CN1216413C - Quick evaluation method for microelectronic device reliability - Google Patents

Abstract

The present invention relates to a quick evaluation method for microelectronic device reliability, which belongs to the field of microelectronic technology. The present invention comprises the steps: 1) the Joule's heat temperature rise of a microelectronic device is firstly measured; 2) the variation data of the failure sensitive parameter P of the microelectronic device along temperature Tj within the range of selected temperature respectively under the conditions of not adding electric stress and adding electric stress is measured, and curves are respectively plotted and are fitted into straight lines; 3) 3 groups of microelectronic devices are taken for a temperature slope test under three different electric stress conditions to obtain the average failure activation energy, the average failure time and the average failure temperature range of each group of microelectronic device; 4) the coefficients of A, m, n in the formula that dp/dt is equal to Aj (n)V(m) e(-Q/kTj) are calculated; 5) the energy of electric heating stress borne by the failure sensitive parameters P is calculated; 6) the service life tau of the microelectronic device when V, j and Tj are respectively numerical values under normal operating conditions is calculated. The present invention has the advantages of test period reduction, few required test sample and great cost reduction, and the service life of a single sample can be simultaneously provided.

Description

The Reliability Issues of Microelectronics Devices fast appraisement method

Technical field

The Reliability Issues of Microelectronics Devices fast appraisement method belongs to microelectronics technology, relates to a kind of method of estimating the microelectronic component performance.

Background technology

At present, many employing accelerated life tests in the reliability evaluation technology, accepted standard is American army mark MIL-STD-883E and national military standard GJB548A-96 relevant provision: 1016 life-spans of method/reliability test.This method adopts the life test of three above temperature spots of constant electric stress, determines the life characteristics of microelectronic component according to the Arrhenius equation, and the life-span is quickened feature, failure rate level.The subject matter of its existence is the variation of measuring element parameter at normal temperatures when the selected test duration of each temperature stress point finishes, and can not provide the life characteristics under the different temperatures simultaneously, and the life-span is quickened feature, failure rate level; The variation of measuring element parameter at normal temperatures when the selected test duration of each temperature stress point finishes, so test period long (more than the 3000hr), the cost height, required sample is many, can not provide the inefficacy activation energy and the life-span of monocyte sample, and can not provide the value of voltage and current density power exponent factor m and n, expect the value of m and n, at least 9 groups of tests of different voltage and current density to be carried out, and the test of 27000hr will be carried out at least.When considering temperature and voltage stress simultaneously, can adopt broad sense Ai Lin (Egring) model, therefore to select for use many temperature and multivoltage stress point to determine dependent constant, according to the test that this model carried out also is when each stress point finishes, the variation of measuring element parameter under the normal temperature.Therefore, the test period is longer, and cost is higher, and required sample is more, can not provide the inefficacy activation energy and the life-span of monocyte sample equally.

Summary of the invention

It is long to the object of the present invention is to provide a kind of Reliability Issues of Microelectronics Devices evaluation method to solve the said method test period, the cost height, and required sample is many, can not provide defectives such as monocyte sample related reliability parameter.

Reliability Issues of Microelectronics Devices fast appraisement method of the present invention is characterized in that, may further comprise the steps:

1) measuring microelectronic component current density to be adopted in experiment with infrared method is that j, voltage are the Peak Junction Temperature T under the electric stress of V _Jpeak, use Peak Junction Temperature T then _JpeakDeduct the temperature T of heating platform ₀The Peak Junction Temperature that is under this electric stress rises Δ T _JpeakOr the average junction temperature that adopts electric method to measure under this electric stress rises Δ T _Javer

2) choose a temperature range that with the working junction temperature of this microelectronic component identical failure mechanism is arranged and be higher than its working junction temperature, example adds the GaAs device can choose 200 ℃ to 300 ℃, silicon device can be chosen 150 ℃ to 250 ℃, the inefficacy sensitive parameter P that measures this microelectronic component in described temperature range with junction temperature T _jThe data that change, and be depicted as curve, as shown in Figure 1, T _J1=T ₀+ β t, T ₀Be the temperature of heating platform, β is a heating rate, and t is the time;

3) 2) in the described temperature range, it is that j, voltage are that heating rate under the electric stress of V is the temperature ramp test of β that microelectronic component is carried out current density, the sensitive parameter P that obtains losing efficacy is with junction temperature T _jThe data that change, and be depicted as curve, as shown in Figure 1, T _J2=T ₀+ β t+ Δ T, T ₀Be the temperature of heating platform, β is a heating rate, and t is the time, and Δ T is the junction temperature liter, according to 1,1) described in the method junction temperature that can obtain two different values rise Δ T _JpeakWith Δ T _Javer, both can choose any one kind of them;

4) establish microelectronic component inefficacy sensitive parameter P under electric heating stress amount of degradation be Δ P, then deterioration velocity is It and current density j, voltage V and temperature T are deferred to following relation:

$\frac{\mathrm{dp}}{\mathrm{dt}}=A{j}^n{V}^m{e}^{\frac{Q}{k{T}_j}}---\left(1\right)$

N, m are the power exponent of j and V in the formula, and Q is the inefficacy activation energy, and k is a Boltzmann constant, and A is a constant; Draw by formula (1):

$\ln \left(T_j^{-2}\frac{\mathrm{\Δp}}{p_0}\right)=\ln \frac{A^{\′}{j}^n{V}^{m}k}{\mathrm{Q\β}}-\frac{Q}{k}\frac{1}{T_j}---\left(2\right)$

P in the formula ₀Be the initial value before the degeneration of inefficacy sensitive parameter, A '=A/P ₀, Δ P=P-P ₀

5) according to the same inefficacy sensitive parameter of same temperature spot P in the difference that adds before and after the electric stress, obtain 2) amount of degradation and the junction temperature T of inefficacy sensitive parameter P in the described temperature range _jThe related data that changes is done

$\ln \left(T^{-2}\frac{\mathrm{\Δp}}{p_0}\right)=\ln \frac{A^{\′}{j}^n{V}^{m}k}{\mathrm{Q\β}}-\frac{Q}{k}\frac{1}{T_j}$

Curve fits to straight line, and the slope of establishing straight line is S, then

Q＝-kS；

6) get 3 groups, every group quantity L for more than or equal to 6 microelectronic component, 2) the inherent three kinds of different electric stresss of described temperature range are that electric stress is respectively j ₁, V ₁, j ₂, V ₂, j ₃, V ₃Condition under, carry out heating rate and be the temperature ramp test of β, obtain the inefficacy activation energy Q of each microelectronic component respectively _Il(i=1,2,3; L=1,2,3,4,5,6 ... L), invalid temperature scope T _Il1～T _Il2(i=1,2,3; L=1,2,3,4,5,6 ... L) and out-of-service time t _Il(i=1,2,3; L=1,2,3,4,5,6 ... L), and by the average inefficacy that following formula draws every group of microelectronic component respectively activate Q _i, mean time to failure, MTTF t _iWith average invalid temperature scope T _I1～T _I2

$Q_i=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{Q}_{\mathrm{il}}/L---\left(3\right)$

$t_i=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{t}_{\mathrm{il}}/L---\left(4\right)$

$\left.\begin{array}{c}{T}_{i1}=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{T}_{\mathrm{il}1}/L\\ T_{i2}=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{T}_{\mathrm{il}2}/L\end{array}\right\}---\left(5\right)$

7) set up the simultaneous equations of the inefficacy sensitive parameter P under the different electric heating stress:

$\left\{\begin{array}{c}\frac{\mathrm{dp}}{\mathrm{dt}}=A{j}_1^n{V}_1^m{e}^{-\frac{Q_1}{\mathrm{<figure-callout\; id="1"\; label="k\; T\; j"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">k</figure-callout>}{T}_{j_{}}{{}_1}_{}}}\\ \frac{\mathrm{dp}}{\mathrm{dt}}=A{j}_2^n{V}_2^m{e}^{-\frac{Q_2}{k{T}_{j_2}}}\\ \frac{\mathrm{dp}}{\mathrm{dt}}=A{j}_3^n{V}_3^m{e}^{-\frac{Q_3}{k{T}_{J_3}}}\end{array}\right\}---\left(6\right)$

To each formula both sides integration in the formula (6), take the logarithm, obtain:

$\left\{\begin{array}{c}\ln \left({\&Integral;}_{p_{01}}^{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}\mathrm{dp}\right)=\ln \left(A\right)+\mathrm{<figure-callout\; id="1"\; label="m\; ln\; V"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">m</figure-callout>}\ln V_{}{}_1+\mathrm{<figure-callout\; id="1"\; label="n\; ln\; j"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">n</figure-callout>}\ln j_{}{}_1+\ln {\&Integral;}_0^{t_1}{e}^{-\frac{Q_1}{k(T_0+\mathrm{\&Delta;T}+\mathrm{\&beta;t})}}\mathrm{dt}\\ \ln \left({\&Integral;}_{p_{02}}^{p_2}\mathrm{dp}\right)=\ln \left(A\right)+m\ln V_2+n\ln j_2+\ln {\&Integral;}_0^{t_2}{e}^{-\frac{Q_2}{k(T_0+\mathrm{\&Delta;T}+\mathrm{\&beta;t})}}\mathrm{dt}\\ \ln \left({\&Integral;}_{p_{03}}^{p_3}\mathrm{dp}\right)=\ln \left(A\right)+m\ln V_3+n\ln j_3+\ln {\&Integral;}_0^{t_3}{e}^{-\frac{Q_3}{k(T_0+\mathrm{\&Delta;T}+\mathrm{\&beta;t})}}\mathrm{dt}\end{array}\right\}---\left(7\right)$

Solve A, the value of m and n, p in the formula ₀₁, p ₀₂, p ₀₃Be the initial value before the degeneration of inefficacy sensitive parameter, p ₁, p ₂, p ₃Value when reaching failure criteria for the inefficacy sensitive parameter, (T ₀+ β t+ Δ T) adopt 1,3) middle T _J2Relational expression calculate, Δ T is the junction temperature liter, can adopt 1,1) Peak Junction Temperature rises Δ T _JpeakRise Δ T with average junction temperature _JaverThe arbitrary value of the two;

8) according to formula:

$E={\&Integral;}_0^{t_0}{j}^n{V}^m{e}^{-\frac{Q}{k{T}_j}}\mathrm{dt}---\left(8\right)$

Calculating microelectronic component is the failure criteria time t that inefficacy sensitive parameter P begins to degenerate to regulation under j, the V condition from accelerated tests at electric stress ₀The time electric heating stress that born ENERGY E;

9) according to formula:

$\mathrm{\&tau;}=\frac{E}{V^m{j}^n{e}^{-\frac{Q}{k{T}_j}}}---\left(9\right)$

Calculate microelectronic component at V, j and T _jBe respectively the life-span τ under the normal running conditions.

In the present invention by formula:

$\frac{\mathrm{dp}}{\mathrm{dt}}=A{j}^n{V}^m{e}^{-\frac{Q}{k{T}_j}}---\left(1\right)$

Can draw:

$(\mathrm{dp}/\mathrm{dt})/P_0=A^{\&prime;}{j}^n{V}^m\exp [-Q/k{T}_j]---\left(10\right)$

A ' in the formula=A/P ₀, adopt the temperature ramp method, promptly to microelectronic component apply the temperature ramp that rises by given pace β (quasistatic, 1 ℃ of heating rate/3-4hr), then t constantly the junction temperature of device be: T _j=T ₀+ β t+ Δ T, T ₀Be the temperature of heating platform, β is a heating rate, and Δ T is that microelectronic component applies the temperature rise that is caused by Jiao Erre behind certain electric stress.By dT _j=β dt can obtain: dt=dT _j/ β, and after substitution (10) formula:

$\mathrm{dP}/P_0=\frac{A^{\&prime;}}{\mathrm{\&beta;}}{j}^n{V}^m\exp [-Q/k{T}_j]d{T}_j---\left(11\right)$

(11) formula both sides integration

$\frac{1}{P_0}{\&Integral;}_{p_0}^p\mathrm{dP}=\frac{A^{\&prime;}{j}^n{V}^m}{\mathrm{\&beta;}}{\&Integral;}_{T_0}^{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}\exp (-Q/k{T}_j)d{T}_j---\left(12\right)$

Because of Q/kT _j＞＞1, then have:

${\&Integral;}_{T_0}^{T_j}\exp (-Q/k{T}_j)d{T}_j=\frac{k}{Q}[{T_j}^2\exp (-Q/k{T}_j)-{T_0}^2\exp (-Q/k{T}_0)]---\left(13\right)$

Because T ₀Less, T _j ²Exp (Q/kT _jThe T of)＞＞ ₀ ²Exp (Q/kT ₀), so second of following formula can ignore,

(11) formula both sides integration:

$\frac{\mathrm{\&Delta;P}}{P_0}=\frac{A^{\&prime;}{j}^n{V}^{m}k{T_j}^2}{\mathrm{\&beta;Q}}\exp (-Q/k{T}_j)---\left(14\right)$

(14) can obtain above-mentioned formula (2) after take the logarithm in the formula both sides:

$\ln \left({T_j}^{-2}\frac{\mathrm{\&Delta;P}}{P_0}\right)=\ln \left[\frac{A^{\&prime;}{j}^n{V}^{m}k}{\mathrm{Q\&beta;}}\right]-Q/k{T}_j---\left(2\right)$

If $C=\frac{A^{\&prime;}{j}^n{V}^{m}k}{\mathrm{Q\&beta;}},$ Then (14) formula becomes

$\ln \left({T_j}^{-2}\frac{\mathrm{\&Delta;P}}{P_0}\right)=\ln C-\frac{Q}{k}\frac{1}{T_j},$ And obtain a straight line through linear match, and the slope of establishing straight line is S, Q=-kS then, and Q is the inefficacy activation energy of device.

Method of the present invention can make the test period foreshorten to 1000 hours, and cost reduces more than 1/3, and required test piece reduces half, can provide the value of the voltage and current density power exponent factor and the life-span of monocyte sample simultaneously.

Description of drawings

Fig. 1 is embodiment of the invention GaAs FET I _DSSWith temperature T _jThe curve chart that changes;

Embodiment

With GaAs X011 is the example explanation, and the responsive electrical quantity of inefficacy is decided to be drain saturation current I _DSS, failure criteria is that drain saturation current degenerates 20%, i.e. Δ I _DSS=20%I _DSS0, I _DSS0Be the drain saturation current initial value.

1) chooses 200 ℃～300 ℃ temperature range, measure GaAs FET I _DSSWith junction temperature T _jThe curve that changes, as shown in Figure 1;

2) with the Peak Junction Temperature T of infrared method measurement under a certain electric stress _Jpeak, Peak Junction Temperature T _JpeakDeduct the temperature T of heating platform ₀The Peak Junction Temperature that is under this electric stress rises Δ T _Jpeak

3) choose 200 ℃～300 ℃ temperature range, at V _DC=8.0V, I _DSCarry out the temperature ramp test under the electric stress condition of=125mA, can obtain I _DSSWith junction temperature T _jDegenerated curve, as shown in Figure 1;

4) get the GaAs X011 sample that 3 groups, every group quantity L equals 6, the electric stress that applies is respectively V _DS1=8.0V, I _DS1=125mA; V _DS2=6.0V, I _DS2=170mA; V _DS3=4.0V, I _DS3=250mA carries out the temperature ramp test that heating rate is β respectively 200 ℃～300 ℃ temperature ranges, obtains the inefficacy activation energy Q of each GaAs X011 sample respectively _Ij(i=1,2,3 j=1,2,3,4,5,6 ... L), invalid temperature scope T _Il1～T _Il2(i=1,2,3 l=1,2,3,4,5,6 ... L) and out-of-service time t _Il(i=1,2,3l=1,2,3,4,5,6 ... L), and by the average inefficacy that following formula draws every group of GaAs X011 sample respectively activate Q _i, mean time to failure, MTTF t _iWith average invalid temperature scope T _I1～T _I2

$Q_i=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{il}}/L---\left(3\right)$

$t_i=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{t}_{\mathrm{il}}/L---\left(4\right)$

$\left.\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="T\; i"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">T</figure-callout>}}_i=\underset{l=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="L\; T\; il"\; filenames="C0315752600131.png"\; state="\{\{state\}\}">L</figure-callout>}}{\mathrm{\&Sigma;}}}{T}_{\mathrm{il}}{1}_{}/L\\ T_{i2}=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{T}_{\mathrm{il}2}/L\end{array}\right\}---\left(5\right)$

The data of calculating are as shown in table 1.

5) set up equation group according to formula (7), solve the value of m and n, in this example: A=472.5, m=4.7, n=8.4.

6) can draw GaAs X011 sample respectively under above-mentioned three kinds of electric stresss and T according to formula (8) and formula (9) _jLife-span τ in the time of=110 ℃ ₁=1.05 * 10 ⁵Hr, τ ₂=6.63 * 10 ⁴Hr, τ ₃=2.14 * 10 ⁴Hr.

The required sample of method of the present invention is few, the test period only needs 1000 hours, has shortened the test period greatly, has reduced cost, but also can provide the value of the voltage and current density power exponent factor and the life-span of monocyte sample.

Table 1

Group	Stress condition	Inefficacy activation energy (ev)	Average inefficacy activation energy (ev)	Invalid temperature scope (k)	Average invalid temperature scope (k)	Out-of-service time (hr)	Mean time to failure, MTTF (hr)	Life-span τ (hr)
									1	V DS＝8.0V I DS＝125mA	1.35	1.38	473～540	473～551	201	234	1.05× 10 5(T j＝110 ℃)
1.20	473～563	270
			1.45	473～545	216
1.25	473～566	279
			1.50	473～543	210
1.46	473～550	231
			2	V DS＝6.0V I DS＝170mA	1.45	1.41	473～553	473～543			300		210		6.63× 10 4(T j＝110 ℃)
1.30	473～536	249
					1.50		473～540		261
1.35	473～527	222
					1.30		473～556		309
1.55	473～548	285
					3		V DS＝4.0V I DS＝250mA		1.36	1.43	473～538	473～535		297		186	2.14× 10 4(T j＝110 ℃)
0.27	473～543	312
			1.60	473～533		282
1.55	473～528	267
			1.51	473～520		249
1.30	473～546	321

Claims (1)

1, a kind of Reliability Issues of Microelectronics Devices fast appraisement method is characterized in that, may further comprise the steps:

1) measuring microelectronic component current density to be adopted in experiment with infrared method is that j, voltage are the Peak Junction Temperature T under the electric stress of V _Jpeak, use Peak Junction Temperature T then _JpeakDeduct the temperature T of heating platform ₀Be the peak value temperature rise Δ T under this electric stress, be referred to as Peak Junction Temperature and rise Δ T _JpeakOr the average junction temperature that adopts electric method to measure this electric stress rises Δ T, is referred to as average junction temperature and rises Δ T _Javer

2) choose a temperature range that with the working junction temperature of this microelectronic component identical failure mechanism is arranged and be higher than its working junction temperature, the inefficacy sensitive parameter P that measures this microelectronic component in described temperature range with junction temperature T _jThe data that change, and be depicted as curve, T _J1=T ₀+ β t, T ₀Be the temperature of heating platform, β is a heating rate, and t is the time;

3) 2) in the described temperature range, it is that j, voltage are that heating rate under the electric stress of V is the temperature ramp test of β that microelectronic component is carried out current density, the sensitive parameter P that obtains losing efficacy is with junction temperature T _jThe data that change, and be depicted as curve, T _J2=T ₀+ β t+ Δ T, T ₀Be the temperature of heating platform, β is a heating rate, and t is the time, and Δ T is the junction temperature liter, according to 1,1) described in the method junction temperature that can obtain two different values rise Δ T _JpeakWith Δ T _Javer, both can choose any one kind of them;

4) establishing the amount of degradation of microelectronic component inefficacy sensitive parameter P under electric heating stress is Δ P, and then deterioration velocity is

It and current density j, voltage V and temperature T are deferred to following relation:

$\frac{\mathrm{dp}}{\mathrm{dt}}={\mathrm{Aj}}^n{V}^m{e}^{-\frac{Q}{k{T}_j}}---\left(1\right)$

N, m are the power exponent of j and V in the formula, and Q is the inefficacy activation energy, and k is a Boltzmann constant, and A is a constant; Draw by formula (1):

$\ln \left(T^{-2}\frac{\mathrm{\&Delta;p}}{p_0}\right)=\ln \frac{A^{\&prime;}{j}^n{V}^{m}k}{\mathrm{Q\&beta;}}-\frac{Q}{k}\frac{1}{T_j}---\left(2\right)$

P in the formula ₀Be the initial value before the degeneration of inefficacy sensitive parameter, A '=A/P ₀, Δ P=P-P ₀

5) according to the same inefficacy sensitive parameter of same temperature spot P in the difference that adds before and after the electric stress, obtain 2) amount of degradation and the junction temperature T of inefficacy sensitive parameter P in the described temperature range _jThe related data that changes is done $\ln \left(T_j^{-2}\frac{\mathrm{\&Delta;p}}{p_0}\right)=\ln \frac{A^{\&prime;}{j}^n{V}^{m}k}{\mathrm{Q\&beta;}}-\frac{Q}{k}\frac{1}{T_j}$ Curve fits to straight line, and the slope of establishing straight line is S, then Q=-kS;

6) get 3 groups, every group quantity L for more than or equal to 6 microelectronic component, 2) the inherent three kinds of different electric stresss of described temperature range are that electric stress is respectively j ₁, V ₁, j ₂, V ₂, j ₃, V ₃Condition under, carry out heating rate and be the temperature ramp test of β, obtain the inefficacy activation energy Q of each microelectronic component respectively _Il(i=1,2,3; L=1,2,3,4,5,6 ... L), invalid temperature scope T _Il1～T _Il2(i=1,2,3; L=1,2,3,4,5,6 ... L) and out-of-service time t _Il(i=1,2,3; L=1,2,3,4,5,6 ... L), and by the average inefficacy that following formula draws every group of microelectronic component respectively activate Q _i, mean time to failure, MTTF t _iWith average invalid temperature scope T _I1～T _I2

$Q_i=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{il}}/L---\left(3\right)$

$t_i=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{t}_{\mathrm{il}}/L---\left(4\right)$

$\left.\begin{array}{c}{T}_{i1}=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{T}_{\mathrm{il}1}/L\\ T_{i2}=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{T}_{\mathrm{il}2}/L\end{array}\right\}---\left(5\right)$

7) set up the simultaneous equations of the inefficacy sensitive parameter P under the different electric heating stress:

$\left\{\begin{array}{c}\frac{\mathrm{dp}}{\mathrm{dt}}={\mathrm{Aj}}_1^n{V}_1^m{e}^{-\frac{Q_1}{{\mathrm{kT}}_{j1}}}\\ \frac{\mathrm{dp}}{\mathrm{dt}}={\mathrm{Aj}}_2^n{V}_2^m{e}^{-\frac{Q_2}{{\mathrm{kT}}_{j2}}}\\ \frac{\mathrm{dp}}{\mathrm{dt}}={\mathrm{Aj}}_3^n{V}_3^m{e}^{-\frac{Q_3}{{\mathrm{kT}}_{j3}}}\end{array}\right\}---\left(6\right)$

To each formula both sides integration in the formula (6), take the logarithm, obtain:

$\left\{\begin{array}{c}\ln \left({\&Integral;}_{p_{01}}^{p_1}\mathrm{dp}\right)=\ln \left(A\right)+m\ln V_1+n\ln j_1+\ln {\&Integral;}_0^1{e}^{-\frac{Q_1}{k(T_0+\mathrm{\&Delta;T}+\mathrm{\&beta;t})}}\mathrm{dt}\\ \ln \left({\&Integral;}_{p_{02}}^2\mathrm{dp}\right)=\ln \left(A\right)+m\ln V_2+n\ln j_2+\ln {\&Integral;}_0^2{e}^{-\frac{Q_2}{k(T_0+\mathrm{\&Delta;T}+\mathrm{\&beta;t})}}\mathrm{dt}\\ \ln \left({\&Integral;}_{p_{03}}^{p_3}\mathrm{dp}\right)=\ln \left(A\right)+m\ln V_3+n\ln j_3+\ln {\&Integral;}_0^3{e}^{-\frac{Q_3}{k(T_0+\mathrm{\&Delta;T}+\mathrm{\&beta;T})}}\mathrm{dt}\end{array}\right\}---\left(7\right)$

Solve A, the value of m and n, p in the formula _O1, p _O2, p _O3Be the initial value before the degeneration of inefficacy sensitive parameter, p ₁, p ₂, p ₃Value when degenerating to failure criteria for the inefficacy sensitive parameter, (T _o+ β t+ Δ T) adopt 1,3) middle T _J2Relational expression calculate, Δ T is the junction temperature liter, can adopt 1,1) Peak Junction Temperature rises Δ T _JpeakRise Δ T with average junction temperature _JaverThe two one of arbitrary value;

8) according to formula:

$E={\&Integral;}_0^{t_0}{j}^n{V}^m{e}^{-\frac{Q}{k{T}_j}}\mathrm{dt}---\left(8\right)$

Calculating microelectronic component is the failure criteria time t that inefficacy sensitive parameter P begins to degenerate to regulation under j, the V condition from accelerated tests at electric stress ₀The time electric heating stress that born ENERGY E;

9) according to formula:

$\mathrm{\&tau;}=\frac{E}{V^m{j}^n{e}^{-\frac{Q}{{\mathrm{kT}}_j}}}---\left(9\right)$

Calculate microelectronic component at V, j and T _jBe respectively the life-span τ under the normal running conditions.

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