Method and system of direct writing a superconducting nanojunction

Abstract

Described herein is a method (200) of forming a superconducting nanojunction in a superconducting material. The method (200) comprises, at step (201), pre-patterning a superconducting strip from the superconducting material. At step (202), the position, temperature and applied force of a thermal scanning probe is selectively controlled to selectively apply heat energy to a region of the superconducting strip under ambient atmospheric conditions to remove or change the superconducting properties of the region. This process forms a superconducting nanojunction between two sections of the superconducting material.

Description

METHOD AND SYSTEM OF DIRECT WRITING A SUPERCONDUCTING NANOJUNCTIONFIELD OF THE INVENTION

[0001] The present application relates to superconducting devices and in particular to methods of fabricating superconducting devices.

[0002] Embodiments of the present invention are particularly adapted for fabricating superconducting nanojunctions using a thermal scanning probe. However, it will be appreciated that the invention is applicable in broader contexts and other applications.BACKGROUND

[0003] High-transition-temperature superconductors (HTSs) have attracted significant attention in both fundamental research and practical applications. The primary advantage of these HTS materials is their ability to become superconducting around liquid nitrogen temperature (~77 K), requiring simpler cryogenic systems for operation than low temperature superconductors (LTSs). Researchers have explored various methods to fabricate Josephson junctions in HTSs.

[0004] Josephson junctions are quantum mechanical devices formed from two superconductor materials separated by a short length of non-superconducting material (e.g. an insulator). These junctions experience the Josephson effect, which is a quantum mechanical phenomenon that allows highly accurate measurement of properties such as voltage and frequency of materials. Quantum phase slip junctions are similar quantum mechanical devices that enable discrete transitions in the quantum phase of a wavefunction across a junction.

[0005] Josephson junctions and quantum phase slip junctions have important applications in quantum-mechanical circuits, such as Superconducting Quantum Interference Devices (SQUIDs) and in other quantum computing applications. Josephson junctions also have uses in sensors to measure physical quantities with extreme precision. For example, to measure tiny variations in magnetic fields from muscle activity and nerve paths. This provides great potential in fields such as medical diagnosis. Such magnetic field sensors can also be used for military purposes like navigation.

[0006] One approach to fabricating Josephson junctions is to define a nanoscale region within a superconducting strip or “microbridge” to create a well-defined, nanoconstriction.However, fabricating these nanobridges from HTS materials, specifically from YBa2Cu3O7-8 (YBCO) remains challenging due to the short and anisotropic superconducting coherence lengths in this material. By way of example, the coherence length of YBCO is typically about 2 nanometers in the a-b plane and 0.2 nanometers along the c axis. This makes the electrical properties of these Josephson Junctions highly sensitive to chemical variations and structural defects at the atomic scale, which can occur during the fabrication process.

[0007] Other common methods for fabricating Josephson junctions in HTS include maskless focused ion beam etching and electron beam lithography. In many cases, a focused particle beam is used to directly write the Josephson junctions into the superconducting materials. In other conventional patterning processes, multiple lithography steps are required, which can degrade these materials. Another approach for fabricating Josephson junctions in HTS involves using an atomic force microscope (AFM) to create nanojunctions. However, this method is timeconsuming process and require a cleaning of the residual material afterwards.

[0008] US Patent 10,224,275 to Cybart et al. entitled “Method for fabricating superconducting devices using a focused ion beam” discloses a method of directly writing Josephson junctions in HTS using a focused ion beam. However, this method requires operation in a vacuum environment, and involves equipment that is difficult to operate and requires regular calibration.

[0009] Any discussion of the background art throughout the specification should in no way be considered as an admission that such art is widely known or forms part of common general knowledge in the field.SUMMARY OF THE INVENTION

[0010] In accordance with a first aspect of the present invention, there is provided a method of forming a superconducting nanojunction in a superconducting material. The method comprises the step of pre-patterning a superconducting strip from the superconducting material. The method also comprises the step of selectively controlling the position, temperature and applied force of a thermal scanning probe to selectively apply heat energy to a region of the superconducting strip under ambient atmospheric conditions. This application of heat energy removes or changes the superconducting properties of the region to thereby form a superconducting nanojunction between two sections of the superconducting material.

[0011] In some embodiments, the superconducting material comprises a YBa2Cu3O7-8 (YBCO) thin film.

[0012] In some embodiments, the thermal scanning probe is controlled to move across the superconducting strip at a velocity in the range of 0.05 pm / s to 0.2 pm / s. In some embodiments, the thermal scanning probe is controlled to move stepwise across the superconducting strip in 2 nm steps. In some embodiments, the thermal scanning probe is controlled to move stepwise across the superconducting strip. Preferably, the stepwise movement is such that, at each step, the probe tip remains at a fixed position for a period in the range of 40 ps to 60 ps.

[0013] In some embodiments, the width of the superconducting nanojunction is less than 400 nm. In some embodiments, the width of the superconducting nanojunction is in the range of 100 nm to 300 nm.

[0014] In some embodiments, the temperature of the thermal scanning probe is controlled to be greater than 1000 degrees Celsius. In some embodiments, the temperature of the thermal scanning probe is controlled to be in the range of 1300 to 1400 degrees Celsius.

[0015] In some embodiments, the step of patterning a superconducting strip comprises etching the superconducting strip in the superconducting material using a photolithography technique. In some embodiments, the etching comprises projecting an Argon ion beam at the superconducting material.

[0016] In some embodiments, the superconducting strip has a width in the order of 1 pm to 10 pm. In some embodiments, the superconducting strip has a width of 2 pm.

[0017] In some embodiments, the superconducting nanojunction has a length in the range of 50 nm to 300 nm.

[0018] In some embodiments, selectively applying heat energy to a region of the superconducting strip acts to change a local area of the superconducting strip from a superconducting material to a non-superconducting material. In other embodiments, selectively applying heat energy to a region of the superconducting strip acts to thermally etch the region of the superconducting strip to form the superconducting nanojunction that has a narrower width than the superconducting strip.

[0019] In some embodiments, the thermal scanning probe comprises a tip having a radius in the range of 1 nm to 10 nm. In some embodiments, the thermal scanning probe etches the region of the superconducting strip with a linewidth in the range of 10 nm to 20 nm.

[0020] In some embodiments, the step of selectively controlling the position, temperature and applied force of a thermal scanning probe comprises moving a tip of the thermal scanning probe in a stepwise manner across the region of the superconducting strip. In some embodiments, the tip of the thermal scanning probe is moved in steps of 1 nm to 5 nm across the region of the superconducting strip. In some embodiments, the tip of the thermal scanning probe is moved in steps of 1 nm, 2 nm, 3 nm, 4 nm or 5 nm across the region of the superconducting strip.

[0021] In some embodiments, the tip of the thermal scanning probe is held at each step location for a period in the range of 20 ps to 60 ps. In some embodiments, the tip of the thermal scanning probe is held at each step location (dwell time) for a period of 48 ps. In some embodiments, the tip of the thermal scanning probe is held at each step location for a period of 20 ps, 30 ps, 40 ps, 50 ps or 60 ps.

[0022] In some embodiments, the superconducting nanojunction exhibits Josephson junction effects. In some embodiments, the superconducting nanojunction exhibits quantum phase slip junction effects.

[0023] In accordance with a second aspect of the present invention, there is provided a quantum mechanical device incorporating a superconducting nanojunction formed by the method of the first aspect. The quantum mechanical device may comprise a superconducting quantum interference device (SQUID).

[0024] In accordance with a third aspect of the present invention, there is provided a system for forming a superconducting nanojunction in a superconducting material. The system comprises a thermal scanning probe tip connected to a position controllable mount. The system also comprises a controller configured to selectively control the position, temperature and applied force of the thermal scanning probe tip to selectively apply heat energy to a region of a pre-patterned superconducting strip formed from the superconducting material under ambient atmospheric conditions. This application of heat energy acts to remove or change the superconducting properties of the region to thereby form a superconducting nanojunction between two sections of the superconducting material.

[0025] In addition to (or alternative to) forming a superconducting nanojunction, the system may be configured to trim, cut or otherwise modify an existing superconducting nanojunction formed in a superconducting material.

[0026] The controller may be configured to set one or more of a tip temperature, forward height, dwell time, and / or scan velocity. In some embodiments, the controller is configured to generate curvilinear junctions. The curvilinear junctions may comprise an S-shaped trajectory.

[0027] In accordance with a fourth aspect of the present invention, there is provided a superconducting nanojunction formed in a superconducting material. The nanojunction is formed by a fabrication method. The fabrication method comprises the step pre-patterning a superconducting strip from the superconducting material. The fabrication method also comprises the step of selectively controlling the position, temperature and applied force of a thermal scanning probe to selectively apply heat energy to a region of the superconducting strip under ambient atmospheric conditions. This application of heat energy acts to remove or change the superconducting properties of the region to thereby form the superconducting nanojunction between two sections of the superconducting material.

[0028] The superconducting nanojunction may comprise a width in the range of 10 nm to 400 nm. The superconducting nanojunction may comprise a width in the range of 10 nm to 30 nm. The superconducting nanojunction may comprise a length in the range of 50 nm to 300 nm. The superconducting nanojunction may have a critical current that is at least one order of magnitude lower than a critical current of the unmodified superconducting strip.BRIEF DESCRIPTION OF THE FIGURES

[0029] Example embodiments of the disclosure will now be described, by way of example only, with reference to the accompanying drawings in which:Figure 1 is a schematic system diagram of a thermal scanning probe lithography system;Figure 2 is a process flow diagram illustrating the primary steps in a method of forming a superconducting nanojunction in a superconducting material using a thermal scanning probe lithography system such as that of Figure 1 ;Figure 3 schematically illustrates an experimental setup (panel a) to pre-pattern superconducting strips, together with example etches (panels b and c) to form nanojunctions and corresponding spatial profiles (panels d and e) of the nanojunctions;Figure 4 schematically illustrates a tip of the thermal scanning probe lithography system being used to thermally etch a region from a superconducting strip to form a nanojunction;Figure 5 illustrates two width profiles of superconducting nanojunctions formed using the present invention;Figure 6 illustrates a graph of current-voltage (l-V) curves from two microbridges (Bridge1 and Bridge 2), showing critical currents Ic of 4.9 mA and 5.4 mA, respectively, with the slope of the l-V curves giving normal resistances Rn of 619 Q and 693 Q, respectively;Figure 7 illustrates a graph of critical current Ic of the two microbridges of Figure 6 as a function of bridge width (circles and squares), along with calculated Ic values assuming a uniform Jc(x) along the bridges;Figure 8 illustrates a graph of normal resistance Rn at high bias currents for the microbridges of Figures 6 and 7 (circles and squares), proving the localization effect of the thermal scribing technique;Figure 9 illustrates a graph of the effect of external magnetic field on the critical current of the microbridge Bridge 1 from Figures 6 to 8;Figure 10 illustrates critical current versus temperature (circles) of nanobridge 1 with exponential fits (dashed line), and RN as a function of temperature (square);Figure 11 illustrates measured de I -V behaviours of the junction with and without microwave radiation of different frequencies at 77 K, the inset is an AFM scan performed by the thermal scanning probe;Figure 12 illustrates l-V curves of a Josephson junction under microwave radiation (19.8 GHz) with different RF power levels, the inset shows the Ic as a function of RF power; andFigure 13 illustrates graphs of oxygen stoichiometry analysis of Bridge 1 (a) and Bridge2 (b) extracted from Raman spectra.DESCRIPTION OF THE INVENTIONThe embodiments described herein use YBa2Cu3O7-8 (YBCO) thin films as the substrate superconducting material. However, it will be appreciated that other suitable superconductingmaterial may also be processed using the methods described herein to form Josephson junctions or quantum phase slip junctions and nanowires.System overview

[0030] Prior to describing the method of forming a superconducting nanojunction in accordance with the present invention, a brief overview of the lithography system is described.

[0031] The invention utilizes a thermal scanning probe lithography system, which, to the knowledge of the inventor, has not been used to form a superconducting nanojunction. There are difficulties in controlling a thermal scanning probe to accurately create an efficient superconducting nanojunction without damaging the material. These include determining the correct values of temperature and forward height of the probe tip and calculating appropriate nanojunction dimensions to suit the lithography system so that the junction is not destroyed or damaged in the process.

[0032] Embodiments of the invention utilize the NanoFrazor t-SPL thermal scanning probe lithography system developed by Heidelberg Instruments. However, it will be appreciated that other thermal scanning probe lithography systems may be employed to implement the present invention.

[0033] The NanoFrazor is a nanofabrication tool that utilizes a heated probe to locally evaporate resist material, enabling the direct writing of high-resolution nanoscale patterns without the need for additional development steps typical in traditional lithography processes. The NanoFrazor allows for directly writing patterns onto the resist material using a heated tip, eliminating the need for masks or additional chemical development steps. This can significantly simplify the fabrication process and reduce contamination risks.

[0034] Figure 1 schematically illustrates the main components of a thermal scanning probe lithography system 100 like that of the NanoFrazor. System 100 comprises a probe tip 102, which is an ultrasharp structure that is typically formed of silicon. Tip 102 has a radius in the order of nanometres, such as 2 nm and has a length in the order of hundreds of nanometres, such as 750 nm. In other embodiments, tip 102 has a radius in the range of 10 nm to 20 nm.

[0035] The software of the NanoFrazor offers precise control over the etching size, including width, length, and depth. The temperature is adjustable within the range of 300-1400°C, and the resolution of the etch cut is approximately 15 nm. A benefit of thermal scanning probe lithography systems such as the NanoFrazor is that they can operate under normal ambientatmospheric conditions and do not need a vacuum environment. In particular, tip 102 is not contained within a vacuum so the tip can be replaced simply within minutes.

[0036] Another advantage of the Nanofrazor is its ability to cut materials more effectively than conventional AFM techniques. The combination of heat and force plays a crucial role in cutting superconducting materials. Given the small tip diameter i.e. 2 nm, the tip can achieve pressures of up to 4 GPa. The applied heat lower the material's breaking strength, thus enabling the tip to achieve sufficient pressures for cutting these materials. Tip 102 is mounted to or integrated into a flexible cantilever arm 104 that supports the probe tip 102 and allows it to be selectively moved relative to a substrate 106. Cantilever arm 104 is connected to a system of actuators 108, which, in conjunction with an actuator controller 110, selectively accurately controls the position of tip 102 in three dimensions. The x and y dimensions specify the lateral position of tip 102 across substrate 106 while the z direction specifies the vertical height (or “forward height”) of tip 102 relative to a surface of substrate 106.

[0037] A heater 112 is provided for heating tip 102 to a high temperature for thermal etching of substrate 106. Heater 112 may comprise a resistive heater integrated into cantilever arm 104, which is electrically controlled by a heater controller 112. Heater 112 is preferably configured to heat tip 102 to temperatures of greater than 1000°C. An on-tip thermometer or thermal sensor may be included to provide temperature feedback to controller 112.

[0038] A system controller 114 is provided for providing input to controllers 110 and 112. However, in some embodiments, all control elements of system 100 may be integrated into a single control module. System controller 114 may be configured to receive input from one or more sensors (not illustrated) embedded in or near tip 102 and cantilever arm 104 to monitor parameters such as temperature and position of tip 102 and, in response, provide closed loop feedback control to controllers 110 and 112. This allows the system to provide real-time feedback on the depth during the etching process. Furthermore, the system controller 114 may be responsive to user input to specify an etching pattern, linewidth parameters, cutting lengths, step size and other parameters.

[0039] The substrate 106 is mounted on a base mount 116 having a sample holder 118. Mount 118 may be fixed or laterally or rotatably movable in various directions to move substrate 106. Movement of base mount 116 may be manually controlled by a user and / or controlled by system controller 114.

[0040] Substrate 106 comprises an upper resist layer 106A where the patterning / etching occurs and a base layer 106B on which the resist layer 106A is coated. Resist layer 106A is a layer of thermally sensitive resist material (e.g., a polymer) coated on the substrate. The base layer 106B may comprise silicon, glass, magnesium oxide (MgO) or another semiconductor material. In embodiments of the present invention, the resist layer is replaced with the superconductor YBa2Cu3O7-b (YBCO), while the base layer 106B comprises magnesium oxide.

[0041] As such, a scanning probe lithography system such as system 100 uses a resistively heated nanoscale probe tip with precise control, closed-loop feedback, and minimal damage to the substrate. The probe tip is brought into close proximity to the substrate to apply localized thermal energy for material modification and / or thermomechanical etching of the material. The localized thermal energy is not particle based like in an ion beam system but is radiant in nature. The system operates under ambient atmospheric conditions the probe temperature is precisely controlled, typically in the range of 1000°C to 1400°C. The system preferably includes closed- loop feedback to monitor and adjust etching depth in real time. The probe tip is moved in a stepwise or continuous manner with nanometre-scale resolution. The system does not rely on particle beams, vacuum environments, for material modification.Method

[0042] In embodiments of the present invention, a thermal scanning probe lithography system such as system 100 described above is used to form a superconducting nanojunction. Referring now to Figure 2, there is illustrated a method 200 of forming a superconducting nanojunction in a superconducting material using a system such as that of Figure 1 .

[0043] At step 201 , method 200 comprises pre-patterning a superconducting strip from the superconducting material. The superconducting strip is a portion of superconducting material in which one dimension is significantly shorter than the other dimension such as a rectangle. In some embodiments, this step is performed separately to the subsequent steps of the method and even performed at a different time and / or location.

[0044] Panel a. of Figure 3 schematically illustrates the experimental setup to pre-pattern the superconducting strips (also called “microbridges”). Creation of four superconducting strips is illustrated in Figure 3. Initially, the superconducting strips are patterned into the YBCO thin film, which is deposited on a 10 mm x 10 mm MgO (100) substrate. The initial patterning is performedusing conventional photolithography and argon ion beam milling techniques. This fabrication process results in devices consisting of multiple (e.g. 4, 8, 12, 24 or 32) blocks of superconducting strip arrays, with widths ranging from 2 to 8 pm and lengths ranging from 20 pm to 50 pm. In one embodiment, the superconducting strips are 2 pm-wide and 30 nm thick. The length of the superconducting strips can be customized by pre-designed photolithography masks. The masks may be designed using software such as LayoutEditor, developed by Juspertor GmbH or Klayout, an open source software package available under the GNU license agreement.

[0045] Panels b. and c. of Figure 3 show thermal scanning probe images of two different cuts, with dashed lines indicating the corresponding profile locations. Panel b. shows a single nanobridge with a width of 100 nm and a length of 300 nm. Panel c. shows an S-shaped nanobridge with a width of 150 nm. Panels d. and e. of Figure 3 illustrate profiles of the cuts shown in panels b. and c., respectively, providing nanoscale features of the corresponding cuts.

[0046] By way of example, a 113 nm-thick epitaxial c-axis YBCO film with a 50 nm in situ gold film may be deposited on the MgO substrate using e-beam evaporation. More generally, the gold film may have a thickness in the range of 30 nm to 100 nm. In some embodiments, the YBCO or other superconducting material may have a thickness in the range of 20 nm to 150 nm to define a thin film. The Au / YBCO film is then patterned and etched to form the microbridges. The in-situ gold is removed from the junction area using an Argon sputtering technique. A second lithography step can be conducted to make gold contact pads of ~ 300 nm thick. The in situ gold film has two roles - the first role is to protect the YBCO film during the shipping; the second role is to act as an adhesion layer for the second deposition of gold electrodes for electrical transport measurements. If it is too thin <20 nm, the gold film might not be continuous; if it is too thick, then valuable gold material is wasted.

[0047] Referring again to Figure 2, at step 202, the pre-patterned superconducting strips are loaded into the thermal scanning probe lithography system 100 (e.g. a Nanofrazor device). This includes placing the strips onto sample holder 118 and properly aligning the strips on holder 118 for accurate etching. The sample holder 118 is then inserted into the thermal scanning probe lithography system 100 and initiating the system as required. The superconducting strip should be aligned perpendicular to the tip scan axes of the system 100. A user may specify etching design parameters, including a pattern, speed, tip force (via the forward heigh), linewidth, step distance, tip temperature any others.

[0048] At step 203, system 100 is operated to selectively control the position, temperature and applied force of tip 102 to selectively apply heat energy to a region of the superconducting strip under ambient atmospheric conditions. The amount of heat energy applied to the region is proportional to the temperature of the tip. The force is provided by the forward height (vertical height relative to the surface of the substrate) and voltage.

[0049] The selective application of heat energy and the force to region 404 act to remove completely the material or change the superconducting properties of the region to thereby form a nanoconstriction between two sections of the superconducting material. This is illustrated schematically in Figure 4, which shows a pre-patterned superconducting strip 402 formed in a YBCO superconducting material being subject to heat from tip 102 in region 404. Tip 102 is selectively moved across region 404 of superconducting strip 402 to form a nanojunction having a width W and a length L.

[0050] In some applications, selectively applying heat energy to region 404 of the superconducting strip 402 acts to change a local area of the superconducting strip from a superconducting material to a non-superconducting material. In other words, the material is changed but not removed. The non-superconducting material may be a conductor or an insulator. In some embodiments, the heat applied to region 404 reduces the superconducting properties of the region sufficiently that the surrounding superconducting strip 402 can still experience Josephson effects and act as a nanojunction. In some embodiments, selectively applying heat energy to a region of the superconducting strip acts to thermomechanically etch the region of the superconducting strip to form the superconducting nanojunction that has a narrower width than the superconducting strip. In these embodiments, material is physically removed from the superconducting strip 402 to form the nanojunction. The resulting width of the nanojunction is less than the original width of the pre-patterned superconducting strip 402 as illustrated in Figure 4.

[0051] Operation of system 100 is performed by system controller 114, which may be based in part on user input. In some embodiments, the thermal scanning probe tip 102 is controlled by controller 114 to move across the superconducting strip 402 at a velocity in the range of 0.05 pm / s to 0.2 pm / s. The tip 102 may be controlled to move stepwise across the superconducting strip in predetermined step increments across the region of the superconducting strip 402. These step increments may be in the range of steps of 1 nm to 5 nm. In one embodiment, the step increment is 2 nm steps. However, in other embodiments, these step increments may belarger than 5 nm or smaller than 1 nm depending on the application and desired nanojunction size / shape. The tip 102 may follow a predefined path such as following a raster or spiral pattern. In some embodiments, the nanojunction is formed by gradually trimming the superconducting strip from a side to a center region. The linewidth of the path is dependent on the radius of tip 102 but is generally in the range of 10 nm to 20 nm.

[0052] The tip 102 may be controlled to move stepwise across the superconducting strip such that, at each step, the probe tip remains at a fixed position for a period in the range of 40 ps to 60 ps. This is referred to as a dwell time. The longer the dwell time, the greater the etching depth at that location. However, a longer dwell time increases the overall etching time of the nanojunction. In one particular embodiment, the tip 102 is held at each step location for a dwell time period of 48 ps.

[0053] During the thermal etching, controller 112 preferably controls the temperature of tip 102 to be greater than 1000 degrees Celsius. Preferably the temperature of tip 102 is controlled to be in the range of 1300 to 1400 degrees Celsius. In one embodiment, during the thermal etching process, the tip 102 is heated and maintained at a writing temperature of 1350 degrees Celsius.

[0054] Preferably the width of the resulting superconducting nanojunction is less than 400 nm. The width of the superconducting nanojunction may be as thin as 10 nm. In some embodiments, the width of the superconducting nanojunction is in the range of 100 nm to 300 nm. In some embodiments, the superconducting nanojunction has a width in the range of 10 nm to 30 nm. In various embodiments, the width of the superconducting nanojunction may be in the range of 10 nm to 400 nm, 100 nm to 300 nm, 50 nm to 100 nm, 30 nm to 50 nm, 10 nm to 50 nm, 10 nm to 40 nm, 10 nm to 30 nm, 10 nm to 20 nm, 20 nm to 50 nm, 20 nm to 40 nm or 20 nm to 30 nm or any range therebetween. In general, the width of the superconducting nanojunction may be less than 30 nm, 40 nm, 50 nm, 75 nm, 100 nm, 150 nm, 200 nm, 250 nm or 300 nm. Preferably the resulting superconducting nanojunction has a length in the range of 50 nm to 300 nm, which can be formed in conjunction with any of the width ranges mentioned above. .

[0055] An advantage of using a thermal scanning probe lithography system such as the Nanofrazor is that it allows for imaging the surface before, during, and after patterning, similar to an atomic force microscope. The imaging process is carried out by measuring the difference in heat exchange between the cantilever's read heater and the substrate's topography.

[0056] The NanoFrazor images the surface topography in contact mode. In this mode, the tip 102 maintains continuous contact as it is scanned over the surface of the substrate 106. The deflection of the cantilever arm 104 is measured by monitoring the heat exchange between the heater 112 and the substrate 106. To perform the measurement, a constant voltage is applied to the heater 112 via a series resistance, and the NanoFrazor measures the current flowing through the heater 112. When the cantilever arm 104 bends up due to a feature on the surface, the heat exchange with the surface decreases and the reader warms up. When the cantilever arm 104 bends down due to a recess in the surface topography, the reader cools down. The NanoFrazor detects these changes in temperature via the change in current flow through the heater 112. The reader signal is converted into depth using the calibration given by the Piezo Approach.

[0057] The method described above is capable of producing superconductor-normal- superconductor (S-N-S) or superconductor-poor superconductor-superconductor (S-S’-S) type nanojunctions that exhibit Josephson junction effects.Example embodiments and experimental results

[0058] In one embodiment, method 200 is performed optimal scribing conditions that comprise a combination of temperature of 1350°C, a forward height of 0 nm and a tip velocity of around 0.1 pm / s, enabling the system to etch through a 30 nm thick YBCO bridge in a single pass of less than 60 seconds. More generally, the forward height range may be controlled to be between -50 nm to 250 nm. 5 illustrates the width profiles of two nanojunctions formed with the control parameters described above. The top panel illustrates a narrow nanojunction with a width of about 50 nm while the bottom panel illustrates a somewhat broader nanojunction having a width of about 500 nm. The width of the nanojunction is set by the linewidth, which can be controlled by setting parameters such as the temperature, forward height and dwell time. In this embodiment, the minimum linewidth, determined by the tip radius, is 15 nm, which is three times better than some AFM studies.

[0059] To investigate the properties of the nanojunctions created by thermal scribing, the width of the nano-constrictions (W) was gradually decreased by trimming from the left to right side of the bridge illustrated in Figure 4. During etching, the critical current (lc) of the structures was monitored. Two 2-pm-wide YBCO microbridges, each with a thickness of 113 nm and an initial critical current density (Jc) of 2.4 MA. cm-2, were aligned perpendicular to the tip scan axes and scanned in imaging mode using a NanoFrazor device. Subsequently, the tip was loweredinto contact at the desired position for creating the nano-constrictions, directly scribing onto YBCO with 2 nm pixel steps and a 48 ps tip contact time per pixel. During the thermal scribing process, the probe was heated and maintained at a writing temperature of Tw= 1350°C using an on-tip resistive heater and monitored by an on-tip thermometer.

[0060] The current-voltage characteristics (IVC) of the bridges were measured using standard 4-terminal methods on a custom-built probe within a dip probe system shielded with mu-metal and cooled with liquid nitrogen to 77 K. An Advantest TR6143 source measure unit was used as a current source and a Hewlett-Packard 3458A multimeter was used to measure the voltage across the superconducting bridge. Temperature dependence critical current and Fraunhofer diffraction pattern measurements were carried out in low fields up to 140 mT in a Physical Property Measurement System (PPMS, Cryogenic Ltd).

[0061] The IcRnfactor, where Rnis the normal state resistance and lcis the critical current, is one of the main quality parameters of a Josephson junction. Measurements performed at 77 K demonstrate a reduction of Icby over an order of magnitude. However, The fabricated nanojunctions also exhibit a high IcRnvalue at 70 K. In various embodiments, the nanojunctions exhibit an IcRnfactor in the order of millivolts at temperatures in the range of 65 K to 77 K.

[0062] Figure 6 illustrates the initial l-V curves of two 2 pm-wide microbridges (superconducting strips) in the same block. Bridge 1 exhibited an lcof 4.9 mA and a normal resistance (Rn) of 619 Q, while bridge 2 showed an lcof 5.4 mA and Rnof 693 Q. As shown in Figure 7, when the remaining width of Bridge 1 was reduced to around 200 nm and the length is ~ 300 nm, the lcdecreased to ~0.3 mA, a reduction of approximately 94 % from the initial lcof 4.9 mA. This demonstrates the potential of using this technique to actively modify the lcof nanojunctions in existing superconducting circuits without the need of multiple lithography steps.

[0063] The lcvalues decreased as a function of the bridge width and followed the calculated values assuming the Jcof the film remained unchanged, indicating that the technique is highly localized and not damaging the surrounding areas. As shown in Figure 8, the normal resistance (Rn) of the bridges as a function of bridge width remained unchanged, further supporting the localization of the thermal scribing technique. The effective width (we) of these two nanobridges, however, are not resolved completely as there is residual YBCO on the edge.

[0064] To better understand the Josephson behaviours and investigate the effective width of the nano-constrictions, the dependence of lcof Bridge 1 was measured on an external magnetic field (Ba). The resulting relationship between lcand Bais illustrated in Figure 9, where the inset represents the corresponding AFM scan of the nanojunction.

[0065] When a field is applied perpendicular to the plane of the junction of width w, a uniform junction (Jc(x) = constant across w) would show the Fraunhofer behaviour, which is given by lc= Ico |sin k / k|, where k =7rB°fteW, heis effective thickness of the barrier, and O0is the flux density.<POAt 70 K, a Fraunhofer-like diffraction pattern was obtained for Bridge 1 , as shown in Figure 9. The pattern is reasonably symmetric around Ba= 0, indicating the presence of the DC Josephson effect. However, this is not an ideal Fraunhofer pattern, as evidenced by non-zero minima and non-uniform spacing of the minima, which suggests a non-uniform Jc(x) along the junction width.

[0066] The magnetic field response of the nanojunction between two superconducting electrodes yields a periodicity of ~27 mT. This periodicity aligns well with an analytical model described in Rosenthal, P. A.; Beasley, M. R.; Char, K.; Colclough, M. S.; Zaharchuk, G., Flux focusing effects in planar thin-film grain-boundary Josephson junctions. Applied Physics Letters 1991, 59 (26), 3482-3484. This model accounts for flux focusing of the flat electrodes, significantly altering the period such that AB0= 1.84O0 / w2. This model predicts a junction width of ~200 nm for a periodicity of ~27 mT, confirming that the present nanobridge is indeed a nanojunction with a width of ~200 nm.

[0067] The temperature dependence of lcand (Rn) is shown in Figure 10. The decrease in Rnas temperature is lowered indicates that the weak link behaves as a conductor. The critical current lcscales with (1 - T / Tc)a, yielding an a value of 1.3 after fitting, which is consistent with the expected behaviour of an SNS-type junction. For short nanobridges, the exponent is expected to be in the range of 1-1.5, whereas for long bridges, it is typically 2-2.517'19. The present nanobridge length of approximately 300 nm falls within the regime of short nanobridges. The resistance (~20 Q) is approximately 200 times larger than typical nanolithography and ion- irradiated weak links (e.g. those described in Cybart, S. A.; Ke, C.; Dynes, R. C., Planar YBa / sub 2 / Cu / sub 3 / O / sub 7- / spl delta / / ion damage Josephson junctions and arrays. IEEE Transactions on Applied Superconductivity 2005, 75 (2), 241-244.) and two orders of magnitude higher than the recent direct write SNS junctions using helium ion irradiation described inCybart, S. A.; Cho, E. Y.; Wong, T. J.; Wehlin, B. H.; Ma, M. K.; Huynh, C.; Dynes, R. C., Nano Josephson superconducting tunnel junctions in YBa2Cu3O7-5 directly patterned with a focused helium ion beam. Nature Nanotechnology 2015, 10 (7), 598-602. The IcRnproduct is approximately 5.9 mV at 70 K.

[0068] Next, the AC Josephson effect was studied in nanobridge 1 . The AC Josephson effect established the following voltage-frequency relationship:GHz0.4836 -V (1)

[0069] Where Vois the DC voltage across the junction when biased above its critical current 2,6 GHzIo. Given that — = 0.4836—, for Voranging from V to mV, the frequency f spans microwave, mm, and sub-mm or THz bands. Under RF radiation, ladder-like voltage steps, known as Shapiro steps, form and are determined by the frequency-voltage relationship.

[0070] Figure 11 shows the microwave responses of nanobridge 1 at frequencies of 19.6 GHz and 19.8 GHz, while Figure 12 presents l-V curves of a Josephson junction under microwave radiation (19.8 GHz) at various power levels at 77K. Measurements at 50 GHz were unsuccessful due to inefficient RF coupling, caused by a mismatch in frequency transmission, which failed to suppress lc. Effective RF power coupling to the nanobridge was achieved only at approximately 20 GHz.

[0071] For the cryogen-free cooling process to perform RF measurements, the sample was housed in a copper enclosure and mounted onto the cold head of a two-stage pulse-tube cryocooler (Janis Research Inc., model PTSHI-SRP-062B). Each DC line connected the device contact pads to a printed circuit board (PCB), which featured a simple filter with a 1 kQ resistor and a 1.5 nF capacitor in series between the DC line and the ground plane. A battery-operated current source applied the current, and the IV characteristics were captured using Pico Scope software. For the RF measurements, a coaxial cable was connected to the sample through an SMA connector, and an RF signal with a frequency of 20-50 GHz was generated using an Agilent Technologies E8257D signal generator. The microwaves were delivered directly to the nanobridges via the coaxial cable.

[0072] To confirm the localization of this technique, the microbridges were further characterized after writing using Raman spectroscopy. Raman spectroscopy measurementswere performed using a 514 nm laser at room temperature with a Renishaw InVia Reflex spectrometer equipped with a Peltier-cooled charged coupled device detector. The Raman spectra were recorded in a backscattering geometry and the laser power was set to 50 mW, using a 50x objective (NA = 0.75), resulting in a nominal spot size of approximately 1 pm. The laser spot was used to probe local structure and oxygen content within the YBCO film along the microbridge.

[0073] Figure 13 shows the oxygen stoichiometry calculated from Raman spectra for two of the microbridges used in the experiment. The calculation is performed based on the correlation between the peak position of the O(4)-Ag phonon mode and the oxygen deficiency within the YBCO crystal structure where a blue-shift in the position of this peak represents an increase in oxygen stoichiometry. Positions along the length of the YBCO microbridge were chosen for investigation by Raman spectroscopy to characterise the relative oxygen content present to assess the damage done to the bridge by the thermal probe.

[0074] Along the bridge, a consistent oxygen concentration was observed within the crystal lattice, averaging around 6.9 mol per formula unit (f.u.), indicating the material remains undamaged. The spectra from the nano-constriction areas, however, clearly show a reduction in oxygen stoichiometry, suggesting oxygen depletion in these regions. Despite this depletion, the areas remain within the superconducting range, specifically above a mole ratio of 6.2 O / f.u., further indicating the formation of an SNS-type junction.Advantages

[0075] Embodiments of the invention described above provide a novel fabrication method that allows for the rapid direct writing of Josephson nanojunctions from high-temperature superconducting materials such as YBCO using the thermal scanning probe. The nanojunctions obtained show evidence of Josephson effects in an SNS-type JJs.

[0076] The present invention offers several advantages, including the speed and simplicity of fabricating junctions and the flexibility to integrate them in desired locations on pre-patterned circuits without the need for further complex lithography processes. Additionally, the method allows for the direct trimming of pre-existing junctions to modify critical current, which can enhance the performance of SQUIDs.

[0077] The method of the present invention is more efficient than typical AFM techniques, which require either a diamond-like coated tip or several hundred cycles of back-and-forth AFMtip movement to create a single structure, and an additional cleaning step to remove residual materials. This efficiency is attributed to the thermal effect, which accelerates the scribing process. The combination of heat and force plays a crucial role in cutting superconducting materials. Given the small tip diameter i.e. 2 nm, the tip can achieve pressures of up to 4 GPa. The applied heat reduces the material's breaking strength, thus enabling the tip to achieve sufficient pressures for cutting these materials.

[0078] When compared to step-edge junctions, the present invention enables a single-step fabrication process. In contrast, step-edge junctions require multiple lithography steps to define the junction geometry. Moreover, step-edge junctions, where weak links form at grain boundaries, offer little control over junction properties due to inherently random nature of these weak links. By providing finer spatial resolution through the small tip diameter, the present invention achieves a higher degree of control, resulting in a simpler and more versatile junction fabrication method.

[0079] Another advantage of this technique is the ease of controlling the depth of the cut through the closed-loop patterning process incorporated into the thermal scanning probe lithography system such as the NanoFrazor device, which provides real-time feedback on the depth during writing.

[0080] The thermomechanical etching process is more localized and does not damage the surrounding superconducting material such as YBCO compared to other techniques such as Focused ion beam

[0081] Finally, the thermomechanical etching method can operate under ambient atmosphere, eliminating the need for vacuum control.

[0082] In addition to (or alternative to) forming a superconducting nanojunction, the thermal scanning probe system of the present invention may be configured to trim, cut or otherwise modify an existing superconducting nanojunction formed in a superconducting material.

[0083] Given the localization of this technique, it holds potential for extending its application to other high-temperature superconductors that are sensitive to disorders and chemicals, where traditional lithography methods may be challenging and prone to damage the junctions during fabrication.Interpretation

[0084] Unless specifically stated otherwise, as apparent from the following discussions, it is appreciated that throughout the specification discussions utilizing terms such as "processing," "computing," "calculating," “determining”, analyzing” or the like, refer to the action and / or processes of a computer or computing system, or similar electronic computing device, that manipulate and / or transform data represented as physical, such as electronic, quantities into other data similarly represented as physical quantities.

[0085] In a similar manner, the term “controller” or "processor" may refer to any device, portion of a device or plurality of devices that processes electronic data, e.g., from registers and / or memory to transform that electronic data into other electronic data that, e.g., may be stored in registers and / or memory. A “computer” or a “computing machine” or a "computing platform" may include one or more co-located or distributed processors.

[0086] Reference throughout this specification to “one embodiment”, “some embodiments” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. Thus, appearances of the phrases “in one embodiment”, “in some embodiments” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0087] As used herein, unless otherwise specified the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.

[0088] In the claims below and the description herein, any of the terms “comprising”, “comprised of’, “which comprises” or similar are open terms that mean including at least the elements / features that follow, but not excluding others. Thus, the term “comprising” and its variations, when used in the claims or description, should not be interpreted as being limitative to the means or elements or steps listed thereafter. For example, the scope of the expression a device comprising A and B should not be limited to devices consisting only of elements A and B. Similarly, any of the terms “including”, “which includes”, “that includes” or similar as usedherein are also open terms that also mean including at least the elements / features that follow the term, but not excluding others. Thus, “including” is synonymous with and means “comprising”.

[0089] It should be appreciated that in the above description of exemplary embodiments of the disclosure, various features of the disclosure are sometimes grouped together in a single embodiment, Fig., or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claims require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the Detailed Description are hereby expressly incorporated into this Detailed Description, with each claim standing on its own as a separate embodiment of this disclosure.

[0090] Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the disclosure, and form different embodiments, as would be understood by those skilled in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0091] In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the disclosure may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0092] Similarly, it is to be noticed that the term coupled, when used in the claims, should not be interpreted as being limited to direct connections only. The terms "coupled" and "connected", along with their derivatives, may be used. It should be understood that these terms are not intended as synonyms for each other. Thus, the scope of the expression a device A coupled to a device B should not be limited to devices or systems wherein an output of device A is directly connected to an input of device B. It means that there exists a path between an output of A and an input of B which may be a path including other devices or means. "Coupled" may mean that two or more elements are either in direct physical, electrical or optical contact, or that two or more elements are not in direct contact with each other but yet still co-operate or interact with each other.

[0093] Embodiments described herein are intended to cover any adaptations or variations of the present invention. Although the present invention has been described and explained in terms of particular exemplary embodiments, one skilled in the art will realize that additional embodiments can be readily envisioned that are within the scope of the present invention.

Claims

What is claimed is:1 . A method of forming a superconducting nanojunction in a superconducting material, the method comprising: pre-patterning a superconducting strip from the superconducting material; selectively controlling the position, temperature and applied force of a thermal scanning probe to selectively apply heat energy to a region of the superconducting strip under ambient atmospheric conditions to remove or change the superconducting properties of the region to thereby form a superconducting nanojunction between two sections of the superconducting material.

2. The method of claim 1 wherein the superconducting material comprises a YBa2Cu3O7-8 (YBCO) thin film.

3. The method of claim 1 or claim 2 wherein the thermal scanning probe is controlled to move across the superconducting strip at a velocity in the range of 0.05 pm / s to 0.2 pm / s.

4. The method of any one of the preceding claims wherein the thermal scanning probe is controlled to move stepwise across the superconducting strip in 2 nm steps.

5. The method of any one of the preceding claims wherein the thermal scanning probe is controlled to move stepwise across the superconducting strip such that, at each step, the probe tip remains at a fixed position for a period in the range of 40 ps to 60 ps.

6. The method of any one of the preceding claims wherein the width of the superconducting nanojunction is less than 400 nm.

7. The method of claim 6 wherein the width of the superconducting nanojunction is in the range of 100 nm to 300 nm.

8. The method of any one of the preceding claims wherein the temperature of the thermal scanning probe is controlled to be greater than 1000 degrees Celsius.

9. The method of claim 8 wherein the temperature of the thermal scanning probe is controlled to be in the range of 1300 to 1400 degrees Celsius.

10. The method of any one of the preceding claims wherein the step of patterning a superconducting strip comprises etching the superconducting strip in the superconducting material using a photolithography technique.11 . The method of claim 6 wherein the etching comprises projecting an Argon ion beam at the superconducting material.

12. The method of any one of the preceding claims wherein the superconducting strip has a width in the order of 1 pm to 10 pm.

13. The method of claim 12 wherein the superconducting strip has a width of 2 pm.

14. The method of any one of the preceding claims wherein the superconducting nanojunction has a length in the range of 50 nm to 300 nm.

15. The method of any one of the preceding claims wherein selectively applying heat energy to a region of the superconducting strip acts to change a local area of the superconducting strip from a superconducting material to a non-superconducting material.

16. The method of any one of the preceding claims wherein selectively applying heat energy to a region of the superconducting strip acts to thermally etch the region of the superconducting strip to form the superconducting nanojunction that has a narrower width than the superconducting strip.

17. The method of any one of the preceding claims wherein the thermal scanning probe comprises a tip having a radius in the range of 1 nm to 10 nm.

18. The method of claim 16 wherein the thermal scanning probe etches the region of the superconducting strip with a linewidth in the range of 10 nm to 30 nm.

19. The method of any one of the preceding claims wherein the step of selectively controlling the position, temperature and applied force of a thermal scanning probe comprises moving a tip of the thermal scanning probe in a stepwise manner across the region of the superconducting strip.

20. The method of claim 18 wherein the tip of the thermal scanning probe is moved in steps of 1 nm to 5 nm across the region of the superconducting strip.

21. The method of claim 19 wherein the tip of the thermal scanning probe is moved in steps of 2 nm across the region of the superconducting strip.

22. The method of any one of claims 18 to 20 wherein the tip of the thermal scanning probe is held at each step location for a period in the range of 20 ps to 60 ps.

23. The method of claim 21 wherein the tip of the thermal scanning probe is held at each step location for a period of 48 ps.

24. The method of any one of the preceding claims wherein the superconducting nanojunction exhibits Josephson junction effects.

25. The method of any one of the preceding claims wherein the superconducting nanojunction exhibits quantum phase slip junction effects.

26. A quantum mechanical device incorporating a superconducting nanojunction formed by the method of any one of the preceding claims.

27. A device of claim 26 comprising a superconducting quantum interference device (SQUID).

28. A system for forming a superconducting nanojunction in a superconducting material, the system comprising: a thermal scanning probe tip connected to a position controllable mount; a controller configured to selectively control the position, temperature and applied force of the thermal scanning probe tip to selectively apply heat energy to a region of a pre-patterned superconducting strip formed from the superconducting material under ambient atmospheric conditions to remove or change the superconducting properties of the region to thereby form a superconducting nanojunction between two sections of the superconducting material.

29. The system of claim 28, wherein the controller is configured to generate curvilinear junctions.

30. The system of claim 29 wherein the curvilinear junctions comprise an S-shaped trajectory.31 . A superconducting nanojunction formed in a superconducting material, the nanojunction formed by a method comprising the steps: pre-patterning a superconducting strip from the superconducting material; selectively controlling the position, temperature and applied force of a thermal scanning probe to selectively apply heat energy to a region of the superconducting strip under ambient atmospheric conditions to remove or change the superconducting properties of the region to thereby form the superconducting nanojunction between two sections of the superconducting material.

32. The superconducting nanojunction of claim 31 comprising a width in the range of 10 nm to 400 nm.

33. The superconducting nanojunction of claim 31 comprising a width in the range of 10 nm to 30 nm.

34. The superconducting nanojunction of any one of claims 31 to 33 comprising a length in the range of 50 nm to 300 nm.

35. The superconducting nanojunction of any one of claims 31 to 34 having a critical current that is at least one order of magnitude lower than a critical current of the unmodified superconducting strip.

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