Simulation excitation method for signal integrity of through silicon via interconnect structure based on core particle conformal technology

Abstract

The application discloses a kind of based on conformal technology's core particle through silicon via interconnection structure signal integrity simulation excitation method, using time domain finite difference method analysis core particle interconnection structure application scene, to through silicon via structure model using conformal technology is analyzed;Overall calculation region is divided into excitation region and structure calculation region two sub-regions;Using total field / scattering field boundary technology, the result of excitation region is introduced as incident wave into structure calculation region, as excitation source to through silicon via structure is excited;The surface power integration at port in total field and scattering field is calculated, and by Fourier transform is converted into frequency domain calculation each port S parameter.The present application reduces the step approximation error of time domain finite difference method using conformal technology, by dividing the calculation region into two sub-regions solve the high-order mode crosstalk problem existing in typical coaxial structure such as through silicon via, and greatly improve the calculation precision of through silicon via structure signal integrity.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic simulation technology, specifically relating to a simulation excitation method for signal integrity of a core-particle through-silicon via interconnect structure based on conformal technology. Background Technology

[0002] In electromagnetic computation methods, the Finite-Difference Time-Domain (FDTD) method has demonstrated excellent application in electromagnetic problem analysis due to its accuracy and flexibility. This method is easy to program, can effectively analyze various structures, and facilitates observation of electromagnetic field changes over time. However, when analyzing signal integrity issues in structures such as Through Silicon Vias (TSVs) and Coaxial Through Silicon Vias (CTSVs), the FDTD method suffers from problems such as stepped approximation errors and high-order mode crosstalk. Specifically, the FDTD method uses a hexahedral mesh discretization mode of Yee cells. When fitting structures such as TSVs or CTSVs, a stepped approximation method is required for modeling, which introduces stepped approximation errors. For typical coaxial or quasi-coaxial structures such as TSVs and CTSVs, coaxial excitation methods facilitate the introduction of excitation sources. However, these structures are typical fine interconnected units, usually with small feature sizes, dense arrangements, and significant multi-scale effects. If excitation is applied directly to the TSV or CTSV body structure, the geometric constraints of the fine structure will make it difficult for the excitation electric field to completely match the TEM mode distribution, which will easily excite higher-order modes and affect the signal integrity analysis results of such structures. Summary of the Invention

[0003] The purpose of this invention is to provide a simulation excitation method for signal integrity of a chip silicon through-hole interconnect structure based on conformal technology. It utilizes the finite-difference time-domain method and introduces conformal technology to reduce the step approximation error. At the same time, the overall calculation region is divided into two sub-regions, namely the excitation region and the structure calculation region, to avoid the influence of higher-order modes.

[0004] The technical solution to achieve the purpose of this invention is: a signal integrity simulation excitation method for a die-cell through-silicon via interconnect structure based on conformal technology, comprising the following steps:

[0005] Step 1: Establish the geometric structure model of the through-silicon via (TSV) chip, and use tetrahedral mesh to divide the geometric structure to obtain the number of the divided tetrahedrons, material number, node number, and three-dimensional coordinate information of the nodes.

[0006] Step 2: Determine the line ratio, surface ratio, and dielectric constant of the Yee cell hexahedral mesh in each direction based on the information of the tetrahedral mesh in the FDTD method;

[0007] Step 3: After completing the geometric structure model identification under the FDTD method, perform model signal integrity calculation and divide the overall calculation area of ​​the model into the excitation area and the structural calculation area.

[0008] Step 4: Apply excitation at any point on the inner or outer conductor at one end of the coaxial structure in the excitation region. After transmission over a distance, a TEM wave without the influence of higher-order modes is formed.

[0009] Step 5: Using the total field / scattered field boundary technique, the TEM wave, which is not affected by higher-order modes, is introduced into the structural calculation region as an excitation source, with the TEM wave being the incident wave.

[0010] Step 6: Calculate the surface power integral at the port in the total field and the scattered field, and convert it to the frequency domain using Fourier transform to calculate the S-parameters of each port.

[0011] Furthermore, in step 3, the excitation region is an ideal coaxial transmission line whose length satisfies the requirement of sufficient attenuation of higher-order modes. An excitation source is applied at the input end of the excitation region, and after transmission through the excitation region, the field distribution at the output end forms the TEM master mode.

[0012] Furthermore, in step 3, the structural calculation region includes the TSV or CTSV body and surrounding interconnection structure. Its input end and the output end of the excitation region are seamlessly coupled through the continuity conditions of electric field and magnetic field, and directly receive the incident field of TEM mode without higher-order mode.

[0013] Furthermore, by employing the total field / scattered field boundary technique, TEM waves without higher-order mode influence are introduced as incident waves into the structural computational domain, specifically including:

[0014] To the right of the grid for the total field and the scattered field, i.e. along The positive direction is the total field region. Using conformal techniques, the magnetic field of the scattered field region is added to the incident magnetic field, and the total field magnetic field components are calculated as follows:

[0015]

[0016]

[0017] in These are the coordinates of points in a rectangular coordinate system in each direction. Let be the spatial discrete lengths in each direction of the FDTD rectangular coordinate system. These represent the electromagnetic field values ​​in each direction of a rectangular coordinate system. To introduce a magnetic field into the incident field The directional component corresponds to the value of the magnetic field in the excitation region at the separation boundary. All are coefficients;

[0018] By introducing conformal techniques, the electric field components of the scattered field are calculated by subtracting the incident electric field from the electric field in the total field region:

[0019]

[0020]

[0021] in To introduce a magnetic field into the incident field The directional component corresponds to the value of the electric field in the excitation region at the separation boundary. is a coefficient.

[0022] Furthermore, the coefficient for:

[0023]

[0024]

[0025]

[0026]

[0027] in, The time discrete length of FDTD, For the model in Directional conductivity and dielectric constant For FDTD mesh in The ratio of lines in the direction.

[0028] Furthermore, the coefficient for:

[0029]

[0030]

[0031]

[0032]

[0033] in, The time discrete length of FDTD, For the model in Directional permeability and permeability coefficient For FDTD mesh in The aspect ratio in the direction.

[0034] Furthermore, the S-parameters are calculated as follows:

[0035]

[0036] in For reflected power, For incident power, This is the symbol for the Fourier transform.

[0037] A computer storage medium storing an executable program, the executable program being executed by a processor to implement the steps of the signal integrity simulation excitation method for a die-core through-silicon via interconnect structure based on conformal technology.

[0038] Compared with the prior art, the significant advantages of this invention are:

[0039] (1) It can realize accurate modeling of TSV structure by finite difference time domain method, effectively capture actual geometric features, and significantly improve the accuracy and reliability of signal integrity simulation results.

[0040] (2) By dividing the overall computational region into an excitation region and a structural computational region, the problem of higher-order modes that may exist on the coaxial line is solved. The results of the excitation region are introduced as incident waves using the total field / scattered field boundary technique, making the signal integrity simulation results more accurate.

[0041] (3) It is applicable to various typical coaxial structures, with wide applicability and good adaptability, and can meet the needs of different fields and application scenarios. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the coaxial structure excitation source setup in this invention.

[0043] Figure 2 This is a schematic diagram showing the division of the total field region and the scattering field region in this invention.

[0044] Figure 3 This is a schematic diagram illustrating the original problem and the equivalent problem of the incident wave problem in this invention, which uses the equivalence principle.

[0045] Figure 4 This is a schematic diagram of the grid connecting the total field and the scattered field in this invention.

[0046] Figure 5 This is a schematic diagram of the TSV-type coaxial model in this invention.

[0047] Figure 6 This is a top view of the TSV-type coaxial model in this invention.

[0048] Figure 7 This is a schematic diagram of the cross-section of the TSV-type coaxial model in this invention.

[0049] Figure 8 This is a comparison result diagram of the TSV-type coaxial model S11 in this invention.

[0050] Figure 9 This is a comparison result diagram of the TSV-type coaxial model S21 in this invention. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings.

[0052] This invention is a simulation excitation method for signal integrity of a die-core silicon through-hole interconnect structure based on conformal technology, the steps of which are as follows:

[0053] Step 1: Establish a geometric structure model. Use tetrahedral mesh to divide the geometric structure and obtain the tetrahedral number, material number, node number, and three-dimensional coordinate information of the nodes.

[0054] Step 2: Determine the line ratio, surface ratio, and dielectric constant of the Yee cell hexahedral mesh in each direction based on the various information of the tetrahedron.

[0055] Step 3: After completing the geometric structure model identification under the FDTD method, perform model signal integrity calculation. Divide the overall calculation area into two sub-regions, namely the excitation area and the structure calculation area, to handle the influence of higher-order modes.

[0056] Step 4: Apply excitation at any point on the inner or outer conductor at one end of the coaxial structure in the excitation region. After transmission over a distance, a TEM wave without the influence of higher-order modes is formed.

[0057] Step 5: Using the total field / scattered field boundary technique, the TEM wave obtained from solving the excitation region without the influence of higher-order modes is introduced into the structural calculation region as the excitation source, which is the incident wave.

[0058] Step 6: Calculate the surface power integral at the port in the total field and the scattered field, and convert it to the frequency domain using Fourier transform to calculate the S-parameters of each port.

[0059] In step 1, a geometric structure model is determined and established, and software is used to perform tetrahedral meshing on the geometric structure to obtain information such as the number of the tetrahedrons, material number, node number, and three-dimensional coordinates of the nodes.

[0060] In step 2, the information such as the number, material number, node number, and three-dimensional coordinates of the tetrahedron are read. Based on the positional relationship between the grid points, lines, and faces of the Yee cell hexahedral mesh and the tetrahedron in the FDTD method, the line ratio, face ratio, and dielectric constant of the hexahedral mesh in each direction are determined, thereby mapping the model to the relevant parameters of the hexahedral mesh in FDTD.

[0061] In step 3, combined with Figure 1 , Figure 1This diagram illustrates the excitation region and the structural computation region, both coaxial in the transmission direction. The excitation region is typically designed as an ideal coaxial transmission line, with a length sufficient to attenuate higher-order modes. An excitation source is applied at the input end of this region to ensure that the field distribution at the output end forms the dominant TEM mode after transmission through this region. The structural computation region includes the TSV or CTSV body and its surrounding interconnects. Its input end is seamlessly coupled to the output end of the excitation region through electric and magnetic field continuity conditions, directly receiving the incident field of the TEM mode without higher-order modes. The core advantage of this regional design is that it avoids direct interaction between the excitation source and the fine structure through physical isolation, fundamentally suppressing the excitation and coupling of higher-order modes while ensuring the accuracy of the incident field. This allows the structural computation region to guarantee the true electromagnetic response of the interconnect structure, significantly improving the accuracy and reliability of numerical simulations of multi-scale core-particle interconnect systems. At each time step, the electromagnetic fields in the two regions are calculated separately, and the results from the excitation region are introduced as the incident wave using TF / SF boundary techniques to excite the structure to be calculated.

[0062] In step 4, when using this method for excitation, the excitation region only needs to be added at any point on the inner or outer conductor at one end of the coaxial structure. After a certain distance of transmission, a TEM wave without the influence of higher-order modes can be formed. The result of introducing the excitation region using TF / SF boundary technology is used as the incident wave to excite the structure to be calculated.

[0063] In step 5, for the electromagnetic scattering problem, the total field in space can be expressed as the sum of the incident field and the scattered field, that is:

[0064] (1)

[0065] One of the core challenges in solving electromagnetic scattering problems using the FDTD method is accurately separating the incident and scattered waves while avoiding interference from reflections at non-physical boundaries. To address this issue, this invention employs the TF / SF boundary technique, strictly dividing the entire computational space into two functionally defined regions: the total field region and the scattering field region. A schematic diagram of this spatial division is shown below. Figure 1 As shown, the key to the TF / SF boundary technique, which serves as the physical interface between the two types of regions, lies in the fact that the total field region outside the boundary simultaneously contains the superposition field of incident and scattered waves, and is the main region where incident waves interact with the scatterer. Conversely, the scattered field region inside the boundary only contains outward traveling waves generated by the scatterer, and has no incident wave component, thus achieving physical separation of incident and scattered waves. By introducing equivalent current or magnetic current sources at the TF / SF boundary, not only can the field continuity condition at the boundary be strictly satisfied, but the precise design of the source terms can also achieve reasonable connection between different grid regions.

[0066] Let the incident electromagnetic wave be , ,like Figure 2 As shown. Based on the equivalence principle, an equivalent surface electromagnetic current is set on the transformed boundary A, and the field inside A is assumed to be zero, as follows. Figure 2 As shown. Therefore, the electromagnetic current on the transformed boundary A is:

[0067] (2)

[0068] To achieve accurate excitation of incident waves from coaxial structures and efficient numerical simulation of the electromagnetic scattering characteristics of multi-scale core-particle interconnected structures, this invention separates excitation generation and structural calculation physically and numerically. A dedicated independent mesh space is designated as the excitation region, while the interconnected structure to be analyzed is placed within another independent structural calculation region. A schematic diagram of the specific region division is shown below. Figure 3 As shown, a coaxial incident wave is iteratively generated within the excitation region and introduced into the mesh space of the structural computation region. Absorbing boundary conditions are applied at both ends of the excitation region to absorb outward waves, ensuring that only the required incident wave exists within the region. To achieve distortion-free transmission of the incident wave from the excitation region to the structural computation region, the interface between the two regions must satisfy strict mesh matching constraints, which is a crucial prerequisite for ensuring the continuity of the field quantities and numerical accuracy. The coaxial cross-sections of the excitation region and the structural computation region at the separation boundary must be completely identical to ensure that the propagation path of the incident wave precisely matches the structural interface. Furthermore, the meshing parameters of the transverse mesh must be strictly uniform, requiring not only… Grid step size in direction ( To ensure complete equality, it is crucial to guarantee strict alignment of the spatial coordinates of corresponding grid nodes to avoid field interpolation errors caused by node position offsets. The computational grid of the structural computation domain is divided into a total field region and a scattering field region. In the total field region, the total field is calculated using the difference scheme of Maxwell's equations for all grid points. In the scattering field region, the difference scheme is only used to calculate the scattering field; the incident field is added at the boundary connecting the total field region and the scattering field region.

[0069] Consider a grid connecting the total field region and the scattered field region. Figure 4 yes Figure 1 A schematic diagram of the grid connecting the total field and the scattered field in the computational region of the medium structure. Assume that on the right side of the grid connecting the total field and the scattered field, i.e., along... The positive direction is the total field area, connecting the grid. The iteration requires the magnetic field of the scattered field region. Calculating the total magnetic field component requires adding the incident magnetic field to the magnetic field of the scattered field region. Introducing a conformal technique, the iteration formula is as follows:

[0070] (3)

[0071] (4)

[0072] in To introduce a magnetic field into the incident field Directional components, corresponding Figure 4 The value of the magnetic field at the separation boundary in the excitation region. The coefficients in equations (3) and (4). They are respectively:

[0073] (5)

[0074] (6)

[0075] (7)

[0076] (8)

[0077] On the left side of the grid used to calculate the total field and scattered field at the connection surface, i.e., along Magnetic field component of the scattered field in the negative direction When calculating the electric field components of this scattered field, the electric field of the total field region connecting the grid is required. The electric field of the total field region needs to be subtracted from the incident electric field. Introducing a conformal technique, the iterative formula is as follows:

[0078] (9)

[0079] (10)

[0080] in To introduce a magnetic field into the incident field Directional components, corresponding Figure 4 The electric field value at the separation boundary in the excitation region. The coefficients in equations (9) and (10) for.

[0081] (11)

[0082] (12)

[0083] (13)

[0084] (14)

[0085] In step 6, each port of the computational model is determined. Throughout the time-domain simulation, the electromagnetic field values, such as electric field strength and magnetic field strength, within the designated monitoring area of ​​each port at each time step are continuously and accurately collected and recorded to ensure the temporal sequence integrity and spatial sampling accuracy of the field value data. Based on the recorded electromagnetic field values ​​of the ports at each time moment, the electromagnetic power of each port at each time moment is calculated using the principle of electromagnetic power calculation and the relevant formulas for surface power integrals, obtaining the surface power integral results of each port in the time domain as a function of time, thus achieving a quantitative characterization of the port's electromagnetic power in the time domain. On this basis, using the mathematical method of Fourier transform, the surface power integral data of each port in the time domain is converted from the time domain to the frequency domain to obtain the power characteristic data of each port within the frequency domain. Then, combined with the definition of S-parameters, using the frequency domain power data as the core basis, the S-parameters between each port of the computational model are solved and calculated, ultimately obtaining the S-parameters of each port within the desired frequency band.

[0086] The Po Yinting vector can be represented as:

[0087] (15)

[0088] Record the electromagnetic field values ​​at each port surface. Under the FDTD method, the relationship between the surface power integral and the Poynting vector is as follows:

[0089] (16)

[0090] The surface power integral data of each port in the time domain is transformed from the time domain to the frequency domain to obtain the power characteristic data of each port in the frequency domain, and the S-parameters are calculated. The calculation method of S11 is as follows:

[0091] (17)

[0092] in For reflected power, This represents the incident power.

[0093] To verify the correctness and effectiveness of this invention, numerical examples will be analyzed below to verify its effects.

[0094] Figure 5 This is a schematic diagram of a TSV-type coaxial model. Figure 6 This is a top view of a TSV-like coaxial model, showing the layout of the source signal TSV, the reference ground TSV, and the air gap. Figure 7 The figure shows a cross-sectional view of the TSV-like coaxial model, illustrating the materials used and key structural parameters. The material properties are shown in Table 1, and the specific parameters of each part of the model are shown in Table 2. The input waveform is a modulated Gaussian signal, and the signal integrity simulation frequency is 1GHz-50GHz.

[0095] Table 1 Material Properties of TSV Coaxial Model

[0096]

[0097] Table 2 Parameters of TSV-like Coaxial Model

[0098]

[0099] The S-parameter results of the TSV coaxial model are as follows: Figure 8 and Figure 9 As shown in the figure. The results show that there is a certain gap between the calculation results using the FDTD method and the calculation results using the simulation software CST, while the calculation results using the CFDTD method are basically consistent with the calculation results using CST, with a relative error of no more than 1%, proving that the conformal coaxial excitation method proposed in this paper has higher solution accuracy. For this TSV-like coaxial model, in the range of 1GHz-50GHz, the return loss (S11) parameter of both the CFDTD calculation results and the calculation results of the simulation software CST are less than -10dB, and the insertion loss (S21) parameter is greater than -0.32dB, indicating good transmission performance.

[0100] The following describes a non-volatile computer-readable storage medium according to exemplary embodiments of the present invention. The present invention also provides a non-volatile computer-readable storage medium storing computer-executable instructions, which are executed by a processor to implement the steps in the chip-based through-silicon via interconnect structure signal integrity simulation excitation method according to various exemplary embodiments of the present invention.

[0101] This invention employs the finite-difference time-domain (FDTD) method to analyze the application scenarios of chip interconnect structures, and utilizes conformal techniques to analyze the through-silicon via (TSV) structure model. The overall computational domain is divided into two sub-regions: an excitation region and a structural computational region. Using the total field / scattered field boundary technique, the results from the excitation region are introduced as incident waves into the structural computational region as excitation sources to excite the TSV structure. The surface power integrals at the ports in the total field and scattered field are calculated and transformed into frequency domain S-parameters for each port using Fourier transform. This invention reduces the stepped approximation error of the FDTD method by utilizing conformal techniques, and solves the problem of high-order mode crosstalk in typical coaxial structures such as TSVs by dividing the computational domain into two sub-regions, significantly improving the computational accuracy of signal integrity calculations for TSV structures.

[0102] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0103] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations to the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for simulating signal integrity of a chip-based through-silicon via interconnect structure based on conformal technology, characterized in that, Includes the following steps: Step 1: Establish the geometric structure model of the through-silicon via (TSV) chip, and use tetrahedral mesh to divide the geometric structure to obtain the number of the divided tetrahedrons, material number, node number, and three-dimensional coordinate information of the nodes. Step 2: Determine the line ratio, surface ratio, and dielectric constant of the Yee cell hexahedral mesh in each direction based on the information of the tetrahedral mesh in the FDTD method; Step 3: After completing the geometric structure model identification under the FDTD method, perform model signal integrity calculation and divide the overall calculation area of ​​the model into the excitation area and the structural calculation area. Step 4: Apply excitation at any point on the inner or outer conductor at one end of the coaxial structure in the excitation region. After transmission over a distance, a TEM wave without the influence of higher-order modes is formed. Step 5: Using the total field / scattered field boundary technique, the TEM wave, which is not affected by higher-order modes, is introduced into the structural calculation region as an excitation source, with the TEM wave being the incident wave. Step 6: Calculate the surface power integral at the port in the total field and the scattered field, and convert it to the frequency domain using Fourier transform to calculate the S-parameters of each port.

2. The signal integrity simulation excitation method for a chip-based through-silicon via interconnect structure based on conformal technology according to claim 1, characterized in that, In step 3, the excitation region is an ideal coaxial transmission line whose length satisfies the requirement of sufficient attenuation of higher-order modes. An excitation source is applied at the input end of the excitation region, and after transmission through the excitation region, the field distribution at the output end forms the TEM master mode.

3. The signal integrity simulation excitation method for a chip-based through-silicon via interconnect structure based on conformal technology according to claim 1, characterized in that, In step 3, the structural calculation region includes the TSV or CTSV body and surrounding interconnection structure. Its input end and the output end of the excitation region are seamlessly coupled through the continuity of electric field and magnetic field, and it directly receives the incident field of TEM mode without higher-order mode.

4. The signal integrity simulation excitation method for a chip-based through-silicon via interconnect structure based on conformal technology according to claim 1, characterized in that, The TEM wave, unaffected by higher-order modes, is introduced as the incident wave into the structural computational domain using the total field / scattered field boundary technique. Specifically, this includes: To the right of the grid for the total field and the scattered field, i.e. along The positive direction is the total field region. Using conformal techniques, the magnetic field of the scattered field region is added to the incident magnetic field, and the total field magnetic field components are calculated as follows: in These are the coordinates of points in a rectangular coordinate system in each direction. Let be the spatial discrete lengths in each direction of the FDTD rectangular coordinate system. These represent the electromagnetic field values ​​in each direction of a rectangular coordinate system. To introduce a magnetic field into the incident field The directional component corresponds to the value of the magnetic field in the excitation region at the separation boundary. All are coefficients; By introducing conformal techniques, the electric field components of the scattered field are calculated by subtracting the incident electric field from the electric field in the total field region: in To introduce a magnetic field into the incident field The directional component corresponds to the value of the electric field in the excitation region at the separation boundary. is a coefficient.

5. The signal integrity simulation excitation method for a chip-based through-silicon via interconnect structure based on conformal technology according to claim 4, characterized in that, The coefficient for: in, The time discrete length of FDTD, For the model in Directional conductivity and dielectric constant For FDTD mesh in The ratio of lines in the direction.

6. The signal integrity simulation excitation method for a chip-based through-silicon via interconnect structure based on conformal technology according to claim 4, characterized in that, The coefficient for: in, The time discrete length of FDTD, For the model in Directional permeability and permeability coefficient For FDTD mesh in The aspect ratio in the direction.

7. The signal integrity simulation excitation method for a chip-based through-silicon via interconnect structure based on conformal technology according to claim 1, characterized in that, The S-parameters are calculated as follows: in For reflected power, For incident power, This is the symbol for the Fourier transform.

8. A computer storage medium, characterized in that, The computer storage medium stores an executable program, which is executed by a processor to implement the steps of the signal integrity simulation excitation method for a die-core silicon through-hole interconnect structure based on conformal technology as described in any one of claims 1-7.

Images