Complete multi-chip module (MCM) interconnection reliability analysis method

Abstract

The invention discloses a complete multi-chip module (MCM) interconnection reliability analysis method. The method comprises MCM three-dimensional automatic modeling, load condition application, interconnection reliability analysis under an MCM alternating current working state, interconnection reliability analysis under transient heat, interconnection reliability analysis under multiple parameters and MCM interconnection reliability evaluation and design guidance. The core adopts an ANSYS parameterized design language to realize three-dimensional automatic modeling of a high-integration dual-channel MCM chip. Secondly, on the basis of the atomic flux divergence theory, interconnection reliability analysis of the MCM multifunctional chip under alternating current, thermal stress and multi-parameter changes is achieved through a finite element analysis method. Compared with a traditional experimental method, the method can perform coupling analysis on attributes such as temperature, line width, current and material, has the advantages of high accuracy, high efficiency, strong operability and the like, can effectively predict the interconnection reliability of the chip, provides important reference for layout design of the chip, and is an important measure for guaranteeing the reliability of the MCM chip.

Description

Technical Field

[0001] This invention relates to the field of circuit reliability and circuit design research, and more specifically, to a complete method for reliability analysis of multi-chip module (MCM) interconnects. Background Technology

[0002] With the development of wireless communication technology, high integration, multifunctionality, multi-channel, and low power consumption are inevitable development trends for integrated circuits. In particular, given their advantages of miniaturization, multifunctionality, and high performance, integrated chips have evolved from single-function to multifunctional, and from single-channel to multi-channel, and are widely used in wireless communication systems. Meanwhile, MCM technology, as the mainstream of multifunctional chip design, enables the integrated packaging of different single-function chips, significantly improving system integration and giving it a more compact size, diverse functions, and superior performance.

[0003] However, with the increasing integration density of MCMs and the continuous shrinking of interconnect dimensions, interconnect reliability has become an indispensable factor in evaluating multi-chip modules. Given the high integration density, small linewidth, multiple heat sources, and complex structure of MCM chips, they are more prone to deformation, short circuits, and open circuits. Especially when the interconnect width approaches its physical limit, interconnect failure has become a significant threat to MCM chips, and the residual reliability tolerance in their design and manufacturing gradually decreases, making their interconnect reliability difficult to predict and analyze. MCMs are more susceptible to interconnect failure under the influence of multiple factors, posing a severe challenge to the overall performance and reliability of multi-chip modules, urgently requiring research on the interconnect reliability of MCMs. Summary of the Invention

[0004] The purpose of this invention is to study the interconnect reliability of MCM chips and to propose a complete method for analyzing the interconnect reliability of multi-chip modules (MCMs), providing an important reference for the study of interconnect reliability of MCM chips.

[0005] The technical method and solution of the present invention to solve the above-mentioned interconnect reliability research is as follows: a complete multi-chip module (MCM) interconnect reliability analysis method, including MCM three-dimensional automatic modeling, load condition application, interconnect reliability analysis under MCM AC working state, interconnect reliability analysis under transient thermal conditions, interconnect reliability analysis under multiple parameters, and MCM interconnect reliability assessment and design guidance. S1. The 3D automatic modeling of the MCM is programmed using the ANSYS parametric language. First, the appropriate unit type and metric unit are selected according to the chip layout structure and parameters. Second, drawing commands such as BLOCK are used to complete the construction of the chip's 3D model. Next, the VMESH statement is used to mesh the model entity. Finally, according to the process requirements, the MP command is used to add material properties to the model, and the final finite element model of the MCM is obtained. S2. The load conditions are applied by using the coupling of electric and temperature fields to determine the initial conditions. First, the positions and value ranges of VDD and GND in the finite element model are determined according to the layout structure of the MCM chip. Second, the heat dissipation method, thermal conductivity, convection coefficient, and thermal radiation system of the MCM chip, as well as the constraint positions of the finite element model, are determined based on the actual working environment of the chip and the theories of heat conduction, heat convection, and heat radiation. Finally, the initial conditions and constraints of the finite element analysis are obtained. S3. The interconnect reliability analysis of the MCM under AC operating conditions is achieved by combining the atomic flux divergence (AFD) theory and the APDL finite element analysis method. First, the chip current and voltage under saturation state are obtained by testing the MCM. At the same time, in order to avoid the negative conductivity of the material in ANSYS, the resistivity used here is the absolute value of the current-to-voltage ratio. The ratio of MCM voltage to current is calculated, and the curve of the simulated MCM resistance changing with time is obtained. In order to obtain the law of AFD_MAX changing with time, a DC load is first applied to bring the circuit to a relatively stable state. Then, a periodic AC load is applied to perform calculations under the AC state of the MCM. In order to improve the accuracy, the DC load value here uses the root mean square of the AC signal. At this time, the instantaneous power dissipated and the average power are the same, which can well simulate the thermal stability state of the MCM. S4. The interconnect reliability analysis of MCM under transient thermal conditions combines thermal stress coupling analysis, structural analysis, and APDL finite element analysis to achieve interconnect reliability analysis. In the analysis, the steady-state analysis of MCM is performed first, and the temperature field results are imported into the thermoelectric analysis. The actual working state of MCM can be simulated by applying boundary conditions such as voltage and temperature. The load applied in the transient thermal analysis is the same as that in the steady-state thermal analysis. The initial temperature of the module is set, the analysis type is transient, the analysis time and time step are set, and the automatic time step is enabled. The minimum and maximum step sizes are set, the time integration option is enabled, and the integration time period is set. Since the applied load is constant in each load step, the load is set as a step load STEPPED. Finally, the solver SOLVE is used to solve the problem. When the temperature stabilizes, its reliability is predicted, and the interconnect reliability change curve of MCM under transient thermal conditions is finally obtained. S5. The reliability analysis of MCM interconnection under different temperatures, currents, and linewidths is based on the temperature distribution and AFD plotted under different conditions to evaluate the degree and trend of the influence of temperature, linewidth, and current factors on the reliability of MCM interconnection. S6, MCM interconnect reliability assessment and design guidance: Based on the relationship curves between each factor and AFD, the first partial derivative is solved to obtain the sensitivity results of AFD to each factor and plot the curves. Finally, the complementary relationship analysis of the influence of temperature, linewidth and current factors on the reliability of MCM interconnect is carried out, and the feasible region interval under fixed AFD is plotted.

[0006] The beneficial effects of the technical solution of this invention are as follows: The core of this invention uses the ANSYS parametric design language (APDL) to realize the three-dimensional automatic modeling of a highly integrated dual-channel MCM chip. Secondly, based on the atomic flux divergence (AFD) theory, the finite element analysis method is used to analyze the interconnect reliability of the MCM multifunctional chip under AC operating conditions, different thermal stresses, and different temperatures, currents, and linewidths. This is a complete study on the interconnect reliability of the MCM chip. Compared with traditional experimental methods, this modeling and simulation method can perform joint coupling analysis of attributes such as temperature, linewidth, and current in the circuit, and has advantages such as high accuracy, high efficiency, and strong operability. This invention can effectively predict and analyze the interconnect reliability of the chip, and thus provide an important reference for the layout design of the chip, which is an important measure to ensure the reliability of the MCM chip.

[0007] Furthermore, the S1's MCM is a highly integrated dual-channel receiver front-end chip, including two channels: RF-IN-A and RXOUT-A, and RF-IN-B and RXOUT-B. It uses an LGA package and is powered by a single positive voltage supply. Internally, it mainly integrates two low-noise amplifiers implemented using GaAs pHEMT 0.25 μm technology and two high-power switching chips implemented using silicon-on-insulator technology.

[0008] The beneficial effects of the above-mentioned further solutions are as follows: The MCM chip used in this invention is composed of two SOI high-power switches and two GaAs pHEMT low-noise amplifiers. The component types and interconnection levels are simple, the geometric-physical model has low dimensionality, and it can perform one-click parametric modeling and quickly generate sparse meshes, which significantly reduces the finite element preprocessing time and storage overhead, and provides efficient and lightweight simulation conditions for subsequent electromagnetic-thermal-mechanical coupling analysis.

[0009] Furthermore, the formula for calculating AFD of S3 is: , in, Represents total atomic flux. This represents the atomic flux generated by electron wind migration. Represents the atomic flux generated by temperature gradient migration, This represents the atomic flux generated by thermomechanical stress migration. Represents the transfer of heat; Represents Boltzmann's constant; T represents absolute temperature; A gradient representing absolute temperature; It is the electron constant; The self-diffusion coefficient represents the pre-factor; The activation energy represents the self-diffusion energy of metal interconnects; Represents atomic volume; The gradient represents the local static stress. This represents the failure time of the interconnect. This represents the atomic flux divergence.

[0010] The beneficial effects of the above-mentioned further solutions are: by transforming the interconnect reliability of MCM chips into quantifiable data indicators and presenting them in intuitive forms such as charts and numerical curves, the original implicit reliability information becomes clear at a glance. This not only greatly improves the evaluation efficiency, but also provides a clear and visualized decision-making basis for subsequent design optimization and failure warning.

[0011] Furthermore, the interconnect reliability, sensitivity, and feasible domain space of the MCM under AC operating conditions, different thermal stresses, and different temperatures, currents, and linewidths were analyzed, and the results are mainly used to guide the chip layout design.

[0012] The beneficial effects of the above-mentioned further solutions are: by further analyzing the interconnection reliability, data sensitivity and feasible domain space of MCM under AC operation, thermal stress and multi-physics coupling, the present invention realizes the circuit layout of thermal-electric synergy. Attached Figure Description

[0013] Figure 1 This is the research method flow of the present invention; Figure 2 For a complete MCM interconnect reliability analysis process; Figure 3 Based on the principle of MCM; Figure 4 For MCM 3D model; Figure 5 These represent the chip current and chip voltage in saturation state. Figure 6 This represents the chip voltage to current ratio and the simulated chip resistance value. Figure 7 The curve showing the relationship between load current and AFD_MAX over time within one cycle; Figure 8 The curve of AFD_MAX changing over time under AC load; Figure 9 This is a cloud map showing the temperature distribution at the nodes for steady-state thermal analysis. Figure 10A contour plot of MCM node temperature over time; Figure 11 This is the time history of the highest and lowest temperatures of the MCM. Figure 12 The curves showing the AFD_MAX as a function of temperature for transient and steady-state heat; Figure 13 The curves showing the relationship between AFD_MAX and temperature for different linewidths; Figure 14 The curves showing the relationship between AFD_MAX and current at different temperatures; Figure 15 The curves showing the relationship between AFD_MAX and linewidth for different currents; Figure 16 The sensitivity curves of AFD_MAX of MCM with respect to temperature for different linewidths; Figure 17 The sensitivity curves of AFD_MAX of the MCM model with respect to temperature under different currents are shown. Figure 18 The sensitivity curves of AFD_MAX with respect to current for the MCM model under different linewidths; Figure 19 To determine the feasible region for fixing the line width and current of the AFD; Figure 20 To select a feasible region for current and temperature under fixed AFD; Detailed Implementation

[0014] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0015] This invention provides a complete method for reliability analysis of multi-chip module (MCM) interconnects, including automatic 3D modeling of MCMs, application of load conditions, interconnect reliability analysis under AC operating conditions of MCMs, interconnect reliability analysis under transient thermal conditions, interconnect reliability analysis under multiple parameters, and MCM interconnect reliability assessment and design guidance.

[0016] like Figure 1 As shown, a method for analyzing the reliability of multi-chip module (MCM) interconnects includes MCM three-dimensional automatic modeling, load condition application, interconnect reliability analysis under MCM AC operating conditions, interconnect reliability analysis under transient thermal conditions, interconnect reliability analysis under multiple parameters (temperature, current, linewidth), and MCM interconnect reliability assessment and design guidance.

[0017] like Figure 2As shown, the MCM 3D automatic modeling uses a parametric language. During construction, the SOLID98 cell type and metric units (Kg, μm, s, ℃, mA, μN, V) are selected according to the chip design. Secondly, based on... Figure 3 The layout structure of the mid-chip design was created by drawing 864 3D entities using programming commands such as WPOFF, K, V, BLOCK, and VADD. Next, VMESH statements were used to mesh the entities. Finally, according to process requirements, material properties such as copper, gold, gallium arsenide, silicon, and epoxy resin were added to the model using the programming language MP, resulting in the MCM finite element model. Figure 4 As shown.

[0018] The load conditions are determined by coupling the electric field and the temperature field. First, based on the chip layout, the positions of the two VDD pins and 25 GND pins are determined in the finite element model of the MCM, with the VDD pin voltage set to 5 V and the GND voltage set to 0 V. Second, based on the actual working environment of the chip and the theories of heat conduction, heat convection and heat radiation, the heat dissipation method of the MCM chip is determined to be mainly solid conduction and air convection conduction, with an air convection coefficient h = 20 W / (m2·℃). The location is on the outer surface of the housing in contact with the air. Finally, the initial conditions and constraints for the finite element analysis are obtained.

[0019] Interconnect reliability analysis of the MCM under AC operating conditions is achieved by combining atomic flux divergence (AFD) theory and APDL finite element analysis. First, the MCM is tested to obtain the chip current and voltage under saturation conditions, such as... Figure 5 As shown, and to avoid the case where the material conductivity in ANSYS is negative, the resistivity used here is the absolute value of the current-to-voltage ratio, such as... Figure 6 As shown, the calculated ratio of MCM voltage to current is used to obtain the simulated curve of MCM resistance changing over time, as shown in the figure. Figure 7 As shown, to obtain the time-varying law of AFD_MAX, a DC load is first applied to bring the circuit to a relatively stable state. Then, a periodic AC load is applied to calculate the MCM under AC conditions. To improve accuracy, the DC load value here uses the root mean square of the AC signal. At this time, the instantaneous power dissipation and the average power are the same, which can well simulate the thermal stability state of the MCM. Figure 8 As shown, it is obvious that the value of AFD continues to increase with the increase of current. The negative current only means that the direction of the current is opposite to the initial current. In fact, the absolute value of the current is constantly increasing.

[0020] Transient thermal interconnect reliability analysis of the MCM combines thermal stress coupling analysis, structural analysis, and APDL finite element analysis to achieve interconnect reliability analysis. During the analysis, a steady-state analysis of the MCM is first performed, such as... Figure 9 As shown, the temperature field results are imported into the thermoelectric analysis. The actual working state of the MCM can be simulated by applying boundary conditions such as voltage and temperature. The load applied in the transient thermal analysis is the same as that in the steady-state thermal analysis. The initial temperature of the module is set, the analysis type is transient, the analysis time and time step are set, and automatic time stepping is enabled. The minimum and maximum step sizes are set, the time integration option is enabled, and the integration time period is set. Since the applied load is constant in each load step, the load is set as a step load (STEPPED). Finally, the solver SOLVE is used for solving the problem. Figure 10 As shown, the reliability of the MCM is predicted when the temperature is stable, and the interconnect reliability change curve of the MCM under transient thermal conditions is finally obtained. The time history of the highest and lowest temperatures of the MCM is as follows. Figure 11 As shown in the figure, the temperature of the MCM basically stabilizes at 2 s, indicating that the temperature has basically reached its maximum. Therefore, a time interval of 2 s is used as the time step to calculate AFD. The AFD_MAX curves of transient and steady-state heat as a function of temperature are shown in the figure. Figure 12 As shown, it can be observed that AFD_MAX increases exponentially with increasing temperature; however, AFD_MAX under transient thermal analysis is significantly lower than that under steady-state thermal analysis.

[0021] The reliability analysis of MCM interconnection under different temperatures, currents, and linewidths is based on the temperature distribution and AFD (Automatic Detection and Deposition) curves plotted under different conditions. For example, when the operating voltage is 5 V, the relationship curves between AFD_MAX and temperature for different linewidths are shown below. Figure 13 As shown, it can be observed that AFD_MAX decreases with increasing line width, and at the same operating voltage, the higher the temperature, the larger the AFD_MAX value. When the minimum interconnect size is 50 μm, the relationship between AFD_MAX and current at different temperatures is shown in the curves. Figure 14 As shown, it can be observed that the AFD_MAX value increases sharply with increasing temperature, and at the same temperature, the larger the current, the larger the AFD_MAX value. The relationship between AFD_MAX and linewidth at different currents when the temperature is 50 ℃ is shown in the curves below. Figure 15 As shown, as the current increases, AFD_MAX first remains almost constant and then increases; the larger the linewidth, the smaller the AFD_MAX value.

[0022] MCM interconnect reliability assessment and design guidance, based on the relationship curves between various factors and AFD, calculate the first partial derivatives to obtain the sensitivity results of AFD to each factor and plot the curves. Figure 16It can be seen that when the temperature is below 70 ℃, the growth rate of ∂AFD_MAX / ∂T changes steadily under different voltages. When the temperature exceeds 70 ℃, the growth rate of ∂AFD_MAX / ∂T under different voltages increases significantly. Figure 17 It can be seen that when the current is below 33.5 mA, ∂AFD_MAX / ∂T gradually increases with increasing temperature, but the change curve is relatively flat. However, when the current is above 33.5 mA, the growth rate of ∂AFD_MAX / ∂T increases significantly with increasing temperature. Figure 18 It can be seen that when the current is below 12.5 mA, the growth rate of ∂AFD_MAX / ∂Current remains almost constant. However, when the current is above 12.5 mA, the growth rate of ∂AFD_MAX / ∂Current increases sharply. This is because in the MCM, the linewidth is inversely proportional to the current density. With a fixed AFD, the feasible region for linewidth and current selection is as follows: Figure 19 As shown, it can be observed that when AFD is 1.5*10 7 toms·μm -3 s -1 At this time, the linewidth can be selected as 50 μm, the current is 34.4 mA, and the feasible range of current and temperature selection under fixed AFD is as follows: Figure 20 As shown, it can be observed that the temperature, current, and area beneath each curve meet the design requirements of AFD, especially when AFD is 5.0*10. 7 toms·μm -3 s -1 At that time, a temperature of 95 ℃ and a current of 27.5 mA can be selected. Under the same AFD budget, when the current is 44.5 mA, the temperature can be reduced to 74 ℃ to meet the AFD requirements. Therefore, in order to meet different AFD budgets, a variety of minimum interconnect size and voltage, as well as line width and temperature combinations can be provided.

[0023] In summary, the application of a method for analyzing the reliability of multi-chip module (MCM) interconnects can provide important reference and guidance for reliability research and chip design of radio frequency microwave circuits.

[0024] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for complete multi-chip module (MCM) interconnect reliability analysis, comprising: The MCM three-dimensional automatic modeling includes MCM three-dimensional automatic modeling, load condition application, MCM interconnection reliability analysis under alternating current working state, MCM interconnection reliability analysis under transient heat, MCM interconnection reliability analysis under multiple parameters, and MCM interconnection reliability evaluation and design guidance. S1, the MCM three-dimensional automatic modeling is programmed by using ANSYS parameterized language, and unit type selection, three-dimensional model construction, mesh division and material attribute addition are sequentially completed, and finally an MCM finite element model is obtained. S2, the load condition application is to determine the initial condition by using the coupling of electric field and temperature field, to calibrate the VDD / GND position and value in the MCM finite element model according to the layout, to set the heat dissipation parameters and constraints according to the heat theory, and to form the initial condition and boundary; S3, the MCM interconnection reliability analysis under alternating current working state is realized by combining the atomic flux divergence (AFD) theory and the APDL finite element analysis method, based on the AFD theory, a direct current steady load is applied first, and then an alternating current load is applied, the root mean value of the alternating current signal is used to obtain the MCM resistance-time curve and the AFD_MAX evolution law; S4, the MCM interconnection reliability analysis under transient heat is realized by combining the thermal stress coupling analysis, the structure analysis and the APDL finite element analysis method, first steady heat analysis is performed, then the temperature field in the steady state is imported for thermal-electric coupling transient analysis, the step load and time step are set, and the reliability change curve under transient heat is solved; S5, the MCM interconnection reliability analysis under different temperatures, currents and line widths is to draw the relationship curve of temperature distribution and AFD under different conditions, and to evaluate the influence degree and trend of temperature, line width and current factors on the MCM interconnection reliability; S6, the MCM interconnection reliability evaluation and design guidance is based on the sensitivity calculated by the first partial derivative of AFD to each factor, the sensitivity curve is drawn, the complementary relationship analysis of temperature, line width and current factors on the MCM interconnection reliability is performed, and the feasible region interval under fixed AFD is drawn.

2. The method of claim 1, wherein the method is a complete MCM interconnect reliability analysis method, characterized by, The MCM of S1 is a high-integration dual-channel receiver front-end chip, including RF-IN-A and RXOUT-A, RF-IN-B and RXOUT-B two channels, using LGA packaging, using positive voltage single power supply, and mainly integrating 2 low-noise amplifiers realized by GaAs pHEMT 0.25 μm process and 2 high-power switch chips realized by silicon-on-insulator process inside.

3. The method of claim 1, wherein the method is a complete MCM interconnect reliability analysis method, characterized by, The AFD calculation formula of S3 is: ， wherein, represents the total atomic flux, represents the atomic flux generated by electron wind migration, represents the atomic flux generated by temperature gradient migration, represents the atomic flux generated by thermo-mechanical stress migration; represents the heat transport; represents the Boltzmann constant; T represents the absolute temperature; represents the gradient of the absolute temperature; is the electron constant; represents the pre-exponential factor of the self-diffusion coefficient; represents the activation energy of the self-diffusion of the metal interconnect; represents the atomic volume; represents the gradient of the local static stress; represents the failure time of the interconnect line, represents the atomic flux divergence.

4. The method of claim 1, wherein the method is a complete MCM interconnect reliability analysis method. The MCM interconnection reliability under alternating current working state, different thermal stresses, different temperatures, currents and line widths, sensitivity and feasible region space are analyzed, which are mainly used to guide the layout design of the chip.

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