A Modeling and Optimization Method for a Magnetic Tunnel Junction Device

Abstract

The present invention discloses a method for modeling and optimizing a magnetic tunnel junction device, belonging to the technical field of integrated circuits. The method includes extracting initial parameters by data fitting before MTJ modeling, and performing parameter optimization on the initial parameters by using an objective function combined with a simulated annealing algorithm after modeling. The present invention extracts initial parameters by fitting and performs parameter optimization by using the simulated annealing algorithm, solves the problem of lack of accurate modeling parameters for MTJ, and achieves the effect of accurate modeling. According to the method of the present invention, model parameters are determined by parameter extraction from the data obtained through experimental tests on actual devices, effectively reducing the modeling deviation caused by inaccurate modeling parameters, improving the practical application value of the model, and having broad application prospects in the fields of modeling of magnetic tunnel junction devices and design and simulation of MRAM.

Description

Technical Field

[0001] The present invention relates to a method for modeling and optimizing a magnetic tunnel junction device, and belongs to the field of integrated circuit technology. Background Art

[0002] A magnetic tunnel junction device (Magnetic Tunnel Junction, MTJ) is a core device of a spin-transfer torque magnetic random access memory (Spin-Transfer Torque Magnetic Random Access Memory, STT-MRAM). STT-MRAM is a new type of non-volatile magnetic random access memory that realizes information writing through spin current, and is considered to be one of the most potential new memories to replace Flash, and has broad application prospects in fields related to computer storage.

[0003] The magnetization direction relationship of the internal magnetic vectors of the two ferromagnetic layers of the MTJ determines that the MTJ has two different states: a low-resistance state (representing 0) when the magnetization directions are parallel, and a high-resistance state (representing 1) when the magnetization directions are antiparallel. The magnetization direction of the ferromagnetic layer can be controlled by a write current. Therefore, the resistance state of the MTJ can be controlled by the write current to write 0 and 1. The MTJ model can characterize the electrical characteristics and switching behavior of the MTJ device, and is essential for the design and simulation of MRAM; moreover, an accurate MTJ model can not only be used to study the working characteristics of the MTJ, but also be used to simulate its static, transient characteristics and the working state of the entire circuit. Therefore, for circuit designers, if they can use the MTJ model to perform simulation analysis before designing the circuit, it will save a large amount of product development costs and time for the designers; for manufacturers, an accurate MTJ model can be used to understand the internal working mechanism of the MTJ and to improve the device structure.

[0004] Currently, there are multiple MTJ device models, including static models and dynamic models; the static model only focuses on whether the MTJ state flips and sets the MTJ resistance accordingly, without considering the magnetic vector flipping process and the change of electrical characteristics during the flipping process; the dynamic model generally tracks the magnetization vector state in real time based on the Landau-Lifshitz-Gilbert (LLG) equation, but the simulation speed is slow and it is not easy to converge.

[0005] In addition, most of the modeling parameters used in the existing models are from theory or literature, rather than obtained through experiments, and do not have practical value. Theoretical parameters cannot accurately show the device characteristics of the MTJ. Without parameter extraction, the model cannot reflect the changes in device processes. Precise modeling parameters are required for MTJ-related circuit and system simulations. Summary of the Invention

[0006] In order to solve the existing problem of lack of accurate modeling parameters, the present invention provides a modeling and optimization method for a magnetic tunnel junction device.

[0007] The present invention proposes a modeling and optimization method for a magnetic tunnel junction device (MTJ). According to the technical solution of the present invention, first, parameter extraction is performed based on the structural parameters of the MTJ. The parameter extraction method is obtained by fitting the experimental measurement and test data of the MTJ with the existing formula. Then, these initial parameters are written into the MTJ model, and the simulation deviation is obtained by comparing the modeling results with the test data by generating an objective function. Further, the parameters are optimized using a simulated annealing (SA) algorithm to obtain a more consistent modeling result. The optimized model results are compared with the experimental test data of the MTJ again to verify the effectiveness of the invention.

[0008] Specifically, a modeling and optimization method of a magnetic tunnel junction device according to the present invention includes the following steps:

[0009] Step 1: Extract the initial parameters for MTJ modeling based on the experimental test data of MTJ;

[0010] Step 2: Write the extracted initial parameters into the MTJ model;

[0011] Step 3: Compare the JR data obtained by the MTJ model with the JR initial data of the MTJ obtained by the test, and generate an objective function, and obtain the simulation deviation of the MTJ model from the objective function;

[0012] Step 4: Use simulated annealing algorithm to optimize the initial parameters;

[0013] Step 5: Rewrite the optimized initial parameters into the MTJ model to obtain accurate modeling results.

[0014] According to the technical solution of the present invention, in step 1 of the method, the initial parameters used for MTJ modeling include:

[0015] Structural parameters: MTJ diameter D, oxide layer thickness t ox , free layer thickness t FL ; Electrical parameters: tunneling magnetoresistance TMR at zero bias voltage 0 , tunneling magnetoresistance TMR is equal to TMR 0 The corresponding bias voltage V h , resistance area product RA, polarization factor P; magnetic parameters: saturation magnetization M S , magnetocrystalline anisotropy constant K b , interface anisotropy constant K i, effective anisotropy field strength H Keff , damping factor a;

[0016] According to the technical solution of the present invention, the diameter D, oxide layer thickness t of the structural parameter MTJ ox and free layer thickness t FL are obtained by experimental measurement.

[0017] According to the technical solution of the present invention, in step one of the method, before extracting the initial parameters, the J-R data based on the MTJ current density-resistance obtained by testing is symmetrically processed.

[0018] As Figure 2 shown in the data flow diagram of the technical solution of the present invention, according to the technical solution of the present invention, in step one of the method, the extraction of electrical parameters and magnetic parameters in the initial parameters is obtained by fitting data with existing formulas, including:

[0019] Extract the tunneling magnetoresistance TMR at zero bias voltage from the symmetrically processed J-R data 0 , the bias voltage V 0 corresponding to half of the tunneling magnetoresistance TMR equal to TMR h and polarization factor P;

[0020] Extract the resistance area product RA from the MTJ diameter-square root of conductance D-G 0.5 data observed based on Transmission Electron Microscopy (TEM), where the conductance G is the conductance in the parallel state of MTJ;

[0021] Extract the saturation magnetization M S from the magnetization curve at the interface of the free layer and the oxide layer;

[0022] Extract the anisotropy constant K FL -Kt FL from the t b -Kt i data measured based on Vibrating Sample Magnetometer (VSM), where Kt FL is the area effective magnetic anisotropy energy density;

[0023] Extract the effective anisotropy field strength H R from the magnetic field angle-resonance field strength θ-H Keff data measured based on Ferro-Magnetic Resonance (FMR);

[0024] Extract the damping factor α from the magnetic field angle - Full - Width at Half - Maximum (FWHM) θ - FWHM data based on ferromagnetic resonance (FMR) measurement.

[0025] According to the technical solution of the present invention, more specifically, TMR 0 , V h is obtained by fitting the V - TMR curve and the formula TMR = TMR 0 / (1 + V 2 / V h 2 ), where the V - TMR curve is obtained from the J - R data and RA; P is obtained by the formula TMR0 = 2P 2 / (1 + P 2 ), where TMR 0 = RP 0 –RAP 0 is obtained from the J - R data; the resistance area RA is obtained by fitting the D - G 0.5 data and the formula G = π(D TEM - D 0 ) 2 / 4RA; the saturation magnetization Ms S is obtained by linearly fitting the magnetization curve at the interface of the free layer and the oxide layer; the anisotropy constants K b , K i are obtained by linearly fitting t FL - Kt FL ; the effective anisotropy field strength Heff Keff is obtained from the θ - H R data and the formulas f = μ 0 γ(H R + H Keff ) / 2π, θ = 0° and f = μ 0 γ[H R (H R - H Keff )] 0.5 / 2π, θ = 90°.

[0026] According to the technical solution of the present invention, in the second step, the process of MTJ modeling based on the initial parameters extracted in the first step is as follows:

[0027] The electrical characteristics and switching behavior of the MTJ are characterized by existing formulas. The modeling includes resistance and TMR models, and current density switching models. Among them, the resistance and TMR models are used to characterize the resistance value of the MTJ, and the current density switching model characterizes the MTJ state under different current densities. The low resistance is obtained according to the Brinkman model, the high resistance is obtained from the TMR model, and the switching behavior of the MTJ is characterized by the switching model, that is, when both the current magnitude and the pulse are satisfied, the MTJ switches.

[0028] According to the technical solution of the present invention, in the second step, the MTJ model established according to the initial parameters extracted in the first step is:

[0029] Parallel state resistance

[0030] Antiparallel state resistance R AP (V,T) = R P ×(1 + TMR(V,T));

[0031] Tunneling magnetoresistance ratio

[0032] Critical current density

[0033] Switching current density J SW = J C0 [1 - ln(taup / τ 0 ) / Δ];

[0034] Where, t ox is the thickness of the oxide layer, F is a parameter determined by RA, F = 3322 / RA, the surface area Area is determined by the diameter D of the MTJ, and is defaulted to 0.4. V is the bias voltage across the MTJ, T is the ambient temperature; e is the elementary charge, e = 1.602×10 -19 C, γ is the gyromagnetic constant, μ B is the Bohr magneton, α is the damping factor, E is the energy barrier, for SBMTJ, For DBMTJ, Where μ 0 is the vacuum permeability, δN is the shape anisotropy coefficient, determined by the structural parameters of the MTJ, that is Where g is the spin polarization rate, for SBMTJ, g = g SV ±g tunnel , For DBMTJ, g = P / (1 - P 4 cos 2 θ 0 ); Where θ 0is the angle between the initial magnetization vector and the z-axis (0 or π). Taup is the width of the current pulse applied to the MTJ, τ 0 is 1 ns, Δ is the thermal stability factor; Δ = E / k B T, k B is the Boltzmann constant.

[0035] According to the technical solution of the present invention, in the third step, the objective function used to compare the J-R data obtained from the MTJ model with the initial J-R data of the tested MTJ is:

[0036]

[0037] where g s (R i ) is the J-R data characterized by the model, and g e (R i ) is the J-R data obtained from the test; N is the number of data points of g s (R i ), and the number of data points of g e (R i ) is also N; the result of the objective function represents the simulation deviation of the MTJ model.

[0038] According to the technical solution of the present invention, in the fourth step, the process of parameter optimization using the simulated annealing algorithm includes:

[0039] Step A1: Starting from the initial parameters extracted in step one, randomly select new parameters within the predetermined floating range of each initial parameter to replace the initial parameter;

[0040] Step A2: Use the Metropolis sampling criterion to determine whether to accept the new initial parameters;

[0041] Step A3: By repeating the above steps A1 and A2, obtain a smaller objective function value and the new initial parameters corresponding to the objective function value to complete the parameter optimization.

[0042] According to the technical solution of the present invention, the method can be used for modeling and optimization of STT-SBMTJ and STT-DBMTJ; where STT-SBMTJ (Spin Transfer Torque-Single Barrier Magnetic Tunnel Junction) is a magnetic tunnel junction of single-layer MgO driven by spin transfer torque; STT-DBMTJ (Spin Transfer Torque-Double Barrier Magnetic Tunnel Junction) is a magnetic tunnel junction of double-layer MgO driven by spin transfer torque.

[0043] The beneficial effects of the present invention are as follows:

[0044] According to the technical solution of the present invention, the initial parameters required for MTJ modeling are classified, and before the initial parameters are extracted, the J-R data based on the MTJ current density-resistance obtained by testing is symmetrically processed; since the high and low resistance values of the MTJ are both symmetric, but the J-R curve obtained by testing generally includes the switching behavior of the MTJ, and the resistance symmetry is broken. After the symmetric processing, for different current densities, the values of R P and R AP can be obtained, and the high and low resistance values characterized by the resistance and the TMR model are also symmetric, so that it is easy to compare and generate the objective function; then, fitting extraction is performed according to different types of initial parameters respectively to obtain the initial parameters for MTJ modeling.

[0045] According to the technical solution of the present invention, an accurate parameter extraction method is adopted, and the simulation deviation of the MTJ model is compared by using the objective function; further, according to the result of the objective function, the initial parameters are optimized by using the simulated annealing algorithm, so as to provide the initial parameters for accurate MTJ modeling, effectively reducing the modeling deviation caused by inaccurate modeling parameters and improving the reliability of the modeling result. It has application value for the development of MTJ devices and the simulation of hybrid MTJ / CMOS circuits.

[0046] According to the technical solution of the present invention, the results of modeling for STT-MTJ confirm that for STT-SBMTJ, the objective function values before and after parameter optimization are 0.3221 and 0.0022 respectively, and for STT-DBMTJ, the objective function values before and after parameter optimization are 0.2378 and 0.0500 respectively.

[0047] According to the technical solution of the present invention, the results of the above objective function values prove that through fitting for parameter extraction and parameter optimization by using the simulated annealing algorithm, the modeling accuracy of the MTJ is greatly improved, so that according to the method of the present invention, the problem of lack of accurate modeling parameters is solved, and the purpose of accurate modeling of STT-MTJ is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0049] Figure 1It is a schematic flow chart of a method for modeling and optimizing a magnetic tunnel junction device according to the present invention;

[0050] Figure 2 It is a schematic data flow diagram in the parameter extraction process according to the present invention;

[0051] Figure 3 It is a schematic flow chart of a parameter optimization method according to the present invention. Detailed implementation manners

[0052] To make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0053] Embodiment 1

[0054] A method for modeling and optimizing a magnetic tunnel junction device provided according to this embodiment, in combination with Figure 1 as shown, includes the following steps:

[0055] Step 1: Based on the experimental test data of the MTJ, extract the initial parameters for MTJ modeling;

[0056] Step 2: Write the extracted initial parameters into the MTJ model;

[0057] Step 3: Compare the J-R data obtained from the MTJ model with the initial J-R data of the tested MTJ, and generate an objective function, and obtain the simulation deviation of the MTJ model from the objective function;

[0058] Step 4: Optimize the initial parameters by using the simulated annealing algorithm;

[0059] Step 5: Rewrite the optimized initial parameters into the MTJ model to obtain an accurate modeling result.

[0060] According to the technical solution of this embodiment, in step 1 of the method, the initial parameters include:

[0061] Structural parameters: the diameter D of the MTJ, the thickness t of the oxide layer ox , the thickness t of the free layer FL ; Electrical parameters: the tunneling magnetoresistance ratio TMR under zero bias voltage 0 , the bias voltage V corresponding to when the tunneling magnetoresistance ratio TMR is equal to half of TMR 0 , the resistance area product RA, the polarization factor P; Magnetic parameters: the saturation magnetization M h , the magnetocrystalline anisotropy constant K S , the interface anisotropy constant K b , the effective anisotropy field strength H i , the damping factor a; Keff

[0062] According to the technical solution of the present invention, the diameter D, the thickness t of the oxide layer of the structural parameter MTJ ox and the thickness t of the free layer FL are obtained by experimental measurement.

[0063] According to the technical solution of the present invention, in step one of the method, before extracting the initial parameters, the J-R data based on the MTJ current density-resistance obtained by testing is symmetrically processed.

[0064] As Figure 2 shown in the data flow diagram of parameter extraction in the technical solution of the present invention, according to this embodiment, in step one of the method, the extraction of the electrical parameters and magnetic parameters in the initial parameters is obtained by fitting the data with existing formulas, including:

[0065] Extract the tunneling magnetoresistance ratio TMR at zero bias voltage from the symmetrically processed J-R data 0 , the tunneling magnetoresistance ratio TMR is equal to the bias voltage V 0 corresponding to half of TMR h and the polarization factor P;

[0066] Extract the resistance area product RA from the MTJ diameter-square root of conductance D-G 0.5 data observed based on Transmission Electron Microscopy (TEM), where the conductance G is the conductance in the parallel state of MTJ;

[0067] Extract the saturation magnetization M from the magnetization curve at the interface of the free layer and the oxide layer S ;

[0068] Extract the anisotropy constant K FL -Kt FL from the t b 、K i data measured based on Vibrating Sample Magnetometer (VSM), where Kt FL is the area effective magnetic anisotropy energy density;

[0069] Extract the effective anisotropy field strength H R from the magnetic field angle-resonance field strength θ-H Keff data measured based on Ferro-Magnetic Resonance (FMR);

[0070] Extract the damping factor α from the magnetic field angle - Full - Width at Half - Maximum (FWHM) θ - FWHM data based on ferromagnetic resonance (FMR) measurement.

[0071] More specifically, TMR 0 , V h is obtained by fitting the V - TMR curve and the formula, where the V - TMR curve is obtained from the J - R data and RA; P is obtained by the formula TMR 0 = 2P 2 / (1 + P 2 ), where TMR 0 = RP 0 – RAP 0 is obtained from the J - R data; the resistance area RA is obtained by fitting the D - G 0.5 data and the formula G = π(D - D 0 ) 2 / 4RA; the saturation magnetization Ms S is obtained by linearly fitting the magnetization curve at the interface of the free layer and the oxide layer; the anisotropy constants K b , K i are obtained by linearly fitting t FL - Kt FL ; the effective anisotropy field strength He Keff is obtained from the θ - H R data and the formulas f = μ 0 γ(H R + H Keff ) / 2π, θ = 0° and f = μ 0 γ[H R (H R - H Keff )] 0.5 / 2π, θ = 90°.

[0072] In the second step, the process of MTJ modeling according to the initial parameters extracted in the first step is as follows:

[0073] Characterize the electrical properties and switching behavior of the MTJ through existing formulas. The modeling includes a resistance and TMR model, and a current density switching model. Among them, the resistance and TMR model is used to characterize the resistance value of the MTJ, and the current density switching model characterizes the MTJ state under different current densities. The low resistance is obtained according to the Brinkman model, the high resistance is obtained from the TMR model, and the switching behavior of the MTJ is characterized by the switching model, that is, when the current magnitude and pulse both meet the conditions, the MTJ switches.

[0074] In the second step, the MTJ model established according to the initial parameters extracted in the first step is:

[0075] Parallel state resistance

[0076] Antiparallel state resistance R AP (V,T) = R P ×(1 + TMR(V,T));

[0077] Tunneling magnetoresistance ratio

[0078] Critical current density

[0079] Switching current density J SW = J C0 [1 - ln(taup / τ 0 );

[0080] Wherein, t ox is the thickness of the oxide layer, F is a parameter determined by RA, F = 3322 / RA, the surface area Area is determined by the diameter D of the MTJ, default is 0.4; V is the bias voltage across the MTJ, T is the ambient temperature; e is the elementary charge, e = 1.602×10 -19 C, γ is the gyromagnetic constant, μ B is the Bohr magneton, α is the damping factor, E is the energy barrier; for SBMTJ, For DBMTJ, Wherein μ 0 is the vacuum permeability, δN is the shape anisotropy coefficient, determined by the structural parameters of the MTJ, i.e., Wherein g is the spin polarization rate, for SBMTJ, g = g SV ±g tunnel , For DBMTJ, g = P / (1 - P 4 cos 2 θ 0 ); wherein θ 0 is the angle between the initial magnetization vector and the z-axis (0 or π); taup is the width of the current pulse applied to the MTJ, τ 0 is 1 ns, Δ is the thermal stability factor; Δ = E / k B T, k B is the Boltzmann constant.

[0081] In the third step, the objective function used to compare the J-R data obtained from the MTJ model with the initial J-R data of the MTJ obtained by testing is:

[0082]

[0083] Wherein, g s(R i ) is the J-R data of the model representation, and g e (R i ) is the J-R data obtained from testing; N is the number of data points of g s (R i ), and the number of data points of g e (R i ) is also N; the result of the objective function represents the simulation deviation of the MTJ model.

[0084] In the fourth step, the process of parameter optimization using the simulated annealing algorithm includes:

[0085] Step A1: Starting from the initial parameters extracted in step one, randomly select new parameters within the predetermined floating range of each initial parameter to replace the initial parameter;

[0086] Step A2: Use the Metropolis sampling criterion to determine whether to accept the new initial parameters;

[0087] Step A3: By repeating the above steps A1 and A2, obtain a smaller objective function value and the new initial parameters corresponding to the objective function value, and complete the parameter optimization.

[0088] Embodiment 2:

[0089] This embodiment provides an accurate modeling method for STT-SBMTJ. Refer to Figure 1 , and in combination with Embodiment 1, the method includes: parameter extraction, STT-SBMTJ modeling, and parameter optimization.

[0090] For STT-SBMTJ, its structural parameters include: D, t ox , t FL , and the initial structural parameters are obtained by measurement as known quantities; TMR, V h are obtained by fitting the V-TMR curve and the formula TMR = TMR 0 / (1 + V 2 / V h 2 ), where the V-TMR curve is obtained from the J-R data and RA; P is obtained by the formula TMR 0 = 2P 2 / (1 + P 2 ), where TMR 0 = RP 0 - RAP 0 is obtained from the J-R data; the resistance area product RA is obtained by fitting the D-G 0.5 data and the formula G = π(D - D 0 ) 2 / 4RA; the saturation magnetization MS Obtained by linear fitting of in-plane and out-of-plane magnetization curves; anisotropy constant K b , K i Through t FL -Kt FL Linear fitting gives; effective anisotropy field H Keff Through θ-H R Data and formula f = u 0 γ(H R +H Keff ) / 2π, θ = 0°; f = u 0 γ[H R (H R -H Keff )] 0.5 / 2π, θ = 90° is obtained; damping factor a is obtained from θ–FWHM data.

[0091] Using the initial parameters to model and characterize the resistance and switching behavior of the MTJ, and comparing with the J-R data to obtain the objective function value. Define the objective function where g s (R i ) is the model result of the J-R data, g e (R i ) is the J-R data from experimental tests, N is the number of J-R data points, and the objective function value obtained according to the above formula is 0.3221; using the objective function to evaluate the deviation between the model and the experiment, and this value indicates a large deviation.

[0092] Therefore, use the simulated annealing algorithm to optimize the initial parameters. The input of the SA algorithm includes the initial parameters and the objective function, and the output is the new parameters and their corresponding objective function values. Its iterative process is as Figure 3 shown. Randomly select new points within the search interval of the predetermined floating range to update the parameters for the initial parameters extracted by fitting, and update the corresponding modeling results and their objective function values, and then use the Metropolis sampling criterion to judge whether to accept the new solution. By continuously iterating, finally obtain a smaller objective function value and new parameters to complete the parameter optimization.

[0093] In this embodiment, the parameter optimization is specifically achieved in two steps. The parameters are divided into 2 groups: Parameter set 1 is the initial parameters affecting the MTJ resistance value, including D, t ox , TMR 0 , RA and V h ; Parameter set 2 is the initial parameters affecting the critical switching current density, including t FL , a, M S , K b , K i , H KeffAnd P. First, optimize parameter set 1 to obtain a more accurate resistance value, and then optimize parameter set 2 to obtain a more accurate switching current density. The specific optimization steps are as follows:

[0094] First, write the processed J-R data and the resistance value data characterized by the resistance and TMR models (excluding the switching behavior) into the objective function, and obtain a new parameter set 1 through the first SA iteration.

[0095] Then, use the new parameter set 1 and the initial parameter set 2 together as the input for the second SA iteration. At this time, the input objective function includes the original J-R data and the J-R data characterized by the MTJ model (including the switching behavior). Continuously iterate to finally obtain a new parameter set 2 and complete the parameter optimization.

[0096] Finally, use the new parameters to model again. At this time, the deviation of the built model simulation is 0.0022.

[0097] Example 3:

[0098] This example provides the modeling and optimization process of STT-DBMTJ. The difference between STT-DBMTJ and STT-SBMTJ in the resistance model is that it has one more oxide layer in structure than STT-SBMTJ. Therefore, the structure parameters include two oxide layer thicknesses t ox , that is, the structure parameters of STT-DBMTJ include: D, t FL , t ox1 , t ox2 . Its resistance model is:

[0099] DBMTJ high resistance R(H) = R 1 (H) + R 2 (L)

[0100] DBMTJ low resistance R(L) = R 1 (L) + R 2 (H)

[0101]

[0102] R 1,2 (H) = R 1,2 (L)(1 + TMR)

[0103] In addition, the initial parameter extraction method and the parameter optimization process are the same as those of STT-SBMTJ.

[0104] For STT-DBMTJ, its implementation process is similar to that of the second embodiment. The modeling and simulation deviations before and after parameter optimization are 0.2378 and 0.0500 respectively. Therefore, this example effectively reduces the modeling and simulation deviations caused by inaccurate modeling parameters and has broad application prospects in the field of magnetic tunnel junction modeling and MRAM design and simulation.

[0105] Some steps in the embodiments of the present invention can be implemented by software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0106] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for modeling and optimizing a magnetic tunnel junction device, Characterized in that, The method includes: Step 1: Based on the experimental test data of the MTJ, extract the initial parameters for MTJ modeling; Step 2: Write the extracted initial parameters into the MTJ model; Step 3: Compare the J-R data obtained from the MTJ model with the initial J-R data of the tested MTJ, and generate an objective function, and obtain the simulation deviation of the MTJ model from the objective function; Step 4: Use the simulated annealing algorithm to optimize the initial parameters; Step 5: Rewrite the optimized initial parameters into the MTJ model to obtain an accurate modeling result; In step 1 of the method, the initial parameters for MTJ modeling include: Structural parameters: diameter D of the MTJ, thickness t of the oxide layer ox , thickness t of the free layer FL ; Electrical parameters: tunneling magnetoresistance ratio TMR at zero bias voltage 0 and the tunneling magnetoresistance ratio TMR is equal to TMR 0 when it is half of that, the corresponding bias voltage V h , resistance area product RA, polarization factor P; Magnetic parameters: saturation magnetization M S , magnetocrystalline anisotropy constant K b , interface anisotropy constant K i , effective anisotropy field strength H Keff , damping factor α; Among them, the diameter D of the structural parameter MTJ, the thickness t of the oxide layer ox and the thickness t of the free layer FL are obtained by experimental measurement; In step 1 of the method, before extracting the initial parameters, symmetric processing is performed on the J-R data of the current density-resistance based on the MTJ obtained by testing; In step 1 of the method, the extraction of electrical parameters and magnetic parameters in the initial parameters is obtained by fitting data with existing formulas, including: Extract the tunneling magnetoresistance ratio TMR at zero bias voltage from the symmetrically processed J-R data 0 The tunneling magnetoresistance ratio TMR is equal to TMR 0 The bias voltage V corresponding to half of h and the polarization factor P; Extract the resistance area product RA from the MTJ diameter - square root of conductance D - G data based on transmission electron microscope observations, where the conductance G is the conductance in the parallel state of the MTJ; 0.5 ​ Extract the saturation magnetization M from the magnetization curve based on the interface between the free layer and the oxide layer S ; Extract the anisotropy constants K FL FL -Kt FL FL from the data measured by a vibrating sample magnetometer, where Kt b b and K i i are the area-effective magnetic anisotropy energy densities; FL FL ​ Extract the effective anisotropy field strength H from the angular-resonance field strength θ-H data based on ferromagnetic resonance measurement R Keff ;​ Extract the damping factor a from the magnetic field angle-full width at half maximum θ-FWHM data based on ferromagnetic resonance measurement; In the third step described above, the objective function used is: Among them, g s (R i ) is the J-R data represented by the model, and g e (R i ) is the J-R data obtained from experimental tests; N is the number of data points of g s (R i ), and the number of data points of g e (R i ) is also N; The result of the objective function represents the simulation deviation of the MTJ model.

2. The method according to claim 1, Characterized in that, In step 2, the process of MTJ modeling according to the initial parameters extracted in step 1 is as follows: Characterize the electrical characteristics and switching behavior of the MTJ through existing formulas. The modeling includes a resistance and TMR model and a current density switching model; among them, the resistance and TMR model is used to characterize the resistance value of the MTJ, and the current density switching model characterizes the MTJ state under different current densities.

3. The method according to claim 2, Characterized in that, The MTJ model established in step 2 according to the initial parameters extracted in step 1 is: Antiparallel state resistance R AP (V,T) = R P ×(1 + TMR(V,T)); Reversal current density J SW = J C0 [1 - ln(taup / τ 0 ) / Δ]; where t ox is the thickness of the oxide layer, F is a parameter determined by RA, F = 3322 / RA, and the surface area Area is determined by the diameter D of the MTJ, which is defaulted to 0.4; V is the bias voltage across the MTJ, T is the ambient temperature; e is the elementary charge, γ is the gyromagnetic constant, μ B is the Bohr magneton, α is the damping factor, E is the energy barrier; g is the spin polarization rate; θ 0 is the angle between the initial magnetization vector and the z-axis; taup is the width of the current pulse applied to the MTJ, τ 0 is 1 ns, Δ is the thermal stability factor; Δ = E / k B T, k B is the Boltzmann constant.

4. The method according to claim 3, Characterized in that, In step 4, the process of parameter optimization using the simulated annealing algorithm includes: Step A1: Starting from the initial parameters extracted in step 1, randomly select new parameters within the predetermined floating range of each initial parameter to replace the initial parameter; Step A2: Use the Metropolis sampling criterion to judge whether to accept the new initial parameters; Step A3: By repeating the above steps A1 and A2, obtain a smaller objective function value and the new initial parameters corresponding to the objective function value to complete the parameter optimization.

5. The method according to claim 1, Characterized in that, The method can be used for modeling and optimizing STT-SBMTJ and STT-DBMTJ.

6. The method according to any one of claims 1-5, Characterized in that, The modeling simulation deviation of the method for STT-SBMTJ can be reduced from 0.3221 to 0.022; the modeling simulation deviation of the method for STT-DBMTJ can be reduced from 0.2378 to 0.0500.

Images