System and method for trimming metal-insulator-metal junctions

Abstract

The present disclosure relates to a method and a system for tuning an operational resistance of a metal-insulator-metal junction. The method for tuning an operational resistance of one or more, metal-insulator-metal, MIM, junctions comprises determining if a first characteristic resistance of a certain MIM junction comprised in the one or more MIM junctions is below a predetermined MIM junction resistance threshold value. In an instance that the first characteristic resistance of that certain MIM junction is determined to fall below the predetermined MIM junction resistance threshold value, the method further comprises tuning the first characteristic resistance of that MIM junction to a second characteristic resistance by trimming that MIM junction by means of applying a first electrical signal to that MIM junction. The method further comprises determining if the second characteristic resistance of that MIM junction corresponds to the predetermined MIM junction resistance threshold value.

Description

[0001] TITLE

[0002] System and method for trimming metal-insulator-metal junctions

[0003] TECHNICAL FIELD

[0004] The present disclosure relates to a junction trimmer. Particularly, embodiments and aspects of the present disclosure relate to metal-insulator-metal, MIM, junctions and a method, a system and an apparatus for tuning an operational resistance of the mentioned MIM junctions. The embodiments and aspects herein also relate to quantum devices for quantum computing applications comprising such MIM junctions.

[0005] BACKGROUND

[0006] MIM junctions are considered amongst the most promising candidates for applications in high frequency regime. Example applications include a non-exhausting list of applications such as rectifier diodes, local oscillators or magnetic tunnel junctions. Certain MIM material combinations may also qualify as superconductor-insulator-superconductor, SIS, junctions, also known as Josephson junctions, at cryogenic temperatures. SIS junctions find additional applications for superconducting quantum interference devices (SQUID), superconducting quantum computers (Qubits), voltage references, as well as rapid single flux quantum (RSFQ).

[0007] As an example, the MIM junctions may be utilized as one of the building blocks of quantum circuits and devices. However, fabrication of MIM junctions comprised in such quantum circuits may be subject to both on wafer and wafer-to-wafer variations, which may significantly affect the operational frequency and overall performance of the associated quantum devices. Many researchers, governments and companies have been investing substantial amounts of time and money for the advancement of quantum computing which faces significant technological bottlenecks. Prospects of future applications of quantum computing are envisioned to have an enormous impact on human societies and improving quality of life. Among others, very prominent suggested applications are in the fields of developing new drugs (protein folding), optimize and organize delivery chains and flight schedules (traveling-salesman problem) or encrypted communication. To build such quantum computers, substantial technological developments are necessary since the mentioned devices are based on specific operational frequencies and operational temperatures. Therefore, tackling the intended applications of quantum devices, efficient calibration methods and well-defined properties of quantum circuits need to be developed.

[0008] Accordingly, there is a need in the field of MIM junctions as well as quantum devices with applications in quantum computing for development of versatile designs and solutions, which at least address some of the above-mentioned drawbacks.

[0009] SUMMARY

[0010] It is accordingly an object of the present invention to improve the current state of the art and to mitigate at least some of the above mentioned drawbacks.

[0011] These and other objects are achieved by providing a method, a system and an apparatus for tuning an operational resistance of one or more MIM junctions as defined in the appended independent claims. The term exemplary is in the present context to be understood as serving as an instance, example or illustration.

[0012] According to a first aspect of the present disclosure, there is provided a method for tuning an operational resistance of one or more, metal-insulator-metal, MIM, junctions. The method comprises determining if a first characteristic resistance of a certain MIM junction comprised in the one or more MIM junctions is below a predetermined MIM junction resistance threshold value. In an instance that the first characteristic resistance of that certain MIM junction is determined to fall below the predetermined MIM junction resistance threshold value, the method further comprises tuning the first characteristic resistance of that MIM junction to a second characteristic resistance by trimming that MIM junction by means of applying a first electrical signal to that MIM junction. Further, the method comprises determining if the second characteristic resistance of that MIM junction corresponds to the predetermined MIM junction resistance threshold value.

[0013] Accordingly, the present inventors have realized that by injecting electrical energy e.g. by means of injecting an electrical current signal through the MIM junctions, the characteristic resistance of the MIM junctions will increase. Since the MIM resistance can be measured and calibrated concurrently, a closed feedback loop can be utilized to tune the operational resistance of the MIM junctions and thus achieve the intended operational resistance.

[0014] In some exemplary embodiments, the first electrical signal may comprise a first waveform having one or more tuning amplitudes and one or more tuning periods. Accordingly, the method may further comprise applying the first electrical signal to the MIM junction for one or more tuning rounds, each tuning round having a respective first waveform.

[0015] Accordingly, tuning rounds may have waveform characteristics, predetermined amplitudes, cycle durations, etc. which may be modified adaptively, thus making the tuning process controllable and notably accurate.

[0016] According to some aspects and embodiments, the method may further comprise determining if the second characteristic resistance of the certain MIM junction is below the predetermined MIM junction resistance threshold value. In an instance that the second characteristic resistance of that MIM junction is determined to fall below the predetermined MIMjunction resistance threshold value, the method may further comprise trimming that M IM junction by means of applying the first electrical signal to that MIM junction.

[0017] In various exemplary embodiments, wherein the first electric signal may at least be associated with a predetermined control voltage or power set to be smaller than a corresponding predetermined breakdown voltage or power of the one or more MIM junctions.

[0018] In some exemplary embodiments, the first electric signal may at least be associated with the predetermined control voltage and power.

[0019] This way it is ensured that the energy can be pumped into the junction for tuning the operational resistance without jeopardizing structural or operational integrity of the MIM junctions.

[0020] In several exemplary embodiments, wherein the method may further comprises determining the first characteristic resistance of each MIM junction and / or the second characteristic resistance of the certain MIM junction at least by measuring the first and / or second characteristic resistance by means of applying a second electrical signal to each respective MIM junction for one or more measurement rounds.

[0021] In some exemplary embodiments, the method may further comprise determining, by applying the second electrical signal, the second characteristic resistance of the certain MIM junction concurrently during a tuning round of the one or more tuning rounds, or at a measurement round of the one or more measurement rounds during which applying the first electrical signal to that MIM junction may be paused. In several aspects and embodiments, each MIM junction may comprise a superconductor-insulator- superconductor junction.

[0022] In several aspects and embodiments, the one or more MIM junctions may be comprised in one or more respective qubit junctions of one or more superconductor qubits.

[0023] As mentioned earlier MIM junctions have several applications in different fields of technology and may e.g. be comprised in rectifier diodes, local oscillators or magnetic tunnel junctions. Similarly, SIS junctions find additional applications for superconducting quantum interference devices (SQUID), superconducting quantum computers (Qubits), voltage references, as well as rapid single flux quantum devices (RSFQ).

[0024] In several aspects and embodiments, the method may further comprise cooling the one or more MIM junctions, having the first or the second characteristic resistance corresponding to the predetermined junction resistance threshold value, to a predetermined temperature set to preserve the first and the second characteristic resistance.

[0025] In several embodiments, the first electrical signal may be applied to that MIM junction via a galvanic contact.

[0026] According to a second aspect of the present disclosure, there is provided a computer- readable storage medium comprising instructions which, when executed by one or more processors, causes the one or more processors to carry out at least some of the embodiments of the methods herein.

[0027] According to a third aspect of the present disclosure, there is provided a computer program product comprising instructions which, when the program is executed by one or more processors, causes the one or more processors to carry out at least some of the embodiments of the methods herein.

[0028] According to a fourth aspect of the present disclosure, there is provided a system for tuning an operational resistance of one or more metal-insulator-metal, MIM, junctions. The system comprises signal application means configured for applying a first electrical signal and / or a second electrical signal to a respective MIM junction of the one or more MIM junctions. The system further comprises processing circuitry configured for determining if a first characteristic resistance of a certain MIM junction is below a predetermined MIM junction resistance threshold value. In an instance that the first characteristic resistance of that MIM junction is determined to fall below the predetermined MIM junction resistance threshold value, the processing circuitry is further configured for tuning the first characteristic resistance of that MIM junction to a second characteristic resistance by trimming that MIM junction by applying the first electrical signal to that MIM junction by means of the signal application means. Furthermore, the processing circuitry is configured for determining if the second characteristic resistance of that MIM junction corresponds to the predetermined MIM junction resistance threshold value.

[0029] According to a fifth aspect of the present disclosure, there is provided an apparatus for tuning an operational resistance of one or more metal-insulator-metal, MIM, junctions, the apparatus comprising at least one tuning module, wherein the at least one tuning module comprises the system according to any one of the embodiments of the system of the fourth aspect.

[0030] Further features and advantages of the invention will become apparent when studying the appended claims and the following description. The skilled person in the art realizes that different features of the present disclosure may be combined to create embodiments other than those explicitly described hereinabove and below, without departing from the scope of the present disclosure.

[0031] Further embodiments of the different aspects are defined in the dependent claims.

[0032] It is to be noted that all the embodiments, elements, features and advantages associated with the first aspect also analogously apply to the second, third, fourth and the fifth aspects of the present disclosure.

[0033] These and other features and advantages of the present disclosure will in the following be further clarified in the following detailed description.

[0034] BRIEF DESCRIPTION OF DRAWINGS

[0035] Further objects, features and advantages of embodiments of the disclosure will appear from the following detailed description, reference being made to the accompanying drawings. The drawings are not to scale.

[0036] Fig. la shows a cross-sectional side view of an exemplary MIM junctions according to several embodiments of the present disclosure. Fig. lb shows a circuit comprising a MIM junction according to several embodiments of the present disclosure.

[0037] Fig. 2a show a MIM junction tuning setup according to several embodiments of the present disclosure.

[0038] Fig. 2b shows an array of MIM junctions according to several embodiments of the present disclosure.

[0039] Figs. 3-5 show exemplary graphs according to several embodiments of the present disclosure.

[0040] Fig. 6 shows a flowchart of a method according to several embodiments of the present disclosure.

[0041] DETAILED DESCRIPTION

[0042] In the present detailed description, embodiments of the present disclosure will be discussed with the accompanying figures. In the following description of exemplary embodiments, the same reference numerals denote the same or similar components. It should be noted that the person skilled in the art will understand that the invention may be practiced without these details and in any other types or variants of the elements or features than the embodiments shown in the appended drawings.

[0043] The following description may use terms such as "top", "bottom", "inner", "outer", "side", "edge", "ridge", "distal", "proximal", "front", "back" etc. These terms generally refer to the views and orientations as shown in the drawings. The terms are used for the reader's convenience only and shall not be construed as limiting.

[0044] It is also to be understood that the terminology used herein is for purpose of describing particular embodiments only, and is not intended to be limiting. It should be noted that, as used in the specification and the appended claim, the articles "a", "an", "the", and "said" are intended to mean that there are one or more of the elements unless the context clearly dictates otherwise. Thus, for example, reference to "a unit" or "the unit" may refer to more than one unit in some contexts, and the like. Furthermore, the words "comprising", "including", "containing" do not exclude other elements or steps. It should be emphasized that the term "comprises / comprising" when used in this specification is taken to specify the presence of stated features, integers, steps, or components. It does not preclude the presence or addition of one or more other features, integers, steps, components, or groups thereof. The term "and / or" is to be interpreted as meaning "both" as well and each as an alternative. The term "obtaining" is herein to be interpreted broadly and encompasses receiving, retrieving, collecting, acquiring, and so forth.

[0045] It will also be understood that, although the term first, second, etc. may be used herein to describe various elements or features, these elements should not be limited by these terms. These terms are only used to distinguish one element from another.

[0046] Various aspects of the disclosure will hereinafter be described in conjunction with the appended drawings to illustrate and not to limit the disclosure, wherein like designations denote like elements, and variations of the described aspects are not restricted to the specifically shown embodiments, but are applicable on other variations of the disclosure.

[0047] As mentioned earlier, in practice, the fabrication process of the MIM junctions is subject to both on wafer and wafer-to-wafer variations, which is reflected as variations in the room temperature resistance of the MIM junctions compared to the desired design target room temperature resistances. In some exemplary embodiments, MIM junctions may also be utilized as MIM diodes. The MIM junctions may be designed for certain applications e.g. high frequency applications having specific and precise operational frequency characteristics. For instance, in some examples and embodiments, the MIM junctions may be comprised in superconductive qubits. Superconducting qubits can be regarded as resonators consisting of a well-defined capacitance and a nonlinear inductance which are designed for operating in a precise resonance frequency. The inductance of the qubits is typically achieved by the qubit junction which may in several example embodiments disclosed herein comprise the MIM junctions. The MIM junctions in turn may comprise superconductor-insulator- superconductor (SIS) junctions. . It is imperative to achieve the precise qubit-frequency, i.e., the resonance frequency for which the qubit is designed and intended to be operated, with tolerances as small as possible. The reported fabrication processes are not able to deliver this level of precision, and thus a post-fabrication calibration of the junction resistance and thereby qubit-frequency is typically required. To verify whether a MIM junction will perform according to the expectations and the designed target resonance frequency, a corresponding room temperature resistance of the MIM junction may be measured.

[0048] Conventionally, calibrating the resistance of MIM junctions for quantum devices have been achieved by heating the whole wafer or quantum chip on a hot plate after fabrication of the qubits. In this approach all junctions will be heat-treated in the same way and no individual tuning of the resistance is possible.

[0049] In another conventional approach, laser-heating of the qubit junctions is carried out. A green laser may be focused on the area around the junction to heat it indirectly. However, the optical setup and application of laser light to the junctions is complex, tedious and expensive.

[0050] With increasing device complexity and numbers of MIM junctions which may be present in a device for the intended exemplary applications such as the quantum devices or other high frequency devices comprising the MIM junctions, demand of well-calibrated MIM junctions will increase drastically. By providing an efficient, flexible, and easy to implement solution for this demand according to the present disclosure enormous amounts of time and resources can be utilized in a significantly more efficient manner. In comparison to the conventional approaches, the proposed solution herein is flexible, and scalable. Furthermore, a parallel production approach is proposed that enables addressing every MIM junction comprised in a plurality of MIM junctions individually and / or simultaneously.

[0051] Fig. la shows a schematic cross-sectional side view illustration of a MIM junction 1 according to several embodiments and aspects herein. The MIM junction 1 may be fabricated with any methods and fabrication processes such as material evaporation, deposition, etching or lithography patterning techniques known in the art. In some exemplary embodiments, one or more MIM junctions 1 may be comprised in one or more respective qubit junctions of one or more superconductor qubits. In several aspects and embodiments herein, each MIM junction 1 may comprise a superconductor-insulator-superconductor (SIS) junction. The skilled person is fully informed that depending on the intended applications, the MIM junction 1 may be referred to as the SIS 1 junction for which the following elements, features, fabrication processes and functional advantages are equally applicable. In several exemplary embodiments, a SIS junction may be a Josephson junction 1.

[0052] More specifically, a MIM junction 1 is a collection of material combinations that include variations wherein a metallic layer is arranged on either side of an insulating barrier as shown in Fig. la and explained in more detail further below. In exemplary applications of using the MIM junctions 1 in quantum circuits and devices, it is known in the art that these devices operate at designated operation states e.g. in cryogenic temperature conditions at which the metallic components of the MIM junction 1 of the junction may assume superconductor characteristics in the so called SIS junctions 1. In several aspects and embodiments, the MIM junction structure 1 comprises aluminium - aluminium oxide - aluminium combination. The proposed methods and systems for tuning and calibration of the MIM junctions 1 herein may be adapted to room temperature conditions. The terms tuning and calibration may be used interchangeably in the rest of this description and are to be construed broadly and pertain to alterations and modifications made to an element or feature such as a characteristic resistance of a MIM junction 1 in order to adjust that resistance to a desired or target operational resistance for the MIM junction 1. In several aspects and embodiments herein, one or more functionalities of the proposed solutions may be carried out by a system comprising processing circuitry.

[0053] The mentioned MIM junction 1 comprises a first metallic layer 11 being made of a first metal. The metal in several embodiments may be aluminium (Al). The Al layer 11 may constitute a first metallic electrode layer 11 of the qubit junction 1. The fabrication process may make use of a silicon (Si) wafer as substrate 200. The Al layer 11 may be deposited on the Si substrate 200 using any known fabrication method in the art. The MIM junction 1 further comprises an insulator barrier 12 which may also be referred to as a metal oxide layer 12.The insulator barrier 12 may simply be referred to as the barrier 12 or the oxide barrier 12.The insulator barrier 12 may be Al-oxide. The MIM junction 1 may further comprise a second metallic layer 13, which in several examples may be an Al-layer 13 constituting a second metallic electrode layer 13. The first metallic electrode 11 may be referred to as the bottom electrode 11 and the second metallic electrode layer may be referred to as the top electrode 13. The barrier 12 may be configured to limit the tunnelling of a current through the MIM junction 1, which means that the thickness of the barrier 12 may determine the resistance "R" through the MIM junction 1. The present inventors have realized that when energy e.g. by means of an injected current is injected through the MIM junction 1, the structure of the MIM junction 1 is trimmed locally, which in turn leads to evening-out the barrier 12, which usually has an uneven morphology after the manufacturing steps. The step of trimming as disclosed in the embodiments herein advantageously provides a more uniform barrier 12 thickness. With fewer thin points across the barrier 12 as a result of the proposed trimming method, the resistance "R" through the barrier 12 is judged such that the operational resistance of the MIM junction 1 is increased. It has also been realized by the present inventors that the barrier 12 in case of being an oxide layer 12 may eventually be restructured to a higher order of oxide (e.g. gamma AIO), which will contribute to the increase in the MIM junction resistance.

[0054] In some examples, the step of trimming increases the operational resistance of the MIM junction by at least 5%. In some of these examples, the operational resistance increases by at least 10%, at least 20%, or at least 30%.

[0055] It is to be understood that the impact of trimming is dependent on the properties of the MIM junction being trimmed, such as its insulator thickness or the amount of oxides at the insulator. An exhaustive list of MIM junction designs and the expected impact of trimming said junctions is beyond the purview of this description.

[0056] Fig. lb is an illustration of the MIM junction 1 incorporated in a construction or an exemplary circuit, which may be referred to as a butterfly cell 100 hereinafter. The butterfly cell 100 comprises a butterfly pattern including two contact wings 101 and 102 extending opposite each other. The butterfly cell 100 further comprises a central portion 103 depicted in the solid square which indeed comprises the core MIM junction 1, a scanning electron microscopy (SEM) image of which is also depicted in Fig. lb circumvented with the same solid square 103.

[0057] Accordingly, there is provided a process for tuning an operational resistance of one or more, MIM, junctions 1 as depicted in Fig. lb. In several embodiments of the methods and systems herein, it is determined if a first characteristic resistance of a certain MIM junction 1 is below a predetermined MIM junction resistance threshold value. The certain MIM junction 1 may be comprised in one or more MIM junctions as shown in Fig. 2b. The one or more MIM junctions 1 in Fig. 2b may be incorporated into an intended device or circuit such as a quantum circuit or a quantum device comprising a plurality of quantum circuits. In an instance that the first characteristic resistance of that certain MIM junction 1 is determined to fall below the predetermined MIM junction resistance threshold value, that MIM junction 1 is trimmed by means of applying a first electrical signal to that MIM junction 1. In several embodiments, the first electrical signal is applied to the MIM junction under tuning via a galvanic contact. For instance, the exemplary MIM junction la and MIM junction lb are shown in Fig. 2b. The MIM junction la is determined to have an operational resistance substantially corresponding to the predetermined MIM junction resistance threshold value. However, the MIM junction lb is determined to have an operational resistance which falls below the predetermined MIM junction resistance threshold value and thus will undergo a tuning procedure. The predetermined MIM junction resistance threshold value in several aspects and embodiments may be the junction resistance value, which is associated with the designed and intended operation of the MIM junctions. For instance, in several aspects and embodiments, the characteristic resistance of the MIM junctions 1 may be associated with a precise and specific resonance frequency e.g. of a qubit comprising the MIM junctions 1. Accordingly, the predetermined MIM junction resistance threshold value may be the junction resistance value, which is associated with the intended resonance frequency for which the MIM junctions 1 are designed. Moving on, the first characteristic resistance of that certain MIM junction falling below the junction threshold value is tuned to a second characteristic resistance by means of trimming the certain MIM junction 1 according to several embodiments herein. Further, it is determined after the first trimming is applied to the certain MIM junction e.g. MIM junction lb, if the second characteristic resistance of that MIM junction lb corresponds to the predetermined MIM junction resistance threshold value. In other words, certain MIM junctions amongst a plurality of MIM junctions may be selected based on measured respective characteristic resistances and individually trimmed until the intended operational resistance corresponding to the intended MIM junction resistance threshold value is obtained. Stated differently, the operational resistance of the MIM junction are tuned by applying the first electrical signal to the junctions, trimming the junctions, determining the resulting resistance and continuously performing the tuning process until the desired operational resistance is achieved.

[0058] The term trimming relates to adjusting specific properties of the insulator layer to optimize device performance. Typically, trimming involves adjusting insulator thickness, surface roughness, and / or dielectric constant of the insulator.

[0059] In some examples, trimming the MIM junction 1 comprises driving an oxidation at said junction by applying the first electrical signal, such as applying an electric field over said junction.

[0060] In several aspects and embodiments herein, the first electrical signal may have a first waveform having one or more tuning amplitudes and one or more tuning periods. In several exemplary embodiments, the waveform may include an electrical signal e.g. a voltage or current signal having a constant amplitude applied to the MIM junctions for a certain duration. In several embodiments waveform may include pulsed signals having one or more amplitudes, and one or more cycles i.e. tuning periods. The waveform may alternatively or additionally include sweeping signals, various pulse shapes such as jigsaw or any other suitable pule shape, and be applied in one or more time intervals. The waveform may be a DC, AC or RF signal. In several aspects and embodiments, the first electrical signal may be applied to the MIM junctions for one or more tuning rounds, each tuning round having a respective first waveform. Stated differently, tuning rounds may have waveform characteristics, predetermined amplitudes, cycle durations, etc. which may be modified adaptively. By a tuning round in the present context is it to be understood a tuning instance or episode.

[0061] The waveform of the first electrical signal may also be applied in one or more predetermined time intervals. During at least some of the intervals, application of the first signal may be paused to introduce a rest period to the junctions such that the applied energy is dissipated from the junctions before application of another tuning round.

[0062] In some examples and embodiments, the entire tuning duration of each tuning round may correspond to a duration of the waveform of the first signal applied in that round. Alternatively, or additionally, in at least some of the one or more tuning rounds, each tuning round may comprise application of a waveform having one or more tuning cycles. Accordingly, each tuning cycle may have a predetermined tuning duration and one or more tuning amplitude values.

[0063] The trimming of the certain MIM junctions lb may be performed by applying the first electrical signal to the MIM junction lb at a predetermined tuning amplitude value. For instance, the first electric signal may comprise a direct (DC) or alternating (AC) current signal. The first electrical signal may be an RF signal. The first electrical signal may be a pulsed signal. The current signal may be applied by means of an exemplary current source 110 as shown in Fig. 2a.

[0064] Accordingly, the present inventors have realized that by injecting electrical energy e.g. by means of injecting the sufficient electrical signal above a predetermined threshold value through the MIM junctions, the characteristic resistance of the MIM junctions will increase. The injected power through the MIM junctions may in some examples be applied above a lower power limit determined for the resistance tuning to take effect. This effect could be attributed to the resistive heating that in turn rearranges or grows the oxide layer 12 in between the metal contacts 11 and 13 in the MIM junction, leading to the increase of the MIM resistance. Since the MIM resistance can be measured and calibrated concurrently, a closed feedback loop can be utilized to achieve a defined operational resistance above the initial resistance of the MIM junction.

[0065] In some exemplary embodiments, the waveform of the first signal applied to the MIM junction lb may comprise sweeping the first electrical signal over a range of one or more tuning amplitude values comprised between a first and a second predetermined tuning amplitude value as mentioned earlier.

[0066] In several embodiments, the first electrical signal e.g. the DC or AC current is applied to the MIM junction lb under tuning for one or more tuning rounds, each tuning round having a predetermined tuning duration. In other words, a current or a voltage waveform of a certain amplitude can be applied to the MIM junction lb for a certain period of time in order to trim the MIM junction lb.

[0067] In several embodiments, steps of measurement and calibration of the operational resistance of MIM junctions disclosed herein may be performed by means of a so-called 4 point measurement approach. It should be appreciated that any suitable number of probes or points as well as other measurement and calibration approaches known in the art may be used. The electrical signals disclosed herein i.e. first and / or second electrical signals as will become apparent in the following, may in several embodiments be applied to the MIM junctions via galvanic contacts. The first and / or second electrical signals may in several embodiments be applied to the MIM junctions via one or more probes, wherein at least one probe may be configured to galvanically contact the MIM junctions.

[0068] At least one probe e.g. probes 104 - 107 from a tuning apparatus (not specifically shown) may be configured to galvanically contact the two contact wings 101 and 102 of the butterfly cell 100 at either side of the butterfly pattern. For instance, as shown in Fig. 2a, probes 104, 105 are connected to the wing 101 at its respective left and right sides and probes 106, 107 are analogously connected to the wing 102.

[0069] In several aspects and embodiments, the first electric signal may at least be associated with a predetermined control voltage, wherein the control voltage may set to be smaller than a predetermined breakdown voltage of the one or more MIM junctions. In some embodiments, the first electric signal may further be associated with a predetermined threshold power of the one or more MIM junctions which is smaller than the power required for causing a junction breakdown. It should be appreciated by the skilled person that some of the MIM junctions comprised in the one or more MIM junctions may have certain physical characteristics such as different junction overlap area or barrier thickness. Accordingly, the breakdown voltage and / or the threshold power of the one or more MIM junctions may be associated with the respective physical characteristics of the MIM junctions which may be vary among the MIM junctions. In some examples, the one or more MIM junctions 1 may comprise several groups of MIM junctions, each group being designed with its respective physical and operational characteristics.

[0070] In some examples, the one or more MIM junctions have a breakdown voltage in the range of IV to 1.2V. In some of these examples, the one or more MIM junctions have a breakdown voltage in the range of 1.05V to 1.15V. In some examples, the first electric signal is arranged to cause at most a 1.2V potential across the one or more MIM junctions.

[0071] In several embodiments and aspects, the first characteristic resistance of each MIM junction

[0072] 1, la and / or the second characteristic resistance of the certain MIM junction lb may be determined by measuring the first and / or second characteristic resistance by means of applying a second electrical signal to each respective MIM junction 1, la, lb. In several exemplary embodiments, the measured resistances of the MIM junctions are compared with tabular data denoting the intended operational resistances and any differences may be recorded to be used during a subsequent tuning procedure. The tabular data may be continuously updated based on adaptive tuning and measurement data. In some exemplary embodiments, analogous to the first electrical signal, the second electrical signal may have a second waveform having one or more measurement amplitudes and one or more measurement periods e.g. measurement cycles.

[0073] In several embodiments, determination of the first characteristic resistance i.e. the initial characteristic resistance of the MIM junctions or determining the second characteristic resistance of the MIM junction under tuning e.g. MIM junction lb at any given point during the calibration may be carried out using the second electrical signal applied by means of a galvanic contact. The second electrical signal should be applied in such a way that it does not change the resistance characteristics of the MIM junctions. In other words, measuring the resistance of the MIM junctions according to the proposed solution is carried out such that it does not affect the characteristics of the barrier layer 12 in the MIM junction and neither the resistance of the MIM junctions. In several exemplary embodiments, determining, by applying the second electrical signal, the second characteristic resistance of the certain MIM junction may be carried out concurrently during a tuning round. Additionally or alternatively, the second characteristic resistance of the certain MIM junction may be measured and determined at a measurement round during which applying the first electrical signal to that MIM junction is paused. In some embodiments, the second signal may be the same as the first signal or the first signal may be utilized as the second electrical measurement signal. The junction resistance may accordingly be determined and calculated based on the readouts from the MIM junctions in response to applying the first signal. In several embodiments, the first electrical signal may be applied to the MIM junction lb at one or more predetermined time intervals as mentioned earlier. Stated differently, the first electrical signal may be applied to the MIM junction lb at a first instance having a respective duration. The application of the first electrical signal to the MIM junction lb may be subsequently paused. The application of the first electrical signal to the MIM junction lb may be subsequently resumed after the duration of the pause. In several embodiments, the second electrical signal, may be applied to the MIM junction lb during at least one time interval, comprised in the one or more predetermined time intervals, during which applying the first electrical signal to the MIM junction is paused. This way the characteristic resistance of the MIM junction lb under tuning may be repeatedly measured, determined, characterized and tuned until the intended operational resistance is attained for that specific MIM junction lb. Further, by introducing rest periods, due care is taken such that the junctions will not be overloaded by constant application of the tuning signal.

[0074] In several embodiments and aspects, it may be determined if the second characteristic resistance of the certain MIM junction e.g. the MIM junction lb under tuning is still below the predetermined MIM junction resistance threshold value after application of the first electric signal. In an instance that the second characteristic resistance of that MIM junction is determined to fall below the predetermined MIM junction resistance threshold value, that MIM junction lb will be further trimmed by means of applying the first electrical signal to that MIM junction lb. Stated differently, the MIM junction having a characteristic resistance which does not correspond to the intended resistance undergoes the tuning or calibration procedure continuously, until the intended operational resistance for that MIM junction lb is achieved. Thus, the present inventors have realized that by forming a feedback loop comprising at least one measurement of the characteristic resistance of the MIM junction lb, and at least one tuning step of the characteristic resistance of the MIM junction lb, the characteristic resistance of the MIM junction lb can be adaptively tuned. Consequently, the intended operational resistance for that MIM junction lb can be advantageously attained. In several embodiments, the feedback loop may be applied in the mentioned adaptive manner, wherein the differences between the measured resistance i.e. the first and / or the second resistances of the MIM junctions and the target operational resistance would eventually determine the shape, type, waveform, amplitude and duration of the first electrical signal being applied in the next calibration instance or round. Stated differently, based on the outcome of the determination of the characteristic resistance of the MIM junction lb e.g. after respective measurement rounds, the subsequent tuning steps, if required, would be adapted accordingly. An advantage of this approach is that, always the appropriate amount of energy needed to tune the characteristic resistance to the intended operational resistance will be delivered to the MIM junctions accurately and in a controlled manner. Accordingly, issues such as overloading the junctions e.g. by exceeding junction breakdown voltage or power will be eliminated.

[0075] In several embodiments, the tuning apparatus (not specifically shown) may comprise signal application means such as probes which may comprise 20, 40, 80, 160 or any appropriate number of probes or groups of probes, configured for both tuning and measurement of the characteristic resistances of one or more M IM junctions 1 individually or in parallel. In several embodiments the tuning apparatus may comprise at least one tuning module, wherein the at least one tuning module comprises the probes for both tuning and measurement of the characteristic resistances of one or more MIM junctions 1 individually or in parallel.

[0076] In several embodiments, signal application means may comprise one or more signal injector probes configured for applying the first electrical signal to the respective MIM junction of the one or more MIM junctions. In several embodiments, signal application means may further comprise one or more measurement probes configured for applying the second electrical signal to the respective MIM junction of the one or more MIM junctions. In several embodiments, the same probes may be utilized for both functionalities as signal injector probes and the measurement probes.

[0077] In some exemplary embodiments, the tuning apparatus may be a SMU instrument (source / measure unit) placed in parallel via a switch (not specifically shown) that selects which probes of the tuning module are activated. The switch may switch the SMUs to various butterfly cells 100a - lOOn (for "n" MIM junctions la-ln comprised in an intended device, both "a" and "n" being real number used simply to denote an exemplary number of butterfly cells or circuits) as shown in Fig. 2b.

[0078] The tuning apparatus may be configured for measuring the MIM junctions in parallel e.g. after measuring or tuning a first group of MIM junctions, the probes may be moved over to perform the same procedures on a second, third, fourth or more groups of butterfly cells 100a - lOOn comprising the respective MIM junctions.

[0079] The measurement and tuning instances may comprise intervals of injecting the first electrical signal to the certain MIM junctions and subsequent measurement of the resistance of those MIM junctions by means of the second electrical signal. For instance, the initial resistance of the MIM junction lb in circuit 100b in Fig. 2b may be measured by injecting a measurement current i.e. the second electrical signal having an exemplary amplitude between -1 pA to +1 pA. In some exemplary embodiments, the measurement current may be swept between -1 pA to +1 pA in measurement cycles having 0.1 pA incrementing steps. Either of the first or second electrical signals may be associated with a control voltage which may be set to be smaller than a threshold voltage corresponding to a predetermined breakdown voltage of the MIM junctions. In some examples the threshold voltage smaller than the breakdown voltage may be 0.8V, 0.85V, 0.9V, IV or similar and may be set as a design parameter based on the intended implementations and applications. Thus, the injected measurement current or the injected tuning current may be limited if the resulting voltage across the MIM junction should exceed the threshold voltage. The threshold voltage may be a design parameter associated with a thickness of the MIM junctions e.g. the thickness of the oxide layer 12 of the MIM junctions.

[0080] Each individual measurement waveform e.g. in the current sweep measurement cycles may have a predetermined duration e.g. 10 ms, 20 ms, 30 ms or the like. In several embodiments, the waveforms of the measurement or tuning instances may comprise more than one measurement or tuning cycles e.g. 10 cycles, 100 cycles, 1000 cycles, etc. Each cycle may have the same duration or amplitude. In some embodiments, the duration or amplitude of cycles may be different. It should be appreciated that the amplitude and / or duration of the second electrical signal e.g. the measurement current is configured such that the characteristic resistance of the MIM junctions will be unaffected by the resistance measurement and determination. The skilled person would readily realize that the above- mentioned amplitude values, number of cycles, cycle durations or waveform characteristics are merely non-limiting examples for further elucidating various aspects of the presented technology herein.

[0081] Similarly, in various embodiments, the first electrical signal e.g. a calibration or tuning current may be injected into the MIM junctions e.g. MIM junction lb via the contacts 101 and 102 of the butterfly cell 100 and by means of the probes e.g. probes 104 - 107. The tuning current may have an exemplary amplitude between 100 pA to 1 mA as the first and the second predetermined tuning amplitude values and be injected in one or more tuning rounds having a specific duration e.g. 100ms, 500ms, Is, 10s, 60s, and so forth. In some embodiments, the tuning current may be swept in one or more tuning cycles between the exemplary amplitudes 100 pA to 1 mA with 100 pA steps.

[0082] Similarly, the tuning current may be associated to the breakdown voltage or maximum power tolerable by the MIM junctions, wherein it is ensured that the breakdown values will not be exceeded by the injected tuning currents.

[0083] Fig. 3 shows an exemplary graph 300 illustrating the results of characterizing the breakdown voltage for MIM junctions having various exemplary sizes or footprints e.g. 100 nm, 150 nm, 200 nm, 250 nm, 300 nm, 350 nm, 400 nm, 450 nm, and so forth. Test current sweeps having exemplary amplitudes between 10 pA - 1 mA are injected into the MIM junctions. Based on the characterization results, the present inventors have realized that an exemplary maximum breakdown voltage threshold around IV may be an experimentally validated benchmark to be followed during the tuning and measurement processes for tuning the operational resistances of the MIM junctions. However, it should be appreciated that the maximum breakdown voltage threshold value may be adjusted accordingly as a design parameter based on the respective MIM junctions.

[0084] Fig. 4 shows an exemplary graph 400 depicting results of a first example attempt for tuning the resistance of several MIM junctions by applying the first electrical signal having an exemplary waveform including a current sweep according to a first tuning procedure of the present disclosure. Between measurement intervals 1 - 2, 2 - 3, 4 - 5, 5 - 6, 6 - 7, 8 - 9 and 9 - 10, so-called calibration or tuning current sweeps were performed on the MIM junctions, which are represented by the boxes 401 - 407 at the bottom of the graph. The calibration sweep is performed wherein the tuning current is varied from exemplary values lOOpA to lOOOpA where each step was held for an exemplary cycle duration of 10, 100, 1000 or 2000 ms. Different curves represent the response of MIM junctions having different sizes as stated above. Some of the junctions, which have experienced a breakdown during the calibration process have been depicted.

[0085] Each applied waveform included a certain number of cycles that are repeated and applied at a certain voltage limitation i.e. the voltage smaller than the breakdown voltage of the MIM junctions. These parameters together determine the energy that the MIM junctions are exposed to, the duration of tuning i.e. the amount of energy pumped into the MIM junctions and whether the MIM junctions are allowed a rest period between the tuning cycles. In this example embodiment, the initial V-threshold is set to 0.8V < 1.095V experimentally discovered breakdown voltage value in Fig. 3. The V-threshold can then be modified to 0.9 and 0.95 V in a stepwise manner. For instance, box 401 represents 100 cycles of 10 ms duration at a control voltage of 0.8 v, box 405 represents 100 cycles of 1000 ms duration at a control voltage of 0.95 v and so forth.

[0086] The present inventors realized that it is the pumped amount of energy into the MIM junctions which may play an important role in tuning the operational resistance of the MIM junctions.

[0087] In a second exemplary tuning procedure depicted in the exemplary graph 500 in Fig. 5, the tuning current sweep is introduced such that the number of cycles of the waveform injecting the tuning current signal is modified. For instance in one example, from box 501 to box 502 for measurement interval 2 - 3, the number of cycles were increased from 100 cycles having a duration of 100 ms to 1275 cycles having the same duration of 100 ms for each cycle and a control voltage at 0.85 V.

[0088] Boxes 503, 504, and 505 have exemplary parameters e.g. 100 cycles of 100 ms, voltage 0.9 V; 100 cycles of 200 ms, voltage 0.9 V; and 100 cycles of 500 ms, voltage 0.9 V respectively. Similar to Fig. 4, different curves represent the response of MIM junctions having different sizes as stated above. Some of the junctions, which have experienced a breakdown during the calibration process have been depicted.

[0089] With this approach a nearly 30% increase could be applied to the characteristic resistances of the MIM junctions and the intended operational resistances could be attained accordingly.

[0090] Fig. 6 shows a flowchart of a method 600 according to several embodiments and aspects of the present disclosure. The method 600 for tuning an operational resistance of one or more metal-insulator-metal, MIM, junctions, comprises determining 601 if a first characteristic resistance of a certain MIM junction comprised in the one or more MIM junctions is below a predetermined MIM junction resistance threshold value. The method further comprises, in an instance that the first characteristic resistance of that certain MIM junction is determined 603 to fall below the predetermined MIM junction resistance threshold value: tuning 607 the first characteristic resistance of that MIM junction to a second characteristic resistance by trimming 605 that MIM junction by means of applying a first electrical signal to that MIM junction. The method further comprises determining 609 if the second characteristic resistance of that MIM junction corresponds to the predetermined MIM junction resistance threshold value.

[0091] In some exemplary embodiments, the first electrical signal may comprise a first waveform having one or more tuning amplitudes and one or more tuning periods. The method may further comprises applying 611 the first electrical signal to the MIM junction for one or more tuning rounds, each tuning round having a respective first waveform.

[0092] In some embodiments, the method may further comprise applying the waveform of the first electrical signal to the MIM junction in one or more predetermined time intervals.

[0093] In several embodiments, the method may further comprise applying the first electrical signal to the MIM junction for one or more tuning rounds, each tuning round having a predetermined tuning duration.

[0094] In some exemplary embodiments, each of the one or more tuning rounds may comprise application of a waveform having one or more tuning cycles, each cycle having a predetermined tuning duration and a respective one or more tuning amplitude values.

[0095] According to several embodiments, the method may further comprise determining 613 if the second characteristic resistance of the certain MIM junction is below the predetermined MIM junction resistance threshold value; and in an instance that the second characteristic resistance of that MIM junction is determined 615 (the alternative "YES" in the flowchart of Fig. 6) to fall below the predetermined MIM junction resistance threshold value, the method may further comprise trimming 617 that MIM junction by means of applying the first electrical signal to that MIM junction. In several embodiments, the shape, amplitude, duration, number of tuning instances and / or cycles of tuning by means of applying the first electrical signal for the subsequent tuning of the MIM junction still not meeting the intended resistance requirements, thus may be determined in an adaptive manner i.e. based on the determination step 613 of the MIM junction resistance. Accordingly, the waveform characteristics, predetermined amplitudes, cycle durations, etc. may be modified dynamically based on the junction resistance determinations and measurements. Consequently, if it is determined that the second characteristic resistance of the certain MIM junction corresponds (as a result of the trimming and resistance tuning process) to the predetermined MIM junction resistance threshold value i.e. the desired operational resistance value, the trimming and tuning process for that MIM junction is terminated 620. (Alternative "NO") in the flowchart of Fig. 6.

[0096] In several embodiments, the first electric signal may comprise a direct or alternating current signal.

[0097] In several embodiments, the first electric signal may at least be associated with a predetermined control voltage or power set to be smaller than a predetermined breakdown voltage or power of the one or more MIM junctions.

[0098] In some embodiments, the method may further comprise determining 619 the first characteristic resistance of each MIM junction and / or the second characteristic resistance of the certain MIM junction at least by measuring 619 the first and / or second characteristic resistance by means of applying a second electrical signal to each respective MIM junction for one or more measurement rounds. In some embodiments, the step of determining may further comprise any suitable analytical or numerical calculations which may be based on the performed measurements.

[0099] In some exemplary embodiments, the method may further comprise determining 621, by applying the second electrical signal, the second characteristic resistance of the certain MIM junction concurrently during a tuning round of the one or more tuning rounds. Alternatively or additionally, determining 621 the second characteristic resistance of the certain MIM junction may be performed at a measurement round of the one or more measurement rounds, during which applying the first electrical signal to that certain MIM junction may be paused.

[0100] In some embodiments, each MIM junction may comprise a superconductor-insulator- superconductor (SIS) junction. In several exemplary embodiments, a SIS junction may be a Josephson junction. In some embodiments, the one or more MIM junctions may be comprised in one or more respective qubit junctions of one or more superconductor qubits. Accordingly, tuning and calibrating the operational resistances of the MIM junctions corresponding to operational resonance frequencies of the qubits ensures that the qubits will operate in the intended precise resonance frequency.

[0101] In some exemplary embodiments, the method may further comprise cooling 623 the one or more MIM junctions, having the first or the second characteristic resistance corresponding to the predetermined junction resistance threshold value, to a predetermined temperature set to preserve the first and the second characteristic resistance. Cooling the one or more MIM junctions may be performed in a controlled manner i.e. in a controlled atmosphere which may be moisture free and / or oxygen free. Accordingly, when it is determined that the second characteristic resistance of the certain MIM junction corresponds (as a result of the trimming and resistance tuning process) to the predetermined MIM junction resistance threshold value i.e. the desired operational resistance value, the attained resistance value may be preserved by applying the cooling process. In some embodiments a cooling means configured for cooling the respective MIM junctions of the one or more MIM junctions, may be used. The Cooling means may comprise a thermoelectric cooling plate e.g. a Peltier plate, or liquid nitrogen cooling, or any other suitable cooling or freezing equipment known in the art.

[0102] In some aspects and embodiments, at least some of the embodiments of the methods described herein may be carried out by a computing device e.g. a computing device of the tuning apparatus comprising one or more processors. Thus, at least some of the embodiments may be computer-implemented method embodiments. Accordingly, there is provided a computer-readable storage medium comprising instructions which, when executed by one or more processors, causes the one or more processors to carry out at least some of the embodiments of the methods herein.

[0103] A computer program product is also provided, wherein the computer program product comprises instructions which, when the program is executed by one or more processors, causes the one or more processors to carry out at least some of the embodiments of the methods herein.

[0104] It will be appreciated that the above description is merely exemplary in nature and is not intended to limit the present disclosure, its application or uses. While specific examples have been described in the specification and illustrated in the drawings, it will be understood by those of ordinary skill in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the present disclosure as defined in the claims. Furthermore, modifications may be made to adapt a particular situation or material to the teachings of the present disclosure without departing from the essential scope thereof.

[0105] Therefore, it is intended that the present disclosure not be limited to the particular examples illustrated by the drawings and described in the specification as the best mode presently contemplated for carrying out the teachings of the present disclosure, but that the scope of the present disclosure will include any embodiments falling within the foregoing description and the appended claims. Reference signs mentioned in the claims should not be seen as limiting the extent of the matter protected by the claims, and their sole function is to make claims easier to understand.

Claims

CLAIMS1. A method for tuning an operational resistance of one or more, metal- insulator-metal, MIM, junctions, the method comprising: determining if a first characteristic resistance of a certain MIM junction comprised in the one or more MIM junctions is below a predetermined MIM junction resistance threshold value; and in an instance that the first characteristic resistance of that certain MIM junction is determined to fall below the predetermined MIM junction resistance threshold value: tuning the first characteristic resistance of that MIM junction to a second characteristic resistance by trimming that MIM junction by means of applying a first electrical signal to that MIM junction; determining if the second characteristic resistance of that MIM junction corresponds to the predetermined MIM junction resistance threshold value.

2. The method according to claim 1, wherein the first electrical signal comprises a first waveform having one or more tuning amplitudes and one or more tuning periods; and wherein the method further comprises: applying the first electrical signal to the MIM junction for one or more tuning rounds, each tuning round having a respective first waveform.

3. The method according to any one of claims 1 or 2, wherein the method further comprises: determining if the second characteristic resistance of the certain MIM junction is below the predetermined MIM junction resistance threshold value; and in an instance that the second characteristic resistance of that MIM junction is determined to fall below the predetermined MIM junction resistance threshold value: trimming that MIM junction by means of applying the first electrical signal to that MIM junction.

4. The method according to any one of claims 1 - 3 , wherein the first electric signal is at least associated with a predetermined control voltage or power set to be smallerthan a corresponding predetermined breakdown voltage or power of the one or more MIM junctions.

5. The method according to any one of the preceding claims, wherein the method further comprises: determining the first characteristic resistance of each MIM junction and / or the second characteristic resistance of the certain MIM junction at least by measuring the first and / or second characteristic resistance by means of applying a second electrical signal to each respective MIM junction for one or more measurement rounds.

6. The method according to claim 5, wherein the method further comprises: determining, by applying the second electrical signal, the second characteristic resistance of the certain MIM junction concurrently during a tuning round of the one or more tuning rounds, or at a measurement round of the one or more measurement rounds during which applying the first electrical signal to that MIM junction is paused.

7. The method according to any one of the preceding claims, wherein each MIM junction comprises a superconductor-insulator-superconductor junction.

8. The method according to any one of the preceding claims, wherein the one or more MIM junctions are comprised in one or more respective qubit junctions of one or more superconductor qubits.

9. The method according to any one of the preceding claims, wherein the method further comprises: cooling the one or more MIM junctions, having the first or the second characteristic resistance corresponding to the predetermined junction resistance threshold value, to a predetermined temperature set to preserve the first and the second characteristic resistance.

10. The method according to any one of the preceding claims, wherein the first electrical signal comprises any one of a direct, alternating, or RF voltage or current signal.

11. A system for tuning an operational resistance of one or more metal- insulator-metal, MIM, junctions, the system comprising: signal application means configured for applying a first electrical signal and / or a second electrical signal to a respective MIM junction of the one or more MIM junctions; wherein the system further comprises processing circuitry configured for: determining if a first characteristic resistance of a certain MIM junction is below a predetermined MIM junction resistance threshold value; and in an instance that the first characteristic resistance of that MIM junction is determined to fall below the predetermined MIM junction resistance threshold value: tuning the first characteristic resistance of that MIM junction to a second characteristic resistance by trimming that MIM junction by applying the first electrical signal to that MIM junction by means of the signal application means; and determining if the second characteristic resistance of that MIM junction corresponds to the predetermined MIM junction resistance threshold value.

12. The system according to claim 11, wherein the first electrical signal comprises a first waveform having one or more tuning amplitudes and one or more tuning periods; and wherein the processing circuitry is further configured for: applying the first electrical signal to that MIM junction for one or more tuning rounds, each tuning round having a respective first waveform.

13. The system according to any one of claims 11 or 12, wherein the first electrical signal is applied to that MIM junction via a galvanic contact.

14. The system according to any one of claims 11 - 13, wherein the one or more MIM junctions are comprised in one or more respective qubit junctions of one or more superconductor qubits.

15. The system according to any one of claims 11 - 14, wherein the system further comprises:a cooling means configured for cooling the respective MIM junctions of the one or more MIM junctions, having a first or second characteristic resistance corresponding to the predetermined junction resistance threshold value, to a predetermined temperature set to preserve the first and the second characteristic resistance.

16. The system according to any one of claims 11 - 15, wherein the signal application means comprises: one or more signal injector probes configured for applying the first electrical signal to the respective MIM junction of the one or more MIM junctions; or one or more measurement probes configured for applying the second electrical signal to the respective MIM junction of the one or more MIM junctions.

17. An apparatus for tuning an operational resistance of one or more metal- insulator-metal, MIM, junctions, the apparatus comprising at least one tuning module, wherein the at least one tuning module comprises the system according to any one of claims 11 - 16.

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