A method for implementing a physically unclonable function in a self-rectifying memristor array

Abstract

The present invention belongs to the field of semiconductor technology, and relates to a method for realizing a physical unclonable function in a self-rectifying memristor array, the method comprising: designing a self-rectifying memristor based on the conduction mechanism of P-F emission and Schottky emission; testing the electrical characteristics of the self-rectifying memristor to determine whether the electrical characteristics of the self-rectifying memristor meet preset requirements; analyzing and fitting the P-F emission and Schottky emission of the self-rectifying memristor to verify the conduction mechanism of the self-rectifying memristor; realizing the input stimulation of the physical unclonable function based on the role of the self-rectifying memristor as an entropy source and the randomness of its conductance self-attenuation; analyzing and verifying the bit error rate and high temperature resistance of the physical unclonable function, and determining that the physical unclonable function realized by the self-rectifying memristor meets the preset bit error rate and high temperature resistance requirements. Its beneficial effect is that the physical unclonable function hardware based on the self-rectifying memristor array can achieve a BER as low as 0 and high temperature resistance characteristics.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor technology, and in particular to a method for realizing a physical unclonable function in a self-rectifying memristor array. Background Art

[0002] In the wave of big data and the Internet of Things, data security and privacy protection have become particularly critical. With hundreds of millions of devices connected to the network, from smart homes to industrial automation, every touchpoint may become a potential risk point for data leakage. Traditional encryption technology is powerless in the face of such a huge data flow and diverse access points.

[0003] Memristors, as a new generation of nonlinear electronic components, have brought new hope to the field of data encryption with their unique physical properties and ability to simulate human brain neural networks. The resistive switching characteristics of memristors enable them to show extremely high flexibility and stability in data storage and processing. In the field of encryption, this characteristic can be transformed into a powerful data protection mechanism. The nonlinearity and volatility of memristors give them a natural advantage in implementing complex encryption algorithms and can provide a higher level of security. In addition, the low energy consumption and fast response characteristics of memristors make it possible to realize real-time data encryption and decryption in IoT devices, thereby ensuring data security without sacrificing performance. Therefore, the application of memristors in the field of encryption not only responds to the demand for data security in the big data era, but also provides a new solution for the security of IoT devices.

[0004] In a memristor crossbar array, due to the resistance difference between devices and the limitation of circuit design, non-target devices may generate interference current, i.e. sneak path current, during the read or write operation. This will not only affect the accuracy of the read data, but also limit the scalability and reliability of the memristor array. The mainstream method to solve this problem is to connect a diode, transistor or selector in series with the memristor to limit the sneak path current, but this will reduce the area efficiency of the circuit, thus seriously hindering the miniaturization of integrated circuits. The self-rectifying memristor is a neuromorphic device with unique electrical characteristics, and its working principle is based on the nonlinear resistance effect of the internal structure. This memristor can realize the rectification function through its own nonlinear resistance characteristics without external circuit control, thereby suppressing the crosstalk problem in array integration and significantly improving the integration and energy efficiency of the device. The self-rectifying memristor has the inherent ability to suppress negative current, which can significantly suppress the sneak path current in a single unit, while greatly simplifying the back-end process of CMOS. Like the general memristor, the self-rectifying memristor also has rich randomness and can be used for the deployment of physically unclonable functions, but there is a lack of related research work.

[0005] The Physical Unclonable Function is an innovative hardware security technology that creates a unique digital fingerprint for each chip by exploiting the random physical changes produced during the semiconductor manufacturing process. Because these changes are unpredictable and cannot be replicated, the Physical Unclonable Function provides a method to generate unique and secure keys, enhancing the anti-counterfeiting and security of the device. The advantage of the Physical Unclonable Function technology is that it does not store keys, but generates them instantly when needed through a challenge-response mechanism, thus providing a non-volatile, tamper-proof security solution suitable for a variety of security application scenarios such as device authentication, key generation and storage.

[0006] However, most of the current research only provides the concept of self-rectifying memristors and simple electrical characterization, but does not provide systematic content applied to the field of hardware security. Summary of the invention

[0007] Technical issues to be solved

[0008] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method for implementing a physical unclonable function in a self-rectifying memristor array, which solves the technical problem that the existing self-rectifying memristors have not been systematically applied in the field of hardware security.

[0009] Technical Solution

[0010] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0011] The present invention provides a method for implementing a physical unclonable function in a self-rectifying memristor array, comprising:

[0012] The structure of the self-rectifying memristor is designed based on the conduction mechanism of PF emission and Schottky emission;

[0013] Testing the electrical characteristics of the self-rectifying memristor to determine whether the electrical characteristics of the self-rectifying memristor meet preset requirements;

[0014] Analyze and fit the PF emission and Schottky emission of the self-rectifying memristor to verify the conduction mechanism of the self-rectifying memristor;

[0015] Based on the role of the self-rectifying memristor as an entropy source and the randomness of its conductance self-attenuation, the input stimulation of the physical unclonable function is realized;

[0016] The bit error rate and high temperature resistance performance of the physical unclonable function are analyzed and verified, and it is determined that the physical unclonable function implemented by the self-rectifying memristor meets the preset bit error rate and high temperature resistance requirements.

[0017] Optionally, the PF emission is analyzed and fitted based on the following formula:

[0018] ;

[0019] where μ represents the electron drift mobility, Nc is the density of states in the conduction band, and E is the applied electric field across the oxide. φ T is the depth of the trapped potential well, k is the Boltzmann constant, T is the absolute temperature, q is the elementary charge, and ε is the dielectric constant of the oxide.

[0020] Optionally, the Schottky emission is analyzed and fitted based on the following formula:

[0021] ;

[0022] Among them, α represents a constant, m0 is the mass of the electron, m* is the effective mass of the electron, φ B is the junction barrier height.

[0023] Optionally, the conductance self-decay of the self-rectifying memristor during the relaxation period complies with the following formula: ;

[0024] Where β is the decay coefficient, G0 is the raw conductivity of a self-decaying cycle, γ represents the temperature correction factor, and t is the decay time experienced.

[0025] Optionally, the bit error rate is analyzed and verified based on the following formula:

[0026] ;

[0027] Where n represents the total number of bit streams, p o and p c represents the standard response stored in the database and the actual response under different conditions, and HD is the Hamming distance between two random bit streams.

[0028] Optionally, the self-rectifying memristor is a 32×32 self-rectifying memristor cross-bar array.

[0029] Optionally, the cross section of each self-rectifying memristor device is a circle with a diameter of 3 μm.

[0030] Optionally, the structure of the self-rectifying memristor is Pt / HfO2-x / WO3-x / TiN.

[0031] Beneficial Effects

[0032] The beneficial effects of the present invention are as follows: a method for implementing a physical unclonable function in a self-rectifying memristor array of the present invention implements a physical unclonable function with zero BER (Bit Error Rate) and a high temperature resistant physical unclonable function based on all possible self-rectifying memristors of PF (Poole-Frenkel) emission and Schottky emission mechanisms. Compared with the related art, the physical unclonable function hardware based on the self-rectifying memristor array implemented in the present application can achieve a BER as low as 0 and high temperature resistance, and realizes an ultra-high reliability physical unclonable function instance while greatly improving the area efficiency of the integrated circuit. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A schematic diagram of the energy band of the conduction mechanism of the self-rectifying memristor provided in an embodiment of the present invention;

[0034] Figure 2 A schematic diagram of the self-attenuation mechanism of the conductance of a self-rectifying memristor provided in an embodiment of the present invention;

[0035] Figure 3 A schematic diagram of a conductance self-decay curve of a self-rectifying memristor as a physical unclonable function entropy source provided by an embodiment of the present invention;

[0036] Figure 4 A distribution histogram of the conductance self-decaying constants of 1000 groups of 1024 devices in the single self-rectifying memristor array provided in an embodiment of the present invention is counted;

[0037] Figure 5 A dotted line graph showing the variation of BER with operation cycle under different temperature conditions provided by an embodiment of the present invention;

[0038] Figure 6 A BER comparison bar chart corresponding to five physical unclonable function examples of different process batches provided in an embodiment of the present invention;

[0039] Figure 7 A scanning electron microscope image of a 32×32 self-rectifying memristor crossbar array provided in an embodiment of the present invention;

[0040] Figure 8 A schematic diagram of the electrical characterization wiring method of the self-rectifying memristor provided in an embodiment of the present invention;

[0041] Fig. 9 A schematic diagram of a current-voltage DC characteristic curve of a self-rectifying memristor provided in an embodiment of the present invention;

[0042] Fig.10 This is a comparison diagram of the changes in the electrical characteristic curves of the self-rectifying memristor provided in an embodiment of the present invention just after manufacturing and after being placed in the air for two months. DETAILED DESCRIPTION

[0043] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below in conjunction with the accompanying drawings through specific embodiments. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a clearer and more thorough understanding of the present invention and to be able to fully convey the scope of the present invention to those skilled in the art.

[0044] This embodiment provides a method for implementing a physical unclonable function in a self-rectifying memristor array, including:

[0045] The structure of the self-rectifying memristor is designed based on the conduction mechanism of PF emission and Schottky emission;

[0046] Testing the electrical characteristics of the self-rectifying memristor to determine whether the electrical characteristics of the self-rectifying memristor meet preset requirements;

[0047] Analyze and fit the PF emission and Schottky emission of the self-rectifying memristor to verify the conduction mechanism of the self-rectifying memristor;

[0048] Based on the role of the self-rectifying memristor as an entropy source and the randomness of its conductance self-attenuation, the input stimulation of the physical unclonable function is realized;

[0049] The bit error rate and high temperature resistance performance of the physical unclonable function are analyzed and verified, and it is determined that the physical unclonable function implemented by the self-rectifying memristor meets the preset bit error rate and high temperature resistance requirements.

[0050] The conductive mechanism of the self-rectifying memristor proposed in the present invention is based on Poole-Frenkel (PF) emission and Schottky emission, so the mechanism is also applicable to the self-rectifying memristor with the following structure: When designing an oxide-based self-rectifying memristor, the conductive mechanism based on PF emission and Schottky emission can be realized by carefully selecting the materials of the insulating layer and the resistive layer. For example, high-insulating films such as HfO2, TiO2, and Al2O3 are used as insulating layers. These materials have high resistivity and excellent electrical insulation properties and can effectively suppress the tunneling of charges. The resistive layer can be selected from films with high oxygen vacancy defect concentrations such as IGZO, WO3-x, and ZnO. The oxygen vacancies of these materials can serve as trap centers for charges and affect the conductivity of the device. The selection of electrodes is also critical. Inert high-conductivity electrodes such as Pt, Au, TiN, Ta, and Pd can be selected. These electrodes not only have good conductivity, but also have high chemical stability and can form a stable interface with the oxide layer. For example, in the Pt / TiO2 / WO3-x / Pt structure, Pt acts as an electrode combined with the TiO2 insulating layer and the WO3-x resistive layer, which may form a Schottky barrier at the Pt / TiO2 interface, while charge tunneling may be carried out through the PF emission mechanism at the TiO2 / WO3-x interface.

[0051] The conductive mechanism of the self-rectifying memristor proposed in the present invention is explained as follows: When positive and negative bias voltages are applied to the two ends of the self-rectifying memristor, the internal energy band structure of the device is as follows: Figure 1 As shown. At room temperature, when the negative voltage is lower than 2V, electrons cannot pass through the Pt / HfO2-x barrier from the cathode Pt to the anode TiN, so the negative current is significantly suppressed. On the contrary, at 150°C, under sufficient thermal excitation, the electrons partially pass through the barrier (Schottky emission) after obtaining sufficient energy, and are subsequently trapped in the WO3-x layer, followed by PF emission, resulting in a small negative current and a switching window. When a positive bias is applied at room temperature, as the voltage increases, electrons are able to pass through the TiN / WO3-x barrier and undergo strong PF emission in the WO3-x and HfO2-x resistor layers, resulting in a high level of forward current. As mentioned earlier, the presence of the TiN / WO3-x and WO3-x / HfO2-x barriers prevents electrons from obtaining sufficient energy and performing Schottky emission and PF emission at low voltages.

[0052] In order to verify the accuracy of the self-rectifying memristor conduction mechanism, we conducted a comprehensive analysis and fitting of two important aspects of the mechanism. First, the basic principle of PF emission lies in the electrons being excited into the conduction band of the oxide. In addition, the essence of Schottky emission lies in the injection of thermally activated electrons from the energy barrier into the conduction band of the oxide.

[0053] Optionally, the PF emission is analyzed and fitted based on the following formula:

[0054] ;

[0055] where μ represents the electron drift mobility, Nc is the density of states in the conduction band, and E is the applied electric field across the oxide. φ T is the depth of the trapped potential well, k is the Boltzmann constant, T is the absolute temperature, q is the elementary charge, and ε is the dielectric constant of the oxide.

[0056] Optionally, the Schottky emission is analyzed and fitted based on the following formula:

[0057] ;

[0058] Among them, α represents a constant, m0 is the mass of the electron, m* is the effective mass of the electron, φ B is the junction barrier height.

[0059] like Figure 2 As shown in the figure, the reason for the self-attenuation of the conductivity of the memristor is the self-diffusion in the continuous conductive path. When a continuous negative bias is applied to both ends of the SRM (self-rectifying memristor), oxygen vacancies in the WO3-x and HfO2-x layers will accumulate at the bottom of the oxide layer, respectively. Subsequently, a continuous positive electrical stimulus is applied to both ends of the device, causing the oxygen vacancies to gradually migrate to the top of the oxide layer until a continuous conductive path with a small amount of electron flow is finally formed. After removing any electrical stimulus and maintaining the device in a relaxed state, due to the small number and fine shape of the continuous conductive paths, they will continue to self-diffuse in the device, resulting in spontaneous attenuation of conductivity.

[0060] Here, we take four devices in a 32×32 array as an example. Figure 3 As shown, the randomness of the conductance self-decay and its role as an entropy source are demonstrated to achieve input stimulation of a physically unclonable function.

[0061] Optionally, the conductance self-decay of the self-rectifying memristor during the relaxation period complies with the following formula: ;

[0062] Where t is the decay time experienced, β is the decay coefficient, G0 is the raw conductivity of a self-decaying cycle, and γ represents the temperature correction factor to account for decay cycles shorter than one second at different temperatures. Due to the randomness of manufacturing, the device-to-device variation in the array (random β) enables the physical unclonable function to be realized. Since the output response (β) corresponding to the same input challenge (electrical pulse sequence) is the same, the reconfigurability and security of the physical unclonable function are perfectly guaranteed.

[0063] Figure 4The distribution of entropy sources used to implement a physical unclonable function in a single chip is shown. 1000 sets of attenuation curves are counted for each device, and the sum of the β distributions of 1024 devices is a normal distribution with an average value of 3.598, which is marked as the reference line. Values ​​less than the reference line are assigned "0" and values ​​greater than the reference line are assigned "1", which can then output a series of binary physical unclonable function mappings.

[0064] Subsequently, it is necessary for the present invention to analyze the reliability of the physical unclonable function. The bit error rate (BER) is crucial for evaluating the stability of the physical unclonable function under different environmental conditions (such as ambient temperature). A lower bit error rate value means that the physical unclonable function can stably generate the expected response corresponding to the unique challenge response pair under different conditions, which is necessary to ensure the reliability of the physical unclonable function in security applications.

[0065] Optionally, the bit error rate is analyzed and verified based on the following formula:

[0066] ;

[0067] Where n represents the total number of bit streams, p o and p c represents the standard response stored in the database and the actual response under different conditions, and HD is the Hamming distance between two random bit streams.

[0068] Different from the traditional conductance state change, the β acquisition in this work relies on the real-time fitting of the conductance curve to ensure that the mapping generated by the physical unclonable function is highly accurate and reliable. Groundbreakingly, the physical unclonable function based on the self-rectifying memristor can be used at 25°C, 10 5 The BER is as low as 0 in 10 repeated operation cycles, which is the most advanced in the field of security primitives and even unified security hardware. 5 The worst-case BER in the repeated operation cycle also reached a breakthrough 1.859×10 -4 %,like Figure 5 shown. Figure 6 The BER statistics of PUC instances from five different manufacturing batches are shown. The BER of all PUC instances can be kept at 0 at 25°C, while the BER of all PUC instances at 150°C remains at the same level, which strongly proves that the proposed unified security hardware can maintain high reliability even at extreme temperatures.

[0069] Optionally, the self-rectifying memristor is a 32×32 self-rectifying memristor cross-bar array.

[0070] Scanning electron microscope images Figure 7 shown.

[0071] Optionally, the cross section of each self-rectifying memristor device is a circle with a diameter of 3 μm.

[0072] Optionally, the structure of the self-rectifying memristor is Pt / HfO2-x / WO3-x / TiN.

[0073] This unique structural design gives the device a significant self-rectifying property. The working principle of the self-rectifying memristor is based on the high asymmetry of the positive and negative directions of its internal energy band structure, which leads to different conductive properties under the action of positive and reverse voltages. Specifically, when the forward bias is applied, the lower potential barrier promotes the injection of charge, while when the negative bias is applied, the higher potential barrier hinders the flow of charge, thereby achieving a rectification effect. This self-rectifying function is not limited to the specific material combination used in the present invention. In fact, other material combinations or designs with similar energy band structure characteristics may also achieve similar self-rectifying functions. For example, by adjusting the doping level of the material, changing the film thickness, or using a combination of different materials, a memristor with different rectification characteristics can be designed. In addition, by optimizing the interface characteristics of the device and utilizing the inherent defects of the material, a self-rectifying effect can also be achieved. In the innovative field of self-rectifying memristors, material selection is the key to achieving efficient self-rectifying functions. In addition to the Pt / HfO2-x / WO3-x / TiN structure mentioned in the present invention, there are many possible material combinations, each of which uses different physical mechanisms to achieve self-rectifying characteristics. For example, metal-insulator-metal structures have demonstrated rectification capabilities through the combination of metal electrodes and insulating layers, such as Pt / Al2O3 / Ni or Au / HfO2 / Pt. Metal-semiconductor-metal structures exploit the intrinsic rectifying behavior of semiconductors, such as Pt / n-Si / Pt. Double-layer or multilayer oxide structures achieve self-rectification by adjusting the band structure of the oxides, such as Pt / TiO2 / Nb2O5 / TiN. Transition metal dichalcogenides, such as MoS2 / WSe2 heterostructures, provide new rectification pathways with their layered properties. Organic-inorganic hybrid materials, such as PEDOT:PSS / HfO2 / Au, combine the tunability of organic materials with the stability of inorganic materials. Two-dimensional materials, such as graphene / MoS2 / graphene, provide self-rectification capabilities with their unique electronic properties. Perovskite materials, such as Au / CH3NH3PbI3 / Ti, have attracted much attention due to their high electron mobility and tunable band gap. Amorphous materials, such as Au / a-Si:H / Au, have unique electronic behaviors due to their disordered structures. The diversity and adjustability of these material combinations provide a broad space for the design of self-rectifying memristors, and they have great potential to be developed and applied in the field of hardware encryption.

[0074] To characterize the electrical properties of the device, we connected the bottom electrode Pt to the input power supply and the top electrode TiN to ground. Figure 8 shown. Fig. 9 The current-voltage DC characteristic curve of the self-rectifying memristor of the present invention is shown, and its rectification ratio (Rectification Ratio, RR) exceeds 10 6 , nonlinearity (NL) exceeds 10 3 When a positive bias voltage is applied across the self-rectifying memristor, when the scan voltage is lower than 0.8V, the output current passes through a nonlinear region (i.e., the forward current limiting region), where the current is limited to the pA range and does not increase significantly. When the scan voltage is greater than 0.8V to 2V, the logarithm of the output current increases rapidly and linearly with the increase in voltage until the peak value approaches or exceeds 1μA. As the voltage is swept back, the on-off ratio gradually reaches about 10 3 , until the output current finally returns to the pA range. When the negative current is swept from 0V to -2V, the output current is always suppressed to about 1pA, achieving negative current limitation, thus further achieving more than 10 6 At the same time, after preparing the self-rectifying memristor and completing all characteristic tests, we exposed all devices and arrays to air for two months and obtained the latest DC characteristic curves, such as Fig.10 shown.

[0075] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include these modifications and variations.

[0076] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for implementing a physically unclonable function in a self-rectifying memristor array, characterized in that: include: The structure of the self-rectifying memristor is designed based on the conduction mechanism of PF emission and Schottky emission; Testing the electrical characteristics of the self-rectifying memristor to determine whether the electrical characteristics of the self-rectifying memristor meet preset requirements; Analyze and fit the PF emission and Schottky emission of the self-rectifying memristor to verify the conduction mechanism of the self-rectifying memristor; Based on the role of the self-rectifying memristor as an entropy source and the randomness of its conductance self-attenuation, the input stimulation of the physical unclonable function is realized; The bit error rate and high temperature resistance of the physical unclonable function are analyzed and verified to determine that the physical unclonable function implemented by the self-rectifying memristor meets the preset bit error rate and high temperature resistance requirements; The PF emission is analyzed and fitted based on the following formula: ； in, is the current density dominated by the PF emission mechanism, μ represents the electron drift mobility, Nc is the density of states in the conduction band, E is the external electric field across the oxide, φ T is the depth of the trapped potential well, k is the Boltzmann constant, T is the absolute temperature, q is the elementary charge, and ε is the dielectric constant of the oxide; The Schottky emission is analyzed and fitted based on the following formula: ； in, is the current density dominated by the Schottky emission mechanism, α represents a constant, m0 is the electron mass, m* is the electron effective mass, φ B is the junction barrier height.

2. The method for implementing a physical unclonable function in a self-rectifying memristor array according to claim 1, characterized in that: The self-attenuation of the conductance of the self-rectifying memristor during the relaxation period conforms to the following formula: ; Where β is the decay coefficient, G0 is the raw conductivity of a self-decaying cycle, γ represents the temperature correction factor, and t is the decay time experienced.

3. The method for implementing a physical unclonable function in a self-rectifying memristor array according to claim 1, characterized in that: The bit error rate is analyzed and verified based on the following formula: ； Where n represents the total number of bit streams, p o and p c represents the standard response stored in the database and the actual response under different conditions, and HD is the Hamming distance between two random bit streams.

4. The method for implementing a physical unclonable function in a self-rectifying memristor array according to claim 1, characterized in that: The self-rectifying memristor is a 32×32 self-rectifying memristor cross-bar array.

5. The method for implementing a physical unclonable function in a self-rectifying memristor array according to claim 1, characterized in that: The cross-section of each self-rectifying memristor device is a circle with a diameter of 3 μm.

6. The method for implementing a physical unclonable function in a self-rectifying memristor array according to claim 1, characterized in that: The structure of the self-rectifying memristor is Pt / HfO2-x / WO3-x / TiN.

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