CN110298126A - A kind of polynary Copula power device method for evaluating reliability based on the physics of failure - Google Patents

A kind of polynary Copula power device method for evaluating reliability based on the physics of failure Download PDF

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CN110298126A
CN110298126A CN201910597236.0A CN201910597236A CN110298126A CN 110298126 A CN110298126 A CN 110298126A CN 201910597236 A CN201910597236 A CN 201910597236A CN 110298126 A CN110298126 A CN 110298126A
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physical model
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付桂翠
郭文迪
万博
苏昱太
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Beihang University
Beijing University of Aeronautics and Astronautics
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    • G06F30/30Circuit design
    • G06F30/36Circuit design at the analogue level
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Abstract

The present invention relates to a kind of polynary Copula power device method for evaluating reliability based on the physics of failure, comprising the following steps: step 1: power device information is collected, and determines actual condition, internal structure and existing failure mechanism;Step 2: failure physical model application and model parameter randomization determine the edge distribution of each structural life-time;Step 3: power device reliability assessment compares Monte Carlo competing failure method;Its theory based on the physics of failure, from power device, existing failure mechanism and failure physical model are started under actual condition, the parameter lacked in model is obtained using emulation, the reliability expression of power device under more failure mechanisms is derived using polynary Archimedean Copula.Pass through comparison Monte Carlo-competing failure method for evaluating reliability, it was demonstrated that polynary Copula model belongs to component reliability assessment technique field it can be considered that cross-influential factors between each mechanism.

Description

A kind of polynary Copula power device method for evaluating reliability based on the physics of failure
(1) technical field:
The present invention relates to a kind of polynary Copula power device method for evaluating reliability based on the physics of failure, it is based on losing The theory of physics is imitated, existing failure mechanism and failure physical model are started under actual condition from power device, analysis failure Parameter value in physical model obtains the parameter of missing using emulation.Derive lose using polynary Archimedean Copula more Imitate the reliability expression of power device under mechanism.By comparing Monte Carlo-competing failure method for evaluating reliability, it was demonstrated that more First Copula model belongs to component reliability assessment technique field it can be considered that cross-influential factors between each mechanism.
(2) background technique:
As microelectronic component develops to small size, extensive and high-performance direction, its method for evaluating reliability is also mentioned Higher requirement is gone out.Model-driven and data-driven two major classes can be divided into for the reliability evaluation of device at present.Based on mistake The evaluation of effect physical model needs analysis elements device inside failure mechanism, understands physics, the chemical process for leading to failure, is to improve The basic research of product reliability.
However, often obtaining most weak point using single failure physical model for the reliability evaluation of power device at present The lifetime results of position, and there are complicated more ambient stress sections in a practical situation, the evaluation under simple stress is not accurate enough. And consider that competing failure thought is then widely applied in the device reliability evaluation under the influence of failure mechanism, it is not intended that between failure mechanism Existing cross-influential factors, such as temperature, power will affect multiple reliability of structures in device.For this purpose, this method considers The power device reliability evaluation of each structural failure service life distribution correlation, proposes a kind of consideration caused by public influence factor The power device method for evaluating reliability of more failure mechanisms, more failpoints.For the service life merged more failure mechanisms, consider each structure The power device reliability evaluation for being distributed correlation provides Evaluation example, establishes higher efficiency and more inexpensive evaluation method stream Journey.
(3) summary of the invention:
1, purpose: the object of the present invention is to provide a kind of, and the polynary Copula power device reliability based on the physics of failure is commented Valence method.This method is distributed correlation in view of service life of the structure each inside power device under different failure mechanisms, examines simultaneously Consider assessed cost and matter of time, the unknown parameter in failure physical model is obtained by finite element simulation, passes through Monte Carlo Influence of the sampling consideration stochastic variable to each structural life-time of device, the reliability assessment for power device in engineering practice provide reason By guidance.
2, technical solution: the present invention is a kind of polynary Copula power device reliability evaluation side based on the physics of failure Method, it includes the following steps:
Step 1: power device information is collected, and determines actual condition, internal structure and existing failure mechanism;
Step 2: failure physical model application and model parameter randomization determine the edge distribution of each structural life-time;
Step 3: power device reliability assessment compares Monte Carlo competing failure method;
Wherein, function under power device information, including analysis power device internal structure and actual condition is collected in step 1 Failure mechanism existing for rate device.Overcurrent, over-voltage, excessively high junction temperature can all cause to fail when due to power device work, this All there is substantial connection with temperature.Excessively high junction temperature will cause PN junction breakdown, and lasting temperature alternating also will cause device interconnection knot The fatigue failure of structure, if bonding line fails, weldering knot layer aging etc..Therefore main to consider chip and failure of both interconnection, it grinds Study carefully failure physical model relevant to temperature, the service life for assessing each structure for subsequent applications failure physical model provides input.
Wherein, power device geometry, material, working environment and the identification obtained in step 2 based on research Weak part and existing failure mechanism, consider that Monte Carlo randomization is applied in influence of the stochastic variable to device lifetime The structural parameters of device, material parameter, technological parameter into.Using failure physical model as input, using the parameter value of randomization Calculate the failure probability distributions that each structure is obeyed.The feature of these service life distribution is described using Gaussian Kernel Density function, it is close Degree function and distribution function may be expressed as:
In formula, hXIndicate the window width of Marginal density function, calculation formula are as follows:
hx=0.9 × N-0.2×min(std,iqr/1.34)
In formula, N indicates that sample total, std are sample standard deviation, and iqr is quartile in sample sequence.
Wherein, consider that failure physical model input parameter exists in step 3 to intersect.Such as Fig. 3, temperature, power, electric current etc. The life prediction value of multiple structures in power device may be all influenced, the calculated result of failure physical model can not be considered It is complete independent.The edge distribution of each structural life-time obtained in step 2 is connected to obtain using multivariable Copula theory Obtain joint distribution function.If thinking, the life value that the failure physical model of device is calculated after stochastic parameter is random becomes Amount, obeys continuous edge distribution F1(t1), F2(t2) ..., Fn(tn);Then by sklar theorem it is found that n failure physical model The joint distribution function uniquely determined is obeyed in obtained cumulative failure distribution:
H(t1,t2,...,tn)=C (F1(t1), F2(t2) ..., Fn(tn))
With the dependency structure of Archimedean Copula race reflection life variance, unknown parameter in estimation function is needed.Here Using Kendall τ coefficient ταRelationship between parameter alpha estimates parameter value.
If { (x1,y1),(x2,y2),...,(xn,yn) be continuous random vector (X, Y) n sample observations, (X, Y) Copula function be Cα, kendall τ coefficient is τα, defined according to the Kendall τ of sample, ταEstimated value are as follows:
In Clayton copula functionIn Gumbel copula functionFrank function Unknown parameter is acquired using Maximum-likelihood estimation.
According to AIC and BIC criterion, the optimal joint probability Distribution Model in power device service life is determined.
Derive that the device reliability comprising n failure mechanism meets series model:
With using following competing failure thought, the service life using the TTF minimum value of possible failure structure as device is carried out No matter all advantageous from evaluation result reasonability and arithmetic speed comparison, this method be.
TTF=min { T1,T2,T3,,......TN}
(4) Detailed description of the invention:
Fig. 1 implementation steps flow diagram
Fig. 2 temperature cycles section
The key structure of Fig. 3 power device and existing typical failure mechanism
Fig. 4 excess carrier service life is distributed
Fig. 5 bonding wire service life is distributed
Fig. 6 welding layer thermal fatigue failure service life is distributed
Two method Reliability assessment Comparative result of Fig. 7
(5) specific embodiment:
Below in conjunction with attached drawing and specific implementation case, to the polynary Copula function of the present invention based on the physics of failure Rate device reliability evaluation method is described in detail.
The present invention illustrates the polynary Copula power device based on the physics of failure by taking IRGB4059DPBF type IGBT device as an example Part reliability evaluation process.
Step 1: power device information is collected;
Firstly, considering the Thermal cycling conditions that device may be undergone under actual condition, tried with reference to GJB128A temperature cycles B conditions of proved recipe method determine environment section such as Fig. 2.Consider the inside key structure and existing failure mechanism such as Fig. 3 of device.It examines Consider chip, three welding layer, bonding wire weak links, analysis corresponds to the physics of failure mould of failure mechanism under Fig. 2 environment section Type.
Carrier determines many dynamics of device and static characteristic in IGBT device base region.Excess carrier concentration with Temperature is increased and is increased, and when majority carrier concentration increases, minority carrier recombination slows, so that under device shutdown rate Drop.The excess carrier service life obeys following formula in chip:
In formula, τ is hot carrier lifetime, unit s, NtFor carrier recombination centers density, unit cm-3, p is that cavity is close Degree, unit cm-3, T refers to temperature, unit K.
Chip emission pole is connected by bonding wire with DCB layers of copper, constantly has thermal stress tired under temperature shock repeatedly Product arrives the contact area of lead and DCB, it may appear that bonding wire falls off.Bonding line Root Stress indicates are as follows:
In formula, αwAnd αsThe thermal expansion coefficient of lead material and base material is respectively corresponded, Δ T is range of temperature.2L For wire length, unit m;2D is lead mutual conductance, unit m;R is wire cross-sectional radius surface, unit m;EWFor lead elasticity modulus, Unit Pa;
The relationship of bonding line thermal fatigue life and Root Stress is expressed as:
In formula, CwFor the tensile fatigue coefficient for being bonded wire material, usually 5~7;mwFor tensile fatigue coefficient.
Due to the inhomogeneities of solder itself and the thermal expansion coefficient difference of welding layer both sides material, caused by temperature fluctuation Thermal stress makes the weakness of solder layer subtle crackle occur because of shear stress.Using Engelmaier heat fatigue model, calculate The thermal fatigue life of welding layer:
In formula, Nf 1For welding layer thermal fatigue life under operating ambient temperature section;Δγ1For welding layer plasticity shear strain; ε'fFor fatigue ductile coefficient;C is fatigue ductility index, is calculated as follows:
In formula, TDTime, unit min are immersed for high/low temperature.
Solder joint plasticity shear strain Δ γ1Calculation formula is as follows:
Δ α LT in formulac, Δ α LTsThe thermal diffusion for characterizing chip and copper base respectively, calculates such as formula:
In formula, LxFor solder joint maximum spacing on the direction x or pad array span, unit mm;LyMost for solder joint on the direction y Big spacing or pad array span, unit mm;αcxFor the thermal expansion coefficient of device on the direction x, unit is ppm/ DEG C;αcyFor y The thermal expansion coefficient of device on direction, unit are ppm/ DEG C;αsxFor the thermal expansion coefficient of circuit board on the direction x, unit ppm/ ℃;αsyFor the thermal expansion coefficient of circuit board on the direction y, unit is ppm/ DEG C.Tc max, Tc minRespectively chip is highest and lowest Temperature, Ts max, Ts minThe respectively highest and lowest temperature of substrate.
Step 2: failure physical model application and model parameter randomization;
The service life of chip, bonding wire and welding layer in failure physical model assessment power device in applying step one.Benefit Default parameters in failure physical model are obtained with finite element simulation method: including each structure temperature, stress, strain.Emulation solves The temperature of chip, welding layer, bonding line, parameter value such as table 1 in failure physical model.
1 failure physical model parameter value of table
The service life distribution of each structure under the influence of failure mechanism is determined using Monte Carlo stochastic parameter;It is taken out by angular distribution The geometric dimension and material thermal parameters of sample device, by the temperature parameter of Normal distribution sampling structure, with Gaussian Kernel Density function The feature of these distributions is described, obtains the lower three kinds of structures of each failure mechanism corresponding service life distribution such as Fig. 5, Fig. 6, Fig. 7.
Step 3: power device reliability assessment;
After determining marginal distribution function, select 3 Archimedean Copula races Typical Representative Gumbel, Clayton and Frank Copula is calculated, and determines parameter alpha, corresponds to τ between acquiring 3 distributions using the definition of kendall ταWith parameter alpha and AIC Value such as table 2:
2 Copula parameter Estimation of table and AIC value
Calculated result shows that Clayton function is optimal Copula function, according to the reliable of series model calculating device Function is spent, this method compares Monte Carlo-competing failure method reliability calculating result such as Fig. 7.Contrast sample's number is The reliability evaluation result of two methods and operation time such as table 3 when 50000.
3 liang of method evaluation results of table and operation time comparison
As seen from Table 3, consider that the reliability evaluation result of each failure physical model correlation is compared and be completely independent hypothesis Under evaluation result it is higher.The MTTF result explanation of two methods does not consider the model calculation phase as caused by cross parameter The reliability evaluation of closing property may judge the service life of device by accident.The operation time of two methods when contrast sample's number is 50000 simultaneously It can be seen that this method compared with Monte Carlo competing failure evaluation method arithmetic speed faster.

Claims (4)

1. a kind of polynary Copula power device method for evaluating reliability based on the physics of failure, it is characterised in that: utilize failure Physical model, Monte Carlo sampling, polynary Copula function evaluate reliability of the power device under actual condition, and Common Monte Carlo competing failure evaluation method illustrates the advantage of this method in comparison engineering.The specific steps of this method are such as Under:
Step 1: power device information is collected, and determines actual condition, internal structure and existing failure mechanism;
Step 2: failure physical model application and model parameter randomization determine the edge distribution of each structural life-time;
Step 3: power device reliability assessment compares Monte Carlo competing failure method.
2. power device information according to claim 1 is collected, actual condition, internal structure and existing failure machine are determined Reason, it is characterised in that consider that overcurrent, over-voltage, excessively high junction temperature can all cause to fail when power device work, these all with temperature Degree has substantial connection.Excessively high junction temperature will cause PN junction breakdown, and lasting temperature alternating also will cause the tired of device interconnected structure Labor failure, if bonding line fails, weldering knot layer aging etc..Therefore main to consider failure of both chip and interconnection, research and temperature Relevant failure physical model is spent, the service life for assessing each structure for subsequent applications failure physical model provides input.
3. failure physical model application according to claim 1 and model parameter randomization, determine the side of each structural life-time Fate cloth, it is characterised in that based on research obtain power device geometry, material, working environment and identification it is thin Weak position and existing failure mechanism consider that Monte Carlo randomization device is applied in influence of the stochastic variable to device lifetime Structural parameters, material parameter, technological parameter into.Using failure physical model as input, using the parameter value calculation of randomization The failure probability distributions that each structure is obeyed.The feature of these service life distribution, density letter are described using Gaussian Kernel Density function Several and distribution function may be expressed as:
In formula, hXIndicate the window width of Marginal density function, calculation formula are as follows:
hx=0.9 × N-0.2×min(std,iqr/1.34)
In formula, N indicates that sample total, std are sample standard deviation, and iqr is quartile in sample sequence.
4. power device reliability assessment according to claim 1 compares Monte Carlo competing failure method, failure is considered Physical model inputs parameter and there is intersection.Such as Fig. 3, temperature, power, electric current etc. may all influence multiple structures in power device Life prediction value, the calculated result of failure physical model can not think to be completely independent.It is theoretical using multivariable Copula The edge distribution of each structural life-time obtained in step 2 is connected to obtain joint distribution function.If thinking the mistake of device The life value that effect physical model is calculated after stochastic parameter is stochastic variable, obeys continuous edge distribution F1(t1), F2 (t2) ..., Fn(tn);Then by sklar theorem it is found that the cumulative failure distribution that n failure physical model obtains is obeyed and uniquely determined Joint distribution function:
H(t1,t2,...,tn)=C (F1(t1), F2(t2) ..., Fn(tn))
Reflect the dependency structure of life variance, the unknown parameter in estimation function, using Kendall with Archimedean Copula race τ coefficient ταRelationship between parameter alpha estimates parameter value:
In Clayton copula functionIn Gumbel copula functionFrank function it is unknown Parameter is acquired using Maximum-likelihood estimation.
According to AIC and BIC criterion, the optimal joint probability Distribution Model in power device service life is determined.
Derive that the device reliability comprising n failure mechanism meets series model:
With using following competing failure thought, compared using the service life of TTF minimum value as the device of possible failure structure, No matter all advantageous from evaluation result reasonability and arithmetic speed this method is.
TTF=min { T1,T2,T3,,......TN}。
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