Scalable model modeling method for passive component in advanced packaging process

Abstract

The invention provides a scalable model modeling method for an advanced packaging process passive component, which comprises the following steps of: on the basis of a mathematical expression and an equivalent circuit model for representing a passive component mechanism, combining process information and design requirements, taking a physical size parameter of a model as an independent variable, taking a model component value as a dependent variable, and establishing a scalable model; a Scalable equation form for multivariable parameter fitting is given by adopting a Taylor expansion polynomial, and a radio frequency integrated microsystem scalable model which is high in precision, wide in parameter coverage range and high in expansibility is established; the problems that equivalent circuit models of passive components are incomplete and scalable models are missing in an advanced integrated packaging process for realizing the radio frequency integrated microsystem at present are effectively solved; according to the method, the modeling time of the radio frequency integrated microsystem model is greatly shortened, and the iteration speed of the radio frequency integrated microsystem design is improved.

Description

Technical Field

[0001] The present invention relates to the field of advanced integrated packaging technology, and in particular to a scalable modeling method for passive components in advanced packaging technology. Background Art

[0002] As one of the optional paths of post-Moore technology, the RF integrated microsystem based on advanced integrated packaging technology has the advantages of high integration, low cost, and high performance, which is a major leap from RF integrated circuits to RF integrated systems. As an important part of RF integrated microsystems, passive components (devices: passive devices such as resistors, capacitors, and inductors; components: interconnect structures such as microstrip lines, strip lines, coplanar waveguides, silicon through vias, and ball grid arrays) occupy more than 90% of the volume of the microsystem, and play a decisive role in the transmission quality of RF signals and the overall performance of the system. The system-centered multi-level collaborative design of RF integrated microsystem design brings new challenges to the traditional modeling methods and modeling processes centered on active transistors. The importance of passive devices and interconnect structures is self-evident, and it also brings new challenges to the development of scalable models of devices and structures.

[0003] In the past, the scalable modeling method for passive devices / interconnect structures in advanced integrated packaging processes used model parameter extraction to determine device values. Due to the lack of physically based scalable equations, the model's physical expansion capability was poor, the accuracy was low, and the modeling took a long time. Limited by the small parameter scaling range and poor model accuracy, the optimization range of components inside the RF integrated microsystem is small, resulting in poor signal transmission performance of the microsystem, difficult to control the performance of the finished product, and poor consistency. In addition, there are problems with incomplete equivalent circuit models of passive devices / interconnect structures in advanced integrated packaging processes and the lack of scalable models. Summary of the invention

[0004] In order to solve the problems of poor physical expansion capability, low precision and long modeling time of traditional passive device / interconnection structure models, lack of equivalent circuit models and scalable models of passive components, and establish accurate scalable models of passive components; based on mathematical expressions and equivalent circuit models that characterize the physical mechanisms of passive components, the present invention takes model component values ​​as dependent variables, and adopts Taylor expansion polynomials to give the form of scalable equations for multivariable parameter fitting. A scalable modeling method suitable for passive components of radio frequency integrated microsystems is proposed, which can quickly establish physically interpretable scalable equations, and can combine process information and design requirements of radio frequency integrated microsystems to establish a scalable passive component structure model with the characteristics of high precision, wide parameter scaling coverage, strong scalability, etc., which can greatly and effectively shorten the modeling time of radio frequency integrated microsystem models and improve the iteration speed of radio frequency integrated microsystem design.

[0005] In order to achieve the above object, the present invention provides a scalable modeling method for passive components in advanced packaging processes, which specifically comprises the following steps:

[0006] Based on process information and design requirements, determine the scalable independent variables and size ranges required for the established scalable model of passive components, and design and process test pieces according to the corresponding scalable independent variables and size ranges; use the test pieces to simultaneously establish equivalent circuit models of passive components, calibrate the electromagnetic simulation environment, and establish a three-dimensional electromagnetic simulation environment for passive components;

[0007] Based on the measured and processed test pieces, the test data is obtained and de-embedded; at the same time, the components that are prone to measurement errors are simulated based on the calibrated electromagnetic simulation environment, and the simulated data is supplemented to the de-embedded test data to increase the test sample volume;

[0008] Based on the analysis of passive components, the topology of the corresponding physical-based equivalent circuit model is established; based on the test data or the test data and the supplementary EM simulation data of the components that are prone to measurement errors, the physical-based equivalent model is fitted to establish the Local physical-based equivalent circuit model;

[0009] Based on the analysis of passive components, the form of Scalable equations for variable parameter fitting is given, with scalable size parameters as independent variables and component values ​​of the Local physical basis equivalent circuit model as dependent variables, the undetermined coefficients in the Scalable equations for variable parameter fitting are fitted, and the fitting determination coefficients of the Scalable equations are obtained;

[0010] If the fitting error of the Scalable equation meets the requirements, the Scalable equation is brought into the Local physical basis equivalent circuit model, the inherent component values ​​are replaced, and a Global equivalent circuit model of passive components with scalable size parameters is established.

[0011] Preferably, when determining the scalable independent variables and size range of passive components, the variable size parameters and fixed size parameters in the physical basis equivalent circuit model of the passive components are determined based on process information, and the type and quantity of scalable independent variables and the size variation range or boundary of the independent variables of the scalable physical basis equivalent circuit model to be established are determined based on design requirements, and the test piece is designed based on the determined scalable independent variables and size range.

[0012] Preferably, when determining the scalable independent variables and size ranges, the process further includes:

[0013] Based on the types and quantity of scalable independent variables of the scalable physical-based equivalent circuit model and the size variation range or boundary of the independent variables, the number of Local physical-based equivalent circuit models required to establish the scalable model and the corresponding sizes of different Local physical-based equivalent circuit models are determined. Among them, the physical-based equivalent circuit is an equivalent circuit used to characterize the physical working mechanism. Preferably, after establishing a three-dimensional electromagnetic simulation environment for passive components, the sizes of the Local physical-based equivalent circuit models of components that have been determined but are prone to measurement errors are brought into it, and the EM simulation corresponding to the corresponding size is obtained, and it is added to the test sample.

[0014] Preferably, the analysis content of passive components includes: physical characteristics of passive components, physical calculation formulas, and parasitic analysis of component structure and manufacturing process.

[0015] Preferably, the form of the scalable equation is given by a Taylor expansion polynomial using a physical calculation formula.

[0016] Preferably, the variable parameters of the Scalable equation fitting are single variable, multivariate, or a combination of data.

[0017] Preferably, based on the fitting determination coefficient of the Scalable equation, if the fitting determination coefficient is near the set value, and the deviation between the component value calculated by the Scalable equation and the component value in the Local physical basis equivalent circuit model of the corresponding size is small, and the error index requirement is met, the next step is executed; if the fitting determination coefficient deviates greatly from the set value and does not meet the design index, the component parameters in the physical basis equivalent circuit model of the passive component are adjusted so that their numerical changes are more in line with the trend of the Scalable equation and the Local model simulation results are required to be consistent with the EM and / or test results of the corresponding size.

[0018] Preferably, after obtaining the Global equivalent circuit model, the simulation results of the Global equivalent circuit model at different scaling sizes are compared with one or a combination of EM simulation and test results of the corresponding sizes to verify the error of the Global equivalent circuit model. If the error meets the error index requirements of the RF integrated microsystem, the establishment of the scalable model of the passive components is completed.

[0019] The present invention provides a scalable modeling method for passive components in advanced packaging processes. Compared with the prior art, the method has the following beneficial effects: the method is based on mathematical expressions and equivalent circuit models that characterize the physical mechanisms of passive components, takes model scalable parameters as independent variables, takes model component values ​​as dependent variables, and adopts Taylor expansion polynomials to give the form of scalable equations for multivariable parameter fitting. Physically interpretable scalable equations can be quickly established, and process information and design requirements of radio frequency integrated microsystems can be combined to establish a scalable passive component model with the characteristics of high precision, wide parameter scaling coverage, and strong scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flow chart of a scalable modeling method for passive components in advanced packaging processes provided by the present invention;

[0021] Figure 2 A three-dimensional diagram of the structure of the equivalent circuit model of the physical basis of a flat plate capacitor provided in the first embodiment of the present invention;

[0022] Figure 3 A structural side view of a physical equivalent circuit model of a flat plate capacitor provided in the first embodiment of the present invention;

[0023] Figure 4 The first embodiment of the present invention provides a physical equivalent circuit model diagram of a flat plate capacitor;

[0024] Figure 5 The electromagnetic simulation result / test result diagram of the planar capacitor of the first embodiment provided by the present invention;

[0025] Figure 6 Comparison of simulation and test results of the scalable global model of a flat-plate capacitor provided in Example 1 of the present invention;

[0026] Figure 7 A three-dimensional structural diagram of the physical basis equivalent circuit model of the planar spiral inductor provided in the second embodiment of the present invention;

[0027] Figure 8 The physical basis equivalent circuit model diagram of the planar spiral inductor of the second embodiment provided by the present invention;

[0028] Fig. 9 The electromagnetic simulation result / test result diagram of the second embodiment of the present invention - a planar spiral inductor;

[0029] Fig.10 A comparison chart of simulation and test results of the scalable global model of the planar spiral inductor provided in the second embodiment of the present invention;

[0030] Fig.11A three-dimensional diagram of the physical basis equivalent circuit model of a ball grid array provided in the third embodiment of the present invention;

[0031] Fig.12 A side view of the physical equivalent circuit model of a ball grid array according to the third embodiment of the present invention;

[0032] Fig.13 Embodiment 3 of the present invention provides a ball grid array physical basis equivalent circuit model diagram;

[0033] Fig.14 The third embodiment of the present invention provides a ball grid array electromagnetic simulation result / test result diagram;

[0034] Fig.15 A comparison chart of simulation and test results of the scalable global model of a ball grid array according to the third embodiment of the present invention;

[0035] Fig.16 A schematic diagram of a three-dimensional structure of a complex interconnected structure according to Embodiment 4 of the present invention;

[0036] Fig.17 A copper pillar structure model diagram of a complex interconnect structure of the fourth embodiment provided by the present invention;

[0037] Fig.18 A diagram of a coplanar waveguide model of a complex structure of the fourth embodiment provided by the present invention;

[0038] Fig.19 The equivalent circuit model diagram of the complex structure of the fourth embodiment provided by the present invention;

[0039] Fig. 20 A comparison diagram of simulation results of complex structures with respect to substrate structure and material parameter scaling provided by Example 4 of the present invention;

[0040] Fig.21 A comparison diagram of simulation results of the coplanar waveguide CPW interconnection structure parameter scaling of a complex structure provided by the fourth embodiment of the present invention;

[0041] Fig. 22 Embodiment 4 provided by the present invention - comparison of simulation results of complex structures with respect to layer hole radius parameter scaling. DETAILED DESCRIPTION

[0042] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0043] like Figure 1 As shown, the present invention provides a scalable modeling method for passive components in advanced packaging processes, and the specific steps include:

[0044] S1: Based on process information and design requirements, determine the scalable independent variables and size ranges required for the established scalable model of passive components, and design and process test pieces according to the corresponding scalable independent variables and size ranges; use the test pieces to simultaneously establish equivalent circuit models of passive components, calibrate the electromagnetic simulation environment, and establish a three-dimensional electromagnetic simulation environment for passive components.

[0045] Specifically, the present invention establishes a three-dimensional electromagnetic simulation model of passive components based on advanced integrated packaging technology, and determines the variable size parameters and fixed size parameters in the physical-based equivalent circuit model of the passive components according to the process information; according to the design requirements, the types and quantities of scalable independent variables of the scalable physical-based equivalent circuit model to be established, as well as the size variation range or boundary of the independent variables are determined. Based on the types and quantities of scalable independent variables of the scalable physical-based equivalent circuit model, as well as the size variation range or boundary of the independent variables, the number of local physical-based equivalent circuit models required to establish the scalable model and the sizes (variable parameter values) corresponding to different local physical-based equivalent circuit models are determined; through the above analysis, the scalable independent variables and size range required for the established scalable model of passive components are determined, and the test piece (physical object of passive components) is designed based on the determined scalable independent variables and size range. The test piece is used to simultaneously establish the equivalent circuit model of the passive components, calibrate the electromagnetic simulation environment, and establish a three-dimensional electromagnetic simulation environment for the passive components.

[0046] S2: Based on the measurement of the processed test piece, the test data is obtained and de-embedded; Based on the measurement of the processed test piece, the test data is obtained and de-embedded; At the same time, based on the calibrated electromagnetic simulation environment, the components that are prone to measurement errors are simulated, and the simulated data is supplemented to the de-embedded test data to increase the test sample size, so as to improve the accuracy of the model to be built.

[0047] Specifically, based on the physical base equivalent circuit model to be established, the size variation range of the independent variable can be scaled, and multiple groups of test pieces of different sizes can be processed. After the test is completed, the test results are de-embedded, and at the same time, the three-dimensional electromagnetic simulation environment of the passive components is calibrated using the test pieces so that the simulation results are consistent with the test results. Based on the calibrated three-dimensional electromagnetic simulation environment, a three-dimensional electromagnetic simulation of the passive components is performed, and the simulation results are used to supplement the test results of the test pieces (devices that are not processed in real objects and are prone to measurement errors). Among them, while verifying and calibrating the three-dimensional electromagnetic simulation environment of the passive components, the test pieces are used to establish the equivalent circuit model of the passive components.

[0048] Among them, when determining the scalable independent variables and size range, the process also includes:

[0049] Based on the types and quantity of scalable independent variables of the scalable physical-based equivalent circuit model and the size variation range or boundary of the independent variables, the number of Local physical-based equivalent circuit models required to establish the scalable model and the sizes (scalable parameter values) corresponding to different Local physical-based equivalent circuit models are determined.

[0050] After establishing the three-dimensional electromagnetic simulation environment of passive components, the dimensions of the Local physical basis equivalent circuit model of the components that are determined but prone to measurement errors are brought into it, and the EM simulation corresponding to the corresponding dimensions is obtained. It is added to the test sample and subsequently used as the EM and / or test data source for simulation comparison of scalable models of passive components.

[0051] S3: Based on the analysis of passive components, the topology of the corresponding physical-based equivalent circuit model is established; based on the test data or the test data and the supplementary EM simulation data of the components that are prone to measurement errors, the physical-based equivalent model is fitted to establish the Local physical-based equivalent circuit model.

[0052] Specifically, the topology of the physical-based equivalent circuit model of the passive components is established based on the physical characteristics of the passive components, the physical calculation formulas, and the parasitic analysis of the device structure and manufacturing process. The simulation results of the physical-based equivalent circuit model of the passive components are fitted to the EM and / or test results of the three-dimensional electromagnetic simulation environment (the size of the local physical-based equivalent circuit model) of the corresponding size of the physical-based equivalent circuit model. It is required to finally fit the EM and / or test results of the corresponding size of all Local physical-based equivalent circuit models, that is, after completing the fitting of the physical-based equivalent circuit models equal to the number of Local physical-based equivalent circuit models, the establishment of the Local physical-based equivalent circuit model of the passive components is completed, but at this time the Local physical-based equivalent circuit model does not have the scalability with respect to the size parameters. Among them, components that are prone to measurement errors include:

[0053] S4: Based on the analysis of passive components, the form of the Scalable equation for variable parameter fitting is given, with scalable size parameters as independent variables and component values ​​of the Local physical basis equivalent circuit model as dependent variables. The undetermined coefficients in the Scalable equation for variable parameter fitting are fitted, and the fitting determination coefficients of the Scalable equation are obtained.

[0054] Specifically, based on the topology of the physical equivalent circuit model of passive components, the physical characteristics of passive components, physical calculation formulas, and parasitic analysis of device processes, the Taylor expansion polynomial of the physical calculation formula is used to give the form of the Scalable equation for parameter fitting to accelerate the fitting speed and accuracy of the scalable equation. With the scalable size parameter as the independent variable and the component value of the Local equivalent circuit model as the dependent variable, the undetermined coefficients in the Scalable equation for variable parameter fitting are fitted, and the fitting determination coefficient R of the equation is obtained. 2 , to evaluate the changes in the values ​​of component parameters in the equivalent circuit model topology before and after scaling. The variable parameters fitted by the Scalable equation are single variables, one of multiple variables or a combination of data, and in the present invention, the form of the Scalable equation is preferably the form of Taylor expansion polynomials. In addition, it can also be given by formulas in other forms.

[0055] The fitting determination coefficient based on the Scalable equation is close to the set value (such as the fitting determination coefficient R 2 If the fitting determination coefficient deviates greatly from the set value and does not meet the design index, the component parameters in the physical basis equivalent circuit model of the passive components are adjusted to make their numerical changes more consistent with the trend of the Scalable equation and require that the simulation results of the Local physical basis equivalent circuit model are consistent with the EM and / or test results of the corresponding size.

[0056] S5: If the fitting error of the Scalable equation meets the requirements, the Scalable equation is brought into the Local physical basis equivalent circuit model, the inherent component values ​​are replaced, and a Global equivalent circuit model of passive components with scalable size parameters is established.

[0057] Specifically, based on the Scalable equation, the function or equation relationship between the component values ​​(dependent variables) and the model scalable variables (independent variables) is established. After completing the establishment of the Scalable equation for each component in the topology of the physical-based equivalent circuit model, the relationship is brought into any established Local physical-based equivalent circuit model, replacing the originally fixed component values, and establishing a Global equivalent circuit model of passive components with scalable size parameters, that is, the passive component equivalent model is scalable. After obtaining the Global equivalent circuit model, compare the simulation results of the Global equivalent circuit model under different scaling sizes with the test data of the corresponding size, and verify the error of the Global equivalent circuit model. If the error meets the error index requirements of the RF integrated microsystem, the establishment of the scalable model of the passive component is completed.

[0058] The present invention provides a scalable modeling method for passive components in an advanced packaging process, and provides multiple embodiments. Corresponding scalable models are established for passive components such as planar capacitors, planar spiral inductors, and interconnection structure ball grid arrays, and the scalable model operating frequency bands, transmission performance indicators, and scalable variable quantity requirements are provided. It is required to realize a RF integrated microsystem passive device model that is scalable in length and width for planar capacitors, and to realize a RF integrated microsystem interconnection structure model that is scalable in radius for ball grid arrays.

[0059] In addition, based on the established scalable model of passive components in advanced packaging processes, a complex interconnect structure model is designed according to the interconnection requirements of RF integrated microsystems to realize a scalable model of advanced integrated packaging process parameters.

[0060] Embodiment 1:

[0061] Capacitors are one of the most important basic electronic components in advanced integrated packaging process passive devices. They are widely used in RF integrated microsystems. According to their structural characteristics and RF performance differences, they can be divided into two types of capacitors: metal insulator capacitors (MOM) and metal oxide capacitors (MIM). Taking the physical equivalent circuit model of a flat plate capacitor as an example, its structural diagram is shown in the figure below. Figure 2 , 3 shown.

[0062] Limited by the edge capacitance effect of the capacitor, the charge distribution of the upper and lower plates of the flat plate capacitor is non-uniform. Based on the tip discharge phenomenon, the charge distribution at the edge of the electrode plate is higher than that inside, and further, the charge distribution at the corner is higher than that at the edge. The calculation formula for the flat plate capacitance taking into account the edge capacitance effect and the thickness of the plate metal layer is as follows:

[0063]

[0064] Among them, C main is the main capacitance of the equivalent circuit model of the flat plate capacitor, which determines the intrinsic capacitance of the capacitor; ε0 is the vacuum dielectric constant; ε r is the relative dielectric constant of the oxide layer; W is the width of the upper plate of the flat capacitor; L is the length of the upper plate of the flat capacitor; d is the distance between the upper and lower plates; T ·1 is the thickness of the plate metal layer M1, T ·2 is the thickness of the plate metal layer M2. The shapes of the studied flat capacitors are all square.

[0065] Combined with the parasitic bypass capacitance C caused by the flat capacitor substrate sub With the parasitic resistor R sub , establish the physical basis equivalent circuit model of the flat plate capacitor, such as Figure 4 shown.

[0066] After completing the design of the flat capacitor structure that meets the performance requirements of passive devices in advanced integrated packaging processes. Among them, the flat capacitor model contains scalable variables of the length and width of the plate, and gives the scalable parameter scanning range of the flat capacitor, as shown in the following table. In order to ensure the accuracy of the scaling model while shortening the model establishment time, the number of Local models is set to 5 for the single-variable scalable model, and the number of Local physical-based equivalent circuit models is set to 16 for the dual-variable scalable model. After determining the number of dimensions of the Local physical-based equivalent circuit model, the parameter scanning range should be set in combination with the actual application size range of the device under the premise of meeting the process requirements, as shown in Table 1.

[0067]

[0068] Table 1 Scalable parameter scanning range of flat capacitors

[0069] After determining the scalable parameter scanning range of the flat-plate capacitor, perform a three-dimensional electromagnetic field simulation, set the model operating frequency band to DC to 10 GHz, obtain the EM simulation results, or perform physical device processing to obtain the test data results of the flat-plate capacitor, such as Figure 5 shown.

[0070] Secondly, according to the physical equivalent circuit model and formula of the flat plate capacitor, an equivalent Local model is established to determine the Local value of the device parameter. Based on the Taylor expansion formula of the physical formula, the scalable parameters of the model are used as independent variables, and the values ​​of the model components are used as dependent variables to give the form of the Scalable equation for multivariable parameter fitting. Among them, the main capacitance C of the flat plate capacitor is main The Taylor expansion of is as follows:

[0071] Cmain =a0+a1WL+a2(WL) 2 +a3(WL) 3 +o((WL) 3 )

[0072] Among them, a0 is the intercept term of the scalable equation, a1 is the first-order term of the capacitance value with respect to the area of ​​the flat plate capacitor, a2 is the second-order term of the capacitance value with respect to the area of ​​the flat plate capacitor, a3 is the third-order term of the capacitance value with respect to the area of ​​the flat plate capacitor, and o is an infinitesimal quantity.

[0073] Plate capacitor Main capacitor C main The numerical values ​​of the Taylor expansion coefficients are as follows:

[0074]

[0075] The fitting results of the Scalable equation of the main capacitance of the flat capacitor show that the scalable equation fitting degree R2 about the capacitance value is 1, and the scalable equation fitting effect is good. Table 2 gives the Local physical basis equivalent circuit model values ​​of the main capacitance values ​​under different sizes and the values ​​obtained by scalable equation fitting.

[0076] Serial number Plate length / width Capacitance value (Local) Capacitance(Global) Relative error 1 10μm 81.90fF 82.73fF 1.00％ 2 20μm 304.65fF 303.10fF 0.51％ 3 40μm 1170.42fF 1171.32fF 0.08％ 4 80μm 4628.99fF 4628.80fF 0.04‰ 5 160μm 18516.30fF 18516.31fF 0.00％

[0077] Table 2 Comparison of numerical parameters of the flat capacitor model components before and after scaling under different sizes

[0078] Finally, the established Scalable equation is introduced into the equivalent circuit model, replacing the component values ​​of the original Local physical equivalent circuit model, and establishing a Global equivalent circuit model for the flat plate capacitor to verify the model error and compare the simulation results. Figure 6 shown.

[0079] Embodiment 2:

[0080] Inductors are also one of the basic electronic components in advanced integrated packaging process passive devices. According to their shape and structural characteristics, they can be divided into many types of inductors. Taking the physical basis equivalent circuit model of planar spiral inductors as an example, its three-dimensional structure diagram is as follows: Figure 7 shown.

[0081] The simple calculation formula for inductance value is as follows:

[0082]

[0083] Among them, L main is the main inductance of the equivalent circuit model of the planar spiral inductor, which determines the intrinsic inductance of the inductor; μ0 is the magnetic permeability of vacuum; μ r is the relative magnetic permeability of the metal layer; D outis the outer diameter of the planar spiral inductor; c1, c2, c3, c4 are the coefficients to be determined in the equation; D in is the inner diameter of the planar spiral inductor; N is the number of inductor turns; S is the inductor line spacing; W is the inductor line width.

[0084] Combined with the parasitic bypass capacitance C caused by the planar spiral inductor substrate sub With the parasitic resistor R sub , establish the physical basis equivalent circuit model of planar spiral inductor, such as Figure 8 shown.

[0085] After completing the design of the planar spiral inductor structure that meets the performance requirements of passive devices in advanced integrated packaging processes, the planar spiral inductor model contains a scalable variable for the number of inductor turns and a given parameter scanning range, as shown in Table 3.

[0086]

[0087] Table 2 Scalable parameter sweep range of planar spiral inductors

[0088] After determining the scalable parameter scanning range of the planar spiral inductor, perform a three-dimensional electromagnetic field simulation, set the model operating frequency band to DC to 10 GHz, obtain the EM simulation results, or perform test piece processing to obtain the test data results of the planar spiral inductor, such as Fig. 9 shown.

[0089] Secondly, according to the physical basis equivalent circuit model and formula of the planar spiral inductor, an equivalent Local physical basis equivalent circuit model is established to determine the values ​​of the Local physical basis equivalent circuit model of the component parameters. Based on the Taylor expansion formula of the physical formula, the scalable parameters of the model are used as independent variables, and the values ​​of the model components are used as dependent variables to give the form of the Scalable equation for multivariable parameter fitting. Among them, the main inductance L of the planar spiral inductor is main The Taylor expansion of is as follows:

[0090] L main =a0+a1N+a2N 2 +a3N 3 +o(N 3 )

[0091] Among them, a0 is the intercept term of the scalable equation, a1 is the first-order term of the inductance value with respect to the number of inductor turns, a2 is the second-order term of the inductance value with respect to the number of inductor turns, and a3 is the third-order term of the inductance value with respect to the number of inductor turns.

[0092] Planar spiral inductor main inductance L main The numerical values ​​of the Taylor expansion coefficients are as follows:

[0093]

[0094] Planar spiral inductor main inductance L main The Scalable equation fitting results show that the scalable equation fitting degree R2 about the inductance value is 0.996, and the scalable equation fitting effect is good. Table 4 gives the values ​​of the Local physical basis equivalent circuit model of the main capacitor values ​​under different sizes and the values ​​obtained by scalable equation fitting.

[0095] Serial number Number of turns Inductance(Local) Inductance(Global) Relative error 1 1.5 363.90pH 382.59pH 5.14％ 2 2.5 764.72pH 690.31pH 9.73％ 3 3.5 1390.49pH 1502.34pH 8.04％ 4 4.5 2565.74pH 2491.379pH 2.90％ 5 5.5 3311.37pH 3330.14pH 0.57％

[0096] Table 3 Comparison of numerical parameters of planar spiral inductor model components before and after scaling at different sizes

[0097] Finally, the established Scalable equation is introduced into the equivalent circuit model, replacing the component values ​​of the original Local physical-based equivalent circuit model, and a Global equivalent circuit model for the planar spiral inductor is established to verify the model error and compare the simulation results. Fig.10 shown.

[0098] Embodiment three:

[0099] Ball grid array (BGA) is an important component of the interconnect structure of advanced integrated packaging technology. Taking the physical equivalent circuit model of ball grid array as an example, its structural schematic diagram is shown in Figures 11 and 12. From the three-dimensional structural schematic diagram of BGA, it can be seen that the fixed size parameters of the model are: the thickness of the metal layer M2 T2, the thickness of the dielectric layer P1 d, the thickness of the metal layer M1 T1, and the thickness of the substrate P2; the scalable parameter is: the radius R of the ball grid array.

[0100] In order to establish an accurate physical equivalent circuit model of the ball grid array, first, analyze the particularity of the BGA model structure, split the semicircular structure into upper and lower parts, and analyze the inductance and loss problems in the signal path. Given the height / radius R of the ball grid array structure, the DC loss R of the upper half of the ball grid array can be calculated. BGA,top and the DC loss R in the upper part BGA,bottom , for the resistance calculation of non-uniform conductors, the following integral formula can be used:

[0101]

[0102]

[0103] Among them, ρ BGA is the resistivity of the ball grid array material. To avoid calculating infinite loss, the loss calculation of the upper part is based on the length calculate.

[0104] After completing the calculation of ohmic loss, analyze the inductance value of the ball grid array (the inductance value L in the upper part) BGA,top and the lower inductance value L BGA,bottom ), similarly, for the calculation of the self-inductance of the non-uniform conductor, the average radius of the upper and lower parts is selected and the following formula is used for approximate calculation:

[0105]

[0106]

[0107] The function F(x) is in the form:

[0108] After completing the calculation of the self-inductance and loss of the ball grid array, analyze the parasitic capacitance component from the ball grid array and the pad to the ground. There is a parasitic capacitance C between the upper metal pad and the ground, which is the medium between air and the substrate. Sub,top There is a parasitic capacitance C between the lower metal pad and the ground, with the substrate as the medium. Sub,bottom , ignoring the air medium ε air And the loss of substrate dielectric, follow the following capacitance calculation formula:

[0109]

[0110]

[0111] Where ε0 is the dielectric constant of vacuum, ε air is the relative dielectric constant of air, S is the upper / lower plate area of ​​the ball grid array, d P1 is the height of the air layer, d P2 is the substrate height, ε sub is the relative dielectric constant of the substrate.

[0112] The parasitic capacitance C between the gate array and the metal pad BGA The expression can be determined qualitatively, and the capacitance should be proportional to the surface area of ​​the sphere and inversely proportional to the distance between the pad and the sphere:

[0113] C BGA ∝ε0ε air R[F]

[0114] According to the calculation and analysis of the above formula, the physical equivalent circuit model of BGA is established. The circuit schematic diagram is as follows: Fig.13 shown.

[0115] After completing the design of the ball grid array structure that meets the performance requirements of the interconnect structure of the advanced integrated packaging process. The ball grid array model contains a scalable variable of the solder ball radius and gives the scalable parameter scanning range of the ball grid array, as shown in Table 5.

[0116]

[0117] Table 4 Ball grid array scalable parameter scanning range

[0118] After determining the scalable parameter scanning range of the ball grid array, perform a three-dimensional electromagnetic field simulation, set the model operating frequency band to DC to 34 GHz, obtain the EM simulation results, or perform physical device processing to obtain the test data results of the ball grid array, as shown in Figure 14.

[0119] Secondly, given the ball grid array bypass parasitic capacitance C BGA The Taylor expansion of is as follows:

[0120] C BGA =a0+a1R+a2R 2 +a3R 3 +o(R 3 )

[0121] Among them, a0 is the intercept term of the scalable equation, a1 is the coefficient of the first inverse term of the scalable equation, a2 is the coefficient of the second inverse term of the scalable equation, and a3 is the coefficient of the third inverse term of the scalable equation.

[0122] Ball grid array bypass parasitic capacitance C BGA The numerical values ​​of the Taylor expansion coefficients are as follows:

[0123]

[0124] The fitting results of the Scalable equation of the parasitic capacitance of the ball grid array bypass show that the scalable equation fitting degree R2 about the capacitance value is 0.974, and the scalable equation fitting effect is good. Table 6 gives the values ​​of the Local physical basis equivalent circuit model of the capacitance value at different sizes and the values ​​obtained by the scalable equation fitting. The Taylor expansion scalable equation coefficients of the capacitance are brought into the model. After completing the scalable fitting of the equivalent circuit components, the scalable model of the BGA structure about the solder ball radius is established, that is, the Global equivalent circuit model.

[0125] Serial number Solder ball radius Capacitance value (Local) Capacitance(Global) Relative error 1 150μm 124.837fF 124.463fF 0.30％ 2 155μm 125.794fF 126.033fF 0.19％ 3 160μm 128.000fF 127.023fF 0.76％ 4 165μm 128.542fF 128.790fF 0.19％ 5 170μm 133.043fF 132.687fF 0.27％

[0126] Table 5 Comparison of the parameters of the ball grid array model components before and after scaling at different sizes

[0127] Finally, the established Scalable equation is introduced into the equivalent circuit model, replacing the component values ​​of the original Global equivalent circuit model, and the Global equivalent circuit model of the ball grid array is established to verify the model error. The simulation results are compared. Fig.15 shown.

[0128] Based on the S parameters obtained from EM and / or test results, the established physical-based equivalent circuit models of planar capacitors, planar spiral inductors, and ball grid arrays are used to extract model parameters, and the parameters of 5 Local physical-based equivalent circuit models are obtained respectively. Based on the mathematical expressions and equivalent circuit models that characterize the physical mechanism of passive components, the scalable parameters of the model are used as independent variables, and the values ​​of model components are used as dependent variables. The Taylor expansion polynomial is used to give the form of Scalable equations for multivariate parameter fitting, and then the scaling rules are established to form scalable Global equivalent circuit models of planar capacitors and ball grid arrays. In the entire device working range, the scalable models have high accuracy.

[0129] Embodiment 4:

[0130] The above demonstrates the establishment of a scalable model of discrete passive devices / interconnect structures for advanced integrated packaging processes. In this embodiment, discrete passive devices / interconnect structure scalable models are cascaded to establish a complex interconnect structure that meets the three-dimensional interconnection requirements of RF integrated microsystems, thereby realizing a scalable model of the complex interconnect structure with respect to advanced integrated packaging process parameters.

[0131] The complex interconnect structure consists of the following three parts: gold wire bonding wire, coplanar waveguide wire and copper pillar. The three-dimensional structure diagram is shown in the figure. Figures 16 to 18 Its size parameter information is shown in Table 7.

[0132]

[0133] Table 6 Dimensional parameter information of complex interconnected structures

[0134] By cascading the established discrete scalable gold wire bonding wire model, scalable coplanar waveguide CPW interconnect model and scalable copper pillar model, a scalable complex interconnect structure model for advanced integrated packaging process parameters is established. Its physical base equivalent circuit model is as follows: Fig.19 shown.

[0135] The specific steps to establish it are:

[0136] The first step is to verify the circuit model simulation results of the scalable complex structure model about the substrate structure and material parameter scaling (substrate dielectric thickness H1, surface gold layer thickness H2, bottom gold layer thickness H3 and substrate dielectric constant T) and compare them with the electromagnetic simulation results, such as Fig. 20 The simulation results show that the established complex structure model is scalable with respect to substrate structure and material parameters, and has high accuracy. The blue is the electromagnetic simulation result, and the red is the scalable model simulation result; the scaling range of the substrate structure and material parameters of the complex interconnected structure is shown in Table 8.

[0137]

[0138] Table 7 Substrate structure and material parameter scaling range of complex interconnect structures (unit: μm)

[0139] The second step is to verify the circuit model simulation results of the scalable complex structure model for the coplanar waveguide CPW interconnection structure parameter scaling (surface metal width W, surface metal spacing S, surface metal line length L) and compare the electromagnetic simulation results, such as Fig.21 The simulation results show that the parameters of the CPW interconnection structure of the complex structure model established are scalable with high accuracy. The blue is the electromagnetic simulation result, and the red is the scalable model simulation result; the scaling range of the CPW interconnection structure parameters of the complex interconnection structure is shown in Table 9.

[0140]

[0141] Table 8 Scaling range of coplanar waveguide CPW interconnection structure parameters of complex interconnection structure (unit: μm)

[0142] The third step is to verify the circuit model simulation results of the scalable complex structure model regarding the scaling of the layer hole radius parameters (hole radius R1, hole interconnection PAD radius R2, hole interconnection PAD spacing R3, bottom PAD spacing R4 and bottom PAD radius R5) and compare them with the electromagnetic simulation results, such as Fig. 22 The simulation results show that the established complex structure model is scalable with respect to the layer hole radius parameter and has high accuracy. Among them, the blue is the electromagnetic simulation result, and the red is the scalable model simulation result; the scaling range of the layer hole radius parameter of the complex interconnected structure is shown in Table 10.

[0143]

[0144] From the above verification process, it can be obtained that the scalable complex structure model is scalable with high accuracy for the above substrate structure and material parameters, CPW interconnect structure and layer hole radius, a total of 13 advanced integrated packaging process parameters. The effectiveness of the scalable modeling method for passive components in advanced packaging processes proposed in the present invention has been verified. Based on the mathematical expressions and equivalent circuit models that characterize the physical mechanisms of passive components, combined with the process information and three-dimensional interconnect structure design requirements of the RF integrated microsystem, a complex three-dimensional interconnect structure can be established based on the established physical equivalent circuit model of discrete scalable passive components, and scalability of advanced integrated packaging process parameters can be achieved. The scalable model of the complex three-dimensional interconnect structure has high accuracy, wide parameter coverage, and strong scalability, and can greatly and effectively shorten the time consumption of RF integrated microsystem model modeling and improve the iteration speed of RF integrated microsystem design.

[0145] The above descriptions are only four specific examples of the present invention and do not constitute any limitation to the present invention. Obviously, for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes to the scalable modeling method of the passive device / interconnection structure of the advanced integrated packaging process without departing from the principles and structures of the present invention, but these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A scalable modeling method for passive components in advanced packaging processes, characterized in that: The specific steps include: Based on process information and design requirements, determine the scalable independent variables and size ranges required for the established scalable model of passive components, and design and process test pieces according to the corresponding scalable independent variables and size ranges; use the test pieces to simultaneously establish equivalent circuit models of passive components, calibrate the electromagnetic simulation environment, and establish a three-dimensional electromagnetic simulation environment for passive components; Based on the measured and processed test pieces, the test data is obtained and de-embedded; at the same time, the components that are prone to measurement errors are simulated based on the calibrated electromagnetic simulation environment, and the simulated data is supplemented to the de-embedded test data to increase the test sample volume; Based on the analysis of passive components, the topology of the corresponding physical-based equivalent circuit model is established; based on the test data or the test data and the supplementary EM simulation data of the components that are prone to measurement errors, the physical-based equivalent model is fitted to establish the Local physical-based equivalent circuit model; Based on the analysis of passive components, the form of Scalable equations for variable parameter fitting is given, with scalable size parameters as independent variables and component values ​​of the Local physical basis equivalent circuit model as dependent variables, the undetermined coefficients in the Scalable equations for variable parameter fitting are fitted, and the fitting determination coefficients of the Scalable equations are obtained; If the fitting error of the Scalable equation meets the requirements, the Scalable equation is brought into the Local physical basis equivalent circuit model, the inherent component values ​​are replaced, and a Global equivalent circuit model of passive components with scalable size parameters is established.

2. The scalable modeling method for passive components in advanced packaging processes according to claim 1, characterized in that: When determining the scalable independent variables and size range of passive components, the variable size parameters and fixed size parameters in the physical basis equivalent circuit model of the passive components are determined according to the process information; according to the design requirements, the type and quantity of scalable independent variables and the size variation range or boundary of the independent variables of the scalable physical basis equivalent circuit model to be established are determined, and the test piece is designed based on the determined scalable independent variables and size range.

3. The scalable modeling method for passive components in advanced packaging processes according to claim 2, characterized in that: When determining the scalable variables and size ranges, the process also includes: Based on the types and quantity of scalable independent variables of the scalable physical-based equivalent circuit model and the size variation range or boundary of the independent variables, the number of Local physical-based equivalent circuit models required to establish the scalable model and the corresponding sizes of different Local physical-based equivalent circuit models are determined.

4. The scalable modeling method for passive components in advanced packaging processes according to claim 3, characterized in that: After establishing the three-dimensional electromagnetic simulation environment of passive components, the dimensions of the Local physical basis equivalent circuit model of the components that are determined but prone to measurement errors are brought into it, and the EM simulation data corresponding to the corresponding dimensions are obtained and added to the test samples.

5. The scalable modeling method for passive components in advanced packaging processes according to claim 1, characterized in that: The analysis of passive components includes: physical characteristics of passive components, physical calculation formulas, and parasitic analysis of component structure and manufacturing process.

6. The scalable modeling method for passive components in advanced packaging processes according to claim 1, characterized in that: The form of the scalable equation is given by the Taylor expansion polynomial using the physical calculation formula.

7. The scalable modeling method for passive components in advanced packaging processes according to claim 6, characterized in that: The variable parameters of the Scalable equation fitting are single variable, multiple variables or a combination of data.

8. The scalable modeling method for passive components in advanced packaging processes according to claim 1, characterized in that: Based on the fitting determination coefficient of the Scalable equation, if the fitting determination coefficient is near the set value, and the deviation between the component value calculated by the Scalable equation and the component value in the Local physical basis equivalent circuit model of the corresponding size is small, and the error index requirements are met, then the next step is executed; if the fitting determination coefficient deviates greatly from the set value and does not meet the design index, the component parameters in the physical basis equivalent circuit model of the passive components are adjusted.

9. The scalable modeling method for passive components in advanced packaging processes according to claim 1, characterized in that: After obtaining the global equivalent circuit model, compare the simulation results of the global equivalent circuit model under different scaling sizes with the test data of the corresponding sizes to verify the error of the global equivalent circuit model. If the error meets the error index requirements of the RF integrated microsystem, the establishment of the scalable model of passive components is completed.

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