CN103970954A - High-density integrated circuit packaging optimization method based on robustness design - Google Patents

Abstract

The invention discloses a novel high-density integrated circuit packaging thermal fatigue structure reliability optimization method based on robustness design. The method includes the following steps that a structural design variable to be optimized is determined, and thermal fatigue strain for packaging a main thermal failure component is used as an optimization objective function; according to the determined structural design variable and an optimization objective, three-level two-order robustness experimental design is conducted; thermal fatigue strain finite element analysis and calculation are conducted on three-level two-order robustness experimental design points, and a complete three-level two-order robustness experimental design table is formed; according to the complete three-level two-order robustness experimental design points and corresponding thermal fatigue strain values, the least square method is used for establishing a quadric surface model of a high-density integrated circuit packaging objective function. According to the method, the high-density integrated circuit packaging thermal reliability analysis and design key technology is achieved, and the novel method is provided for high-density integrated circuit packaging thermal reliability analysis and design.

Description

A kind of optimization method of the high density integrated circuit encapsulation based on robust designs

Technical field

The present invention relates to integrated circuit (IC) design and encapsulation technology field, be specifically related to a kind of optimization method of the high density integrated circuit encapsulation based on robust designs.

Background technology

Two large gordian techniquies of integrated circuit fields are ic manufacturing technology and integrated antenna package technology, and integrated circuit will form semiconductor devices by encapsulation, and encapsulation is that CI supports, the necessary condition of protection, is also the important component part that its function realizes.High density integrated circuit encapsulation technology has good interconnection performance, cheap assembly cost and the anti-high-frequency signal advantage such as crosstalk becomes the inexorable trend of development.

Yet, due to highdensity interconnection, make its link particularly encapsulate little soldered ball, under the periodicity break-make and the periodically variable effect of environment temperature of circuit, can produce thermal and mechanical stress strain, cause germinating and the expansion of underbead crack, finally make package failure, the thermomechanical inefficacy that encapsulation particularly encapsulates solder joint becomes the main failure mode of high density integrated circuit.According to the statistics of the mechanisms such as IEEE and JEDEC: in all failure causes of electron device or complete electronic set, approximately have 70% to cause for encapsulation and solder joint thermal failure thereof.High density integrated circuit encapsulation thermomechanical reliability becomes one of focus of microelectronic research, solve this key issue, must carry out thermal reliability optimal design to it, J.T.HANN points out " along with the raising of chip integration and welding spot size more and more less, must carry out thermomechanical reliability design in case thermal failure ".But high density integrated circuit is encapsulated under the Thermal Load of circulation, its hot-machine coupling relation is very complicated, is a dynamic fatigue process, up to now, also do not set up effective heat fatigue Optimization Design, greatly restricted the development of high density integrated circuit encapsulation technology.

Summary of the invention

The deficiency existing for prior art, the object of the present invention is to provide a kind ofly can guarantee the main inoperative component heat fatigue of high-density packages reliability, can guarantee again the optimization method of the high density integrated circuit encapsulation based on robust designs of the robustness of encapsulating structure parameter under disturbance.

For achieving the above object, the invention provides following technical scheme: a kind of optimization method of the high density integrated circuit encapsulation based on robust designs, comprises the steps:

(1) determine structural design variable to be optimized, using the heat fatigue strain of the main thermal failure parts of encapsulation as optimization aim function;

(2), according to definite structural design variable and optimization aim, carry out three horizontal second order robust experimental designs;

(3) 3 horizontal second order robust experimental design points are carried out respectively to finite element analysis and the calculating of heat fatigue strain, form three complete horizontal second order robust experimental design tables;

(4), according to complete 3 horizontal second order robust experimental design points and corresponding heat fatigue strain value, use least square method to build the model of a quadric of high density integrated circuit encapsulation objective function;

(5) model of a quadric of high density integrated circuit encapsulation objective function is carried out to variance test and precision test.If meeting under the confidence level of designing requirement, model is significant, can utilize this model to be optimized; Otherwise must redesign test, build new model of a quadric;

(6) utilize the model of a quadric meet precision and requirement, the level line of making equivalent heat repeated strain, analyzes reciprocation and the influencing characteristic of each structural design variable;

(7) utilize the model of a quadric of having constructed to replace real finite element model, set up the sane Optimized model of heat fatigue structural reliability of the high density integrated circuit encapsulation of multiple constraint, and solve, obtain the encapsulating structure parameter set of optimizing, and verify optimum results.

The present invention is further set to: step (2) comprises following sub-step:

(2.1) according to high density integrated circuit package design, require to determine the marginal range of structural design variate-value, their value of naming a person for a particular job centered by the intermediate value of marginal range is arranged to three levels :+1,0 and-1, they represent higher limit, intermediate value and the lower limit of tolerance value;

(2.2) hypercube of being tieed up by N structural design variable structure N, Mei Wei center and hypercube Mei Bian center arrange respectively an experimental point, sampling produces M experimental point altogether, form three horizontal second order robust experimental design tables, there is not axial point and can be simultaneously in high-level state in three horizontal second order robust experimental designs, make design point all drop on safety zone, there is very strong robustness.

The present invention is also further set to: step (3) comprises following sub-step:

(3.1) according to the structure of high-density packages, with the intermediate value of structural design variable to be optimized, set up the solid model of packaging body finite element;

(3.2) in conjunction with the material properties of each parts of packaging body, the solid model of packaging body finite element is carried out to grid division;

(3.3) by the standard of uniform temperature circulation, the thermal force of circulation is loaded on each node of finite element, four to six temperature cycles under the cycle, each experimental design point in three horizontal second order robust experimental design tables is carried out to FEM (finite element) calculation, obtain the heat fatigue strain value of main inoperative component maximum equivalent, obtain three complete horizontal second order robust experimental design tables.

The method that high density integrated circuit encapsulates main inoperative component heat fatigue strain quadric structure is:

(a) construct quadric basis function: $E\left(\widehat{\mathrm{\α}}\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}({\mathrm{\ϵ}}_j-{\widehat{\mathrm{\ϵ}}}_j)={(\mathrm{\ϵ}-G\widehat{\mathrm{\α}})}^T(\mathrm{\ϵ}-G\widehat{\mathrm{\α}})$

Wherein, G=[1, p ₁..., p _n, p ₁ ², p ₁p ₂..., p ₁p _n, p ₂ ², p ₂p ₃..., p ₂p _n..., p _n-1 ², p _n-1p _n, p _n ²] $\widehat{\mathrm{\α}}={[{\mathrm{\α}}_0,{\mathrm{\α}}_1,\·\·\·,{\mathrm{\α}}_{1n},{\mathrm{\α}}_{11},{\mathrm{\α}}_{12},\·\·\·,{\mathrm{\α}}_{1n},{\mathrm{\α}}_{22},{\mathrm{\α}}_{23},\·\·\·,{\mathrm{\α}}_{2n},\·\·\·,{\mathrm{\α}}_{(n-1)(n-1)},{\mathrm{\α}}_{(n-1)n},{\mathrm{\α}}_{\mathrm{nn}}]}^T$ , for high density integrated circuit encapsulates the output valve of main inoperative component heat fatigue strain quadric, P=(p ₁, p ₂..., p _n) be the structural design variable of encapsulation, matrix of coefficients for corresponding design variable.ε represents the output valve ε=(ε of finite element heat fatigue strain ₁, ε ₂..., ε _m), n is the number of encapsulating structure design variable, m is three horizontal second order robust test design numbers.

(b) basis function is asked local derviation to quadric surface coefficient: obtain quadric matrix of coefficients $\widehat{\mathrm{\α}}={\left(Q^{T}Q\right)}^{-1}{Q}^T\mathrm{\ϵ},$ In formula, $Q=\left[\begin{array}{ccccc}1& q_{11}& q_{12}& ...& q_{1n}\\ 1& q_{21}& q_{22}& ...& q_{2n}\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ 1& q_{m1}& q_{m2}& ...& q_{\mathrm{mn}}\end{array}\right].$ Q _jibe that in three horizontal second order robust experimental design tables, i design variable value put in j experimental design.

(c) set up based on three horizontal second order robust experimental design models of a quadric:

Advantage of the present invention is: the present invention is nonlinear theory, fatigue reliability theory and robust designs theory are incorporated in the thermal design of high density integrated circuit encapsulation, proposed based on three horizontal second order robust test design, the robust heat fatigue reliability Optimum Design method that nonlinear finite element merges mutually with quadric surface, the heat fatigue strain of the main thermal failure parts of encapsulation is carried out to the modeling of thermal reliability optimal design and solved the high-density packages under thermal cycle load as objective function, in scope of design, obtain the optimum structure parameter collection of high density integrated circuit encapsulation, make the inside maximum equivalent heat fatigue strain of main thermal failure parts reduce to minimum, and show that each structural design variable is to the reciprocation of heat fatigue strain and influencing characteristic.The method can guarantee the main inoperative component heat fatigue of high-density packages reliability, can guarantee again the robustness of encapsulating structure parameter under disturbance.This invention has solved the gordian technique of high density integrated circuit encapsulation thermal reliability analysis and design, for high density integrated circuit encapsulation thermal reliability analysis and design provides new method.

Below in conjunction with Figure of description and specific embodiment, the invention will be further described.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the high density integrated circuit encapsulation heat fatigue structural optimization based on reliability of the embodiment of the present invention based on robust designs;

Fig. 2 is the horizontal second order robust of the embodiment of the present invention three design of experiment;

Fig. 3 is embodiment of the present invention FSBGA encapsulation mesh of finite element illustraton of model;

Fig. 4 is the cloud atlas of the solder joint heat fatigue strain FEM (finite element) calculation of an experimental design point of the embodiment of the present invention.

Embodiment

Referring to Fig. 1, Fig. 2, Fig. 3 and Fig. 4, the optimization method of a kind of high density integrated circuit encapsulation based on robust designs disclosed by the invention, comprises the steps:

(1) determine structural design variable to be optimized, using the heat fatigue strain of the main thermal failure parts of encapsulation as optimization aim function;

(2), according to definite structural design variable and optimization aim, carry out three horizontal second order robust experimental designs;

(3) 3 horizontal second order robust experimental design points are carried out respectively to finite element analysis and the calculating of heat fatigue strain, form three complete horizontal second order robust experimental design tables;

(4), according to complete 3 horizontal second order robust experimental design points and corresponding heat fatigue strain value, use least square method to build the model of a quadric of high density integrated circuit encapsulation objective function;

(5) model of a quadric of high density integrated circuit encapsulation objective function is carried out to variance test and precision test.If meeting under the confidence level of designing requirement, model is significant, can utilize this model to be optimized; Otherwise must redesign test, build new model of a quadric;

(6) utilize the model of a quadric meet precision and requirement, the level line of making equivalent heat repeated strain, analyzes reciprocation and the influencing characteristic of each structural design variable;

(7) utilize the model of a quadric of having constructed to replace real finite element model, set up the sane Optimized model of heat fatigue structural reliability of the high density integrated circuit encapsulation of multiple constraint, and solve, obtain the encapsulating structure parameter set of optimizing, and verify optimum results.

The present invention is further set to: step (2) comprises following sub-step:

(2.1) according to high density integrated circuit package design, require to determine the marginal range of structural design variate-value, their value of naming a person for a particular job centered by the intermediate value of marginal range is arranged to three levels :+1,0 and-1, they represent higher limit, intermediate value and the lower limit of tolerance value;

(2.2) hypercube of being tieed up by N structural design variable structure N, Mei Wei center and hypercube Mei Bian center arrange respectively an experimental point, sampling produces M experimental point altogether, form three horizontal second order robust experimental design tables, there is not axial point and can be simultaneously in high-level state in three horizontal second order robust experimental designs, make design point all drop on safety zone, there is very strong robustness.

The present invention is also further set to: step (3) comprises following sub-step:

(3.1) according to the structure of high-density packages, with the intermediate value of structural design variable to be optimized, set up the solid model of packaging body finite element;

(3.2) in conjunction with the material properties of each parts of packaging body, the solid model of packaging body finite element is carried out to grid division;

(3.3) by the standard of uniform temperature circulation, the thermal force of circulation is loaded on each node of finite element, four to six temperature cycles under the cycle, each experimental design point in three horizontal second order robust experimental design tables is carried out to FEM (finite element) calculation, obtain the heat fatigue strain value of main inoperative component maximum equivalent, obtain three complete horizontal second order robust experimental design tables.

The method that high density integrated circuit encapsulates main inoperative component heat fatigue strain quadric structure is:

(a) construct quadric basis function: $E\left(\widehat{\mathrm{\α}}\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}({\mathrm{\ϵ}}_j-{\widehat{\mathrm{\ϵ}}}_j)={(\mathrm{\ϵ}-G\widehat{\mathrm{\α}})}^T(\mathrm{\ϵ}-G\widehat{\mathrm{\α}})$

Wherein, G=[1, p ₁..., p _n, p ₁ ², p ₁p ₂..., p ₁p _n, p ₂ ², p ₂p ₃..., p ₂p _n..., p _n-1 ², p _n-1p _n, p _n2] $\widehat{\mathrm{\α}}={[{\mathrm{\α}}_0,{\mathrm{\α}}_1,\·\·\·,{\mathrm{\α}}_{1n},{\mathrm{\α}}_{11},{\mathrm{\α}}_{12},\·\·\·,{\mathrm{\α}}_{1n},{\mathrm{\α}}_{22},{\mathrm{\α}}_{23},\·\·\·,{\mathrm{\α}}_{2n},\·\·\·,{\mathrm{\α}}_{(n-1)(n-1)},{\mathrm{\α}}_{(n-1)n},{\mathrm{\α}}_{\mathrm{nn}}]}^T$ , for high density integrated circuit encapsulates the output valve of main inoperative component heat fatigue strain quadric, P=(p ₁, o ₂..., p _n) be the structural design variable of encapsulation, matrix of coefficients for corresponding design variable.ε represents the output valve ε=(ε of finite element heat fatigue strain ₁, ε ₂..., ε _m), n is the number of encapsulating structure design variable, m is three horizontal second order robust test design numbers.

(b) basis function is asked local derviation to quadric surface coefficient: obtain quadric matrix of coefficients $\widehat{\mathrm{\α}}={\left(Q^{T}Q\right)}^{-1}{Q}^T\mathrm{\ϵ},$ In formula, $Q=\left[\begin{array}{ccccc}1& q_{11}& q_{12}& ...& q_{1n}\\ 1& q_{21}& q_{22}& ...& q_{2n}\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ 1& q_{m1}& q_{m2}& ...& q_{\mathrm{mn}}\end{array}\right],$ Q _jibe that in three horizontal second order robust experimental design tables, i design variable value put in j experimental design.

(c) set up based on three horizontal second order robust experimental design models of a quadric:

The present invention is nonlinear theory, fatigue reliability theory and robust designs theory are incorporated in the thermal design of high density integrated circuit encapsulation, on the basis of three horizontal second order robust test design, adopt nonlinear finite element and quadric surface method, the heat fatigue strain of the main thermal failure parts of encapsulation has been set up to the high-density packages heat fatigue reliability optimal mathematical model under thermal cycle load as objective function, this model can be analyzed reciprocation and the influencing characteristic to heat fatigue reliability of encapsulating structure parameter complexity, and can in scope of design, obtain high density integrated circuit and encapsulate best heat fatigue structural parameters collection, make the maximum equivalent heat fatigue strain of main thermal failure parts reduce to minimum.The method can guarantee the main inoperative component heat fatigue of high-density packages reliability, can guarantee again the robustness of encapsulating structure parameter under disturbance.This invention has solved the gordian technique of high density integrated circuit encapsulation thermal reliability analysis and design, for high density integrated circuit encapsulation thermal reliability analysis and design provides new method.

The invention provides a kind of new method of heat fatigue structural optimization based on reliability of the high density integrated circuit encapsulation based on robust designs, the high density integrated circuit of take encapsulation FSBGA is step of the present invention as embodiment illustrates, they comprise:

(1) according to high density integrated circuit encapsulation FSBGA heat fatigue reliability effect characteristic, select the height of solder joint, the thickness of the diameter of solder joint, substrate, the thickness of the thickness of PCB, chip and the width of chip as structural design variable to be optimized, using the maximum equivalent heat fatigue strain of the most concentrated solder joint of package thermal stress as optimization aim function;

(2) according to definite structural design variable and optimization aim, carry out three horizontal second order robust experimental designs, comprise following sub-step:

(2.1) according to high density integrated circuit FSBGA package design, require to determine the marginal range of structural design variate-value, their value of naming a person for a particular job centered by the intermediate value of marginal range is arranged to three levels :+1,0 and-1, they represent higher limit, intermediate value and the lower limit of tolerance value, and embodiment is specifically horizontally disposed with as shown in table 1:

Variable symbol	Structural design variable	-1	0	+1
					A	The height of solder joint (mm)	0.28	0.32	0.36
B	The diameter of solder joint (mm)	0.35	0.40	0.45
					C	The thickness of substrate (mm)	0.22	0.30	0.38
D	The thickness of PCB (mm)	1.40	1.57	1.74
					E	The thickness of chip (mm)	0.2	0.5	0.8
F	The width of chip (mm)	21.0	23.0	25.0

Table 1

(2.2) hypercube of being tieed up by 6 structural design variable structures 6, Mei Wei center and hypercube Mei Bian center arrange respectively an experimental point, and specifically referring to Fig. 2, sampling produces 54 experimental points altogether, form three horizontal second order robust experimental design tables, as shown in table 2:

Table 2

(3) 3 horizontal second order robust experimental design points are carried out respectively to finite element analysis and the calculating of heat fatigue strain, form three complete horizontal second order robust experimental design tables, it comprises following sub-step:

(3.1) according to the structure of high density FSBGA encapsulation, with the intermediate value of structural design variable to be optimized, set up the solid model of packaging body finite element;

(3.2) in conjunction with the material properties of each parts of FSBGA packaging body, the solid model of packaging body finite element is carried out to grid division; FSBGA is comprised of the element of multiple heterogeneity material, sets respectively elastic modulus E, Poisson ratio v and the linear expansion coefficient α of each storeroom _l.For reflecting more accurately the impact of the α l difference butt welding point thermal stress of FSBGA encapsulating material, invention is reduced to FSBGA into chip, plastic packaging, substrate, PCB and solder joint, and material parameter is set respectively.Using solder joint as viscoplastic material, adopt Anand model to simulate its deformation characteristic, all the other all adopt linear elastic materials.Welding material is visco-plasticity unit VISCO108, and other parts all adopt Plane82 unit.Finite element model after grid is divided as shown in Figure 3.

(3.3) by the standard of uniform temperature circulation, the thermal force of circulation is loaded on each node of finite element, four temperature cycles under the cycle, each experimental design point in three horizontal second order robust experimental design tables is carried out to FEM (finite element) calculation, obtain the heat fatigue strain value of solder joint maximum equivalent, obtain three complete horizontal second order robust experimental design tables.

The present embodiment carries out temperature cycling test according to the relevant regulations in MILSTD MIL-STD-883, and it follows the warm degree – 55-+125 ℃ of ring, and the temperature cycles cycle is 30min/ week, and wherein high low temperature temperature retention time is 10min, and temperature rate is 36 ℃/min.The three complete horizontal second order robust experimental design tables that obtain, referring to table 3, the cloud atlas of the solder joint heat fatigue strain FEM (finite element) calculation of one of them experimental design point, specifically referring to Fig. 4.

Table 3

(4) according to complete 3 horizontal second order robust experimental design points and corresponding heat fatigue strain value, use least square method to build the model of a quadric of high density integrated circuit FSBGA encapsulation objective function, the method for structure is as follows:

(a) construct quadric basis function: $E\left(\widehat{\mathrm{\α}}\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}({\mathrm{\ϵ}}_j-{\widehat{\mathrm{\ϵ}}}_j)={(\mathrm{\ϵ}-G\widehat{\mathrm{\α}})}^T(\mathrm{\ϵ}-G\widehat{\mathrm{\α}})$

Wherein, m=54, is the number of 3 horizontal second order robust experimental design points,

G＝[1，p ₁，…，p _n，p ₁ ²，p ₁p ₂，…，p ₁p _n，p ₂ ²，p ₂p ₃，…，p ₂p _n，…，p _n-1 ²，p _n-1p _n，p _n ²]， $\widehat{\mathrm{\α}}={[{\mathrm{\α}}_0,{\mathrm{\α}}_1,\·\·\·,{\mathrm{\α}}_{1n},{\mathrm{\α}}_{11},{\mathrm{\α}}_{12},\·\·\·,{\mathrm{\α}}_{1n},{\mathrm{\α}}_{22},{\mathrm{\α}}_{23},\·\·\·,{\mathrm{\α}}_{2n},\·\·\·,{\mathrm{\α}}_{(n-1)(n-1)},{\mathrm{\α}}_{(n-1)n},{\mathrm{\α}}_{\mathrm{nn}}]}^T$ , for the output valve of high density FSBGA encapsulation solder joint maximum equivalent heat fatigue strain quadric, P=(p ₁, p ₂..., p _n) be the structural design variable of encapsulation, n=6 is the number of structural design variable, matrix of coefficients for corresponding design variable.ε represents finite element heat fatigue strain output valve ε=(ε ₁, ε ₂..., ε _m).

(b) basis function is asked local derviation to quadric surface coefficient, and makes partial derivative equal zero: obtain quadric matrix of coefficients $\widehat{\mathrm{\α}}={\left(Q^{T}Q\right)}^{-1}{Q}^T\mathrm{\ϵ},$ In formula, $Q=\left[\begin{array}{ccccc}1& q_{11}& q_{12}& ...& q_{1n}\\ 1& q_{21}& q_{22}& ...& q_{2n}\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ \·& \·& \·& & \·\\ 1& q_{m1}& q_{m2}& ...& q_{\mathrm{mn}}\end{array}\right].$ Q _jibe that in three horizontal second order robust experimental design tables, i design variable value put in j experimental design.

(c) set up based on three horizontal second order robust experimental design models of a quadric:

In the present embodiment, by quadric structure, draw:

$\begin{array}{c}\widehat{\mathrm{\α}}=[-\mathrm{0.068744,0.50895},-0.099014,-4.56161E-003,-\mathrm{0.025348,0.027375},\\ 3.53988E-003,-0.12619,-0.075450,-5.39583E-\mathrm{003,2.34219}E-003,\\ -\mathrm{0.027719,0.034309,0.010996},-1.92500E-\mathrm{004,0.019991},-0.015661,\\ 1.87500E-004,-\mathrm{0.012539,7.31618}E-005,-2.45833E-005,-0.59462,\\ 0.056961,-3.75868E-\mathrm{003,0.014104},-2.68580E-003,-9.43576E-005{]}^T\end{array}$

(5) model of a quadric of high density integrated circuit FSBGA encapsulation objective function is carried out to variance test and precision test.If meeting under the confidence level of designing requirement, model is significant, can utilize this model to be optimized; Otherwise must redesign test, build new model of a quadric; It comprises the following steps:

(5.1) with variance analysis method, quadric surface is carried out to significance test, adopts following formula to calculate variance:

Quadric surface is exported total data fluctuations-square sum of total departure SS _t:

${\mathrm{SS}}_T=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{({\mathrm{\ϵ}}_i-\stackrel{\‾}{\mathrm{\ϵ}})}^2$

Quadratic Surface Fitting point data fluctuations-deviation from regression quadratic sum SS _r:

${\mathrm{SS}}_R=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{({\widehat{\mathrm{\ϵ}}}_i-\stackrel{\‾}{\mathrm{\ϵ}})}^2$

In formula, the sum that m is experimental point, ε _ifor the heat fatigue strain value of FEM (finite element) calculation, for quadric surface output valve, for quadric surface output valve mean value.

Getting P=5% is level of significance, and variance is carried out to significance test, if the result P<0.05 of check, result is significant, and P<0.001, for extremely remarkable, illustrates that model is stable.Table 4 is the result of calculation of embodiment.

Variance	Degree of freedom	Square sum of total departure	Deviation from regression quadratic sum	P value
					Quadric surface	27	2.672E-004	9.249E-004	<0.0001

Table 4

(5.2) use coefficient of multiple correlation R ²with the multiple correlation coefficient AdjR adjusting ²the precision of carrying out verification model, computing method are as follows:

$R^2=1-\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\widehat{\mathrm{\&epsiv;}}}_j-{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_j)}^2}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{\&epsiv;}}_j-{\widehat{\mathrm{\&epsiv;}}}_j)}^2},{R^2}_{\mathrm{adj}}=1-\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\widehat{\mathrm{\&epsiv;}}}_j-{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_j)}^2(m-1)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{\&epsiv;}}_j-{\widehat{\mathrm{\&epsiv;}}}_j)}^2(m-k-1)}$

The result that the present embodiment draws is:

The type of R	R 2	AdjR 2
			The value of R	0.9809	0.9611

Table 5

As seen from Table 5, coefficient of multiple correlation R ²with the multiple correlation coefficient AdjR adjusting ²all approach 1, the precision that model is described is high, can be used for integrated circuit FSBGA to encapsulate and carry out heat fatigue structural optimization based on reliability.

(6) utilize the model of a quadric meet precision and requirement, the level line of making heat fatigue strain, analyzes reciprocation and the influencing characteristic of each structural design variable.

The contour map of making according to model of a quadric, pass through contour plots analysis, can draw to draw a conclusion: the reciprocation between the height of solder joint and other parameters is the strongest, the major parameter that affects the heat fatigue strain of solder joint is the height of solder joint, next is the thickness of substrate, the thickness of the diameter of solder joint, PCB width, chip and PCB thickness, and this result is consistent with the result of document.

(7) utilize the model of a quadric of having constructed to replace real finite element model, set up the sane Optimized model of heat fatigue structural reliability of the high density integrated circuit encapsulation of multiple constraint, and solve, obtain the encapsulating structure parameter of optimizing, and verify optimum results.The Optimized model of setting up is as follows:

Satisfy：p _i1≤p _i≤p _iu

$\mathrm{Minf}\left(P\right)=G\widehat{\mathrm{\&alpha;}}$

In formula, p _i(i=1,2 ..., 6) and be the structural design variable of encapsulation, the present embodiment represents respectively the height of solder joint, the thickness of the diameter of solder joint, substrate, PCB thickness, chip thickness and PCB width, p _i1and p _iuthe lower limit and the higher limit that represent design variable.

The present embodiment, obtains FSBGA encapsulation the most optimized parameter combination and solder joint maximum equivalent heat fatigue strain-responsive value by solving, and the results are shown in Table 6:

Table 6

As can be seen from Table 6, after optimizing, the maximum equivalent heat fatigue strain of encapsulation solder joint reduces to 0.00951976 by 0.01858200, has reduced by 48.77%, is consistent with the result of finite element analysis.

Visible, the present invention can realize heat fatigue Analysis of structural reliability and the optimization of high density integrated circuit encapsulation, has improved widely the heat fatigue reliability of high-density packages.

The present invention is not only confined to above-mentioned embodiment; persons skilled in the art are according to content disclosed by the invention; can adopt other multiple embodiment to implement the present invention; therefore; every employing project organization of the present invention and thinking; do some simple designs that change or change, all fall into the scope of protection of the invention.

Claims (4)

1. an optimization method for the encapsulation of the high density integrated circuit based on robust designs, is characterized in that: comprise the steps:

(1) determine structural design variable to be optimized, using the heat fatigue strain of the main thermal failure parts of encapsulation as optimization aim function;

(2), according to definite structural design variable and optimization aim, carry out three horizontal second order robust experimental designs;

(3) 3 horizontal second order robust experimental design points are carried out respectively to finite element analysis and the calculating of heat fatigue strain, form three complete horizontal second order robust experimental design tables;

(4), according to complete 3 horizontal second order robust experimental design points and corresponding heat fatigue strain value, use least square method to build the model of a quadric of high density integrated circuit encapsulation objective function;

(5) model of a quadric of high density integrated circuit encapsulation objective function is carried out to variance test and precision test.If meeting under the confidence level of designing requirement, model is significant, can utilize this model to be optimized; Otherwise must redesign test, build new model of a quadric;

(6) utilize the model of a quadric meet precision and requirement, the level line of making equivalent heat repeated strain, analyzes reciprocation and the influencing characteristic of each structural design variable;

(7) utilize the model of a quadric of having constructed to replace real finite element model, set up the sane Optimized model of heat fatigue structural reliability of the high density integrated circuit encapsulation of multiple constraint, and solve, obtain the encapsulating structure parameter set of optimizing, and verify optimum results.

2. the optimization method that a kind of high density integrated circuit based on robust designs according to claim 1 encapsulates, is characterized in that: step (2) comprises following sub-step:

(2.1) according to high density integrated circuit package design, require to determine the marginal range of structural design variate-value, their value of naming a person for a particular job centered by the intermediate value of marginal range is arranged to three levels :+1,0 and-1, they represent higher limit, intermediate value and the lower limit of tolerance value;

(2.2) hypercube of being tieed up by N structural design variable structure N, Mei Wei center and hypercube Mei Bian center arrange respectively an experimental point, sampling produces M experimental point altogether, form three horizontal second order robust experimental design tables, there is not axial point and can be simultaneously in high-level state in three horizontal second order robust experimental designs, make design point all drop on safety zone, there is very strong robustness.

3. the optimization method that a kind of high density integrated circuit based on robust designs according to claim 1 and 2 encapsulates, is characterized in that: step (3) comprises following sub-step:

(3.1) according to the structure of high-density packages, with the intermediate value of structural design variable to be optimized, set up the solid model of packaging body finite element;

(3.2) in conjunction with the material properties of each parts of packaging body, the solid model of packaging body finite element is carried out to grid division;

(3.3) by the standard of uniform temperature circulation, the thermal force of circulation is loaded on each node of finite element, four to six temperature cycles under the cycle, each experimental design point in three horizontal second order robust experimental design tables is carried out to FEM (finite element) calculation, obtain the heat fatigue strain value of main inoperative component maximum equivalent, obtain three complete horizontal second order robust experimental design tables.

4. the optimization method that a kind of high density integrated circuit based on robust designs according to claim 3 encapsulates, is characterized in that: the method that high density integrated circuit encapsulates main inoperative component heat fatigue strain quadric structure is:

(a) construct quadric basis function:

Wherein, G=[1, p ₁, p _n, p ₁ ², p ₁p ₂..., p ₁p _n, p ₂ ², p ₂p ₃..., p ₂p _n..., p _n-1 ², p _n-1p _n, p _n ²] , for high density integrated circuit encapsulates the output valve of main inoperative component heat fatigue strain quadric, for the structural design variable of encapsulation, for the matrix of coefficients of corresponding design variable, ε represents the output valve ε=(ε of finite element heat fatigue strain ₁, ε ₂..., ε _m) n is the number of encapsulating structure design variable, m is three horizontal second order robust test design numbers.

(b) basis function is asked local derviation to quadric surface coefficient: obtain quadric matrix of coefficients in formula q _jibe that in three horizontal second order robust experimental design tables, i design variable value put in j experimental design.

(c) set up based on three horizontal second order robust experimental design models of a quadric: .