Multiphysics Numerical Calculation Method for On-Chip Devices with Ferrite Thin Films Loaded

Abstract

The present invention discloses a multi-physics numerical calculation method for an on-chip device loaded with a ferrite thin film, belonging to the fields of integrated circuit technology and computational electromagnetics. First, a hybrid grid meshing is performed on the on-chip device loaded with the ferrite thin film; then, each field component of the three physical fields is arranged in the discrete space; finally, according to the coupling relationship of the three physical fields, the physical field equations are solved and the parameter transfer between the equations is carried out. According to the structural characteristics of the on-chip device, the present invention combines two grid encryption technologies in the conventional FDTD space, significantly improving the modeling accuracy; according to the multi-physics phenomena faced by the on-chip device, on the basis of solving the Maxwell equation by FDTD, the LLG equation and the heat conduction equation are coupled and calculated, and reasonable parameter transfer is carried out, completely restoring the electromagnetic field phenomena, the magnetization and demagnetization processes of the ferrite thin film and their thermal effects when the on-chip device is working, and effectively improving the simulation accuracy of the calculation method for the target.

Description

Technical Field

[0001] The present invention relates to the technical fields of integrated circuit technology and computational electromagnetics, and particularly relates to a multi-physics numerical calculation method for an on-chip device loaded with a ferrite thin film. Background Art

[0002] After years of development, millimeter-wave technology has been widely applied in various civilian and military scenarios, greatly promoting the progress of the electronics industry. On-chip devices are a type of basic device with ultra-high integration, and can be of single-layer or multi-layer structures. As Figure 1 shown in a double-layer on-chip device, which includes a primary coil and a secondary coil, with an isolation material in between, and can be directly integrated on a substrate material.

[0003] On-chip devices play a crucial role in the development of millimeter-wave integrated circuits. To enhance the electromagnetic performance and electromagnetic shielding effectiveness of on-chip devices, loading a soft magnetic thin film (i.e., a ferrite thin film) on its surface is an effective means, as Figure 2 shown. However, the time-varying electromagnetic field characteristics and temperature effects exhibited by electromagnetic devices, as well as the ultra-high magnetic permeability and strong magnetization / demagnetization characteristics of ferrite thin films, make it impossible for a single physical field to accurately describe the device performance. It is necessary to comprehensively solve Maxwell's equations of electromagnetics, the Landau–Lifshitz–Gilbert equations (LLG equations) of magnetization dynamics, and the heat conduction equation in heat transfer. This is essentially a multi-physics coupling problem. If an effective solution method for the above equations cannot be developed, it will severely limit the development and application of high-performance on-chip devices.

[0004] Currently, the multi-physics numerical calculation for on-chip devices loaded with ferrite thin films mainly faces the following difficulties:

[0005] First, after loading the ferrite thin film, the electromagnetic field around the on-chip device will change violently and exhibit strong multi-physics coupling characteristics, posing a great challenge to accurate simulation. Existing commercial software needs to simplify and equivalent it when calculating such problems; for example, the metal layer is equivalent to an ideal electric conductor, and the ferrite thin layer is equivalent to an ideal magnetic conductor or a two-dimensional plane with high magnetic permeability. However, in the actual physical process, the ferrite thin film has a strong binding effect on the magnetic field of the device, making the magnetic field distribution concentrated and the magnetization and demagnetization phenomena inside the material significant. Therefore, the entire process needs to be calculated accurately to obtain the precise electromagnetic field distribution. At the same time, after adding electromagnetic excitation to the on-chip device, electromagnetic effects such as ohmic loss and eddy current loss will cause the temperature to rise in the local space, and then lead to changes in parameters such as the resistivity, thermal conductivity, and dielectric constant of the material. This material nonlinearity makes the solution process more complex.

[0006] Second, after loading the ferrite film on the on-chip device, the overall structure will exhibit strong multi-scale characteristics, posing great challenges to accurate modeling. When performing three-dimensional numerical modeling of the on-chip device, in the vertical direction, the substrate of the on-chip device is usually in the order of hundreds of micrometers, the metal layer of the on-chip device is in the order of micrometers, and the ferrite film is in the order of hundreds of nanometers to micrometers; due to the special properties of ferrite, the thickness direction cannot be ignored, resulting in extremely prominent multi-scale phenomena; on the other hand, the "thin layer" morphology exhibited by the device also shows certain multi-scale characteristics in the horizontal and vertical directions, which greatly increases the difficulty of accurate three-dimensional modeling.

[0007] From the above analysis, it can be seen that accurate modeling and analysis of the on-chip device loaded with the ferrite film are the basis for describing its physical properties. Synchronously solving the Maxwell equation, LLG equation, and heat conduction equation in the time domain can accurately describe the interaction process of its physical fields and achieve the above purpose. However, there is a lack of effective multi-physics simulation analysis software in the current commercial market, and there is a lack of effective numerical calculation methods in the academic community. Therefore, it is urgent to establish an effective numerical calculation method to accurately analyze the distribution state of each physical field in the device, providing necessary theoretical support and efficient simulation means for experiments. Summary of the Invention

[0008] The purpose of the present invention is to provide a multi-physics field numerical calculation method for an on-chip device loaded with a ferrite film to solve the problem that there is a lack of effective numerical methods to accurately simulate the physical properties of the on-chip device after covering the ferrite film.

[0009] To solve the above technical problems, the present invention provides a multi-physics field numerical calculation method for an on-chip device loaded with a ferrite film, including:

[0010] Step one, performing hybrid grid meshing on the on-chip device after loading the ferrite film;

[0011] Step two, arranging each field component of the three physical fields in the discrete space;

[0012] Step three, according to the coupling relationship of the three physical fields, solving the physical field equations and performing parameter transfer between the equations.

[0013] In one implementation, performing hybrid grid meshing on the on-chip device after loading the ferrite film includes: establishing a FDTD calculation space in the Cartesian coordinate system, discretizing the space with cubic grids of side length δ, and on this basis, using two encryption techniques of non-uniform grids and conformal sub-grids to finely mesh the calculation target.

[0014] In one embodiment, according to the structural characteristics of the on-chip device and the loaded ferrite thin film in the vertical direction, the non-uniform grid encryption technology is used in its xOz plane to gradually refine the grid in the specified direction:

[0015] By specifying the grid reduction factor p, the size of the next grid in this direction is 1 / p of the current grid size. Through m consecutive transformations, the grid cell size rapidly reduces from δ×δ in the conventional grid area to δ×(δ / p m )), and the value range of p is set as 1 < p < 1.6, where m is a positive integer.

[0016] In one embodiment, according to the structural characteristics of the on-chip device and the loaded ferrite thin film in the horizontal direction, the conformal sub-grid encryption technology is used in the xOy plane to realize the grid encryption of a specific area:

[0017] By specifying the sub-grid factor d, the grids in the region are refined simultaneously in the x and y directions, and 1 grid in the conventional space becomes d 2 grids, and the grid cell size rapidly reduces from δ×δ in the conventional grid area to (δ / d)×(δ / d) in the fine area. The value range of d is set as an integer of 2 < d < 8.

[0018] In one embodiment, arranging the field components of the three physical fields in the discrete space includes:

[0019] Setting the spatial direction and position according to the physical difference format of the spatial vector, reasonably arranging the physical field quantities in the discrete space, and discretizing them in space and time in the form of central difference;

[0020] Based on the physical field equations and their coupling relationships, a hexahedral grid containing each physical field quantity is established on the basis of the discrete grid of FDTD.

[0021] In one embodiment, the three physical fields are the electromagnetic field, the micro magnetic field, and the thermal field. According to the mutual coupling relationship among the three, parameter transfer and the calculation of all physical fields are performed within one time step of the discrete time.

[0022] In one embodiment, the physical field equations are calculated step by step in the following order:

[0023] First step, with the field boundary conditions of the given port excitation, solve the Maxwell equation to obtain the distributions of the electric field intensity E and the magnetic field intensity H within the entire calculation domain at the current moment. Then, transfer the magnetic field intensity H to the LLG equation and transfer the electric field intensity E to the heat conduction equation, which are respectively used for the electromagnetic field - micro magnetic field coupling and the electromagnetic field - thermal field coupling;

[0024] In the second step, solve the LLG equation in the internal region of the ferrite film. Take the magnetic field strength H in the electromagnetic field as the dynamic component in the effective magnetic field strength Heff. Combine the initial bias magnetic field strength H0, the magnetic anisotropy field strength Hk, and the exchange magnetic field strength Hex to obtain the exchange magnetic field strength Heff at the current moment, and substitute it into the LLG equation to solve the magnetization intensity M of the ferrite film at the current moment to characterize the magnetization process of the ferrite film. Then, calculate the more accurate magnetic field strength H at the current position based on the magnetization intensity M and transfer it back to the Maxwell equation to achieve the coupling of the micro-magnetic field and the electromagnetic field, that is, to form the synchronous bidirectional coupling calculation of the electromagnetic field and the micro-magnetic field.

[0025] In the third step, solve the heat conduction equation. Take the ohmic heat of the device as the heat source and the fixed temperature value or the temperature interpolation function as the background temperature boundary condition to calculate the temperature distribution at the current moment. Then, update each parameter according to the temperature coefficient and the temperature change function of the material, and transfer these parameters back to the Maxwell equation and the LLG equation to form the coupling of the thermal field - electromagnetic field and the thermal field - micro-magnetic field, that is, to complete all the coupling calculations of the electromagnetic field - micro-magnetic field - thermal field in one time step.

[0026] The multi-physics field numerical calculation method for an on-chip device loaded with a ferrite film provided by the present invention has the following beneficial effects:

[0027] (1) Based on the traditional meshing, two encryption techniques are superimposed. By implementing encryption at necessary positions, the error caused by over-simplification is effectively avoided, and at the same time, the huge calculation amount caused by over-encryption is avoided, improving the calculation accuracy while ensuring the calculation efficiency.

[0028] (2) Based on the calculation of the Maxwell equation, the LLG equation and the heat conduction equation are coupled for calculation to completely describe the magnetization and demagnetization processes of the thin film and the temperature phenomenon of the material, truly restoring the physical performance of the device, and effectively improving the simulation accuracy of the device. Description of the Drawings

[0029] Figure 1 It is a schematic structural diagram of an on-chip device with a double-layer structure.

[0030] Figure 2 It is a schematic structural diagram of the on-chip device after loading the ferrite film.

[0031] Figure 3 It is a schematic flow diagram of the multi-physics field numerical calculation method provided by the present invention.

[0032] Figure 4 It is a schematic diagram of the mesh meshing form in the xOz direction.

[0033] Figure 5It is a schematic diagram of the grid meshing form in the xOy direction.

[0034] Figure 6 It is a spatial grid unit based on the FDTD grid settings and includes all physical field quantities in the electromagnetic field, micro-magnetic field, and thermal field. Specific implementation manners

[0035] The following further elaborates in detail a multi-physical field numerical calculation method for an on-chip device loaded with a ferrite thin film proposed by the present invention in combination with the accompanying drawings and specific embodiments. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings all adopt very simplified forms and non-precise scales, and are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention.

[0036] The present invention provides a multi-physical field numerical calculation method for an on-chip device loaded with a ferrite thin film, and its process is as Figure 3 shown, including the following steps:

[0037] Step 1: Establish the basic discrete space and time of the FDTD (Finite difference time domain method) of the object to be solved.

[0038] Establish the FDTD space in the Cartesian coordinate system. The spatial coordinate range of the calculation region is set as Xn→Xp in the x direction, Yn→Yp in the y direction, and Zn→Zp in the z direction. The discrete space step sizes in the x, y, and z directions within the calculation region are all set as δ, and the time step size is set as Δt.

[0039] Step 2: Establish a three-dimensional solid model of the on-chip device and the ferrite thin film, and perform grid meshing.

[0040] Establish a three-dimensional solid model of the on-chip device and the ferrite thin film, and describe the positions of each node in terms of coordinates. According to the node coordinates and the discrete space step size, perform the first grid division on the entire calculation target. On this basis, combine two grid encryption techniques to perform the second discretization on the calculation target. According to the structural characteristics of the on-chip device and the loaded ferrite thin film in the vertical direction, use the "non-uniform grid" encryption technique in the xOz plane to gradually refine the grid in the specified direction, that is, by specifying the grid reduction factor p, the size of the next grid in this direction is 1 / p of the current grid size. Through m consecutive transformations, the grid cell size rapidly shrinks from δ×δ in the conventional grid region to δ×(δ / p m ), achieving the purpose of rapid reduction of the grid size. m is a positive integer, such as Figure 4As shown. In the present invention, the value range of p is set as 1 < p < 1.6. According to the structural characteristics of the on-chip devices and the loaded ferrite thin film in the horizontal direction, such as Figure 5 As shown, the "conformal sub-grid" encryption technology is used in the xOy plane to achieve grid encryption in a specific area, that is, by specifying the sub-grid factor d, the grids in the area are refined simultaneously in the x and y directions, and 1 grid in the conventional space becomes d 2 grids, and the grid cell size is rapidly reduced from δ×δ in the conventional grid area to (δ / d)×(δ / d) in the fine area. In this way, accurate modeling of the local area can be achieved without changing the grid arrangement in the conventional space. In addition, by constructing a sub-grid area along the boundary of the calculation target, the proportion of the fine grid can be minimized, improving the calculation efficiency while ensuring the accuracy. In the present invention, the value range of d is set as an integer of 2 < d < 8.

[0041] Step 3, initialize all physical field components in the calculation area.

[0042] Based on all the coordinates in the discrete space obtained in Step 1 and Step 2, all the physical quantities in the three physical fields of the electromagnetic field, the micro-magnetic field, and the thermal field are initialized. As Figure 6 Shown is the space grid cell including all the physical field quantities in the electromagnetic field, the micro-magnetic field, and the thermal field based on the FDTD grid. The physical field quantities involved in the present invention are: electric field strength E, magnetic field strength H, magnetic induction intensity B, effective magnetic field strength H eff , initial bias magnetic field strength H0, magnetic anisotropy field strength H k , exchange magnetic field strength H ex , magnetization intensity M, saturation magnetization intensity M s , dissipation power P, heat generation Q, time-varying temperature T. Among them, E, H, B, Heff, H0, Hk, Hex, M, and Ms are spatial vectors and have components in the x, y, and z directions in the Cartesian discrete space. Using (i, j, k) to represent the spatial coordinate position and x, y, z to represent the spatial directions of the physical field quantities, initial values are set for the components of each physical field quantity in the x, y, and z directions, that is, E x | i,j,k = 0, E y | i,j,k = 0, E z | i,j,k = 0, H x | i,j,k = 0, H y | i,j,k = 0, H z | i,j,k = 0, B x | i,j,k = 0, B y |i,j,k = 0, B z | i,j,k = 0, H effx | i,j,k = 0, H effy | i,j,k = 0, H effz | i,j,k = 0, H 0x | i,j,k = 0, H 0y | i,j,k = 0, H 0z | i,j,k = 0, H kx | i,j,k = 0, H ky | i,j,k = 0, H kz | i,j,k = 0, H exx | i,j,k = 0, H exy | i,j,k = 0, H exz | i,j,k = 0, M x | i,j,k = 0, M y | i,j,k = 0, M z | i,j,k = 0, M sx | i,j,k = 0, M sy | i,j,k = 0, M sz | i,j,k = 0, P| i,j,k = 0, T| i,j,k = 0; Assign corresponding numerical values to each constant, that is, the permittivity of free space ε0 = 8.854×10 -12 F / m, the permeability of free space μ0 = 4π×10 -7 N / A 2 , the gyromagnetic ratio γ = -1.759×10 11 C / kg, the damping coefficient α = μ0γΔH / 4πf0, where f0 is the operating frequency and ΔH is the magnetic field change; Assign different numerical values to the remaining parameters according to the properties of different materials, including the relative permittivity ε r , the relative permeability μ r , the conductivity σ, the heat capacity C p , the thermal conductivity κ, the temperature coefficient of permeability α μ , the temperature coefficient of permittivity α ε , the temperature coefficient of conductivity α σ , the temperature coefficient of thermal conductivity α μ .

[0043] Step 4: Set the excitation source, background temperature, and initial bias magnetic field strength.

[0044] At the device port, set the excitation electric field at the port according to the following formula:

[0045]

[0046] where n is the number of time-step iterations, C eze , C ezhy , C ezhx are iteration coefficients obtained according to the central difference scheme, expressed as follows:

[0047]

[0048] Δt is the time step, δ is the side length of the cubic grid; f is the excitation source wave function, which can usually be set as a time-harmonic field source, Gaussian pulse source, differential Gaussian pulse source, and modulated Gaussian pulse at a specific frequency.

[0049] The background temperature can be a constant or a function of time. The initial bias magnetic field strength can be a constant or a function of time in one or several directions.

[0050] Step 5: Calculate the Maxwell equations in the entire computational space according to the following method to obtain the spatial electric and magnetic field distributions at the current moment:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] where the iteration coefficients between the various field quantities can be expressed as:

[0058] Iteration coefficient

[0059] Iteration coefficient

[0060] Iteration coefficient

[0061] Iteration coefficient

[0062] Step Six, calculate the LLG equation within the ferrite thin film region and update the H component in the Maxwell equation within the thin film region.

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Step Seven, calculate the heat conduction equation in the entire calculation space using the following method to obtain the spatial temperature distribution at the current moment, and update the material parameters of each node according to the temperature.

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] where ρ is the material density, C p is the material heat capacity, and T0 is the initial temperature.

[0077] Step Eight, within the specified time range, loop through Steps Five, Six, and Seven until the time ends to complete the calculation.

[0078] The above description is only a description of the preferred embodiments of the present invention and does not limit the scope of the present invention in any way. Any changes and modifications made by those of ordinary skill in the art of the present invention based on the above disclosure fall within the scope of protection of the claims.

Claims

1. A multi-physics numerical calculation method for an on-chip device loaded with a ferrite thin film, characterized in that, including: Step 1: Perform hybrid mesh generation on the on-chip device after loading the ferrite film; Step 2: Arrange the field components of the three physical fields in the discrete space; Step 3: According to the coupling relationships of the three physical fields, solve the physical field equations and perform parameter transfer between the equations; where, Performing hybrid mesh generation on the on-chip device after loading the ferrite film includes: establishing a FDTD calculation space in the Cartesian coordinate system, discretizing the space using cubic grids with side length δ, and on this basis, using two encryption techniques of non-uniform grids and conformal sub-grids to finely divide the calculation target; The three physical fields are the electromagnetic field, the micro-magnetic field, and the thermal field. According to the mutual coupling relationships among them, parameter transfer and the calculation of all physical fields are performed within one time step of discrete time; The physical field equations are calculated step by step in the following order: First step: Given the field boundary conditions of the excitation at the ports, solve the Maxwell equations to obtain the distributions of the electric field intensity E and the magnetic field intensity H within the entire calculation domain at the current moment. Then, transfer the magnetic field intensity H to the LLG equation and transfer the electric field intensity E to the heat conduction equation, which are respectively used for the electromagnetic field - micro-magnetic field coupling and the electromagnetic field - thermal field coupling; Second step: Solve the LLG equation within the internal region of the ferrite film. Take the magnetic field intensity H in the electromagnetic field as the dynamic component in the effective magnetic field intensity Heff, and combine the initial bias magnetic field intensity H0, the magnetic anisotropy field strength Hk, and the exchange magnetic field intensity Hex to obtain the exchange magnetic field intensity Heff at the current moment, and substitute it into the LLG equation to solve the magnetization intensity M of the ferrite film at the current moment to characterize the magnetization process of the ferrite film. Then, calculate a more accurate magnetic field intensity H at the current position based on the magnetization intensity M and transfer it back to the Maxwell equation to achieve the micro-magnetic field - electromagnetic field coupling, that is, to form a synchronous two-way coupling calculation of the electromagnetic field and the micro-magnetic field; Third step: Solve the heat conduction equation. Take the ohmic heat of the device as the heat source and the fixed temperature value or the temperature interpolation function as the background temperature boundary condition to calculate the temperature distribution at the current moment. Then, update each parameter according to the temperature coefficient and the temperature change function of the material, and transfer these parameters back to the Maxwell equation and the LLG equation to form the thermal field - electromagnetic field and thermal field - micro-magnetic field couplings, that is, to complete all the couplings of the electromagnetic field - micro-magnetic field - thermal field within one time step.

2. The multi-physics numerical calculation method for the on-chip device loaded with ferrite film according to claim 1, wherein According to the structural characteristics of the on-chip device and the loaded ferrite film in the vertical direction, use the non-uniform grid encryption technology in its xOz plane to gradually refine the grid in the specified direction: By specifying the mesh reduction factor p, the size of the next mesh in this direction is made 1 / p of the current mesh size. Through m consecutive transformations, the mesh cell size rapidly reduces from δ×δ in the regular mesh region to δ×(δ / p m ) in the fine region. Set the value range of p as 1 < p < 1.6, and m is a positive integer.

3. The multi-physics numerical calculation method of the on-chip device loaded with ferrite thin film according to claim 1, characterized in that According to the structural characteristics of the on-chip device and the loaded ferrite film in the horizontal direction, use the conformal sub-grid encryption technology in the xOy plane to achieve grid encryption in specific regions: By specifying the sub-grid factor d, the grids in the region are refined simultaneously in the x and y directions, and one grid in the conventional space is changed into d 2 grids. The grid cell size rapidly shrinks from δ×δ in the conventional grid region to (δ / d)×(δ / d) in the fine region. The value range of d is set as an integer where 2 < d < 8.

4. The multi-physical field numerical calculation method of the on-chip device loaded with ferrite film according to claim 1, characterized in that, Arranging the field components of the three physical fields in the discrete space includes: Set the spatial directions and positions according to the physical difference format of the spatial vectors, reasonably arrange the physical field quantities in the discrete space, and discretize them in space and time in the form of central differences; Based on the discrete grids of FDTD, establish a hexahedral grid containing each physical field quantity according to the physical field equations and their coupling relationships.

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