminum mask intact. The middle constriction was 300 nm wide, lift-off of the middle channel was successful.
48 Results
(a)
(b)
Figure 5.11: SEM images of a follow up design for the side-gated Hall bar. a In this design the structure was increased in size by a factor 3. The side gates are now 300 nm in the design, the main channel 900 nm. Side-gates in this structure are closed for all area doses. b. Close up of the main channel of a Hall bar (labeled 230 in panel a). The structure was exposed to an area dose of 115 μC/cm2. The middle channel is roughly 500 nm wide.
48
5.2 Side-gated Hall bars 49
A Hall bar design using constricted voltage leads was created. The voltage leads now start as 500 nm by 500 nm squares and fan out from there; the width of the central channel was changed to 700 nm. Figure 5.12 shows this pattern, created with an area dose of 145 μC/cm2. The top left piece of AlOx has been chipped, this, however, does not affect the overall structure. Notably all voltage leads for this structure are open, suggest-ing the constriction method combined with the larger size has solved our initial problems. It should be noted that all voltage leads appear different sizes. This suggests that significant thermal drift occurs while the pattern is written, leading to errors when the beam switches between the figures that make up the design.
Figure 5.12: SEM image of the first design using constricted voltage leads. The structure was exposed to an area dose of 145 μC/cm2. In the design the voltage leads were 500 nm wide and the central channel was 700 nm wide. All voltage leads in the image are open, but they are all different sizes.
To avoid thermal drift an ordering is given to the polygons in the de-sign. The pattern is written spiraling out from the center, ensuring errors are minimized between neighboring polygons. The optimal area dose has varied from sample to sample, thus we aim to overdose structures slightly, as this should lead to more consistent results. Several different voltage lead sizes were added to the design to compensate for the higher area dose. Figure 5.13 shows a structure with voltage leads of 700 nm, at an area dose of 210 μC/cm2. All voltage leads are now consistent sizes, al-though slightly too large. Damage can be seen in the sharper corners of
50 Results
the design next to the voltage lead, both in this sample and the previous one. To avoid this damage the corners will be more rounded off in the next design. The distance between the side-gates and the main channel is over a micron, this distance will be reduced in the next design.
Figure 5.13: SEM image of design of the Hall bar with constricted voltage leads using a writing order. The structure was exposed to an area dose of 210 μC/cm2.
In the design the voltage leads were 700 nm wide, the central channel was also 700 nm wide. All voltage leads in the image are roughly 300 nm wide, the central channel is 400 nm wide.
Figure 5.14 shows a SEM image and E-beam design of the final struc-ture. Rounding off the corners has prevent damage as desired. The area dose was raised to 220 μC/cm2, the voltage leads are 700 nm wide, the central channel is 700 nm wide and the distance to the side-gates is only 300 nm. 5.15 shows close up SEM-images of the center and voltage leads of the structure. The observed distances are summarized in table 5.1. The difference between the desired and observed distance is less than 100 nm for all parts of the design. Now that the design works we will use AFM to check quality of the lift-off.
Table 5.1:Sizes of AlOxmask in nm
Desired distance Distance in design Observed distance
Voltage Lead 100 700 160±20
Main channel 300 700 370±20
Side-gates 600 300 565±20
50
5.2 Side-gated Hall bars 51
] (a)
(b)
Figure 5.14: a. SEM image of finalized Hall bar design. The structure was exposed to an area dose of 220 μC/cm2. b. E-beam design of the final structure. In this design the voltage leads are 700 nm wide, the central channel is 700 nm wide and the distance to the side-gates is 300 nm.
52 Results
(a)
(b)
Figure 5.15:Close-up SEM images of the finalized Hall bar design. The structure was exposed to an area dose of 220 μC/cm2. a. Image of the central constriction and the side-gates. The image quality is somewhat poor due to charging effects.
b. Image of two voltage leads.
52
5.2 Side-gated Hall bars 53
5.2.3
Oxygen plasma cleaning
Figure 5.16a shows an AFM image created of the Hall bar shown in figure 5.13. Remainders of resist can be seen near the edges of the AlOx mask, showing that even when all AlOxis removed from a trench some resist will always remain. The sample is exposed to an oxygen plasma for 90 seconds. The oxygen-ions are highly reactive and will remove carbon compounds, such as resist, from the sample, while leaving STO and AlOx relatively unaffected. Figure 5.16c shows the Hall bar after the oxygen plasma etch. All resist previously observed is now removed from the sample. Figure 5.17 shows a close up image of a voltage lead, the STO surface appears flat and clean.
54 Results
(a) (b)
(c) (d)
Figure 5.16: AFM images of the Hall bar shown in figure 5.13. a. AFM image taken before oxygen plasma cleaning. Resist can be seen next to parts of the AlOx
mask, particularly inside the voltage leads. b. Corresponding height profile of a voltage lead shows much resist remains inside the channel. c. AFM image of the same Hall bar after oxygen plasma cleaning. All resist appears to be removed by the plasma. d. Corresponding height profile of a voltage lead shows the resist is indeed removed and the channel is now open.
54
5.2 Side-gated Hall bars 55
(a) (b)
(c)
Figure 5.17: Close up AFM image of a voltage lead from a Hall bar after oxygen plasma cleaning. a. Height map of the voltage lead. The walls of the AlOxmask
are slanted, which is not unexpected for a lift-off process. No resist or AlOx
re-mains in the center of the channel. b. corresponding phase image of the voltage lead. The sporadic growth of the AlOxcan be seen in the phase shift on top of the
mask. The phase on the STO is constant, affirming no adhesives remain on the surface.c. Height profile of the voltage lead as marked in panel a.
Chapter
6
Conclusion
In this project, we have worked towards devices for two different oxide systems. Firstly, we have worked on the optimization of growth parame-ters for the deposition of LSMO films in off-axis sputtering. Using AFM, we find that, for films grown at 650 C◦, the films are quite flat and the step character of the STO substrates is preserved during growth. Using XRD, we obtain a lattice parameter of 0.385 ± 0.001 nm similar to liter-ature values of 0.3873 nm [8]. However, in resistance measurements the films do not show characteristic behavior for LSMO, showing instead a sharp resistance increase at low temperatures. The strange behavior could be explained by an incorrect stoichiometry of the LSMO films. After sev-eral films had been grown, the LSMO target used in this project started to emit particles during sputtering, and could no longer be used.
For future work on the LSMO project, firstly, a higher quality target is needed, which will stay intact during the sputtering of films. The char-acterization of LSMO films must be continued with magnetic and resis-tance measurements. For precise resisresis-tance measurements, we illustrate a lithography procedure which allows for the patterning LSMO films into Hall bar structures. We believe these structures can be used for accurate measurements of the CMR effect in LSMO films, a strong indicator of the stoichiometry and quality of the films.
Next, we have designed a side-gated Hall bar pattern for LAO/ETO/STO devices. Using E-beam lithography we create an AlOx mask of the nega-tive of this pattern on a TiO2-terminated STO substrate. After several de-sign iterations we successfully created a Hall bar of ∼ 350 nm wide and
58 Conclusion
roughly ∼ 150 nm wide. Two side-gates are located roughly ∼ 550 nm next to the main channel. In future work, this structure could allow for the local gating of the LAO/STO interface and for local measurements of spin-polarization by means of the anomalous Hall effect.
58
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