Modeling and simulation method for spin transfer torque and spin orbit torque magnetic tunnel junction

Abstract

The invention provides a modeling and simulation method for a spin-transfer torque and spin-orbit torque magnetic tunnel junction. A framework of the invention adopts a modular construction mode based on a Python language. The influence of temperature on the working state of the device is considered. A low power consumption device control mechanism of a voltage control anisotropy field (VCMA) is added. And meanwhile, the influence of environmental radiation on the MTJ device in a special use scene, which is generally lacked, is considered. The relationship between the model and simulation is unified, all the models and simulation are realized based on a unified platform, and the characteristics of the size effect, randomness and the like of the MTJ device can be freely simulated. And commercial software does not need to be embedded, and direct current (DC) simulation, transient simulation (Tran) and Monte-Carlo simulation (Monte-Carlo) functions are independently supported. Based on the perfect design, flexible modeling and multifunctional simulation of the MTJ device can be realized. The problem that all schemes for MTJ device modeling are not considered perfectly at present is solved.

Description

Technical Field

[0001] The invention relates to the technical field of electronic devices, and in particular to a modeling and simulation method for a spin transfer torque and a spin orbit torque magnetic tunnel junction. Background Art

[0002] Magnetic tunnel junction (MTJ) modeling is a multidisciplinary field that mainly involves magnetic materials, semiconductor physics and spin electronics. Early MTJ modeling focused on the tunnel magnetoresistance effect (TMR) and the classic Jullière model to explain the change in magnetoresistance when current passes through the MTJ. With technological advances, researchers began to introduce the spin transfer torque (STT) model and spin orbit torque (SOT) to describe the relationship between current and magnetic moment reversal, and used the Landau-Lifshitz-Gilbert (LLG) equation to simulate the dynamic behavior of the magnetic moment.

[0003] After 2010, MTJ modeling has gradually become more complex, involving multi-scale modeling, macroscopic magnetization dynamics, etc., to accurately describe the behavior of MTJ at different scales. Coupling with traditional circuit models has also become a focus, especially when integrating MTJ and CMOS circuits, how to optimize the coupling effect of current-voltage characteristics and magnetic behavior is a technical problem. However, the current modeling is mainly based on commercial simulation software Virtuoso and Hspice. In recent years, modeling based on open source software such as NGspice has also begun to appear. For the STT-MTJ modeling part, the model uses the derivation form of the Juliere model for the static resistance of the STT-MTJ device. For the dynamic part, the method of solving the LLGS (Landau-Lifshitz-Gilbert-Slonczewski Equation) equation containing supplementary terms is used. For the coupling field part, anisotropic fields, voltage-controlled anisotropic fields, and demagnetization fields are considered. At the same time, the document considers the influence of temperature on saturation magnetization, spin polarization, and exchange stiffness, based on which the influence of different temperatures on the working performance of the device can be analyzed.

[0004] For the SOT-MTJ modeling part, the article Compact Modeling and Analysis of Voltage-Gated Spin-Orbit Torque Magnetic Tunnel Junction published in the journal Access gives a good summary of the current technical overview of the SOT-MTJ modeling part. For the static resistance part, the Jullière model and the Brinkman model are combined. For the dynamic model part, the method of solving the LLGS (Landau-Lifshitz-Gilbert-Slonczewski Equation) equation containing supplementary terms is adopted, and the equation is converted into spherical coordinates to obtain the precession of the magnetic moment over time. In the multi-field coupling part, perpendicular anisotropy field, voltage-controlled anisotropy field, demagnetization field, exchange bias field and thermal noise field are considered.

[0005] For the simulation framework, CMTJ: Simulation package for analysis of multilayer spintronic devices published in 2023 provides a device simulation package for STT-MTJ, which introduces and uses the RK4 technology, the mainstream solution method in current device modeling. However, the package does not include the modeling and simulation module of SOT-MTJ. It also lacks consideration of temperature.

[0006] From the perspective of device modeling, the first solution has fewer coupled physical fields and does not consider the effects of exchange bias field, thermal noise field and external magnetic field on the device. The second solution does not consider the effects of external magnetic field and temperature effect on the device in the modeling part of the SOT-MTJ model. At the same time, the solution method is based on the spherical coordinate form, and the derivation and conversion of the LLG equation is time-consuming and complicated. Both of the above modeling are based on commercial modeling software, with strong model specificity and poor flexibility. Although the third solution is built in the form of a python library based on an open source platform, the model part is not well considered, the device type is single, and there is a lack of consideration for temperature effects. The simulation support mode is not enough, and it cannot well support the Monte Carlo simulation of various physical parameters as random items. At the same time, none of the above three solutions support the simulation of MTJ devices in special working environments involving radiation.

[0007] In summary, there is an urgent need for a complete modeling and simulation framework for magnetic tunnel junctions for device designers to use. Summary of the invention

[0008] In view of this, in order to solve the current technical problems in modeling MTJ devices, the present invention proposes a modeling and simulation method for spin transfer torque and spin orbit torque magnetic tunnel junctions. The specific technical solution is as follows:

[0009] A modeling and simulation method for a spin transfer torque and spin orbit torque magnetic tunnel junction comprises the following steps:

[0010] First, in step 1, the physical parameters of the device are loaded through the parameter initialization module, including material constants, geometric dimensions, temperature, etc.;

[0011] Then, in step 2, the electromagnetic model of the device is established through the physical field modeling module, taking into account physical phenomena including thermal noise, spin transfer torque effect (STT), and voltage-controlled magnetic anisotropy effect (VCMA). The numerical solution module uses RK4 for time-stepping solution to simulate the dynamic changes of the magnetization direction.

[0012] Finally, in step three, the simulation results are statistically analyzed and visualized through the data analysis module to plot relevant data such as magnetization direction, MTJ resistance and current;

[0013] In step 1, the basic physical constants of the device are input:

[0014] Vacuum magnetic permeability: μ0, gyromagnetic

[0015] Ratio: γ, Boltzmann constant: k B , electron charge: e,

[0016] Reduced Planck constant: Damping coefficient: α, effective gyromagnetic ratio: Input of device size:

[0017] Device diameter: D, free layer thickness: t f , oxide layer thickness: t ox , junction area: A MTJ ;

[0018] In step 2, the energy term of the external magnetic field (Zeeman energy) is as follows:

[0019] E ext =-∫M·H ext dV

[0020] The effective field obtained by the variational method of the magnetic moment M is as follows:

[0021] H ext =H ext

[0022] The anisotropic field energy term is as follows:

[0023]

[0024] The anisotropic fields are obtained as follows:

[0025]

[0026] Among them, M s is the saturation magnetization.

[0027] Demagnetization field energy term:

[0028]

[0029] The demagnetization field is obtained as follows:

[0030]

[0031] Spin transfer torque field energy term:

[0032] E STT =-∫J·MdV

[0033] The contribution of the spin transfer torque in the effective field is obtained as follows:

[0034]

[0035] J is the current density of the ferromagnetic layer

[0036] The thermal noise field simulates the disturbance of thermal fluctuations on magnetization by introducing random force terms, and its noise satisfies the following statistical properties:

[0037] <F thermal (t)·F thermal (t′)>=2k B TαMδ(tt′)

[0038] Therefore, the thermal noise term generally added to the effective field is:

[0039]

[0040] Energy term for the exchange bias field:

[0041] E exbias =-J ex ∫M·M AFM dV

[0042] The contribution of this field in the effective field is obtained as:

[0043]

[0044] Among them J ex is the interface exchange coupling strength, usually obtained through experiments or fitting.

[0045] M FM is the magnetization direction of the ferromagnetic layer, M AFM is the magnetization direction of the antiferromagnetic layer.

[0046] Voltage Controlled Anisotropy:

[0047]

[0048] Where β is the voltage regulation coefficient, m z is the z-axis magnetic moment component of the free layer.

[0049] The resistance formula uses the following:

[0050]

[0051] The dynamics of the device model comes from solving the LLG equation. Taking the LLG equation used in the framework as an example, the solution process implemented by two methods is given:

[0052]

[0053] The equation can be expressed as:

[0054]

[0055] Fourth-order Runge-Kutta: The fourth-order Runge-Kutta method approximates the solution of a differential equation by calculating four slopes. First calculate the slope:

[0056] k1=f(M(t))

[0057]

[0058] k4=f(M(t)+Δt·k3)

[0059] Then calculate the new magnetization vector:

[0060] .

[0062] Furthermore, in step 2, the influence of temperature on the spin transfer torque magnetic tunnel junction includes several aspects:

[0063] Saturation magnetization M s Dependence on temperature:

[0064]

[0065] M s0 is the initial saturation magnetization, T c is the Curie temperature, C Msx is the power factor of the temperature effect

[0066] Magnetic anisotropy constant K i Dependence on temperature:

[0067]

[0068] K i0 is the initial magnetocrystalline anisotropy constant, C γi is the power factor describing the relationship between magnetic anisotropy and magnetization intensity. The dependence of the spin polarization rate P on temperature:

[0069] P=P0·(1-a·T 1.5 )

[0070] P0 is the initial spin polarization, a is the temperature dependence coefficient

[0071] Dependence of voltage regulation coefficient β on temperature:

[0072]

[0073] Furthermore, the influence of radiation on the spin transfer torque magnetic tunnel junction under the special working environment in step 2 includes the following aspects:

[0074] Saturation magnetization M s Degeneration:

[0075]

[0076] D is the radiation dose (Gy, gray), c It is the radiation tolerance threshold, which indicates the radiation tolerance of the material.

[0077] Magnetic anisotropy constant K i Degeneration:

[0078]

[0079] Degradation of Tunneling Magnetoresistivity (TMR)

[0080]

[0081] TMR0 is the initial TMR value, D TMR Describe the radiation tolerance threshold for TMR degradation.

[0082] At the same time, radiation will introduce random perturbations, destroying the magnetization direction of the magnetic tunnel junction.

[0083] The field contribution is modeled as a Gaussian distributed random field:

[0084]

[0085] in σ0 is the disturbance intensity when not irradiated.

[0086] Furthermore, the step 2 also includes modeling of a spin-orbit moment magnetic tunnel junction (SOT-MTJ), as follows:

[0087] Input of basic physical constants of the device:

[0088] Vacuum magnetic permeability: μ0, gyromagnetic ratio: γ, Boltzmann constant: k B , electron charge: e,

[0089] Reduced Planck constant: Damping coefficient: α, effective gyromagnetic ratio: Electronic quality: me

[0090] Input of device size:

[0091] Device diameter: D, free layer thickness: t f , oxide layer thickness: t ox , junction area: A MTJ ,

[0092] Heavy metal layer length: l, heavy metal layer thickness: h, heavy metal layer cross-sectional area: A HM

[0093] Physical Modeling Basics: SOT-MTJ unique supplementary physical modeling section is explained;

[0094] Read status: The read path passed is the same as STT-MTJ;

[0095] Write state: The write state is written by the SOT current of the heavy metal layer, which utilizes spin-orbit coupling (SOC). The following is the LLG equation form used in the write state simulation:

[0096]

[0097] Where m is the normalized magnetic moment, expressed by M / M s Get. σ is the polarization direction of the spin polarized current. and The ratio between different materials is: and Usually between 0 and 0.6. STT and J SOT They are the current density through the magnetic tunnel junction and the current density through the heavy metal layer respectively, and the addition of other effective fields is the same as the above-mentioned STT-MTJ.

[0098] Furthermore, in the modeling of the spin-orbit moment magnetic tunnel junction (SOT-MTJ), the dynamics of the SOT-MTJ device model also comes from the solution of the LLG equation provided above including the supplemented form. The solution process implemented by the algorithm is given by taking the LLG equation used in the framework as an example:

[0099]

[0100] The equation can be expressed as:

[0101]

[0102] Fourth-order Runge–Kutta: The fourth-order Runge–Kutta method approximates the solution of a differential equation by computing four slopes.

[0103] First calculate the slope:

[0104] k1=f(m(t))

[0105]

[0106] k4=f(m(t)+Δt·k3)

[0107] Then calculate the new magnetization vector:

[0108] .

[0110] The above technical solution has the following beneficial effects:

[0111] The framework of the present invention separates physical modeling, numerical solution and data analysis, and users can flexibly combine modules according to specific needs. It supports a variety of custom parameters, such as device size, temperature, radiation environment, etc., and can quickly adapt to different application scenarios. Based on Python development, the code is easy to expand and maintain, which is convenient for secondary development by scientific researchers and engineers.

[0112] Supporting multi-physics coupling modeling, the framework realizes the dynamic coupling of multi-physics fields such as magnetic field, thermal noise field, demagnetization field, magnetic anisotropy field, etc., significantly improving the physical accuracy of modeling. Considering the influence of temperature, size and other conditions on physical parameters, it supports dynamic adjustment of saturation magnetization intensity (Ms), magnetic anisotropy constant (Ki) and tunnel magnetoresistance ratio (TMR) to achieve accurate multi-physics modeling.

[0113] Comprehensive simulation functions and data visualization support DC simulation, transient simulation and Monte Carlo simulation, covering a variety of scenarios such as steady-state analysis, dynamic response and statistical analysis. The simulation framework can dynamically record and visualize the time-varying trends of key parameters such as magnetization direction, current, resistance, etc., facilitating result analysis and optimization.

[0114] Complete radiation effect modeling, supplemented with integrated modeling of the impact of radiation on MTJ devices, including radiation-induced magnetic material degradation, thermal noise enhancement, and resistance characteristic changes. Supports the input of radiation environment parameters (such as dose rate, total dose, etc.), which can be used for performance evaluation and optimization of devices in extreme environments.

[0115] Fast and efficient numerical solution, using the highly accurate Runge-Kutta fourth-order method (RK4)

[0116] The Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation ensures the accuracy and stability of the numerical solution. The random thermal noise and radiation disturbance torque are considered to fully capture the impact of external disturbances on the magnetization dynamics;

[0117] The framework of the present invention adopts a modular construction method based on Python language. Each physical field is written in a modular way, fully considering the contribution of anisotropy field, demagnetization field, exchange bias field, thermal noise field and external magnetic field to the effective field, and comprehensively considering the influence of temperature on the working state of the device. A low-power device control mechanism of voltage-controlled anisotropy field (VCMA) is added. At the same time, the generally missing influence of environmental radiation on MTJ devices in special usage scenarios is considered. The relationship between the unified model and the simulation is all based on a unified platform, and the size effect, randomness and other characteristics of the MTJ device can be freely simulated. No commercial software embedding is required, and direct current (DC) simulation, transient (Tran) simulation and Monte Carlo simulation (Monte-Carlo) simulation functions are independently supported. Based on the above-mentioned perfect design, flexible modeling and multifunctional simulation of MTJ devices can be realized. It solves the problem that each scheme for MTJ device modeling is not perfect. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 It is a schematic diagram of the composition and operation structure of the magnetic tunnel junction simulation framework of the present invention;

[0119] Figure 2 The diagram is a schematic diagram of the STT-MTJ direct current (DC) simulation circuit structure and results of the present invention;

[0120] Figure 3 A schematic diagram of the change in resistance of the magnetic tunnel junction is drawn for 100 DC simulation runs of the STT-MTJ of the present invention;

[0121] Figure 4 The STT-MTJ transient simulation (Tran) simulation circuit structure and output schematic diagram of the present invention

[0122] Figure 5The simulation circuit structure and output schematic diagram of the STT-MTJ transient simulation (Tran) containing thermal noise of the present invention

[0123] Figure 6 Schematic diagram of the 5% process deviation result of the STT-MTJ Monte-Carlo simulation of the present invention

[0124] Figure 7 Schematic diagram of the temperature results of the STT-MTJ Monte-Carlo simulation (200-500K) of the present invention

[0125] Figure 8 Schematic diagram of the thermal noise simulation results of the STT-MTJ Monte-Carlo simulation of the present invention

[0126] Fig. 9 Schematic diagram of the multi-factor deviation simulation of the STT-MTJ Monte Carlo simulation of the present invention

[0127] Fig.10 The SOT-MTJ (including VCMA effect) transient simulation (Tran) circuit structure and output schematic diagram of the present invention

[0128] Fig.11 The STT-SOT collaborative transient simulation (Tran) simulation circuit structure and output schematic diagram of the present invention

[0129] Fig.12 Schematic diagram of the thermal noise simulation results of the SOT-MTJ Monte-Carlo simulation of the present invention

[0130] Fig.13 Schematic diagram of Monte Carlo simulation results of the effect of STT-MTJ radiation on the device of the present invention DETAILED DESCRIPTION

[0131] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0132] Modeling and Implementation of Spin-Transfer Torque Magnetic Tunnel Junction (STT-MTJ)

[0133] Input of basic physical constants of the device:

[0134] Vacuum magnetic permeability: μ0, gyromagnetic

[0135] Ratio: γ, Boltzmann constant: k B , electron charge: e,

[0136] Reduced Planck constant: h, damping coefficient: α, effective gyromagnetic ratio:

[0137] Input of device size:

[0138] Device diameter: D, free layer thickness: t f , oxide layer thickness: t ox , junction area: A MTJ

[0139] Physics Modeling Basics:

[0140] We derive the composition of the effective field taking into account all interactions that affect the magnetization dynamics, and derive the corresponding effective field composition through the energy term based on the LLG equation. That is, the effective field is the negative variation of the total energy of the system with respect to the magnetization direction M: Below we introduce the formula and process derived using this method.

[0141] External Magnetic Field (Zeeman Energy) The energy term of the external magnetic field is as follows:

[0142] E ext =-∫M·H ext dV#(1)

[0143] The effective field obtained by the variational method of the magnetic moment M is as follows:

[0144] H ext =H ext #(2)

[0145] The anisotropic field energy term is as follows:

[0146]

[0147] The anisotropic fields are obtained as follows:

[0148]

[0149] Among them, M s is the saturation magnetization.

[0150] Demagnetization field energy term:

[0151]

[0152] The demagnetization field is obtained as follows:

[0153]

[0154] Spin transfer torque field energy term:

[0155] E STT =-∫J·MdV#(7)

[0156] The contribution of the spin transfer torque in the effective field is obtained as follows:

[0157]

[0158] J is the current density of the ferromagnetic layer

[0159] The thermal noise field simulates the disturbance of thermal fluctuations on magnetization by introducing random force terms, and its noise satisfies the following statistical properties:

[0160] <F thermal (t)·F thermal (t′)>=2k B TαMδ(tt′)#(9)

[0161] Therefore, the thermal noise term generally added to the effective field is:

[0162]

[0163] Energy term for the exchange bias field:

[0164] E exbias =-J ex ∫M·M AFM dV#(11)

[0165] The contribution of this field in the effective field is obtained as:

[0166]

[0167] Among them J ex is the interface exchange coupling strength, usually obtained through experiments or fitting.

[0168] M FM is the magnetization direction of the ferromagnetic layer, M AFM is the magnetization direction of the antiferromagnetic layer.

[0169] Voltage Controlled Anisotropy:

[0170]

[0171] Where β is the voltage regulation coefficient, m z is the z-axis magnetic moment component of the free layer.

[0172] The resistance formula uses the following:

[0173]

[0174] Through the above formulas, we understand the basic modeling theory of spin-transfer torque magnetic tunnel junction. Now we will introduce the effects of temperature and radiation on the device.

[0175] Temperature section:

[0176] The influence of temperature on the spin transfer torque magnetic tunnel junction mainly considers the following aspects:

[0177] Saturation magnetization M s Dependence on temperature:

[0178]

[0179] M s0 is the initial saturation magnetization, T c is the Curie temperature, C Msx is the power factor of the temperature effect

[0180] Magnetic anisotropy constant K i Dependence on temperature:

[0181]

[0182] K i0 is the initial magnetocrystalline anisotropy constant, C γi is the power factor describing the relationship between magnetic anisotropy and magnetization intensity

[0183] The temperature dependence of the spin polarization P is:

[0184] P=P0·(1-a·T 1.5 )#(17)

[0185] P0 is the initial spin polarization, a is the temperature dependence coefficient

[0186] Dependence of voltage regulation coefficient β on temperature:

[0187]

[0188] Radiation part:

[0189] The influence of radiation on the spin transfer torque magnetic tunnel junction under special working environment mainly considers the following aspects:

[0190] Saturation magnetization M s Degeneration:

[0191]

[0192] D is the radiation dose (Gy, gray), c It is the radiation tolerance threshold, which indicates the radiation tolerance of the material.

[0193] Magnetic anisotropy constant K i Degeneration:

[0194]

[0195] Degradation of Tunneling Magnetoresistivity (TMR)

[0196]

[0197] TMR0 is the initial TMR value, D TMR Describe the radiation tolerance threshold for TMR degradation.

[0198] At the same time, radiation will introduce random perturbations, destroying the magnetization direction of the magnetic tunnel junction.

[0199] The field contribution is modeled as a Gaussian distributed random field:

[0200]

[0201] in σ0 is the disturbance intensity when not irradiated.

[0202] Device model numerical implementation:

[0203] The dynamics of the device model comes from solving the LLG equation. The framework design provides two solution methods: the fourth-order Runge-Kutta (RK4) and the Euler method. When the simulation data scale is large, such as Monte Carlo simulation, the Euler method can be used to reduce the amount of calculation. The following takes the LLG equation used by the framework as an example to give the solution process of the two methods:

[0204]

[0205] The equation can be expressed as:

[0206]

[0207] Fourth-order Runge-Kutta: The fourth-order Runge-Kutta method approximates the solution of a differential equation by calculating four slopes. First calculate the slope:

[0208] k1=f(M(t))#(25)

[0209]

[0210] k4=f(M(t)+Δt·k3)

[0211] Then calculate the new magnetization vector:

[0212]

[0213] Euler's method: The basic idea of ​​Euler's method is to approximate the solution of the differential equation by the following formula:

[0214] M(t+Δt)=M(t)+Δt·f(M(t))#(27)

[0215] Modeling implementation of spin-orbit torque magnetic tunnel junction (SOT-MTJ):

[0216] (1) Input of basic physical constants of the device:

[0217] Vacuum magnetic permeability: μ0, gyromagnetic ratio: γ, Boltzmann constant: k B , electron charge: e,

[0218] Reduced Planck constant: h, damping coefficient: α, effective gyromagnetic ratio: Electron mass: m e

[0219] (2) Input of device size:

[0220] Device diameter: D, free layer thickness: t f , oxide layer thickness: t ox , junction area: A MTJ ,

[0221] Heavy metal layer length: l, heavy metal layer thickness: h, heavy metal layer cross-sectional area: A HM

[0222] (3) Physical field modeling foundation:

[0223] Since the main difference between the SOT-MTJ and STT-MTJ structures is the added heavy metal layer, and the difference in operation logic is the read-write separation, the following will explain the unique additional physical modeling part of SOT-MTJ.

[0224] Read status: The read path is the same as STT-MTJ.

[0225] Write state: The write state is written by the SOT current of the heavy metal layer, which utilizes spin-orbit coupling (SOC). The following is the LLG equation form used in the write state simulation:

[0226]

[0227] Where m is the normalized magnetic moment, expressed by M / M s Get. σ is the polarization direction of the spin polarized current. and The ratio between different materials is: and Usually between 0 and 0.6. STT and J SOT The current density through the magnetic tunnel junction and the current density through the heavy metal layer are respectively. The addition of the remaining effective fields is the same as that of the above STT-MTJ and will not be repeated here.

[0228] (4) Numerical implementation of device model:

[0229] The dynamics of the SOT-MTJ device model also comes from solving the LLG equations provided above in supplementary form. The framework design also provides two solution methods: the fourth-order Runge-Kutta (RK4) and the Euler method. When the simulation data scale is large, such as Monte Carlo simulation, the Euler method can be used to reduce the amount of calculation. The following takes the LLG equations used by the framework as an example to give the solution process of the two methods:

[0230]

[0231] The equation can be expressed as:

[0232]

[0233] Fourth-order Runge-Kutta: The fourth-order Runge-Kutta method approximates the solution of a differential equation by calculating four slopes. First calculate the slope:

[0234] k1=f(m(t))#(31)

[0235]

[0236] k4=f(m(t)+Δt·k3)

[0237] Then calculate the new magnetization vector:

[0238]

[0239] Euler's method: The basic idea of ​​Euler's method is to approximate the solution of the differential equation by the following formula:

[0240] M(t+Δt)=m(t)+Δt·f(m(t))#(33)

[0241] Implementation of simulation function

[0242] Tran simulation implementation: The simulation is based on the following steps:

[0243] Initialize physical parameters:

[0244] o Set the MTJ geometry, magnetic parameters, temperature dependence, and initial conditions such as external current and electric field. o Calculate all physical constants related to magnetization dynamics and current.

[0245] Effective magnetic field calculation:

[0246] oIncludes the added physics fields that need to be considered for the above modeling, such as anisotropic magnetic field, demagnetization field, exchange bias field, and thermal noise field. oDynamic calculation of the total effective magnetic field using formulas.

[0247] 2. Magnetization dynamics solution:

[0248] oCalculate the rate of change of magnetization direction with time using the LLG equation.

[0249] oThe magnetization direction is solved using the fourth-order Runge-Kutta (RK4) numerical method.

[0250] Dynamic calculation of resistance:

[0251] oThe transient resistance is dynamically calculated using the tunnel magnetoresistance (TMR) formula based on the angle between the magnetization direction and the reference layer magnetization direction.

[0252] Iterate and update and store the results:

[0253] oIteratively update state variables such as magnetization direction, resistance, and current.

[0254] oStore the results at each time step for subsequent visualization.

[0255] The following hides the specific parameters and gives the core implementation code based on STT-MTJ:

[0256] import numpy as np

[0257] import matplotlib.pyplot as plt

[0258] class Mtj:

[0259] def__init__(self,step_size,t_max,temperature):

[0260] self.step_size = step_size

[0261] self.t_max = t_max

[0262] self.num_steps=int(t_max / step_size)

[0263] self.temperature=temperature

[0264] # Initial magnetization direction and reference layer direction

[0265] self.m = np.array([0,0,1])# Initial magnetization of free layer

[0266] self.m_r = np.array([0,0,1])#reference layer magnetization

[0267] # Parameter simplification

[0268] self.alpha=0.05#damping coefficient

[0269] self.gamma_eff=2.2127e5 / (1+self.alpha**2)#Effective magnetic gyrometry

[0270] self.Hstt_coeff=1e-2#Spin transfer torque coefficient

[0271] #Data Storage

[0272] self.magnetization=np.zeros((self.num_steps,3))

[0273] self.time=np.linspace(0,t_max,self.num_steps)

[0274] def llg(self,m,Heff):

[0275] """LLG equation, simplified form"""

[0276] dmdt=-self.gamma_eff*np.cross(m,Heff)\

[0277] -self.alpha*self.gamma_eff*np.cross(m,np.cross(m,Heff))\

[0278] -self.Hstt_coeff*np.cross(m,np.cross(m,self.m_r))

[0279] return dmdt

[0280] def run(self):

[0281] """Run Simulation"""

[0282] for iin range(self.num_steps):

[0283] #Simplify the effective magnetic field (assuming only thermal noise field)

[0284] Hthermal=0.01*np.random.randn(3)#thermal noise field

[0285] Heff=Hthermal

[0286] #Use RK4 method to update the magnetization direction

[0287] k1=self.step_size*self.llg(self.m,Heff)

[0288] k2=self.step_size*self.llg(self.m+0.5*k1,Heff)

[0289] k3=self.step_size*self.llg(self.m+0.5*k2,Heff)

[0290] k4=self.step_size*self.llg(self.m+k3,Heff)

[0291] self.m+=(k1+2*k2+2*k3+k4) / 6

[0292] self.m / =np.linalg.norm(self.m)#Normalized magnetization direction

[0293] #Store the results

[0294] self.magnetization[i]=self.m

[0295] def plot(self):

[0296] """Plot the magnetization orientation over time"""

[0297] plt.figure(figsize=(10,5))

[0298] plt.plot(self.time,self.magnetization[:,2],label="Mz")

[0299] plt.xlabel('Time(s)')

[0300] plt.ylabel('Magnetization(Mz)')

[0301] plt.title('Magnetization Over Time')

[0302] plt.legend()

[0303] plt.grid(True)

[0304] plt.show()

[0305] #Simulation execution

[0306] mtj=Mtj(step_size=1e-12, t_max=1e-9, temperature=300)

[0307] mtj.run()

[0308] mtj.plot()

[0309] DC simulation implementation:

[0310] Voltage sweep:

[0311] oSet a range of voltage values, such as from -1V to 1V and then back to -1V (forming a complete cycle).

[0312] oEach voltage value V MTJ It will act on the MTJ device, affecting its current, resistance and magnetization direction of the free layer.

[0313] Evolution of magnetization direction:

[0314] oFor each applied V MTJ , the magnetization direction of the free layer is updated using the Landau-Lifshitz-Gilbert (LLG) equation. o Changes in the magnetization direction affect the state of the magnetic tunnel junction and thus its resistance.

[0315] Resistance calculation:

[0316] oCalculate the resistance at the current voltage based on the magnetization direction and voltage value.

[0317] The resistance formula combines the tunnel magnetoresistance ratio (TMR), the parallel state resistance, and the magnetization direction component m z .

[0318] Result storage:

[0319] For each voltage value V MTJ , record the corresponding resistance value after the simulation is completed.

[0320] oStore the results in an array for subsequent analysis and visualization.

[0321] Plot the voltage-resistance curve:

[0322] oThe relationship between voltage and resistance is intuitively displayed through a curve graph.

[0323] Also use the STT-MTJ device as an example to hide the device parameters and part of the effective field, and show the simulation code logic:

[0324]

[0325] Heff = noise

[0326] #Magnetization direction derivative

[0327] dmdt=-self.gamma_eff*np.cross(self.m,Heff)\

[0328] -self.alpha*self.gamma_eff*np.cross(self.m,np.cross(self.m,Heff))

[0329] return dmdt

[0330] def run(self):

[0331] """Run DC simulation"""

[0332] for Vmtj in self.voltage_values:

[0333] #Iterative calculation of magnetization direction

[0334] for_in range(self.num_steps):

[0335] dmdt = self.llg (Vmtj) # Calculate the time derivative of magnetic susceptibility

[0336] self.m=self.m+self.step_size*dmdt#Update magnetization direction

[0337] self.m / =np.linalg.norm(self.m)#Normalized magnetization direction

[0338] # Calculate resistance and store

[0339] resistance=self.calculate_resistance(Vmtj)

[0340] self.resistances.append(resistance)

[0341] def plot_voltage_resistance(self):

[0342] """Draw the voltage-resistance curve"""

[0343] plt.figure(figsize=(10,6))

[0344] plt.plot(self.voltage_values,self.resistances,'o-',label='R vs V')

[0345] plt.xlabel('Voltage(V)')

[0346] plt.ylabel('Resistance(Ohm)')

[0347] plt.title('MTJ Resistance vs Voltage')

[0348] plt.grid(True)

[0349] plt.legend()

[0350] plt.show()

[0351] #Simulation run

[0352] mtj=Mtj(step_size=1e-12, t_max=5e-9, temperature=300)

[0353] mtj.run()

[0354] mtj.plot_voltage_resistance()

[0355] Monte-Carlo simulation implementation: Demonstration method using thermal noise as random term

[0356] 1. Simulation objectives:

[0357] oAt the external voltage V MTJ Under the action of, evaluate whether the magnetic moment of the MTJ free layer is successfully flipped.

[0358] oUse the Monte-Carlo method to introduce random thermal noise and calculate the flip success rate after multiple simulations.

[0359] 2. Simulation parameters:

[0360] o Initial condition: The initial magnetization direction of the free layer is set to m = [0, 0, 1] (positive z direction).

[0361] oFlip judgment: At the end of the simulation, if the flip amount of the z component of the magnetization direction reaches 90%, the flip is considered successful.

[0362] oIntroduction of thermal noise: Random thermal noise is added to the effective magnetic field in each simulation to simulate the effect of thermal disturbance on the magnetization direction.

[0363] 3. Simulation process:

[0364] oSingle simulation: Run the run() method to calculate the change process of magnetization direction from the initial state to the final time point.

[0365] oMultiple Repetitions: Repeat the run() method n times, generating new thermal noise each time and recording the simulation results.

[0366] oStatistical results: Count the number of successful magnetization reversals and calculate the reversal success rate.

[0367] 4. Visualization:

[0368] oThe change of the z-component of the magnetization direction over time during multiple simulations is plotted as a curve to intuitively display the dynamic behavior of magnetization reversal.

[0369] Taking the STT-MTJ device simulation as an example, the code implementation of the hidden parameters is shown with the thermal noise term as a random term:

[0370] import numpy as np

[0371] import matplotlib.pyplot as plt

[0372] import matplotlib.cm as cm

[0373] class Mtj:

[0374] def__init__(self,step_size,t_max,temperature,voltage):

[0375] self.step_size = step_size # time step

[0376] self.t_max=t_max#maximum simulation time

[0377] self.num_steps = int(t_max / step_size) #Number of simulation steps

[0378] self.temperature=temperature#temperature

[0379] self.voltage = voltage#apply voltage

[0380] self.alpha=0.05#damping coefficient

[0381] self.gamma_eff=2.2127e5 / (1+self.alpha**2)#Effective magnetic gyrometry

[0382] self.m_initial=np.array([0,0,1],dtype=np.float64)#initial magnetization direction

[0383] self.m=self.m_initial.copy()#Current magnetization direction

[0384] self.time=np.linspace(0,t_max,self.num_steps)#time array

[0385] self.magnetization = np.zeros((self.num_steps, 3)) #Store magnetization direction

[0386] def llg(self,m,Heff):

[0387] """LLG equation core calculation"""

[0388] dmdt=-self.gamma_eff*np.cross(m,Heff)\

[0389] -self.alpha*self.gamma_eff*np.cross(m,np.cross(m,Heff))

[0390] return dmdt

[0391] def run(self):

[0392] """Single magnetization reversal simulation"""

[0393] for iin range(self.num_steps):

[0394] #Thermal noise field

[0395] thermal_noise=np.random.randn(3)

[0396] thermal_noise / =np.linalg.norm(thermal_noise)#Normalized noise

[0397] Hthermal=0.01*thermal_noise# Thermal noise intensity (simplified)

[0398] #Effective magnetic field (considering only noise and voltage modulation)

[0399] Heff=Hthermal

[0400] #Use RK4 method to update the magnetization direction

[0401] k1=self.step_size*self.llg(self.m,Heff)

[0402] k2=self.step_size*self.llg(self.m+0.5*k1,Heff)

[0403] k3=self.step_size*self.llg(self.m+0.5*k2,Heff)

[0404] k4=self.step_size*self.llg(self.m+k3,Heff)

[0405]

[0406] Since the use and simulation functions of the two devices under the framework are similar, this embodiment is based on STT-MTJ (spin transfer matrix) to demonstrate the electrical and magnetic properties of the magnetic tunnel junction (MTJ) under different working conditions based on this framework, including DC simulation, transient (Tran) simulation, and Monte Carlo. The simulation also takes into account the impact of radiation on device operation in special use scenarios such as aerospace, and supplements radiation-related simulation functions. Different simulation forms for three-terminal devices such as SOT-MTJ will be specifically demonstrated in combination with diagrams.

[0407] The composition and operation structure of the magnetic tunnel junction simulation framework

[0408] like Figure 1As shown, the STT-MTJ simulation framework used in this embodiment consists of multiple modules. First, the system loads the physical parameters of the device (such as material constants, geometric dimensions, temperature, etc.) through the parameter initialization module. Subsequently, the electromagnetic model of the device is established through the physical field modeling module, considering physical phenomena such as thermal noise, spin transfer torque effect (STT), and voltage-controlled magnetic anisotropy effect (VCMA). The numerical solution module uses RK4 for time stepping solution to simulate the dynamic changes of magnetization direction. Finally, the simulation results are statistically analyzed and visualized through the data analysis module to draw relevant data such as magnetization direction, MTJ resistance and current.

[0409] STT-MTJ DC simulation (DC)

[0410] like Figure 2 As shown in the figure, the circuit structure of the STT-MTJ DC simulation includes an input current source and a magnetic tunnel junction device. In the simulation, the input current is driven by voltage to change the magnetization state of the MTJ device. Under the stimulation of the electrical signal and sufficient delay waiting, the resistance state of the MTJ switches between parallel (P) and antiparallel (AP). Figure 2 The image shows that under the stimulation of the write signal, the MTJ switches from the parallel steady state to the antiparallel steady state.

[0411] Resistance variation in STT-MTJ DC simulation

[0412] like Figure 3 As shown, 100 DC simulations were performed based on the DC simulation module in the framework, and the simulation results showed the resistance distribution of STT-MTJ under different operating voltages. Figure 3 The curves in the figure show the resistance distribution of the MTJ device under different voltages, reflecting the difference in resistance when the magnetic tunnel junction changes from a parallel state to an antiparallel state and from an antiparallel state to a parallel state, which is completely consistent with the actual working conditions of the magnetic tunnel junction.

[0413] STT-MTJ transient simulation (Tran)

[0414] Figure 4 The simulation output of the STT-MTJ transient simulation based on the framework transient simulation module is shown. In this simulation, the magnetic tunnel junction is dynamically switched by the write signal. Figure 4 The left side shows the circuit structure and the z-axis magnetic moment precession of the magnetic tunnel junction when writing low resistance state and writing high resistance state. The image output of transient simulation shows the nonlinear resistance change of the MTJ device under transient response, proving its adjustability as a storage unit.

[0415] Thermal Noise Effects in STT-MTJ Transient Simulation

[0416] Figure 5 The circuit structure and output of STT-MTJ transient simulation based on adding thermal noise in the framework are shown. Figure 4 Similarly, the left side includes the circuit structure and the z-axis magnetic moment precession of the magnetic tunnel junction in two written states. In this simulation, the influence of thermal noise on the magnetization dynamics is considered, especially the interference of thermal noise on the magnetization reversal process. Figure 5 The output in Figure 1 shows the time delay of the magnetization reversal process and the fluctuation of the resistance change under the action of thermal noise. Consideration of thermal noise is an important factor in the design of STT-MTJ devices.

[0417] Therefore, this simulation is of great significance.

[0418] STT-MTJ Monte Carlo Simulation—Influence of Process Deviation

[0419] like Figure 6 As shown in the figure, this simulation is based on the function of the Monte Carlo simulation module of the framework simulation module. The Monte Carlo simulation of the STT-MTJ device takes into account the impact of 5% process deviation on device performance. The simulation results show the impact of process deviation on the resistance distribution and magnetization dynamics of the MTJ device through statistics of 100 random simulation samples. The results show that due to process fluctuations, there is a certain degree of randomness in the resistance value and the success rate of switching the magnetization direction of the MTJ device. This shows that in the actual manufacturing process, the impact of process deviation on device performance cannot be ignored, and this simulation function is of great significance for knowing the actual preparation of the device.

[0420] STT-MTJ Monte Carlo Simulation—Temperature Effect

[0421] Figure 7 The effect of temperature change on the performance of STT-MTJ devices is demonstrated, and the simulation temperature range is 200K to 500K. The results show that the increase in temperature causes the success rate of magnetization reversal of MTJ devices to drop significantly. Under high temperature conditions, thermal noise increases, and the magnetization reversal process becomes more difficult, thus affecting the stability of the device. This result shows that the temperature effect is a factor that cannot be ignored when designing STT-MTJ devices. STT-MTJ Monte Carlo Simulation (Monte Carlo) - Thermal Noise Impact

[0422] like Figure 8 As shown in Figure 1, the STT-MTJ device was simulated with thermal noise as a random term. The simulation results show the impact of thermal noise on the device's magnetization reversal process. The simulation results show that thermal noise is a key factor affecting the stability of MTJ devices, especially in low-power applications.

[0423] STT-MTJ Monte Carlo Simulation (Monte Carlo)—Influence of Multi-factor Deviation

[0424] Fig. 9 The Monte Carlo simulation results of STT-MTJ devices are presented under consideration of multiple factors (such as process deviation, temperature fluctuation, thermal noise, etc.). By analyzing the coupling effects of multiple factors, the results show that in actual application environments, the performance stability of MTJ devices is affected by a combination of multiple factors. This simulation result can provide optimization guidance for the design of STT-MTJ devices to improve their reliability in complex environments.

[0425] SOT-MTJ (including VCMA effect) transient simulation (Tran) simulation circuit structure and output schematic diagram

[0426] Since SOT-MTJ is a three-terminal device, the simulation structure in this framework is slightly different from the two-terminal STT-MTJ simulation circuit structure, so it is specially displayed separately. SOT-MTJ has read-write separation, and the magnetic tunnel junction is flipped based on the orbital coupling effect (SOC) under the action of the write current. This simulation shows the writing working conditions of the SOT-MTJ including voltage-controlled various effects (VCMA), and the regulation of anisotropy by the VCMA effect is shown through two-stage voltage control. The upper right end is a schematic diagram of the magnetic moment precession of the magnetic tunnel junction. At present, this kind of regulation technology is an important direction of low-power research on magnetic tunnel junctions, so it is of great significance for the framework to have this function.

[0427] STT-SOT collaborative transient simulation (Tran)

[0428] like Fig.11 As shown in the figure, a transient simulation diagram of SOT-MTJ with STT-SOT working together is shown. This type of SOT-MTJ can guarantee 100% state switching, so it is a very important working mechanism in the research of SOT-MTJ. This simulation shows the framework's support for this type of simulation function.

[0429] SOT-MTJ Monte Carlo simulation function display

[0430] Considering that SOT-MTJ is a three-terminal device, the framework's support for SOT-MTJ Monte Carlo simulation is shown here. This image shows a Monte Carlo simulation with thermal noise as a random term, and the change in magnetic moment reflects the impact of thermal noise on the writing and retention of SOT-MTJ.

[0431] Simulation of STT-MTJ Radiation Effect

[0432] Fig.13The simulation results of the effect of radiation on STT-MTJ devices are shown. This simulation is based on the Monte Carlo simulation function module in the framework. In this simulation, the effect of radiation particles on MTJ devices is considered, especially the response in a high radiation environment. The simulation results show that radiation particles will affect the working state of the device, and the device will be in a fluctuating working range. Fig.13 The results reveal the potential threat of radiation to the stability and reliability of STT-MTJ devices.

[0433] The above images demonstrate the successful construction of two magnetic tunnel junction devices and the successful operation of the three simulation working modes of the simulation platform.

[0434] The basic principles and main features of the present invention are described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for illustrating the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which shall fall within the scope of the present invention to be protected. The scope of protection of the invention shall be defined by the attached claims and their equivalents.

Claims

1. A modeling and simulation method for spin transfer torque and spin orbit torque magnetic tunnel junction, characterized in that: The following steps are involved: First, in step 1, the physical parameters of the device are loaded through the parameter initialization module, including material constants, geometric dimensions, temperature, etc.; Then, in step 2, the electromagnetic model of the device is established through the physical field modeling module, taking into account physical phenomena including thermal noise, spin transfer torque effect (STT), and voltage-controlled magnetic anisotropy effect (VCMA). The numerical solution module uses RK4 for time-stepping solution to simulate the dynamic changes of the magnetization direction. Finally, in step three, the simulation results are statistically analyzed and visualized through the data analysis module to plot relevant data such as magnetization direction, MTJ resistance and current; In step 1, the basic physical constants of the device are input: Vacuum magnetic permeability: μ0, gyromagnetic Ratio: γ, Boltzmann constant: k B , electron charge: e, Reduced Planck constant: Damping coefficient: α, effective gyromagnetic ratio: Input of device size: Device diameter: D, free layer thickness: t f , oxide layer thickness: t ox , junction area: A MTJ ; In step 2, the energy term of the external magnetic field (Zeeman energy) is as follows: Yes ext =-∫M·H ext dV The effective field obtained by the variational method of the magnetic moment M is as follows: H ext =H ext The anisotropic field energy term is as follows: The anisotropic fields are obtained as follows: Among them, M s is the saturation magnetization. Demagnetization field energy term: The demagnetization field is obtained as follows: Spin transfer torque field energy term: E STT J-∫J·MdV The contribution of the spin transfer torque in the effective field is obtained as follows: J is the current density of the ferromagnetic layer The thermal noise field simulates the disturbance of thermal fluctuations on magnetization by introducing random force terms, and its noise satisfies the following statistical properties: <F thermal (t)·F thermal (t ′ )>=2k B TαMδ(t-t ′ ) Therefore, the thermal noise term generally added to the effective field is: Energy term for the exchange bias field: E exbias =-J ex ∫M·M AFM dV The contribution of this field in the effective field is obtained as: Among them J ex is the interface exchange coupling strength, usually obtained through experiments or fitting. M FM is the magnetization direction of the ferromagnetic layer, M AFM is the magnetization direction of the antiferromagnetic layer. Voltage Controlled Anisotropy: Where β is the voltage regulation coefficient, m z is the z-axis magnetic moment component of the free layer. The resistance formula uses the following: The dynamics of the device model comes from solving the LLG equation. Taking the LLG equation used in the framework as an example, the solution process implemented by two methods is given: The equation can be expressed as: Fourth-order Runge–Kutta: The fourth-order Runge–Kutta method approximates the solution of a differential equation by computing four slopes. First calculate the slope: k1=f(M(t)) k4=f(M(t)+Δt·k3) Then calculate the new magnetization vector:

2. The modeling and simulation method of a spin transfer torque and spin orbit torque magnetic tunnel junction according to claim 1, characterized in that: In the step 2, the influence of temperature on the spin transfer torque magnetic tunnel junction includes several aspects: Saturation magnetization M s Dependence on temperature: M s0 is the initial saturation magnetization, T c is the Curie temperature, C Msx is the power factor of the temperature effect Magnetic anisotropy constant K i Dependence on temperature: K i0 is the initial magnetocrystalline anisotropy constant, C γi is the power factor describing the relationship between magnetic anisotropy and magnetization intensity The temperature dependence of the spin polarization P is: P=P0·(1-a·T 1.5 ) P0 is the initial spin polarization, a is the temperature dependence coefficient Dependence of voltage regulation coefficient β on temperature:

3. The modeling and simulation method of a spin transfer torque and spin orbit torque magnetic tunnel junction according to claim 1, characterized in that: The influence of radiation on the spin-transfer torque magnetic tunnel junction under the special working environment in step 2 includes the following aspects: Saturation magnetization M s Degeneration: D is the radiation dose (Gy, gray), c It is the radiation tolerance threshold, which indicates the radiation tolerance of the material. Magnetic anisotropy constant K i Degeneration: Degradation of Tunneling Magnetoresistivity (TMR) TMR0 is the initial TMR value, D TMR Describe the radiation tolerance threshold for TMR degradation. At the same time, radiation will introduce random disturbances and destroy the magnetization direction of the magnetic tunnel junction. The field contribution is modeled as a Gaussian distributed random field: in σ0 is the disturbance intensity when not irradiated.

4. The modeling and simulation method of a spin transfer torque and spin orbit torque magnetic tunnel junction according to claim 1, characterized in that: The step 2 also includes modeling of a spin-orbit moment magnetic tunnel junction (SOT-MTJ), which is as follows: Input of basic physical constants of the device: Vacuum magnetic permeability: μ0, gyromagnetic ratio: γ, Boltzmann constant: k B , electron charge: e, Reduced Planck constant: h, damping coefficient: α, effective gyromagnetic ratio: Electronic quality: me Input of device size: Device diameter: D, free layer thickness: t f , oxide layer thickness: t ox , junction area: AMTJ, Heavy metal layer length: l, heavy metal layer thickness: h, heavy metal layer cross-sectional area: AHM Physical Modeling Basics: SOT-MTJ unique supplementary physical modeling section is explained; Read status: The read path passed is the same as STT-MTJ; Write state: The write state is written by the SOT current of the heavy metal layer, utilizing spin-orbit coupling (SOC). The following is the LLG equation form used in the write state simulation: Where m is the normalized magnetic moment, expressed by M / M s Get. σ is the polarization direction of the spin polarized current. and The ratio between different materials is: and Usually between 0 and 0.

6. J STT and J SOT They are the current density through the magnetic tunnel junction and the current density through the heavy metal layer respectively, and the addition of other effective fields is the same as the above-mentioned STT-MTJ.

5. The modeling and simulation method of a spin transfer torque and spin orbit torque magnetic tunnel junction according to claim 4, characterized in that: In the modeling of the spin-orbit moment magnetic tunnel junction (SOT-MTJ), the dynamics of the SOT-MTJ device model also comes from the solution of the LLG equation provided above including the supplemented form. The solution process implemented by the algorithm is given by taking the LLG equation used in the framework as an example: The equation can be expressed as: Fourth-order Runge–Kutta: The fourth-order Runge–Kutta method approximates the solution of a differential equation by computing four slopes. First calculate the slope: k1=f(m(t)) k4=f(m(t)+Δt·k3) Then calculate the new magnetization vector:

Images