Physically unreplicable function element and cryptographic key generation device using the same

Abstract

This invention provides a physically non-replicable functional element and a cryptographic key generation device using the same. [Solution] The physically unreplicable functional element 100 includes a spin torque generating layer, a magnetization free layer, a tunnel barrier layer, a spacer layer, and an indirect exchange interaction layer. The spin torque generating layer generates a spin orbit torque when current flows in the in-plane direction. The magnetization free layer has perpendicular magnetic anisotropy. The indirect exchange interaction layer includes a first magnetic layer, a non-magnetic intermediate layer, and a second magnetic layer. Depending on the thickness of the non-magnetic intermediate layer, the magnetization direction between the first magnetic layer and the second magnetic layer is determined to be either parallel or antiparallel. When the magnetization direction of the indirect exchange interaction layer is antiparallel, the leakage magnetic fields of the first magnetic layer and the second magnetic layer cancel each other out, preventing switching of the magnetization free layer. When the magnetization direction of the indirect exchange interaction layer is parallel, the leakage magnetic fields mutually reinforce each other, allowing switching of the magnetization free layer to occur.

Description

[Technical Field]

[0001] [Cross-Reference to Related Applications] This application claims the benefit of priority based on Korean Patent Application No. 10-2025-0026634 filed on February 28, 2025 and Korean Patent Application No. 10-2025-0062448 filed on May 14, 2025. All contents disclosed in the documents of the Korean patent applications are incorporated herein by reference in their entirety.

[0002] The present invention relates to a physically unclonable function element and an encryption key generation apparatus using the same. More specifically, the present invention relates to a technique for implementing a physically unclonable function element that generates a unique encryption key through random indirect exchange interaction resulting from uncontrollable process variation, which can maintain perpendicular magnetic anisotropy (PMA) and enable Spin-Orbit Torque (SOT) switching, and to an encryption key generation apparatus using the physically unclonable function element. [Background Art]

[0003] A heterogeneous junction, which is a core element of spin-orbit torque (SOT) switching-based Magnetoresistive random-access memory (MRAM), is composed of a non-magnetic spin torque generation layer (hereinafter referred to as "spin torque layer"), a magnetic layer (magnetization free layer, hereinafter referred to as "free layer"), and a tunnel barrier layer.

[0004] A magnetic tunnel junction (MTJ) is composed of a spin torque layer, a magnetization free layer, a tunnel barrier layer, and a second magnetic layer (magnetization pinned layer, hereinafter referred to as "pinned layer").

[0005] Information is stored using the tunneling magnetoresistance (TMR) phenomenon, where the electrical resistance of the tunnel current passing through the insulating layer changes depending on the relative magnetization direction of the free layer and the fixed layer.

[0006] Recently, a spin-orbit torque phenomenon has been discovered that induces switching of the free layer using the spin Hall effect or Rashba effect, which occurs when current flows in a parallel direction within the plane of a spin torque layer adjacent to the free layer. This is attracting attention as a technology that enables information writing at higher speeds and with lower current consumption than existing spin-transfer torque (STT) writing methods.

[0007] Recently, there has been significant development in innovative data technologies such as artificial intelligence and the Internet of Things (IoT).

[0008] As a result, the amount of data being processed is increasing exponentially, and because personal information is frequently used in this data, the importance of security is growing.

[0009] Traditional software-based cryptographic systems are vulnerable to external attacks and pose risks of being easily duplicated.

[0010] Recently, physically unclonable functions (PUFs), a hardware-based security system that can replace this, have been gaining attention.

[0011] For a physically non-replicable function to be driven efficiently, it must satisfy three performance metrics.

[0012] Entropy is an indicator that represents how randomly the output values ​​(responses) of a function that cannot be physically replicated appear.

[0013] Uniqueness is an indicator of whether a physically non-replicable function has different output patterns for different elements.

[0014] Reliability is an indicator of whether a physically non-replicable function has a unique output value for a given input value (challenge).

[0015] Therefore, it is necessary to ensure a method for realizing a physically non-replicable function that satisfies all the conditions of entropy, uniqueness, and reliability by utilizing spin-orbit torque in a zero-magnetic-field environment. [Prior art documents] [Patent Documents]

[0016] [Patent Document 1] Korean Registered Patent No. 10-2396525 [Patent Document 2] Korean Registered Patent No. 10-2746798 [Non-patent literature]

[0017] [Non-Patent Document 1] IEEE Magnetics Letters 12,4500305(2021) [Overview of the project] [Problems that the invention aims to solve]

[0018] The present invention uses an encryption key implemented by a spin-orbit torque (SOT)-based element. An object of the present invention is to implement a physically unclonable function element that generates a unique encryption key through random indirect exchange interaction caused by uncontrollable process variation in an element which maintains perpendicular magnetic anisotropy (PMA) and enables spin-orbit torque (SOT) switching, and an encryption key generation apparatus using the same.

[0019] An object of the present invention is to implement an encryption key generation apparatus that generates a unique encryption key through random indirect exchange interaction by determining the magnetization direction between a first magnetic layer and a second magnetic layer to be in a parallel state or an antiparallel state according to the thickness of a non-magnetic intermediate layer constituting an indirect exchange interaction layer.

[0020] An object of the present invention is to implement a physically unclonable function that satisfies all the conditions of entropy, uniqueness and reliability, wherein the output value (response) exhibited by the physically unclonable function appears randomly, the physically unclonable function has different output patterns for different elements, and the physically unclonable function has a unique output value for a specific input value (challenge). [Means for Solving the Problem]

[0021] According to an embodiment of the present invention, a physically unclonable function element includes a spin torque generating layer, a free magnetization layer, a tunnel barrier layer, a spacer layer, and an indirect exchange interaction layer, wherein the spin torque generating layer generates spin orbit torque when a current flows in an in-plane direction, the free magnetization layer has perpendicular magnetic anisotropy, the indirect exchange interaction layer includes a first magnetic layer, a non-magnetic intermediate layer, and a second magnetic layer, the magnetization direction between the first magnetic layer and the second magnetic layer is determined to be in a parallel state or an anti-parallel state according to the thickness of the non-magnetic intermediate layer, when the magnetization direction of the indirect exchange interaction layer is in the anti-parallel state, leakage magnetic fields of the first magnetic layer and the second magnetic layer cancel each other out, so that switching of the free magnetization layer does not occur, and when the magnetization direction of the indirect exchange interaction layer is in the parallel state, the leakage magnetic fields reinforce each other, so that switching of the free magnetization layer can occur.

[0022] For an input value input to the spin torque generating layer, an output value determined by a zero-field spin orbit torque switching characteristic depending on whether switching of the free magnetization layer occurs, which is determined by the magnetization direction of the indirect exchange interaction layer, can be generated.

[0023] The indirect exchange interaction layer has indirect exchange interaction characteristics due to process variability based on changes in the thickness of the non-magnetic intermediate layer, and an output value based on the indirect exchange interaction characteristics can be randomly determined.

[0024] The thickness of the non-magnetic intermediate layer may range from 0.9 nm to 3.2 nm.

[0025] The magnetization direction of the indirect exchange interaction layer is determined to be in the anti-parallel state when the thickness of the non-magnetic intermediate layer is 0.9 nm to 1.2 nm, and when the thickness of the non-magnetic intermediate layer increases from 1.3 nm to 1.8 nm, the magnetization direction oscillates from the anti-parallel state to the parallel state and can be determined to be in the parallel state.

[0026] The magnetization direction of the indirect exchange interaction layer may be determined to be the antiparallel state by oscillating from the parallel state to the antiparallel state when the thickness of the nonmagnetic intermediate layer is 1.9 nm to 2.3 nm, and may be determined to be the parallel state by oscillating from the antiparallel state to the parallel state when the thickness is 2.6 nm to 3.2 nm.

[0027] The magnetization direction of the indirect exchange interaction layer can be determined by the RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction between the first magnetic layer and the second magnetic layer.

[0028] The first magnetic layer and the second magnetic layer may be formed of CoFeB, and the non-magnetic intermediate layer may be formed of Ru.

[0029] The array includes a plurality of physically non-replicable functional elements, any one of the plurality of physically non-replicable functional elements includes a spin torque generating layer, a magnetization free layer, a tunnel barrier layer, a spacer layer, and an indirect exchange interaction layer, wherein the spin torque generating layer generates a spin orbit torque when current flows in the in-plane direction, the magnetization free layer has perpendicular magnetic anisotropy, and the indirect exchange interaction layer includes a first magnetic layer, a non-magnetic intermediate layer, and a second magnetic layer, wherein the magnetization direction between the first magnetic layer and the second magnetic layer is determined to be parallel or antiparallel depending on the thickness of the non-magnetic intermediate layer, when the magnetization direction of the indirect exchange interaction layer is antiparallel, the leakage magnetic fields of the first magnetic layer and the second magnetic layer cancel each other out and no switching occurs in the magnetization free layer, and when the magnetization direction of the indirect exchange interaction layer is parallel, the leakage magnetic fields reinforce each other and switching occurs in the magnetization free layer, and due to process variability based on the change in the thickness of the non-magnetic intermediate layer within the array, cryptographic keys can be generated with random output values ​​based on different indirect exchange interaction characteristics.

[0030] Any one of the plurality of physically non-replicable function elements has indirect exchange interaction characteristics due to process variability based on the change in the thickness of the non-magnetic intermediate layer in the indirect exchange interaction layer, and can generate an output value randomly determined based on the indirect exchange interaction characteristics in response to an input value.

[0031] Any one of the aforementioned multiple non-replicable functional elements can perform switching due to the generated spin-orbit torque without an external magnetic field.

[0032] The array in which the plurality of physically non-replicable functional elements are arranged is such that the plurality of physically non-replicable functional elements are arranged in predetermined rows and predetermined columns, and each of the plurality of physically non-replicable functional elements is determined to be in a parallel or antiparallel state by random indirect exchange interaction, thereby determining the zero-field spin-orbit torque characteristics, outputting an output value with the zero-field spin-orbit torque characteristics, and generating an encryption key using the output value. [Effects of the Invention]

[0033] The present invention embodies a physically non-replicable functional element that maintains perpendicular magnetic anisotropy (PMA) and enables spin-orbit torque (SOT) switching, generating a unique cryptographic key through random indirect exchange interaction with uncontrollable process variability, and a cryptographic key generation device using the same.

[0034] The present invention embodies a cryptographic key generation device that generates a unique cryptographic key using random indirect exchange interaction, by determining whether the magnetization direction between the first magnetic layer and the second magnetic layer is parallel or antiparallel depending on the thickness of the non-magnetic intermediate layer constituting the indirect exchange interaction layer.

[0035] The present invention makes it possible to realize a physically non-replicable function that satisfies all the conditions of entropy, uniqueness, and reliability by having the output value (response) shown by the physically non-replicable function appear randomly, having different output patterns for different elements, and having an output value unique for a specific input value (challenge). [Brief explanation of the drawing]

[0036] [Figure 1] This figure illustrates a physically unreplicable functional element according to one embodiment of the present invention. [Figure 2] This figure illustrates a physically unreplicable functional element according to one embodiment of the present invention. [Figure 3A] This figure illustrates the indirect exchange interaction characteristics due to the thickness of the non-magnetic intermediate layer in a physically unreplicable functional element according to one embodiment of the present invention. [Figure 3B] This figure illustrates the indirect exchange interaction characteristics due to the thickness of the non-magnetic intermediate layer in a physically unreplicable functional element according to one embodiment of the present invention. [Figure 4A] This figure illustrates the field-free spin-orbit torque switching characteristics due to indirect exchange interaction characteristics in a physically unreplicable functional element according to one embodiment of the present invention. [Figure 4B] This figure illustrates the field-free spin-orbit torque switching characteristics due to indirect exchange interaction characteristics in a physically unreplicable functional element according to one embodiment of the present invention. [Figure 5A] This figure illustrates the generation of an encryption key based on the magnetic field-free spin-orbit torque switching characteristics of an encryption key generation device composed of multiple physically non-replicable functional elements according to one embodiment of the present invention. [Figure 5B] This figure illustrates the generation of an encryption key based on the magnetic field-free spin-orbit torque switching characteristics of an encryption key generation device composed of multiple physically non-replicable functional elements according to one embodiment of the present invention. [Figure 5C]This figure illustrates the generation of an encryption key based on the magnetic field-free spin-orbit torque switching characteristics of an encryption key generation device composed of multiple physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6A] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6B] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6C] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6D] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6E] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6F] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6G] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6H] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6I] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 6J] This figure illustrates the main characteristics of a plurality of physically non-replicable functional elements according to one embodiment of the present invention. [Figure 7A] This figure illustrates the temperature-dependent reliability and durability characteristics of a physically unreplicable functional element according to one embodiment of the present invention. [Figure 7B] This figure illustrates the temperature-dependent reliability and durability characteristics of a physically unreplicable functional element according to one embodiment of the present invention. [Figure 7C] This figure illustrates the temperature-dependent reliability and durability characteristics of a physically unreplicable functional element according to one embodiment of the present invention. [Figure 8A] This is a diagram illustrating the RKKY interaction, which oscillates between two states, parallel coupling and antiparallel coupling, depending on the thickness of the nonmagnetic intermediate layer according to one embodiment of the present invention. [Figure 8B] This figure illustrates the field-free spin-orbit torque switching characteristics due to the RKKY interaction properties. [Figure 9A] This figure illustrates the exchange field (H(ex)) as a function related to the thickness of the non-magnetic intermediate layer according to one embodiment of the present invention. [Figure 9B] This figure illustrates the exchange field (H(ex)) as a function related to the thickness of the non-magnetic intermediate layer according to one embodiment of the present invention. [Figure 10] This figure illustrates the magnetic properties of a physically unreplicable functional element according to one embodiment of the present invention. [Figure 11] This figure illustrates the field-free spin-orbit torque switching due to a leakage magnetic field in a magnetization layer having in-planar magnetic anisotropy in a physically non-replicable functional element according to one embodiment of the present invention. [Figure 12] This figure illustrates the anomalous Hall resistance due to the thickness of the non-magnetic intermediate layer in a physically unreplicable functional element according to one embodiment of the present invention. [Figure 13] This figure illustrates the measurement results of zero-field switching at a reduced size of a physically unreplicable functional element according to one embodiment of the present invention. [Figure 14] This figure illustrates the analysis of the microstructure of a physically non-replicable functional element according to one embodiment of the present invention. [Figure 15] This figure illustrates the measurement of the anomalous Hall resistance of a 16-bit RKKY spintronic PUF related to a physically unreplicable function element according to one embodiment of the present invention. [Figure 16] This figure illustrates the in-planar magnetic anisotropy of an RKKY layer related to a physically unreplicable functional element according to one embodiment of the present invention. [Figure 17]This figure illustrates the SOT switching characteristics of multiple physically non-replicable functional elements at various operating temperatures according to one embodiment of the present invention. [Modes for carrying out the invention]

[0037] Various embodiments of this specification are described below with reference to the accompanying drawings.

[0038] The examples and the terminology used herein are not intended to limit the technology described herein to any particular embodiment, but should be understood to include various modifications, equivalents, and / or substitutions of such examples.

[0039] In describing various embodiments below, if it is determined that a specific description of a relevant known function or configuration may obscure the gist of the invention, such detailed description will be omitted.

[0040] Furthermore, the terms described later are defined considering the functions in various embodiments, and these may change depending on the intent or conventions of the user or operator. Therefore, their definitions should be based on the content throughout this specification.

[0041] In relation to the description of the drawings, similar reference numerals may be used for similar components.

[0042] A singular expression can contain multiple expressions unless the context clearly indicates a different meaning.

[0043] In this specification, expressions such as "A or B" or "at least one of A and / or B" may include all possible combinations of the items listed together.

[0044] Expressions such as "first," "second," "first," or "second" can modify the constituent elements regardless of their order or importance, and are used only to distinguish one constituent element from others, without limiting it to that constituent element.

[0045] When it is said that one component (e.g., component 1) is "connected" or "linked" to another component (e.g., component 2), that component may be directly connected to the other component or connected via another component (e.g., component 3).

[0046] In this specification, “configured to” may be used interchangeably with, depending on the context, “suitable for,” “capable of,” “modified to,” “made to,” “capable of,” or “designed to,” either in hardware or software.

[0047] In some situations, the expression "a device configured to do ~" can mean that the device "can do ~" together with other devices or components.

[0048] For example, the phrase "a processor configured (or set up) to perform A, B, and C" can mean a dedicated processor for performing those operations (e.g., an embedded processor), or a general-purpose processor (e.g., a CPU or application processor) that can perform those operations by executing one or more software programs stored in a memory device.

[0049] Furthermore, the term "or" here refers to inclusive OR rather than exclusive OR.

[0050] In other words, unless otherwise stated or made clear from the context, the expression "x uses a or b" means one of the natural inclusive permutations.

[0051] The terms "...unit" and "...device" used below refer to a unit that processes at least one function or operation, which can be embodied in hardware, software, or a combination of hardware and software.

[0052] Figures 1 and 2 illustrate a physically unreplicable function element according to one embodiment of the present invention.

[0053] According to one embodiment of the present invention, the physically unreplicable functional element 100 includes a spin torque generating layer 101, a magnetization free layer 102, a tunnel barrier layer 103, a spacer layer 104, and an indirect exchange interaction layer 105.

[0054] As an example, the spin torque generating layer 101 generates a spin orbit torque when an electric current flows in the in-plane direction.

[0055] The magnetized free layer 102 has perpendicular magnetic anisotropy.

[0056] The indirect exchange interaction layer 105 includes a first magnetic layer, a non-magnetic intermediate layer, and a second magnetic layer.

[0057] The indirect exchange interaction layer 105 is configured such that the magnetization direction between the first magnetic layer and the second magnetic layer is either parallel or antiparallel, depending on the thickness of the non-magnetic intermediate layer.

[0058] When the magnetization directions of the indirect exchange interaction layer 105 are antiparallel, the leakage magnetic fields of the first magnetic layer and the second magnetic layer cancel each other out, and no switching occurs in the magnetized free layer.

[0059] When the magnetization directions of the indirect exchange interaction layer 105 are parallel, the leakage magnetic fields of the indirect exchange interaction layer 105 mutually reinforce each other, which can cause switching of the magnetization free layer 102.

[0060] The indirect exchange interaction layer 105 can generate an output value determined by the zero-field spin-orbit torque switching characteristics, which depend on the presence or absence of switching of the magnetization-free layer 102, determined by the magnetization direction of the indirect exchange interaction layer 105, in response to the input value input to the spin torque generation layer 101.

[0061] The indirect exchange interaction layer 105 has indirect exchange interaction characteristics due to process variability based on the change in the thickness of the nonmagnetic intermediate layer, and the output value due to the indirect exchange interaction characteristics can be randomly determined.

[0062] The thickness of the non-magnetic intermediate layer can range from 0.9 nm to 3.2 nm.

[0063] The magnetization direction of the indirect exchange interaction layer 105 is determined to be antiparallel when the thickness of the non-magnetic intermediate layer is 0.9 nm to 1.2 nm, and may oscillate from antiparallel to parallel and then be determined to be parallel when the thickness of the non-magnetic intermediate layer increases from 1.3 nm to 1.8 nm.

[0064] The magnetization direction of the indirect exchange interaction layer 105 can be determined to be antiparallel by oscillating from a parallel state to an antiparallel state when the thickness of the nonmagnetic intermediate layer is 1.9 nm to 2.3 nm, and can be determined to be parallel by oscillating from an antiparallel state to a parallel state when the thickness is 2.6 nm to 3.2 nm.

[0065] The magnetization direction of the indirect exchange interaction layer 105 can be determined by the RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction between the first magnetic layer and the second magnetic layer.

[0066] In the indirect exchange interaction layer 105, the first magnetic layer and the second magnetic layer may be formed of CoFeB, and the non-magnetic intermediate layer may be formed of Ru.

[0067] Therefore, the present invention embodies a cryptographic key realized with a spin-orbit torque (SOT) based element, which maintains perpendicular magnetic anisotropy (PMA) and generates a unique cryptographic key through random indirect exchange interaction due to process variability that cannot be controlled by the element capable of spin-orbit torque (SOT) switching, and a cryptographic key generation device using the same.

[0068] Referring to Figure 2, the structure of the physically unreplicable functional element 200 according to one embodiment of the present invention includes W201, CoFeB202, MgO203, Ti204, CoFeB205, Ru206, CoFeB207, and Ta208.

[0069] The thicknesses of each component of the structure of the physically unreplicable functional element 200 according to one embodiment of the present invention may be as follows: W201 is 5 nm, CoFeB202 is 0.9 nm, MgO203 is 1 nm, Ti204 is 2 nm, CoFeB205 is 2 nm, Ru206 is t nm, CoFeB207 is 2.5 nm, and Ta208 is 2 nm. Here, t is a real number greater than 0 (i.e., a positive real number).

[0070] The thickness of Ru206 is 0.9 nm to 3.2 nm. Here, Si represents the substrate, and the SiO2 layer is a naturally occurring oxide layer formed on the substrate and is amorphous.

[0071] The W layer 201 is a spin torque layer, the CoFeB layer 202 is a magnetic free layer, and the composition of the sputtering target is Co 40 Fe 40 B 20 (at%) is possible.

[0072] The Ti layer 204 may be a spacer layer, the CoFeB / Ru / CoFeB layer may be an indirect exchange interaction layer, and the Ta layer 208 may be a capping layer.

[0073] After thin film deposition, the film is heat-treated at 300°C for 1 hour, with an initial vacuum of 10°C during the heat treatment. -6 The Torr band is present, and during heat treatment, an external magnetic field of 6 kOe may be applied horizontally to the thin film.

[0074] After heat treatment at 300°C, a 16-bit element can be fabricated using a photolithography process for generating encryption keys.

[0075] The element is a Hallbar with a width of 5 μm and a length of 75 μm, with a 5 × 25 μm area in the center. 2 By etching a rectangular bar of a certain size down to layer W 201, it is possible to prevent current injection into the indirect exchange interaction layer.

[0076] Figures 3A and 3B illustrate the indirect exchange interaction characteristics due to the thickness of the non-magnetic intermediate layer in a physically unreplicable functional element according to one embodiment of the present invention.

[0077] Figures 3A and 3B show the indirect exchange interaction characteristics of a physically non-replicable functional element according to one embodiment of the present invention, which is composed of a W / CoFeB / MgO / Ti / CoFeB / Ru / CoFeB / Ta structure and corresponds to the thickness of the Ru, which is a non-magnetic intermediate layer.

[0078] Referring to Figure 3A, Graph 300 shows the indirect exchange interaction characteristics with respect to Ru thickness.

[0079] When the thickness of Ru is 0.9 to 1.2 nm, the two magnetic layers of the indirect exchange interaction layer, which are CoFeB layers, are in an antiparallel state. As the thickness of Ru increases, they oscillate between the antiparallel and parallel states, which is the well-known RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction.

[0080] Graph 300 shows the results of the RKKY interaction in terms of its magnetic properties.

[0081] Referring to Figure 3B, Graphs 310 to 313 show the magnetic properties of the in-planar hysteresis loop of a physically non-replicable functional element as the thickness of Ru changes.

[0082] The behavior of the RKKY interaction oscillates with changes in the thickness of the nonmagnetic intermediate layer.

[0083] Graphs 310 and 312 show the anti-parallel direction, while graphs 311 and 313 show the parallel direction.

[0084] The RKKY interaction is an indirect exchange coupling mechanism between magnetic moments in metals mediated by conduction electrons.

[0085] Through this long-range interaction, magnetic moments can interact over relatively long distances.

[0086] Depending on the thickness of the non-magnetic intermediate layer, it exhibits vibrational behavior between ferromagnetic and diamagnetic coupled states.

[0087] This behavior is related to the oscillation characteristics of the exchange field (Hex) in the RKKY interaction, which characterizes the exchange interaction between magnetic moments separated by a non-magnetic interlayer, and its magnitude indicates the strength of the coupling.

[0088] Graph 310 experimentally shows that indirect interactions between two CoFeB layers in the range of 0.9 nm to 1.2 nm generate antiparallel bonds.

[0089] Graph 311 shows that the RKKY interaction abruptly switches to a parallel coupling once the Ru thickness reaches 1.3 nm.

[0090] In Graphs 312 and 313, as the thickness of Ru increases further, antiparallel and parallel couplings appear alternately, illustrating the overall vibrational behavior.

[0091] In the case of antiparallel coupling, when a sufficiently large magnetic field is applied, the two magnetization directions become parallel.

[0092] However, as the magnetic field gradually decreases, antiparallel alignment occurs due to the RKKY interaction.

[0093] Because the thicker CoFeB layer has an even larger magnetic moment and therefore an even higher Zeeman energy, the thinner CoFeB layer with a thickness of 2.0 nm is converted first.

[0094] When such layers are converted first, the change in the magnetic field can become a diamagnetic exchange field (Hex).

[0095] Hysteresis loops can be observed in other scale ranges, not just within the thickness range mentioned above.

[0096] The leakage magnetic field generated in a planar magnetized ferromagnetic layer can induce zero-field SOT switching in a nearby perpendicular magnetized layer.

[0097] In order to construct a spintronic PUF (physically unclonable function), which is a physically unreplicable function element according to one embodiment of the present invention, a magnetic field-free SOT switching operation is realized through RKKY interaction, enabling SOT switching without an external magnetic field.

[0098] Therefore, the present invention can embody a cryptographic key generation device that generates a unique cryptographic key in random indirect exchange interaction, by determining whether the magnetization direction between the first magnetic layer and the second magnetic layer is parallel or antiparallel depending on the thickness of the non-magnetic intermediate layer constituting the indirect exchange interaction layer.

[0099] Figures 4A and 4B illustrate the field-free spin-orbit torque switching characteristics due to indirect exchange interaction characteristics in a physically non-replicable function element according to one embodiment of the present invention.

[0100] Figure 4A illustrates the field-free spin-orbit torque characteristics due to the indirect exchange interaction characteristics. According to Graphs 400 and 402, in the antiparallel state, the stray fields of the two magnetic layers of the indirect exchange interaction layer, which are CoFeB layers, cancel each other out, preventing the magnetic free layer from switching.

[0101] Conversely, in the parallel state shown in graphs 401 and 403, the leakage magnetic fields reinforce each other, causing the magnetic free layer to switch.

[0102] This demonstrates that this property is maintained even for the two initial states of the indirect exchange interaction.

[0103] To construct a spintronic PUF, we demonstrate a field-free SOT switching operation via RKKY interaction.

[0104] To perform such measurements, we fabricate a cross-shaped Hole bar and demonstrate SOT switching without an external magnetic field.

[0105] Figure 4B shows the behavior of zero-field SOT switching for a heterostructure composed of various Ru thicknesses for the non-magnetic intermediate layer of a physically non-replicable functional element according to one embodiment of the present invention.

[0106] Referring to graphs 410 and 411 in Figure 4B, an external field H(x) was applied along the x-axis to initialize the magnetization direction of the planar magnetized RKKY layer equivalent to the current before measuring the zero-magnetic-field switching, and the initialization field was aligned in the +x direction.

[0107] The switching results can be classified into two operations based on the RKKY interaction type, and it can be confirmed that they generate a binary digital output.

[0108] Parallel coupled samples can deterministically convert the magnetization of the bottommost vertically magnetized CoFeB layer in the absence of a magnetic field.

[0109] This suggests that the total leakage magnetic field emitted from two parallel-coupled ferromagnetic layers provides an effective in-plane magnetic field strong enough to break symmetry, leading to deterministic SOT switching.

[0110] The same results are obtained using a single in-planar magnetized ferromagnetic layer instead of the RKKY interaction layer.

[0111] Unlike parallel-coupled samples, antiparallel-coupled samples emit a negligible total leakage magnetic field, making it impossible to deterministically switch the perpendicularly magnetized CoFeB layer into a zero-field state.

[0112] This suggests that the antiparallel coupled RKKY layer cannot provide a sufficient effective in-plane magnetic field for zero-field SOT switching.

[0113] The bottom CoFeB layer maintains perpendicular magnetic anisotropy across the thickness of all Ru spacers, eliminating the possibility that specific RKKY interactions could interfere with perpendicular magnetic anisotropy and disrupt zero-field SOT switching.

[0114] +x and -x indicate that an external magnetic field Hx was applied along the +x and -x directions, respectively, before the measurement of the zero-magnetic-field switching.

[0115] Antiparallel coupled elements cannot deterministically switch a perpendicularly magnetized CoFeB layer without an external magnetic field, regardless of the direction of the pre-applied external magnetic field.

[0116] This is because, regardless of the two possible parallel configurations depending on the direction of the pre-applied magnetic field, the two opposing magnetic moments in the RKKY interaction layer effectively cancel each other out.

[0117] However, in the case of parallel-coupled devices, the switching polarity changes depending on the direction of the magnetic field applied before the measurement of the zero-magnetic-field switching.

[0118] This indicates that the directions of the leakage magnetic field are opposite in the two possible parallel coupled RKKY interaction configurations.

[0119] The switching operation is maintained regardless of the direction of the external magnetic field applied before the measurement of the zero-magnetic-field switching.

[0120] This indicates that even if transient magnetic modulation occurs due to the structure, the system returns to its initial RKKY interaction state of parallel or antiparallel coupling.

[0121] It is not important that the switching polarity of the parallel coupling unit device changes due to the magnetic field applied before the measurement of the zero-field switching, because the encryption key is determined by the switching capability.

[0122] Figures 5A to 5C illustrate the generation of an encryption key based on the magnetic field-free spin-orbit torque switching characteristics of an encryption key generation device composed of multiple physically non-replicable functional elements according to one embodiment of the present invention.

[0123] Figure 5A illustrates the structure of a cryptographic key generation device composed of multiple physically non-replicable functional elements according to one embodiment of the present invention.

[0124] Referring to Figure 5A, structure 500 is formed by depositing a Ru layer, then non-uniformly etching a portion of the Ru layer using ion milling, resulting in an unpredictable Ru thickness at each location. This induces random indirect exchange interaction characteristics at each location.

[0125] Structure 500 consists of pre-configured rows and columns, exemplified as 4 rows and 4 columns, but the row and column settings can be changed based on user settings.

[0126] Structure 500 demonstrates zero-field spin-orbit torque switching characteristics by fabricating 16 identical unit devices on a single physically non-replicable function element.

[0127] Considering that the RKKY interaction determines the occurrence of zero-field SOT switching, the stochastic distribution of zero-field SOT switching operation can be predicted by randomizing the RKKY interaction.

[0128] After depositing a thin film up to the Ru layer, a portion of the Ru layer is etched using Ar ion milling to induce a desired Ru thickness, and then the deposition of the remaining layer is completed.

[0129] Furthermore, it can be confirmed that the entire PUF manufacturing process does not degrade the perpendicular magnetic anisotropy characteristics of the CoFeB layer, which is magnetized perpendicularly to the bottom.

[0130] Referring to Figure 5B, a 16-bit pattern 510 is shown on one of several physically non-replicable function elements (e.g., PUF1), where the squares of different colors indicate the presence or absence of zero-field SOT switching due to parallel and antiparallel RKKY interactions of the unit device.

[0131] The black area in row 1, column 1 indicates the case where zero-field SOT switching did not occur due to an antiparallel aligned indirect exchange interaction layer, while the gray area in row 1, column 3 indicates the case where zero-field SOT switching occurred due to a parallel aligned indirect exchange interaction layer.

[0132] Referring to Figure 5C, data 520 shows the switching measurements for all unit devices of PUF1.

[0133] In Data 520, parallel (antiparallel) coupled unit devices were shown in gray (black).

[0134] The measurement was performed by sweeping the current between -30mA and +30mA, applying an external magnetic field H(x) along the +x direction, and then performing a zero-field switching measurement.

[0135] Data 520 shows that unit elements with parallel and antiparallel couplings are randomly distributed in a ratio of 7 to 9.

[0136] This ratio is close to the requirements of an ideal PUF, which requires an even distribution of 50:50.

[0137] Data 520 shows that the device displays a binary digital output because two separate RKKY parallel and antiparallel coupling interactions enable two different switching operations.

[0138] Analog PUFs require an analog-to-digital converter that consumes a considerable amount of power, so the lower power consumption of digital PUFs is an advantage over analog PUFs.

[0139] Data 520 shows that current sweep does not require an external magnetic field to generate encryption keys.

[0140] Applying a magnetic field in the +x direction prior to measurements in the absence of a magnetic field was a precautionary step and is not strictly necessary, as the in-plane magnetic anisotropy of the RKKY layer is along the x-axis. Anisotropy can be established by applying a magnetic field along the x-axis during heat treatment.

[0141] Figures 6A to 6J illustrate the main characteristics of a plurality of physically non-replicable function elements according to one embodiment of the present invention.

[0142] Referring to Figure 6A, data 600 illustrates the output results for nine PUF devices, each consisting of 16 unit devices, each representing 16 bits.

[0143] This shows the entire layout with 16 unit devices arranged in a single PUF (Pull-Up Function) device.

[0144] The unit devices have identical dimensions and, except for the non-uniform Ru milling, appear to have undergone the same manufacturing process.

[0145] Data 600 shows the individual 16-bit patterns of the nine PUF devices.

[0146] This pattern is unpredictable and unique to each device; actual switching measurements for PUF devices are further presented through Figures 6C and 6D.

[0147] To evaluate the uniformity characteristics, the entropy (E) value of the RKKY spintronic apparatus is calculated, and this calculation is performed using Equation 1.

[0148]

number

[0149] In Equation 1, p represents the probability of being "0" or "1". 0 and 1 are defined according to the switching operation of the unit device. Thus, a unit device capable of zero-magnetic-field switching is represented as 1, and a unit device that cannot perform zero-magnetic-field switching is represented as 0.

[0150] Since the ideal p-value is 0.5, the E-value can be 1.

[0151] For example, in the first PUF device, 7 out of 16 unit devices are capable of zero-field switching, so the p-value is 0.438.

[0152] Therefore, the E value of the first PUF device can be 0.989.

[0153] Referring to Figure 6B, Graphs 610 and 611 show the zero-field spin-orbit torque switching characteristics for a total of nine physically non-replicable function elements, exhibiting an average entropy of 0.994 and an average uniqueness of 0.457 ± 0.011. The ideal values ​​for entropy and uniqueness are 1.0 and 0.5, respectively, indicating that these values ​​are experimentally close to ideal values.

[0154] Graph 610 shows the total entropy value of the PUF device.

[0155] The entropy value of the device has an average value of 0.994, which is close to 1.

[0156] Next, Graph 611 determines the uniqueness of the spintronic PUF by calculating the Hamming distance (inter-HD) between devices and quantifying the difference between them.

[0157] The Hamming distance (HD) is determined by evaluating the number of non-identical bits between two CRPs and calculating the HD for all possible combinations of two PUFs, each consisting of 16 bits, to determine the inter-HD.

[0158] Therefore, Inter-HD is calculated by performing a 36-bit comparison across the nine PUF devices.

[0159] Graph 611 shows the probability mass function (PMF) as a function of inter-HD, where PMF is the number of specific HD values ​​divided by the total number of comparisons, which is 36, and inter-HD is normalized to the bit length of 16.

[0160] The ideal normalized inter-HD for maximum uniqueness between two PUF devices is 0.5, where half the bits are different from each other and the other half are identical.

[0161] From the Gaussian distribution shown in Graph 611, we can obtain a mean-normalized inter-HD of 0.457 ± 0.011 and a standard deviation of 0.111 ± 0.013, and the curve can be shown to be Gaussian fitting.

[0162] Figures 6C to 6J illustrate the measured values ​​of the field-free spin-orbit torque switching of spintronic PUFs from the 2nd PUF device to the 9th PUF device.

[0163] The data 620 from the second PUF device in Figure 6C, the data 630 from the third PUF device in Figure 6D, the data 640 from the fourth PUF device in Figure 6E, the data 650 from the fifth PUF device in Figure 6F, the data 660 from the sixth PUF device in Figure 6G, the data 670 from the seventh PUF device in Figure 6H, the data 680 from the eighth PUF device in Figure 6I, and the data 690 from the ninth PUF device in Figure 6J may be the result of measurements performed using the same procedure as that used to obtain the data for the first PUF device.

[0164] Figures 7A to 7C illustrate the temperature-dependent reliability and durability characteristics of a physically unreplicable functional element according to one embodiment of the present invention.

[0165] Figures 7A to 7C show the evaluation results of reliability characteristics, illustrating the verification of high reliability and endurance by measuring the zero-magnetic-field spin-orbit torque switching characteristics 20,000 times at room temperature for control unit elements with Ru thicknesses of 1.0 and 1.7 nm.

[0166] We evaluated the zero-field spin-orbit characteristics 200 times for antiparallel and parallel, physically non-replicable function unit elements, demonstrating that they can be driven at -55°C, room temperature, and 150°C.

[0167] Referring to Figure 7A, the start portion 701 and end portion 702 of data 700 show the reliability characteristics of typical control unit devices for parallel and antiparallel RKKY interactions, indicating that the thickness of the Ru nonmagnetic intermediate layer for typical antiparallel and parallel control devices is 1.0 nm and 1.7 nm, respectively, and that the measurements are performed at RT.

[0168] Referring to Figure 7B, Graph 710 shows the reliability characteristics of a typical PUF unit element in relation to parallel RKKY interactions, and the measurement results for both at various temperatures.

[0169] Referring to Figure 7C, Graph 720 shows the reliability characteristics of a typical PUF unit element in relation to antiparallel RKKY interaction, and the measurement results for both at various temperatures.

[0170] After applying an external magnetic field Hx along the +x direction before measuring the zero-magnetic-field switching, the normalized R(AHE) for the number of current pulses of a typical control unit is shown.

[0171] The control unit device can reproduce the same response for up to 20,000 current pulses without a single error bit through RKKY interaction, ensuring reliability and high durability.

[0172] The measured values ​​of continuous current pulses applied to typical PUF unit devices with parallel and antiparallel couplings are shown.

[0173] The PUF unit instrument can reproduce the response due to RKKY interaction, thus ensuring reliability requirements even under high and low temperature conditions of -55°C and 150°C.

[0174] These results demonstrate that an RKKY PUF based on an element according to one embodiment of the present invention meets the requirements for practical applications and offers clear advantages compared to previously reported spintronic PUFs.

[0175] Because it is based on two RKKY interaction types, it is robust to magnetic modulation, and correcting CRP would require permanently altering the RKKY interaction, which is highly unlikely.

[0176] Since the reliability of the PUF is essential to ensure the consistent generation of encryption keys, which are indispensable for security authentication and data protection, the reliability of the RKKY spintronic PUF can be demonstrated.

[0177] Furthermore, it is important to repeatedly guarantee stable generation of encryption keys under various environmental conditions. The high reliability of PUF minimizes the complexity and overhead of error correction algorithms by reducing the need for error correction.

[0178] Figures 8A and 8B illustrate the diagrams of the RKKY interaction in two states, oscillating between parallel coupling and antiparallel coupling, depending on the thickness of the nonmagnetic intermediate layer according to one embodiment of the present invention.

[0179] Referring to Figure 8A, schematic diagram 800 shows that RKKY interaction occurs in two states, oscillating between parallel coupling and antiparallel coupling, depending on the thickness of the nonmagnetic intermediate layer.

[0180] The RKKY interaction in the two states results in different leakage magnetic field behaviors.

[0181] Parallel coupling adds two leakage magnetic fields emitted from individual ferromagnetic layers, while antiparallel coupling generates a leakage magnetic field that is nearly zero due to two opposing magnetic moments.

[0182] The leakage magnetic field of the parallel-coupled RKKY layer exerts an effective field on the bottommost vertically magnetized CoFeB layer, inducing zero-field SOT switching.

[0183] On the other hand, the leakage magnetic field of the antiparallel coupled RKKY layer is close to zero, so this is not the case.

[0184] Referring to Figure 8B, schematic diagram 810 illustrates the measurement of field-free SOT switching in the RKKY spintronic PUF apparatus.

[0185] The probabilistic RKKY interaction distribution results in an unpredictable switching behavior distribution.

[0186] Schematic Figure 800 shows the behavior of the RKKY interaction in an indirect exchange interaction layer composed of a ferromagnetic material (CoFeB) / nonmagnetic material (Ru) / ferromagnetic material (CoFeB).

[0187] As the thickness of the ruthenium (Ru) layer changes, the RKKY interaction oscillates between parallel (ferromagnetic) coupling and antiparallel (antiferromagnetic) coupling.

[0188] These two types of interaction can result in two distinct behaviors.

[0189] When two ferromagnetic layers are coupled in parallel, the leakage magnetic fields emitted from the two magnetic layers reinforce each other, resulting in an overall increase in the leakage magnetic field.

[0190] Conversely, when two ferromagnetic layers are coupled antiparallel, their opposing magnetic moments cancel each other out, and the pure magnetic moment approaches zero, resulting in a leakage magnetic field that is almost zero.

[0191] An indirect exchange interaction layer according to one embodiment of the present invention controls the field-free spin-orbit torque (SOT) switching of the CoFeB layer magnetized perpendicularly to the bottom side.

[0192] In the case of parallel coupling, the total leakage magnetic field emitted from the RKKY interaction layer provides an effective in-plane magnetic field that breaks symmetry, inducing zero-field SOT switching in the lowest perpendicular magnetization CoFeB layer.

[0193] In previous research, we demonstrated the measurement of zero-field SOT switching by utilizing the leakage magnetic field of a magnetized ferromagnetic layer.

[0194] On the other hand, in the case of antiparallel coupling, the leakage magnetic field, which is close to zero, is insufficient for deterministic SOT switching.

[0195] The thickness of the non-magnetic Ru spacer determines the coupling type, and therefore acts as an entropy source in the PUF apparatus.

[0196] As shown in schematic figure 810, the stochastic distribution of the RKKY interaction results in a random distribution of the two zero-field switching types.

[0197] The probabilistic thickness distribution of Ru spacers between devices can generate a unique and unpredictable pattern of the occurrence of the two switches.

[0198] Figures 9A and 9B illustrate the exchange field (H(ex)) as a function related to the thickness of the non-magnetic intermediate layer according to one embodiment of the present invention.

[0199] Data 900 and 910, illustrated in Figures 9A and 9B, demonstrate that, according to the RKKY interaction theory, the exchange field H(ex) oscillates as a function of the thickness of the Ru nonmagnetic intermediate layer.

[0200] Along with the definition of Hex shown in data 900 and data 910, the hysteresis loops of the parallel and antiparallel RKKY interactions are shown as thickness functions of the Ru nonmagnetic intermediate layer.

[0201] As the in-plane magnetic field gradually decreases, the 2.0 nm thick CoFeB layer is converted first because its Zeeman energy is lower than that of the 2.5 nm thick CoFeB layer. The exchange field Hex is the magnitude of the magnetic field when the 2.0 nm thick CoFeB layer is converted.

[0202] The magnitude of the exchange field oscillates depending on the thickness of the Ru nonmagnetic intermediate layer, which corresponds to the RKKY interaction theory.

[0203] Figure 10 illustrates the magnetic properties of a physically unreplicable functional element according to one embodiment of the present invention.

[0204] Referring to Figure 10, graphs 1000 to 1003 show the magnetic properties of the heterostructure β-W 5 / CoFeB 0.9 / MgO 1 / Ti 2 / CoFeB 2 / Ru t / CoFeB 2.5 / Ta 2 (nm).

[0205] Graphs 1000 to 1003 show the in-planar hysteresis loops, specifically those resulting from the thickness of the heterostructured Ru nonmagnetic intermediate layer.

[0206] We demonstrate magnetic hysteresis loops of heterostructures across a diverse scale range and show the magnetic properties of heterostructures as a function of the thickness of the nonmagnetic Ru intermediate layer.

[0207] Graph 1000 shows the results for non-magnetic intermediate layer thicknesses of 0.9 nm to 1.2 nm.

[0208] Graph 1001 shows the results for non-magnetic intermediate layer thicknesses of 1.3 nm to 1.8 nm.

[0209] Graph 1002 shows the results for non-magnetic intermediate layer thicknesses of 1.9 nm to 2.3 nm.

[0210] Graph 1003 shows the results for non-magnetic intermediate layer thicknesses of 2.6 nm to 3.2 nm.

[0211] Figure 11 is a diagram illustrating the field-free spin-orbit torque switching due to the leakage magnetic field of a magnetization layer having in-planar magnetic anisotropy in a physically non-replicable functional element according to one embodiment of the present invention.

[0212] Referring to Figure 11, Graph 1100 shows a magnetic hysteresis loop of a physically unreplicable functional element according to one embodiment of the present invention, and Graph 1101 shows leakage magnetic field induced zero-field SOT switching.

[0213] We demonstrated leakage field-induced zero-field spin-orbit torque switching using a single planar magnetized ferromagnetic layer.

[0214] The in-planar magnetized ferromagnetic layer generates a stray magnetic field that can break inversion symmetry.

[0215] This leads to deterministic, field-free spin-orbit torque switching in a vertically magnetized ferromagnetic layer.

[0216] In Graph 1100, within the structure of a physically unreplicable functional element according to one embodiment of the present invention, two magnetic layers with thicknesses of 0.9 nm and 2 nm, respectively, have magnetic anisotropy in the out-of-planar and in-planar directions, respectively.

[0217] This shows the zero-field spin-orbit torque switching of a structure due to a leakage magnetic field. An external magnetic field H(x) was applied along the +x direction before measuring the zero-field switching. The anomalous Hall resistance is plotted as a function of the current pulse.

[0218] Figure 12 is a diagram illustrating the anomalous Hall resistance due to the thickness of the non-magnetic intermediate layer in a physically unreplicable functional element according to one embodiment of the present invention.

[0219] Referring to Figure 12, a non-magnetic intermediate layer according to one embodiment of the present invention exhibits an anomalous Hall resistance depending on its thickness.

[0220] Graphs 1200, 1201, 1202, and 1203 show the anomalous Hall resistance R(AHE) for various ruthenium thicknesses.

[0221] This indicates that the bottommost CoFeB layer maintained perpendicular magnetic anisotropy across the entire thickness of the Ru layer.

[0222] This suggests that the non-switching operation of the antiparallel RKKY interaction control element is not due to a decrease in the perpendicular magnetic anisotropy of the bottommost CoFeB layer.

[0223] Graph 1200 illustrates data for thicknesses of 0.9 nm to 1.2 nm, Graph 1201 illustrates data for thicknesses of 1.3 nm to 1.6 nm, Graph 1202 illustrates data for thicknesses of 1.7 nm to 2.0 nm, and Graph 1203 illustrates data for thicknesses of 2.3 nm to 3.2 nm.

[0224] Figure 13 illustrates the measurement results of zero-field switching at a reduced size of a physically non-replicable function element according to one embodiment of the present invention.

[0225] Referring to Figure 13, Graphs 1300 and 1301 show the zero-field switching operation due to RKKY interaction with various device sizes, Graph 1300 shows the antiparallel operation with various device sizes, and Graph 1301 shows the zero-field switching measurements of the parallel control device.

[0226] Figure 14 illustrates the analysis of the microstructure of a physically non-replicable functional element according to one embodiment of the present invention.

[0227] Referring to Figure 14, Image 1400 shows the HR TEM image of the entire spintronic PUF thin film stack, and Image 1401 shows the STEM-EDS mapping results of Co and Ru atoms.

[0228] The stack was fabricated using the method described in the sample preparation section of the manuscript, but the RKKY interaction layer was intentionally thickened to a thickness of CoFeB 4 / Ru t / CoFeB 4.5 (nm) to enhance visual clarity.

[0229] Even after partially etching the Ru stack, the entire film stack exhibits a clear and continuous interface, and this continuity is crucial in RKKY interactions.

[0230] This image shows a mapping of Co and Ru atoms captured by scanning transmission electron microscopy (STEM)-energy-dispersive spectroscopy (EDS), illustrating a continuous thin-film stack of RKKY interaction layers.

[0231] Figure 15 illustrates the measurement of the anomalous Hall resistance of a 16-bit RKKY spintronic PUF related to a physically non-replicable function element according to one embodiment of the present invention.

[0232] Referring to Figure 15, data 1500 illustrates the measurement results of R(AHE) for individual unit elements by sweeping an external magnetic field perpendicular to the film plane, confirming that all manufacturing processes constituting the RKKY spintronic PUF do not degrade the perpendicular magnetic anisotropy characteristics of the bottom CoFeB layer.

[0233] This allows us to show the R(AHE) values ​​for all 16 unit devices of a typical PUF apparatus.

[0234] The numbers displayed inside the loop indicate the corresponding position of the unit device in the 4x4 array.

[0235] The measurement results show that the bottommost CoFeB layer, which is magnetized perpendicularly to all unit elements, maintained magnetic anisotropy regardless of its position.

[0236] The graph shows measured anomalous Hall resistance (R(AHE)) values ​​for 16 individual unit devices of a typical 16-bit RKKY spintronic PUF, with the numbers in the loop indicating the position of the unit device.

[0237] Figure 16 is a diagram illustrating the in-planar magnetic anisotropy of an RKKY layer related to a physically unreplicable functional element according to one embodiment of the present invention.

[0238] Referring to Figure 16, Graphs 1600 and 1601 show the in-planar hysteresis loop of the RKKY layer as a function of the measured angle.

[0239] Angles of 0° and 90° correspond to values ​​measured parallel and perpendicular to the x-axis.

[0240] The results indicate that the easy magnetization axis of the RKKY layer is along the x-axis, and the hard magnetization axis is along the y-axis.

[0241] The in-planar magnetic anisotropy of the RKKY layer is induced by applying a magnetic field along the x-axis during heat treatment.

[0242] Graph 1600 shows the in-planar hysteresis loop of an antiparallel bond heterostructure, and Graph 1601 shows the in-planar hysteresis loop of a parallel bond heterostructure.

[0243] Figure 17 is a diagram illustrating the SOT switching characteristics of multiple physically non-replicable function elements at various operating temperatures according to one embodiment of the present invention.

[0244] Referring to Figure 17, Graphs 1700 and 1701 illustrate the temperature-dependent SOT switching behavior of parallel and antiparallel coupled unit devices.

[0245] The antiparallel coupling unit becomes relatively unstable at 150°C, but no field-free SOT switching is observed.

[0246] Graph 1700 shows parallelism across various operating temperatures, and Graph 1701 shows the measurement of field-free SOT switching of an antiparallel coupling PUF unit.

[0247] Therefore, the present invention can realize a physically non-replicable function that satisfies all the conditions of entropy, uniqueness, and reliability by having the output values ​​(responses) shown by the physically non-replicable function appear randomly, having different output patterns for different elements, and having an output value unique for a specific input value (challenge).

[0248] The devices described above may be implemented as hardware components, software components, and / or combinations of hardware and software components. For example, the devices and components described in the embodiments may be implemented using one or more general-purpose or special-purpose computers, such as a processor, controller, ALU (arithmetic logic unit), digital signal processor, microcomputer, FPA (field programmable array), PLU (programmable logic unit), microprocessor, or any other device capable of executing and responding to instructions. The processing device can run an operating system (OS) and one or more software applications run on the operating system. The processing device can also access, store, manipulate, process, and generate data in response to software execution. For convenience of understanding, the processing device has sometimes been described as being used as one, but a person with ordinary skill in the art will see that the processing device may include multiple processing elements and / or multiple types of processing elements. For example, the processing device may include multiple processors or one processor and one controller. Furthermore, other processing configurations, such as parallel processors, are also possible.

[0249] Software may include computer programs, code, instructions, or a combination of one or more of these, which can configure a processing unit to operate as desired, or independently or collectively, instruct the processing unit. Software and / or data may be permanently or temporarily embodied in a certain type of machine, component, physical device, virtual device, computer storage medium or device, or transmitted signal wave, in order to be interpreted by a processing unit or to provide instructions or data to a processing unit. Software may be distributed on a networked computer system and stored or executed in a distributed manner. Software and data may be stored on a recording medium readable by one or more computers.

[0250] As described above, the embodiments have been illustrated with illustrative and limited drawings, but a person with ordinary skill in the art can make various modifications and variations from the above description. For example, the described technique may be performed in a different order than described, and / or the components of the described system, structure, apparatus, circuit, etc. may be combined or assembled in a different manner than described, or substituted or replaced by other components or equivalents, and satisfactory results may be achieved.

[0251] Therefore, other embodiments, other embodiments and equivalents of the claims also fall within the scope of the attached claims.

Claims

1. It includes a spin torque generating layer, a magnetization free layer, a tunnel barrier layer, a spacer layer, and an indirect exchange interaction layer. The spin torque generating layer generates a spin orbit torque when a current flows in the in-plane direction. The magnetization free layer has perpendicular magnetic anisotropy, The indirect exchange interaction layer includes a first magnetic layer, a non-magnetic intermediate layer, and a second magnetic layer, wherein the magnetization direction between the first magnetic layer and the second magnetic layer is determined to be either parallel or antiparallel depending on the thickness of the non-magnetic intermediate layer, and when the magnetization direction of the indirect exchange interaction layer is antiparallel, the leakage magnetic fields of the first magnetic layer and the second magnetic layer cancel each other out, preventing switching of the magnetization free layer, and when the magnetization direction of the indirect exchange interaction layer is parallel, the leakage magnetic fields are mutually reinforced, causing switching of the magnetization free layer, thus creating a physically unreplicable functional element.

2. The physically unreplicable function element according to claim 1, characterized in that it generates an output value determined by the presence or absence of switching of the magnetization free layer, which is determined by the magnetization direction of the indirect exchange interaction layer, in response to an input value input to the spin torque generating layer, the output value being determined by the field-free spin orbit torque switching characteristics of the magnetization free layer, which is determined by the magnetization direction of the indirect exchange interaction layer, and the presence or absence of switching of the magnetization free layer.

3. The indirect exchange interaction layer has indirect exchange interaction characteristics due to process variability based on the change in the thickness of the nonmagnetic intermediate layer, and the output value is randomly determined due to the indirect exchange interaction characteristics, as described in claim 1, a physically non-replicable function element.

4. The physically unreplicable functional element according to claim 3, characterized in that the thickness of the non-magnetic intermediate layer is 0.9 nm to 3.2 nm.

5. The physically unreplicable function element according to claim 4, characterized in that the magnetization direction of the indirect exchange interaction layer is determined to be the antiparallel state when the thickness of the nonmagnetic intermediate layer is 0.9 nm to 1.2 nm, and when the thickness of the nonmagnetic intermediate layer increases from 1.3 nm to 1.8 nm, it vibrates from the antiparallel state to the parallel state and is determined to be the parallel state.

6. The magnetization direction of the indirect exchange interaction layer is such that, when the thickness of the non-magnetic intermediate layer is 1.9 nm to 2.3 nm, it vibrates from the parallel state to the antiparallel state and is determined to be the antiparallel state, and when the thickness is 2.6 nm to 3.2 nm, it vibrates from the antiparallel state to the parallel state and is determined to be the parallel state, as described in claim 5, a physically unreplicable function element.

7. The indirect exchange interaction layer is characterized in that the magnetization direction is determined by the RKKY (Rudeman-Kittel-Kasuya-Yosida) interaction between the first magnetic layer and the second magnetic layer, as described in claim 1, a physically non-replicable functional element.

8. The first magnetic layer and the second magnetic layer are formed of CoFeB. The non-magnetic intermediate layer is formed of Ru, characterized in that the physically non-replicable function element is as described in claim 1.

9. It includes an array in which multiple physically non-replicable functional elements are arranged, Any one of the plurality of physically non-replicable function elements includes a spin torque generating layer, a magnetization free layer, a tunnel barrier layer, a spacer layer, and an indirect exchange interaction layer. The spin torque generating layer generates a spin orbit torque when a current flows in the in-plane direction. The magnetization free layer has perpendicular magnetic anisotropy, The cryptographic key generation device is characterized in that the indirect exchange interaction layer includes a first magnetic layer, a non-magnetic intermediate layer, and a second magnetic layer, and the magnetization direction between the first magnetic layer and the second magnetic layer is determined to be parallel or antiparallel depending on the thickness of the non-magnetic intermediate layer, when the magnetization direction of the indirect exchange interaction layer is antiparallel, the leakage magnetic fields of the first magnetic layer and the second magnetic layer cancel each other out and no switching occurs in the magnetization free layer, when the magnetization direction of the indirect exchange interaction layer is parallel, the leakage magnetic fields are mutually reinforced and switching occurs in the magnetization free layer, and cryptographic keys are generated in the array by process variability based on changes in the thickness of the non-magnetic intermediate layer, using random output values ​​based on different indirect exchange interaction characteristics.

10. The cryptographic key generation device according to claim 9, characterized in that any one of the plurality of physically non-replicable functional elements has indirect exchange interaction characteristics in the indirect exchange interaction layer due to process variability based on a change in the thickness of the non-magnetic intermediate layer, and generates an output value randomly determined based on the indirect exchange interaction characteristics for an input value.

11. The cryptographic key generation apparatus according to claim 10, characterized in that the thickness of the non-magnetic intermediate layer is 0.9 nm to 3.2 nm.

12. The encryption key generation device according to claim 11, characterized in that the magnetization direction of the indirect exchange interaction layer is determined to be the antiparallel state when the thickness of the non-magnetic intermediate layer is 0.9 nm to 1.2 nm, and when the thickness of the non-magnetic intermediate layer increases from 1.3 nm to 1.8 nm, it vibrates from the antiparallel state to the parallel state and is determined to be the parallel state.

13. The encryption key generation apparatus according to claim 12, characterized in that the magnetization direction of the indirect exchange interaction layer is determined to be the antiparallel state when the thickness of the non-magnetic intermediate layer is 1.9 nm to 2.3 nm, and is determined to be the antiparallel state when the thickness is 2.6 nm to 3.2 nm, by oscillating from the antiparallel state to the parallel state.

14. The cryptographic key generation device according to claim 9, characterized in that one of the plurality of physically non-replicable functional elements performs switching by the generated spin-orbit torque without an external magnetic field.

15. The cryptographic key generation device according to claim 9, wherein the array of the plurality of physically non-replicable functional elements is arranged such that the plurality of physically non-replicable functional elements are arranged in predetermined rows and predetermined columns, and each of the plurality of physically non-replicable functional elements is determined to be in a parallel or antiparallel state by random indirect exchange interaction, thereby determining the zero-field spin-orbit torque characteristics, outputting an output value with the zero-field spin-orbit torque characteristics, and generating a cryptographic key using the outputted output value.

Images