Modeling method of electric leakage defect TSV equivalent circuit

Abstract

The invention discloses a modeling method for an electric leakage defect TSV equivalent circuit, and solves the problems that in the prior art, the electric leakage defect may accelerate aging of a chip and a package, shorten the service life of equipment, increase the failure rate and even affect the reliability of a final product. The method comprises the following steps: establishing a distributed equivalent circuit of an electric leakage defect TSV model by adopting a distributed modeling method; respectively simulating the electric leakage defect TSV model and the distributed equivalent circuit to obtain a model simulation result and a circuit simulation result; setting an error threshold, and calculating an error between the model simulation result and the circuit simulation result to obtain an error result; judging the relationship between the error result and an error threshold value, and outputting a distributed equivalent circuit; the construction of a distributed equivalent circuit is realized, the distributed equivalent circuit is simulated, and the mapping of an equivalent circuit model and a leakage defect TSV physical model is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of semiconductor process defect detection, and particularly to a method for modeling an equivalent circuit of a leakage defect TSV. Background Art

[0002] With the continuous development of integrated circuit technology, Through-Silicon Via (TSV) has become one of the core technologies for improving chip performance and density. However, during the manufacturing process of TSV, the problem of leakage defects caused by the rupture of the insulating layer has become an important challenge restricting its wide application and high-performance realization. The main function of the TSV insulating layer is to isolate the current between the metal and the silicon substrate, preventing short circuits and leakage currents between chip layers. Generally, the insulating layer of TSV uses silicon dioxide (SiO2) or other low dielectric constant materials to reduce capacitive coupling and power consumption. However, due to various reasons, the insulating layer may rupture during production or use, thus triggering leakage defects.

[0003] Mechanical stress is a key factor leading to the rupture of the insulating layer. During the manufacturing and packaging processes of TSV, due to the material property differences between the silicon wafer and the filled metal material, large stresses are often generated, especially during temperature changes and thermal cycling. These stresses may cause cracks to occur in local areas of the insulating layer, further expand and eventually rupture. Secondly, thermal expansion mismatch is also a factor that cannot be ignored. The difference in thermal expansion coefficients between the metal material and the silicon substrate will cause stress accumulation under temperature changes, thereby triggering the rupture of the insulating layer, especially during the long-term operation of the chip. During the manufacturing process of TSV, the non-uniformity of the metal filling and insulating material coating processes may result in weak points in local areas, increasing the risk of rupture.

[0004] Leakage defects will cause the electrical performance of the chip to decline, resulting in reduced signal transmission quality, increased power consumption, and even chip failure. Leakage defects will generate parasitic currents, leading to signal interference and increased power consumption, thus affecting the stability of the entire system. Leakage defects will also cause system instability. During high-speed signal transmission or high-frequency operation, leakage may cause voltage fluctuations or noise interference, thereby triggering system errors or abnormal operation. More seriously, leakage defects may accelerate the aging of the chip and the package, shorten the service life of the device, increase the failure rate, and even affect the reliability of the final product.

[0005] Generally speaking, the leakage defects formed by the rupture of the TSV insulating layer are an important factor affecting the reliability of 3D packaging technology. Summary of the Invention

[0006] The present invention provides a method for modeling an equivalent circuit of a TSV with leakage defects, which solves the problems in the prior art that leakage defects may accelerate the aging of chips and packages, shorten the service life of devices, increase the failure rate, and even affect the reliability of the final product, and realizes the construction of a distributed equivalent circuit and the simulation of the distributed equivalent circuit, so that the size and position of the leakage defects can be adjusted, and the leakage defects in the product can be determined.

[0007] The present invention provides a method for modeling an equivalent circuit of a TSV with leakage defects, including:

[0008] Establish a distributed equivalent circuit of the TSV model with leakage defects by using a distributed modeling method, where the distributed equivalent circuit takes into account the variation of current and electric field along the longitudinal direction in the TSV to accurately capture the distribution characteristics of parasitic effects at high frequencies;

[0009] Use HFSS and ADS to simulate the TSV model with leakage defects and the distributed equivalent circuit respectively to obtain model simulation results and circuit simulation results;

[0010] Set an error threshold, calculate the error between the model simulation results and the circuit simulation results to obtain an error result;

[0011] Judge whether the error result is less than the error threshold. If so, output the distributed equivalent circuit;

[0012] If not, correct the distributed equivalent circuit until the error result is less than the error threshold, and output the corrected distributed equivalent circuit.

[0013] In a possible implementation manner, the distributed modeling method includes: dividing the TSV model with leakage defects into multiple sub-regions along the longitudinal direction, establishing equivalent sub-circuits for each sub-region respectively, and then combining the equivalent sub-circuits to form the complete distributed equivalent circuit.

[0014] In a possible implementation manner, the step of dividing the TSV model with leakage defects into multiple sub-regions along the longitudinal direction, establishing equivalent sub-circuits for each sub-region respectively, and then combining the equivalent sub-circuits to form the complete distributed equivalent circuit includes:

[0015] Determine the leakage height of the leakage defect, and divide the TSV model with leakage defects into n segmented TSVs with leakage defects according to the leakage height;

[0016] Determine n equivalent sub-circuits corresponding to the n segmented TSVs with leakage defects respectively, and connect the n equivalent sub-circuits in series to obtain the distributed equivalent circuit.

[0017] In a possible implementation, the leakage defect TSV model is used to characterize the leakage defect of the insulating layer in the leakage defect TSV model according to a leakage factor: The leakage defect TSV model includes: a metal layer, an insulating layer, a substrate layer, and a leakage defect; the leakage defect is in the insulating layer.

[0018] In a possible implementation, the leakage factor is expressed as:

[0019] j = ωh pin / 2πr TSV ;

[0020] where ω represents the radian of the leakage defect; h pin represents the height of the leakage defect; r TSV represents the radius of the conductive metal in the metal layer.

[0021] In a possible implementation, the distributed equivalent circuit includes: a plurality of equivalent circuit units connected in parallel in sequence; where each equivalent circuit unit includes: a metal layer resistance R TSV , a metal layer inductance L TSV , an insulating layer conductance G leak , an insulating layer capacitance C leak , a substrate layer capacitance C S , and a substrate layer conductance G S ;

[0022] The first end of the metal layer resistance R TSV is connected to the input signal, and the second end of the metal layer resistance R TSV is connected to the first end of the metal layer inductance L TSV , the first end of the insulating layer conductance G leak , and the first end of the insulating layer capacitance C leak ;

[0023] The second end of the metal layer inductance L TSV is the output end;

[0024] The second end of the insulating layer conductance G leak is connected to the first end of the substrate layer capacitance C S , the first end of the substrate layer conductance G S , and the second end of the insulating layer capacitance C leak ;

[0025] The second end of the substrate layer capacitance C S is connected in parallel to the second end of the substrate layer conductance G S and grounded.

[0026] In a possible implementation, the insulating layer conductance G leakThe calculation formula is as follows:

[0027]

[0028] Among them, σ 1 represents the conductivity of the insulating layer; l TSV represents the height of the segmented leakage defect TSV; j represents the leakage factor; ε 0 represents the permittivity of vacuum; ε r,air represents the air permittivity; r TSV represents the radius of the conductive metal in the metal layer; t ox represents the thickness of the insulating layer.

[0029] In a possible implementation manner, the insulating layer capacitance C leak The calculation formula is as follows:

[0030]

[0031] Among them, ε r,ox represents the permittivity of the insulating layer; ε 0 represents the permittivity of vacuum; l TSV represents the height of the segmented leakage defect TSV; j represents the leakage factor; r TSV represents the radius of the conductive metal in the metal layer; t ox represents the thickness of the insulating layer.

[0032] In a possible implementation manner, using HFSS and ADS to simulate the leakage defect TSV model and the distributed equivalent circuit respectively to obtain the model simulation result and the circuit simulation result, including:

[0033] When using ADS for simulation, set the first simulation parameters, and simulate the leakage defect TSV model and the distributed equivalent circuit according to the simulation parameters to obtain the model simulation result and the circuit simulation result; the simulation parameters include the signal source, load and transmission line parameters;

[0034] When using HFSS for simulation, set the second simulation parameters, and simulate the leakage defect TSV model and the distributed equivalent circuit according to the second simulation parameters to obtain the model simulation result and the circuit simulation result; the second simulation parameters include the simulation frequency range and boundary conditions.

[0035] One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

[0036] The present invention adopts a method for modeling the equivalent circuit of a TSV with leakage defects. By using a distributed modeling method, a distributed equivalent circuit equivalent to the TSV model with leakage defects is determined, which can more accurately describe the characteristics of the TSV with leakage defects. Moreover, the distributed equivalent circuit can take into account the longitudinal variations of current and electric field in the equivalent circuit of the TSV with leakage defects, and can more precisely capture the distribution characteristics of parasitic effects at high frequencies. Considering the longitudinal variations of current and electric field in the TSV, it can more accurately describe the characteristics of the TSV with leakage defects. A TSV with leakage defects is built and simulated in a High Frequency Structure Simulator (HFSS), and the equivalent circuit model is simulated in ADS. By adjusting the size and position of the leakage defects, while verifying the accuracy of the equivalent circuit model, the influence of the leakage defects on the transmission characteristics of the TSV is also analyzed, providing a method for electrically detecting leakage defects, and the size and position of the internal leakage defects of the TSV can be effectively located through the signal transmission performance of the TSV with leakage defects. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flowchart of the steps of the method for modeling the equivalent circuit of a TSV with leakage defects provided by an embodiment of the present invention;

[0038] Figure 2 is a schematic structural diagram of a TSV with leakage defects provided by an embodiment of the present invention;

[0039] Figure 3 is a schematic diagram of the initially designed distributed equivalent circuit provided by an embodiment of the present invention;

[0040] Figure 4 is a schematic diagram of the corrected distributed equivalent circuit provided by an embodiment of the present invention;

[0041] Figure 5 is a schematic diagram of the curve of the resistance value of the part where the leakage defect is located varying with the void factor provided by an embodiment of the present invention;

[0042] Fig. 6(a) is the S 11 curve varying with the void factor m of the TSV with leakage defects provided by an embodiment of the present invention;

[0043] Fig. 6(b) is the S 12 curve varying with the void factor m of the TSV with leakage defects provided by an embodiment of the present invention;

[0044] Fig. 7(a) is the S 11 curve varying with the position of the void defect of the TSV with leakage defects provided by an embodiment of the present invention;

[0045] Figure 7(b) is a schematic diagram of the S 12 curve varying with the position of the void defect of the TSV with leakage defects provided by the embodiment of the present invention. Specific embodiments

[0046] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] The present invention provides a method for modeling an equivalent circuit of a TSV with leakage defects. Refer to Figure 1 , which includes the following steps S101 to S105.

[0048] S101. Establish a distributed equivalent circuit of the TSV model with leakage defects by using the distributed modeling method. The distributed equivalent circuit takes into account the variation of current and electric field along the longitudinal direction in the TSV to accurately capture the distribution characteristics of parasitic effects at high frequencies.

[0049] Specifically, in step S101, the distributed modeling method includes: dividing the TSV model with leakage defects into multiple sub-regions along the longitudinal direction, respectively establishing equivalent sub-circuits for each sub-region, and then combining the equivalent sub-circuits to form a complete equivalent circuit of the TSV with leakage defects.

[0050] Specifically, dividing the TSV model with leakage defects into multiple sub-regions along the longitudinal direction, respectively establishing equivalent sub-circuits for each sub-region, and then combining the equivalent sub-circuits to form a complete distributed equivalent circuit includes the following steps S1011 to S1012.

[0051] S1011. Determine the leakage height of the leakage defect, and divide the TSV model with leakage defects into n segmented TSVs with leakage defects according to the leakage height.

[0052] S1012. Respectively determine n equivalent sub-circuits corresponding to the n segmented TSVs with leakage defects, and connect the n equivalent sub-circuits in series to obtain a distributed equivalent circuit.

[0053] Specifically, in step S101, the TSV model with leakage defects is used to characterize the leakage defect of the insulating layer in the TSV model with leakage defects according to the leakage factor: the TSV model with leakage defects includes: a metal layer, an insulating layer, a substrate layer, and a leakage defect; the leakage defect is in the insulating layer.

[0054] Here, the leakage factor is expressed as:

[0055] j = ωh pin / 2πr TSV ;

[0056] Where, ω represents the radian of the leakage defect; h pin represents the height of the leakage defect; r TSV represents the radius of the conductive metal in the metal layer.

[0057] Specifically, in step S101, the distributed equivalent circuit includes: multiple equivalent circuit units connected in parallel in sequence; among them, each equivalent circuit unit includes: the metal layer resistance R TSV , the metal layer inductance L TSV , the insulation layer conductance G leak , the insulation layer capacitance C leak , the substrate layer capacitance C S and the substrate layer conductance G S ; the first end of the metal layer resistance R TSV is connected to the input signal, and the second end of the metal layer resistance R TSV is connected to the first end of the metal layer inductance L TSV , the first end of the insulation layer conductance G leak and the first end of the insulation layer capacitance C leak ; the second end of the metal layer inductance L TSV is the output end; the second end of the insulation layer conductance G leak is connected to the first end of the substrate layer capacitance C S , the first end of the substrate layer conductance G S and the second end of the insulation layer capacitance C leak ; the second end of the substrate layer capacitance C S is connected in parallel to the ground with the second end of the substrate layer conductance G S .

[0058] In step S101, the calculation formula of the insulation layer conductance G leak is:

[0059]

[0060] Where, σ 1 represents the conductivity of the insulation layer; l TSV represents the height of the segmented leakage defect TSV; j represents the leakage factor; ε 0 represents the permittivity of vacuum; ε r,air represents the air permittivity; r TSV represents the radius of the conductive metal in the metal layer; t ox represents the thickness of the insulation layer.

[0061] The calculation formula of the insulation layer capacitance C leak is:

[0062]

[0063] Among them, ε r,ox represents the dielectric constant of the insulating layer; ε 0 represents the dielectric constant of vacuum; l TSV represents the height of the segmented leakage defect TSV; j represents the leakage factor; r TSV represents the radius of the conductive metal in the metal layer; t ox represents the thickness of the insulating layer.

[0064] Exemplarily, in the embodiments of the present invention, the structure of the leakage defect TSV is first determined as Figure 2 shown, including a metal layer, an insulating layer, a substrate layer, and a leakage defect. The selection of the materials for each layer in the leakage defect TSV structure should be determined according to the subsequent process parameters and the design requirements of the dielectric material. Generally speaking, the metal layer usually adopts a solid cylindrical copper column, mainly because copper has excellent process compatibility; the material of the insulating layer is the key to preventing signal leakage to the substrate layer, and a dielectric material with a higher resistivity can effectively prevent signal leakage. Therefore, at the same size, the difficulty of signal leakage will also increase; here, silicon dioxide (SiO 2 ) is often used as the insulating layer material; the substrate layer usually selects silicon material; the leakage defect usually appears as an arc-shaped air cavity.

[0065] The distributed method divides the leakage defect TSV model into n parts, and connects each part in series to describe the electrical characteristics of the entire leakage defect TSV model as a whole. The characteristics of each part are represented by a lumped model.

[0066] The equivalent circuit model of the leakage defect TSV model involves four basic parameters: resistance R, inductance L, conductance G, and capacitance C; for a TSV with a metal layer radius of r TSV , a metal layer height of h TSV , and a metal layer resistivity of ρ Cu , the height of each part of the TSV is l TSV , where h TSV = n×l TSV ;

[0067] In the specific embodiments provided by the present invention, refer to Figure 3 which is the distributed equivalent circuit designed for the first time by the present invention.

[0068] During distributed modeling, the length l TSV of each leakage defect TSV model = h pin ; with the small segment where the leakage defect is located as the center, divide it from the upper and lower ends of the leakage defect TSV model to determine the total number of segments n.

[0069] Define x as the normalized parameter of the length of the leakage defect TSV model, where x = 0 indicates that the defect is located at the source end, x = 0.5 indicates that the defect is located at the midpoint of the TSV, and x = 1 indicates that the defect is located at the terminal position. The number of upper segments and the number of lower segments are n 1 = x(h TSV / l TSV ) - 0.5 and n 2 = (1 - x)(h TSV / l TSV ) - 0.5;

[0070] The total number of segments is n = n 1 + n 2 + 1, where n 1 and n 2 are integers; the total number of segments is n = [n 1 + [n 2 + 1 + x 0 , where n 1 or n 2 is not an integer, [·] is the rounding function, and x 0 is the number of non-integers of n 1 and n 2 .

[0071] In the embodiments provided by the invention, when calculating the equivalent sub-circuit corresponding to the segmented leakage defect TSV, the parameters of each electrical component are divided into two parts. Among them, one part is the calculation formula when the equivalent sub-circuit does not include a leakage defect, and the other part is the calculation formula when the equivalent sub-circuit includes a leakage defect.

[0072] When the equivalent sub-circuit does not include a leakage defect:

[0073] The DC resistance R TSV-dc of the metal layer resistance is calculated as follows:

[0074]

[0075] Among them, ρ Cu represents the density of the conductive metal Cu; l TSV represents the height of the segmented leakage defect TSV; r TSV represents the radius of the conductive metal in the metal layer; δ represents the skin depth of the TSV.

[0076] As the frequency increases, the current density gradually increases on the surface of the conductor, while the current density gradually decreases in the central part of the conductor. The current tends to be transmitted through the outer region of the conductor, and almost no current is carried in the interior of the conductor, resulting in the skin effect. Under the action of the skin effect, the high-frequency parasitic resistance R TSV-ac of the TSV is calculated as follows:

[0077]

[0078] Among them, δ represents the skin depth of the TSV, f represents the operating frequency of the TSV, μ 0 represents the permeability of free space, and μ r,Cu represents the permeability of the metal layer.

[0079] The total resistance R of the metal layer TSV is calculated by the formula:

[0080]

[0081] Among them, R TSV-dc represents the DC resistance of the metal layer, and R TSV-ac represents the high-frequency parasitic resistance of the metal layer;

[0082] In the segmented leakage defect TSV, the current loop is located at infinity. The inductance L of the metal layer TSV is calculated by the formula:

[0083]

[0084] Among them, μ 0 represents the permeability of free space; μ r,Cu represents the permeability of the metal Cu in the metal layer; l TSV represents the height of the segmented leakage defect TSV; r TSV represents the radius of the conductive metal in the metal layer; ln(·) represents the natural logarithm.

[0085] The metal layer, the insulating layer, and the substrate layer will form a parasitic capacitance with MOS characteristics. The equivalent circuit model capacitance C includes: the insulating layer capacitance C leak and the substrate layer capacitance C Si Among them, the insulating layer capacitance C leak is expressed as:

[0086]

[0087] The substrate layer capacitance C Si is essentially the series connection of the parasitic MOS capacitance C dep and the substrate capacitance C sub and its calculation formula is:

[0088]

[0089] Among them, ε r,Si represents the dielectric constant of silicon, t ox is the thickness of the insulating layer, w dep is the depletion layer width on the semiconductor side, and r substrate is the thickness of the substrate layer.

[0090] The conductance G of the equivalent circuit model is the conductance G of the insulating layer leak , and the calculation formula is as follows:

[0091]

[0092] where h pin is the height of the leakage defect. When there is no leakage defect, the impedance between the TSV and the silicon substrate is infinite.

[0093] When the equivalent sub-circuit contains a leakage defect, different from the above calculation method, the insulating layer capacitance C leak and the insulating layer conductance G leak . When a leakage defect appears in the insulating layer, a leakage current may be generated between the TSV and the silicon substrate, resulting in a lower breakdown voltage, an increase in the insulating layer conductance, and a decrease in the insulating layer capacitance. The calculation formula is as follows:

[0094]

[0095]

[0096] where ε r,air represents the relative permittivity of the insulating layer; j = ωh pin / 2πr TSV , j is called the leakage factor; ω is the radian of the leakage defect.

[0097] When j = 0, the above expression of G leak is the same as the expressions of the insulating layer conductance G INS and the insulating layer capacitance C ox , indicating that there is no leakage defect in this segmented insulating layer; when j ≠ 0, C leak and G leak represent the size of the leakage defect in the segmented insulating layer.

[0098] S102, respectively simulate the TSV model with leakage defects and the distributed equivalent circuit using HFSS and ADS to obtain the model simulation results and the circuit simulation results;

[0099] Specifically, in step S102, respectively simulate the TSV model with leakage defects and the distributed equivalent circuit using HFSS and ADS to obtain the model simulation results and the circuit simulation results, including:

[0100] When using ADS for simulation, set the first simulation parameters, and simulate the TSV model with leakage defects and the distributed equivalent circuit according to the simulation parameters to obtain the model simulation results and the circuit simulation results; the simulation parameters include the signal source, load, and transmission line parameters;

[0101] When performing simulation using HFSS, set the second simulation parameters, and simulate the TSV model with leakage defects and the distributed equivalent circuit according to the second simulation parameters to obtain the model simulation results and the circuit simulation results; the second simulation parameters include the simulation frequency range and the boundary conditions.

[0102] Exemplarily, in order to verify whether the equivalent circuit of the TSV with leakage defects meets the designed purpose, in the embodiments of the present invention, the designed TSV structure with leakage defects is built in HFSS (High Frequency Structure Simulator), an excitation is applied to it, and simulation analysis is carried out. At the same time, an equivalent circuit model of the TSV with leakage defects is built in ADS (Advanced Design System) for simulation analysis. In the embodiments of the present invention, the accuracy of the equivalent circuit model of the TSV with leakage defects is determined by adjusting the size and position of the leakage defects.

[0103] S103, set an error threshold, calculate the error between the model simulation result and the circuit simulation result to obtain an error result; determine whether the error result is less than the error threshold. If so, output the distributed equivalent circuit; if not, correct the distributed equivalent circuit until the error result is less than the error threshold, and output the corrected distributed equivalent circuit.

[0104] Exemplarily, determine whether the HFSS simulation result and the ADS simulation result meet the error requirement. If so, output the equivalent circuit model of the designed TSV with leakage defects, indicating that the equivalent circuit model of the designed TSV with leakage defects can meet the requirement at this time and no further correction is needed.

[0105] If not, correct the distributed equivalent circuit model, correct the distributed equivalent circuit to obtain a corrected distributed equivalent circuit, see Figure 4 until the HFSS simulation result and the ADS simulation result meet the error requirement.

[0106] In Figure 4 the parasitic conductance of the silicon substrate is added, so that the error between the simulation result of the corrected distributed equivalent circuit and the simulation result of the TSV model with leakage defects is less than the error threshold.

[0107] The calculation formula of the parasitic conductance of the silicon substrate is expressed as: where σ Si represents the conductivity of the insulating layer.

[0108] Figure 5 is a schematic diagram of the change curve of the leakage conductance and the leakage capacitance with the leakage factor in the corrected distributed equivalent circuit. From Figure 5It can be seen that when there is a leakage defect, even if the leakage factor is only 5%, the leakage conductance of the TSV changes from 3×10 -15 μS without defect to 8.5 μS, showing an obvious decrease. As the leakage factor j increases, that is, as the leakage area expands, the leakage conductance increases approximately linearly. This is because the increase in the leakage factor leads to a deterioration of the insulation between the TSV and the substrate, thereby increasing the leakage conductance. At the same time, the capacitance of the insulating layer decreases linearly with the increase in the leakage factor because the increase in the leakage factor reduces the effective area of the insulating layer.

[0109] Figures 6(a) to 6(b) Schematic diagram of the S 11 and S 21 curves of the TSV with leakage defects varying with the leakage factor j. Among them, the proposed mode represents Equivalent circuit simulation ; 3D M simulation represents 3D physical model simulation ; It can be seen from Figures 6(a) to 6(b) that in the low-frequency range, the S 11 curve obtained by the equivalent circuit model simulation overlaps basically with the S 11 curve obtained by HFSS, and the S 21 curve will have a slight rise. In the high-frequency range, the S 11 curve obtained by the equivalent circuit model has a slight decrease relative to the S 11 curve obtained by HFSS, and the S 21 curves overlap basically. In the frequency range of 19 - 20 GHz, as the leakage factor increases, the amplitude of the S 11 will rise slightly. In the frequency range of 0 - 1 GHz, the amplitude of the S 21 of the TSV with leakage defects will decrease, and as the leakage factor increases, the decreasing amplitude becomes larger and larger, and the transmission performance of the TSV deteriorates slightly. As the frequency increases, the current becomes more and more concentrated on the surface of the TSV. The leakage defect destroys the insulating layer that originally blocks the signal, and the signal leaks into the silicon substrate along this conductive path, forming losses. The larger the leakage factor, the greater the leakage conductance, and the more current leaks to the silicon substrate, resulting in a deterioration of the signal transmission performance of the TSV.

[0110] Figures 7(a) to 7(b) Schematic diagram of the S 11 and S 21 curves of the TSV with leakage defects varying with the leakage defect position x. It can be seen from Figures 7(a) to 7(b) that as x increases, that is, as the leakage defect position moves away from the source end, the amplitude of the S 11 remains basically unchanged, and the amplitude of the S 21 will have a slight rise. The main reason is that the farther away from the source end, the smaller the current density, the smaller the current leaking to the substrate at the leakage defect, and the signal transmission performance improves slightly.

[0111] The various embodiments in this specification are described in a progressive manner. For the same or similar parts among the various embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. All or part of the present invention can be used in many general-purpose or special-purpose computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and so on.

[0112] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the present invention; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A modeling method for a leakage defect TSV equivalent circuit, characterized in that: include: A distributed modeling method is used to establish a distributed equivalent circuit of a leakage defect TSV model, wherein the distributed equivalent circuit takes into account the longitudinal changes of current and electric field in the TSV to accurately capture the distribution characteristics of parasitic effects at high frequencies; Using HFSS and ADS to simulate the leakage defect TSV model and the distributed equivalent circuit respectively, to obtain model simulation results and circuit simulation results; Setting an error threshold, calculating the error between the model simulation result and the circuit simulation result, and obtaining an error result; Determine whether the error result is less than the error threshold, and if so, output the distributed equivalent circuit; If not, the distributed equivalent circuit is corrected until the error result is less than the error threshold, and the corrected distributed equivalent circuit is output.

2. The modeling method of the leakage defect TSV equivalent circuit according to claim 1, characterized in that: The distributed modeling method includes: dividing the leakage defect TSV model into multiple sub-areas along the longitudinal direction, establishing an equivalent sub-circuit for each sub-area, and then combining the equivalent sub-circuits to form a complete distributed equivalent circuit.

3. The modeling method of the leakage defect TSV equivalent circuit according to claim 2, characterized in that: The method of dividing the leakage defect TSV model into a plurality of sub-regions along the longitudinal direction, establishing an equivalent sub-circuit for each sub-region, and then combining the equivalent sub-circuits to form a complete distributed equivalent circuit includes: Determine a leakage height of the leakage defect, and divide the leakage defect TSV model into n segmented leakage defect TSVs according to the leakage height; n equivalent subcircuits corresponding to n segmented leakage defects TSV are respectively determined, and the n equivalent subcircuits are connected in series to obtain the distributed equivalent circuit.

4. The modeling method of the leakage defect TSV equivalent circuit according to claim 1, characterized in that: The leakage defect TSV model is used to characterize the leakage defect of the insulating layer in the leakage defect TSV model according to the leakage factor: the leakage defect TSV model includes: a metal layer, an insulating layer, a substrate layer and a leakage defect; the leakage defect is in the insulating layer.

5. The method for modeling a leakage defect TSV equivalent circuit according to claim 4, characterized in that: The leakage factor is expressed as: j=ωh pin / 2πr TSV ; Where, ω represents the arc of the leakage defect; h pin Indicates the height of the leakage defect; r TSV Represents the radius of the conductive metal in the metal layer.

6. The modeling method of the leakage defect TSV equivalent circuit according to claim 1, characterized in that: The distributed equivalent circuit comprises: a plurality of equivalent circuit units connected in parallel in sequence; wherein each equivalent circuit unit comprises: a metal layer resistor R TSV , metal layer inductance L TSV , insulation layer conductivity G leak , insulation layer capacitance C leak , substrate layer capacitance C S and substrate layer conductivity G S ; The metal layer resistance R TSV The first end is connected to the input signal, and the metal layer resistor R TSV The second end of the metal layer inductor L TSV The first end of the insulating layer conducts G leak The first end and the insulating layer capacitance C leak A first end is connected; The metal layer inductance L TSV The second end is the output end; The insulation layer conductivity G leak The second end and the substrate layer capacitance C S The first end of the substrate layer conducts G S The first end and the insulating layer capacitance C leak The second end of the connection; The substrate layer capacitance C S The second end of the substrate layer conducts G S The second end is connected in parallel to the ground.

7. The method for modeling a leakage defect TSV equivalent circuit according to claim 6, characterized in that: The insulation layer conductivity G leak The calculation formula is: Where σ1 represents the conductivity of the insulating layer; l TSV represents the height of the segmented leakage defect TSV; j represents the leakage factor; ε0 represents the dielectric constant of vacuum; ε r,air represents the dielectric constant of air; r TSV Represents the radius of the conductive metal in the metal layer; t ox Indicates the thickness of the insulation layer.

8. The method for modeling a leakage defect TSV equivalent circuit according to claim 6, characterized in that: The insulation layer capacitance C leak The calculation formula is: Among them, ε r,ox represents the dielectric constant of the insulating layer; ε0 represents the dielectric constant of the vacuum; l TSV represents the height of the segmented leakage defect TSV; j represents the leakage factor; r TSV Represents the radius of the conductive metal in the metal layer; t ox Indicates the thickness of the insulation layer.

9. The method for modeling a leakage defect TSV equivalent circuit according to claim 1, characterized in that: The method of using HFSS and ADS to simulate the leakage defect TSV model and the distributed equivalent circuit respectively to obtain model simulation results and circuit simulation results includes: When using ADS for simulation, first simulation parameters are set, and the leakage defect TSV model and the distributed equivalent circuit are simulated according to the simulation parameters to obtain model simulation results and circuit simulation results; the simulation parameters include signal source, load and transmission line parameters; When simulating using HFSS, second simulation parameters are set, and the leakage defect TSV model and the distributed equivalent circuit are simulated according to the second simulation parameters to obtain model simulation results and circuit simulation results; the second simulation parameters include simulation frequency range and boundary conditions.

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