Handbook of High Temperature Superconductor Electronics Part 5 potx

4 Step-Edge Josephson Junctions F. Lombardi Chalmers Institute of Technology and Göteborg University, Göteborg, Sweden A. Ya. Tzalenchuk National Physical Laboratory, Middlesex, England 4.1 INTRODUCTION In the framework of high-critical-temperature Josephson Junctions (HTS-JJs) the development of grain-boundary (GB) junctions has represented an important in- novation. The structures involving “extrinsic” interfaces are well established for metallic low-temperature superconductors. A similar approach in HTS multilayer technology remains very difficult for both physical (the short coherence length) as well as chemical (surface instability) reasons, although significant progress has re- cently been achieved in the fabrication of the ramp-type multilayer JJs. These dif- ficulties have motivated the fabrication methods of HTS-JJs to deeper exploit the unique combination of structure and properties of the high-critical-temperature superconductors. Soon after the discovery of the HTS superconductors, it was re- alized that at least some of the grain boundaries in a polycrystalline material be- have as weak links for the superconducting current. The IBM group (1) first man- aged to separate a single grain boundary and proved that it worked as a Josephson junction. Later, the same group found a method to artificially create individual grain boundaries in otherwise single-crystalline thin films—the bicrystal technol- Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. ogy (2). The intrinsic Josephson effect in the c-axis direction (3) or the use of a controlled nucleation of grains with different crystallographic orientation [the biepitaxial technique (4)] are other examples of valid alternative methods to real- ize Josephson structures. In these methods, “intrinsic” interfaces and/or barrier layers determine the Josephson junction properties. The fabrication of devices, which are useful in complex circuits, requires, however, the optimization and a precise control of these intrinsic interfaces/barriers. Among the possibilities for producing grain-boundary junctions, step-edge junctions (SEJs) represent a step up in technological complexity, compared to bicrystal junctions, but, at the same time, bring the topological freedom necessary for the design and the integration on small and large scales. The idea and the first demonstration are due to Daly et al. (5). SEJs are obtained by the epitaxial growth of a high-T c (transition temperature) film on a step etched in a substrate prior to the film deposition. The preparation of well-defined microstructurally repro- ducible steps is the key point in the step-edge junction technology. The step pattern is defined by either photolithography or electron beam (e-beam) lithography. The step is then produced in the substrate by ion milling. Because etching rates of the common substrate materials are slow and ion etching is very directional, the microstructure of the step depends greatly on the mask properties and especially on its profile. Reflown photoresist masks are commonly used to produce shallow steps. Hard materials, such as carbon (diamondlike or amorphous) and chromium, often in combination with e-beam lithography are used to produce straight steep steps. The step angle and morphology directly af- fect the film growth on the substrate and the structural and transport properties of the GBs that are subsequently formed. In this chapter, we will give an overview of the current state of art of YBa 2 Cu 3 O 7Ϫ␦ (YBCO) step-edge Josephson junctions. First, we will make some general remarks about YBCO growth on differently oriented substrates. It will be followed by a detailed description of the structural properties of the GBs, obtained on the most commonly substrates used for HTS film growth, in correlation with the step-edge profile. A description of the principal fabrication techniques used to form a step in a substrate will then be given. The transport properties of the GBs will be widely discussed in the framework of the well-established theory of the Josephson effect and of the up-to-date understanding of the HTS phenomenology. Then, we will characterize the dc superconducting quantum interference devices (SQUIDs), which represent the most successful application of the SEJs. Through- out the chapter, the performances of the SEJs will be also discussed in compari- son with other HTS Josephson junction technologies. 4.2 YBCO GROWTH ON EXACT AND VICINAL CUT (100)/(110) SUBSTRATES In this section, we will briefly summarize some aspects of YBCO growth on dif- ferently oriented substrates. What is discussed in Sections 4.2.1 and 4.2.2 is meant 104 Lombardi and Tzalenchuk Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. to give a general understanding of the mechanisms which lead to the nucleation of grain boundaries on stepped substrates. A direct correlation between the YBCO growth habits and the microstructure observed is, in fact, needed to clarify the technological key points necessary for the development of reproducible engi- neered grain-boundary Josephson devices. 4.2.1 General Remarks About YBCO Growth on Exact Substrates For a good epitaxial growth of HTS superconductors, the choice of the substrate is quite crucial, as it must be compatible with the superconductor material both structurally and chemically. The types of substrate most commonly used for YBCO growth, are perovskites, such as LaA1O 3 , SrTiO 3 , and NdGaO 3 , but also ZrO 2 , MgO, and sapphire buffered with thin films of CeO or MgO. In Table 4.1, the values of the lattice parameters for these compounds and for the YBCO are summarized. On perovskite substrates, the similarity of the crystal structure and the low lattice mismatch allow epitaxial growth of the YBCO, leading to films with ex- cellent superconducting properties. The crystal cut of the substrate affects the ori- entation of the films. For example, on (100) SrTiO 3 and LaA1O 3 , depending on the deposition conditions, (100) or (001) YBCO orientation is achieved; (110) or (103) growth is, instead, obtained on (110)-oriented perovskites. As a general rule, low substrate temperature, high oxygen pressure, and high deposition rates during film deposition favor in-plane alignment of the YBCO c axis (6–8). Opposite con- ditions are required for optimal growth of (001) and (103) YBCO. On (110) perovskite surfaces, the fourfold rotational symmetry inherent to the (001) surface is broken. In other words, two orthogonal in-plane directions (e.g., the [100] and [11 ¯ 0]) are no longer equivalent. For a (110) growth, the lattice matching is obtained by aligning the c axis and the [11 ¯ 0] YBCO directions respectively with the [001] and [11 ¯ 0] in-plane directions of the substrate Step-Edge Josephson Junctions 105 TABLE 4.1 Lattice Parameters for the YBCO and for Some Compounds Material Lattice parameter (nm) YBCO a ϭ 0.382, b ϭ 0.389, c ϭ 0.1169 LaAlO 3 0.379 SrTiO 3 0.391 NdGaO 3 0.386 MgO 4.21 Al 2 O 3 a ϭ b ϭ 0.476, c ϭ 0.13 Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. ([001] YBCO ሻ [001] sub and [11 ¯ 0] YBCO ሻ [11 ¯ 0] sub ). The a and b YBCO axes will therefore be out of the plane of the substrate, forming an angle of approximately 45° with respect to the normal n to the substrate surface (see Fig. 4.1a). For a (103) growth (Fig. 4.1b), the b axis and the [103 ¯ ]. YBCO direction are aligned respec- tively with the [001] and [11 ¯ 0], directions of the substrate. In this case, the c and a YBCO axes are out of the substrate plane at an angle of about 45° with respect to n. Owing to the twofold axial symmetry of the substrate surface, a (1 ¯ 03) YBCO growth is also possible (see Fig. 5.1b). The (103) and (1 ¯ 03) domains differ by a 90° rotation around the b axis (i.e., the a and c axes are exchanged). The coales- cence and growth of {103} nuclei leads to the formation of triangular grains de- limited by the a-b plane at 45° with the substrate normal. This can be interpreted in the following way (9). Figure 4.2a shows the presence of both the (103) and (1 ¯ 03) domains. They terminate on one side by a basal plane face, which is smooth but slow growing due to the layer-by-layer growth mode of the YBCO and the lack of favorable sites for the nucleation of new layers. The other side, which is very rough, should grow rel- atively fast due to the abundance of steps and kinks provided by the grain mor- phology. On the basis of this hypothesis, the (103) face expands faster on the left (L) side of one grain than it does on the (1 ¯ 03) face on the right (R) side of another grain (see Fig. 4.2a). At the meeting point, they form symmetrical 90° tilt grain 106 Lombardi and Tzalenchuk FIGURE 4.1 Sketch of the possible epitaxial relations between the YBCO cell and a (110) SrTiO 3 substrate: (a) (110) YBCO growth; (b) (103) YBCO growth. The two domains (103) and (1 ෆ 03) are tilted 90° with respect to each other. (a) (b) Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. boundaries (SGB) (Fig. 4.2b). If the two meeting grains have roughly the same height, they will form a triangular grain, with both sides terminating by basal plane face. In the following stages of the film growth, the triangular grain may be covered and embedded by larger nuclei expanding either in the [11 ¯ 0] or in the [1 ¯ 10] direction. This leads to the formation of 90° tilt boundaries of the basal- plane-faced (BPF) type (see Fig. 4.2c). These features account for the character- istic morphology of (103) YBCO films (10) determined by the formation of in- trinsic grain boundaries. On poorly matched substrates such as the MgO for example, the growth habits of the YBCO are quite different. On (100) and (110) substrates, the growth is almost c axis in a wide range of values of deposition parameters. Few reports on a-axis growth on MgO are present in the literature (11). Moreover, a (103) orien- tation has only been obtained on SrTiO 3 -buffered (110) MgO (12). This behavior is a consequence of the large mismatch between the lattice parameters of the YBCO and the MgO. The substrate lattice cannot be a template for the growth, so the orientation which minimizes the free energy at the interface with the MgO is dominant. Step-Edge Josephson Junctions 107 FIGURE 4.2 Schematic representation of the nucleation and domain coales- cence of a (103) YBCO thin film: (a) (103) and (1 ෆ 03) nuclei characterized by a rough side and a side bound by a basal plane (BPF). The coalescence of grains leads to the formation of a (b) 90° symmetric intrinsic GB or a (c) basal- plane-faced intrinsic GB. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. 4.2.2 YBCO Growth on Vicinal Cut Substrates On perovskite (100) substrates, the alignment between the YBCO lattice parame- ters and the crystallographic axis of the substrate is kept, even when the in-plane symmetry of the surface substrate is broken by the introduction of a vicinal cut (13). Figure 4.3a shows the YBCO growth on a perovskite substrate with a small vicinal angle ␣ in the (100) [or (010)] direction. On the atomic scale, the substrate surface is not flat. The ratio between the height h and the width w of the steps is defined by the angle ␣ (tg ␣ϭh/w). It is clear that the normal n to the horizontal surface of the atomically defined steps is still the (001) crystallographic direction of the substrate, whereas the normal nЈ to the macroscopic substrate surface is ro- tated by an angle ␣ with respect to n. The growth mode, characterized by the c axis of the YBCO parallel to the direction locally defined by n is energetically favor- able because of the small mismatch between the lattice parameters of the YBCO and that of the substrate. On poorly matched substrates such as the MgO, the YBCO will, instead, preferably grow, aligning the c direction with the normal nЈ to the macroscopic substrate surface (14) (see Fig. 4.3b). From a microscopic point of view, the presence of a step with an angle ␣ and with the edges aligned with one of the two in-plane directions is equivalent to the introduction of a (001) surface, in the substrate, with a vicinal cut ␣. For small values of ␣, in a perovskite substrate, the direction of the YBCO c axis on the step surface will therefore remain parallel to the c-axis orientation on the top and the bottom flat parts of the step (see Fig. 4.3a). At this point, a question naturally arises: What is the maximum value of ␣ compatible with this kind of growth? Or alternatively, what is the minimum value of ␣ which allows rotation of the YBCO c axis on the step surface and the formation of GBs at the edges of the step? For ␣ approaching 45°, the step surface will have twofold symmetry. On such a kind of 108 Lombardi and Tzalenchuk FIGURE 4.3 YBCO growth on a vicinal cut (a) and perovskite substrate (b) on a MgO substrate. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. surface, as discussed in the previous paragraph, depending on the growth condi- tions, two different orientations are possible: the (110) and the (103). From these considerations, we can, therefore, guess that at the temperatures typical for a c- axis growth on a (001) substrates (T Ϸ 730–800°C), on steps with ␣ Ϸ 45°, we will have a c-axis growth on the upper and bottom flat parts and a preferential (103) growth on the step surfaces. For a step angle ␣Ͼ45°, we would expect a situation similar to that illustrated in Figure 4.4 with two 90° tilt symmetric grain boundaries at the defined edges of the step and a combination of 90° symmetric and basal-plane-faced tilt GBs on the step surface. A more detailed correlation among the morphology of the step, the step angle, and the exact structural prop- erties of the GBs will be discussed in the following sections. 4.2.2.1 Do These Grain Boundaries Behave as Weak Links? Electrical measurements performed on steps with different angles fabricated on a SrTiO 3 substrate give some indications about the transport properties of the YBCO film grown on the step. Figure 4.5 shows the dependence of the critical current density J cm of a microbridge across the step, normalized by J cs of a stripline defined on the flat part of the substrate, as a function of the step angle (15). In this case, the thickness of the YBCO film is less than the step height. It is clear that, up to an angle of 10°, no evident degradation of the superconducting properties is observed. In the range of values 10° Ͻ␣Ͻ40°, J cm is reduced by al- most one order of magnitude compared to J cs . This reduction is related both to the presence of defects between c-axis grains nucleated on two adjacent microscopic steps (16) (like antiphase boundaries) and to the strong out-of-plane anisotropy of the YBCO superconductor. Indeed, the current flows partially along the c-axis di- rection throughout the step, where the critical current density is almost one order of magnitude lower than the corresponding value in the a-b plane. For ␣ Ϸ 65°, J cm is reduced by two orders of magnitude compared with J cs and this is a sign for a weak-link-like behavior (17). Step-Edge Josephson Junctions 109 FIGURE 4.4 Grain-boundary formation on a step with ␣ approaching 45°. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. On poorly matched substrates, such as MgO, the situation is quite different. As discussed earlier, the YBCO c axis on the step should be aligned with the nor- mal n of the macroscopic surface. In this case, the step angle ␣ determines the mis- alignment between the c axes on the flat substrate and on the step surface. If the step edges are well defined (not rounded), even a small step angle may, therefore, introduce [100]/[010] tilt grain boundaries into the structure. These kinds of GBs have been extensively explored by Dimos et al. (18) using bicrystal junctions. From their transport measurements, also in the presence of an external magnetic field, there is clear evidence that [100]/[010] tilt GBs, with an angle as small as 10°, act as Josephson weak links. An interesting features of SEJs on MgO sub- strates is, therefore, represented by the possibility to explore [100]/[010] tilt GBs in a wide angular range. 4.3 MICROSTRUCTURE OF EPITAXIAL YBCO FILMS ON STEP-EDGE PEROVSKITE SUBSTRATES The description of the step surface in terms of atomically defined steps has given a qualitative understanding about the possibility of forming GBs during the 110 Lombardi and Tzalenchuk FIGURE 4.5 Critical current density J cs across the step normalized to the J cm of a stipline, as a function of the step angle ␣ for two different temperatures. (After Ref. 15.) Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. YBCO deposition. In order to study the microstructure of YBCO films across a step, structural investigation on the atomic scale is required. In what follows, a de- scription of the GBs structure is given on the basis of high-resolution transmission electron microscopy (HRTEM) analysis performed on samples fabricated by pulsed laser deposition. The microstructure of the YBCO film is found to vary with the steepness of the step characterized by the angle ␣. Figure 4.6 shows the YBCO growth on two different steps fabricated in SrTiO 3 substrates (19). No grain boundaries are ob- served for a mild slope, ␣ Ϸ 40° (Fig. 4.6a). The c axis does not change the ori- entation across the step, remaining perpendicular to the substrate surface. When ␣ is about 45° (Fig. 4.6b) the microstructure is just like that observed in a (103) growth on a (110) surface (for comparison, see Fig. 4.2c). Multiple GBs consist- ing of a complex combination of 90° symmetric and basal-plane-faced (BPF) GBs are formed along the step and at the edges. This behavior is, therefore, in agree- ment with the arguments presented in the previous section for YBCO growth on well-matched substrates. Figure 4.7 shows the YBCO film growth on a step with ␣ Ϸ 58° in SrTiO 3 (19). Two similar GBs can be clearly distinguished. They are almost of the sym- metrical type, although the presence of small facets and misfit dislocations is also observed. This is typical for symmetric grain boundaries (20). They are located near the top and the bottom edges of the step. A combination of symmetrical GBs and BPF grain boundaries are also visible near the interface between the film and the step surface. When the thickness of the film on the step exceeds 30 nm, these domains are shunted by a larger unidirectional domain. This behavior may be interpreted by Step-Edge Josephson Junctions 111 FIGURE 4.6 High-resolution TEM pictures showing the microstructure of the YBCO film (a) on a 38° step and (b) on a 45° step for ratios t/h Ϸ 1/3 and 1 re- spectively between the film thickness and the step height. (After Ref. 19.) (a) (b) Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. considering the surface of a step with an angle ␣ exceeding 45° as the surface of the (110) substrate with a vicinal angle ␤ Ϸ ␣Ϫ45° in the [11 ¯ 0] direction. On such a kind of surface, one of the two growth modes (103) or (1 ¯ 03) can be se- lected (12). In this way, the (103) YBCO film presents a single domain. At the early stage of growth, however, local variations of the step angle may induce nu- cleation of both domains. By increasing the film thickness on the step, the trian- gular grain formed by the coalescence of (103) and (1 ¯ 03) domains are covered and embedded by larger nuclei of the dominant orientation (see Fig. 4.2 for com- parison). The YBCO microstructure substantially changes as the angle ␣ is increased. Figure 4.8 shows a low-resolution TEM image of a YBCO grown on a steep step (␣ Ϸ 80°) in a LaAlO 3 substrate (21). Two well-defined 90° GBs separate the YBCO c-axis film on the substrate from the film grown on the step, which, in this case, presents a single domain. The film on the step flank is then often referred to as the YBCO a axis. From Figure 4.8, it is evident that the upper YBCO c axis has overgrown the film on the step. Furthermore, in contrast with shallow steps, the following is found: 1. The a-b plane termination on the step are not exposed to the environ- ment (see for comparison, Fig. 4.7). 2. The a-axis YBCO film thickness is much reduced compared with the c- axis component on the top and bottom parts of the step (about one-third of the nominal YBCO film thickness). 3. The top and bottom grain boundaries are very dissimilar. 112 Lombardi and Tzalenchuk FIGURE 4.7 Lattice image of the YBCO film grown on a 58° step. Open arrows indicate the two grain boundaries, and the triangles point to the 90° domains at the interface with the step surface. (After Ref. 19.) Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. [...]... Junctions 1 15 FIGURE 4.10 High- temperature TEM image of the GB formed at the bottom edge of a high- angle LaAlO3 step (From Ref 22.) FIGURE 4.11 (a) Sketch of the wavy step-edge profile patterned in a LaAlO3 substrate SEM micrograph after the deposition of (b) a 50 -nm-thick YBCO film and (c) a 200-nm-thick YBCO film In (b), the open arrows indicate the aaxis grains which nucleates at the apex of the step... upper part of the c-axis film with the subsequent formation of a BPF grain boundary Moreover, the presence of 90° facets of the grain-boundary plane of Figure 4.9a can be explained in a similar way The late nucleation of a-axis grain may also be related to the high directionality of the plasma plume in the plasma laser deposition (PLD) The growth rate turns out to be dependent on the incident angle of. .. 114 Lombardi and Tzalenchuk on top of the BPF part, consists of a random alternating sequence of segments of (100)(001) or (010)(001) boundaries (still of the BPF type) and segments of (013)(013) or (103)(103) boundaries [of the symmetrical(s) type] The length of each facet does not exceed a few unit cells In Figure 4.9b, the top GB consists, instead, essentially of symmetric segments The general trend,... evaporation or, alternatively, a high- power plasma decomposition of methane The ion-milling rate of ␣-C is slightly higher than that of the diamondlike form Very good results in terms of a step-edge profile have been obtained by using an e-beam-defined ␣-C mask (31) The use of e-beam lithography, in place of ordinary photolitography, strongly improves the straightness of the step In the previous section... the 2-mV tunability range of VM leads to a bandwidth of 50 0 GHz around 1 THz The available dc power of the oscillations, when the junction is dc biased on the DLS at a voltage, for example, V ϭ 1 .5 mV and a current I ϭ 0.3 mA, is P ϭ 0. 45 ␮W: Under conditions of perfect matching however, the available power will not be more than half of this amount An estimate of the linewidth of the radiation emitted... Josephson nature of the junctions needs an atomic-level inspection of the microstructure of these specific GBs HRTEM analysis performed on the step-edge junctions showed that the GBs formed at the top and at the bottom edges of the step were very dissimilar (see Fig 4. 25) The top GB (Fig 4.25a) consists of two parts: a 10–20-nm-thick BPF GB and an almost regular S GB of 130–140 nm on top of it The bottom... can be understood in terms of the evolution of BPF GB formed at the top edge of the step The R(T ) dependence was of the semiconductor type and the Tc was reduced compared to the plain microbridges of the same width Nevertheless, at 4.2 K, the critical current density of this type of junctions was high, of the order of 5 ϫ 1 05 A/cm2, with a weak dependence on the magnetic field and the excess current... maximum of the critical current Ic corresponds always to B ϭ 0 and the current–phase relation has the usual sinusoidal form [measured by Il’ichev et al (57 )] The absence of ␲ loops also helps to avoid additional 1/ƒ noise 4 .5. 4 Electrodynamics of the Step-Edge Junction Various mechanisms have been proposed to account for the transport properties of grain boundaries in high critical temperature superconductors... of the step A much higher ion-milling rate of the protecting mask compared to the substrate causes shrinking of the mask edges and the formation of a “bump” at the top edge of the step The growth of such layer, usually a few nanometers thick, can be detected by SEM or atomic force microscopic (AFM) inspection of the substrates The material is usually redeposited in an amorphous form The formation of. .. range of temperature between 4.2 K and the critical temperature Tc of the specific junction After removal of the YBCO stripes, by additional ion milling the I–V characteristics of the SEJs remained unchanged Therefore, these data allow one to correlate the transport properties of these SEJs with the occurrence of only one effective weak link, namely the top GB However, a clear understanding of the . Junctions 1 15 FIGURE 4.10 High- temperature TEM image of the GB formed at the bottom edge of a high- angle LaAlO 3 step. (From Ref. 22.) F IGURE 4.11 (a) Sketch of the wavy step-edge profile patterned. alter- natively, a high- power plasma decomposition of methane. The ion-milling rate of ␣-C is slightly higher than that of the diamondlike form. Very good results in terms of a step-edge profile have. on the flat part of the substrate, as a function of the step angle ( 15) . In this case, the thickness of the YBCO film is less than the step height. It is clear that, up to an angle of 10°, no