1、m (D P EINJEDEC STANDARD Standard Method for Calculating the Electromigration Model Parameters for Current Density and Temperature EINJESD63 FEBRUARY1998 1 I ELECTRONIC INDUSTRIES ASSOCIATION ENGINEERING DEPARTMENT - STD*EIA JESDb3-ENGL 1998 323Lib00 059207b 809 NOTICE EWJEDEC standards and publicat
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8、 as they are fiee to duplicate this document in accordance with the latest revision of JEDEC Publication 2 1 “Manuai of Organization and Procedure“. PRICE: Please refer to the current Catalog of JEDEC Engineering Publications and Standards or call Global Engineering Documents, USA and Canada (1-800-
9、854-7179), International (303-397-7956) Printed in the U.S.A. Ail rights reserved JEDEC Standard No. 63 STD-EIA JESDb3-ENGL 1998 = 323Lib00 0572077 745 D STANDARD METHOD FOR CALCULATING THE ELECTROMIGRATION MODEL PARAMETERS FOR CURRENT DENSITY AND TEMPERATURE CONTENTS Scope Introduction: Significanc
10、e and use Summary of method Precautions and interferences Procedure for calculating the sample estimate of S and its confidence interval 5.1 When tso(3i) values are available from N stress tests 5.2 When tr(Ji j) values are available from N stress tests Procedure for calculating sample estimate of E
11、A and its confidence interval 6.1 When t5o(Tj) values are available from N stress tests 6.2 When t(i j) values are available from N stress tests 7 Procedure for calculating sample estimate of S and EA, and their confidence intervals 7.1 When tso(Ji Ti) values are available from N stress tests 7.2 Wh
12、en ti(Ji,Ti j) or ti(J, ,Ti j) values are available from N stress tests 8 Procedure for calculating sample estimate of S, EA, or both when censored data is used 9 Measures for linearity 10 Reporting 10.1 Minimum data to report 10.2 Additional recommended data and information 11 References 12 List of
13、 selected symbols Figures 1A 1B ANNEX A Example Calculations A. 1 Using procedure 5.2 to calculate the sample estimate S and its confidence interval when failure times tAJi j) are available N stress tests A.2 Using procedure 5.1 to calculate the sample estimate of S and its confidence interval when
14、tx(Ji) values are given from N stress tests A.3 Using procedure 7.2 to calculate the sample estimates of S and EA and their Confidence intervals when tAJi j) values are given from N stress tests A.4 Using procedure 7.1 to calculate sample estimates of S and EA and their confidence intervals when t50
15、(J, ,Ti) values are available from N stress tests AS Using procedures 8 and 7.1 to calculate sample estimates of S and EA and their confidence intervals when censored data is used Page 1 i 2 6 8 8 9 10 10 12 13 13 15 17 19 20 20 21 22 22 4 5 24 26 27 30 32 -1- STD.EIA JESDb3-ENGL 1998 3234b00 059207
16、8 bdl, 9 JEDEC Standard No. 63 Page 1 STANDARD METHOD FOR CALCULATING THE ELECTROMIGRATION MODEL PARAMETERS FOR CURRENT DENSITY AND TEMPERATURE (From JEDEC Council Ballot JCB-97-17, formulated under the cognizance of JC-14.2 Committee on Wafer-Level Reliability) 1 Scope 1.1 The method provides proce
17、dures that use linear regression analyses for calculating sample estimates, and their confidence intervals, of the electromigration model parameters for current density and temperature of thin-film metal interconnects used in microelectronic devices. 1.2 The method assumes that the median time to fa
18、ilure (tm) data from accelerated stress tests of metal interconnect test structures can be satisfactorily modeled by Blacks equation i (see eq. 3.2). Hence, the model parameter for current density, J, is the value of the exponent, n, to which J is raised and the model parameter for temperature is th
19、e activation energy, EA, of the electromigration process. The linear regression analyses calculate sample estimates of EA directly, while sample estimates of n are obtained from analyses that involve the calculation of sample estimates of a slope S, where S = -n. 1.3 The method requires existing fai
20、lure-time (tr) data or median-time-to-failure (t50) data. When t50 data is used, they must be from at least three electromigration stress tests conducted at different stress levels when only the current density or only the temperature is varied. They must come from at least four stress tests if both
21、 current density and temperature are varied to obtain the tm data. 1.4 The method can be used with censored tf data if JEDEC standard JESD37 2 (or its equivalent) is used to convert the censored data to t50 estimates and the method used with these tso values. In the context of this standard, censore
22、d tf data refers to the case where the stress test is halted before all test parts have failed. Hence, the number of tf values available for analysis is less than the sample size of the test. 1.5 Examples of three types of calculations by this method are given in Annex A. One is to obtain sample est
23、imates of n and of their confidence interval when t5o or tf data are available from experiments conducted at different current-density stresses. The second is to obtain sample estimates of both n and EA and of their confidence intervals when tso or tf data are available from experiments conducted at
24、 different current-density and temperature stresses. The third involves calculations with censored data. 1.6 This method does not preclude the use of other methods as long as they have been shown to provide equivalent results. The calculation examples referred to in 1.5 may be used to show equivalen
25、ce. 2 Introduction Significance and use 2.1 Electromigration is a failure mechanism of electrical interconnects that is of great concern, especially for the reliability assessment of very large scale integrated (VLSI) microelectronics. The drivers of the electromigration process in Blacks equation a
26、re the current density and the temperature. STD-EIA JESDb3-ENGL I778 323Lib00 0572077 518 JEDEC Standard No. 63 Page 2 2 Introduction Significance and use (contd) 2.2 To obtain reliability data from thin-film metal interconnect test structures in a time much shorter than their expected lifetime, sam
27、ples of similar interconnects are subjected to accelerated stress tests. These tests provide sets of failure times for current density and temperature conditions that are more severe than would normaily be encountered in use. To assess the reliability of such parts under use conditions requires that
28、 the model parameters for both current density (n) and temperature (EA) be determined and used to extrapolate the results of stress tests to use conditions. Because only sample estimates of the model parameters can be obtained, it is also important to determine the confidence limits for these sample
29、 estimates. 2.3 Confidence intervals for the sample estimates of the model parameters of electromigration are necessary to determine the statistical significance of any differences noted in the values determined: from similar interconnect test structures measured at different times, from test struct
30、ures with different designs, or from interconnects fabricated at different times, at different laboratories, or with different processes. 2.4 This method can be useful in evaluating and optimizing the selection of metal alloys and processes, and in identifying the key input material and process para
31、meters that affect the reliability of interconnects. 3 Summary of method 3.1 To obtain sample estimates and their confidence intervals of the model parameter for the current density, for the temperature, or for both requires a set of median-time-to-failure (tso) data or a set of time- to-fail (tf) d
32、ata obtained from severai electromigration stress tests with different stress conditions. These data are best obtained by following the procedure of the standard electromigration test method 3 and the standard method for determining the joule heating in a test line 4. The electromigration test metho
33、d includes procedures for calculating sample estimates of both tso and CJ from the failure times of the test parts. The sample estimates for tm and G are obtained from the average and the standard deviation, respectively, of the naturai logarithm of the individual failure times. That is, where j run
34、s from 1 to N and N is the sample size. The test method also includes procedures for calculating the confidence intervals for these estimates. In that method 3 1, as in this method, the impact of sample size on confidence intervals is demonstrated. In performing such electromigration tests and in fo
35、llowing this method, it must be understood that the stress temperature of the structures being stressed is the sum of the local ambient stress temperature and of the temperature increase of the test line due to power dissipation in the test structure and elsewhere on the wafer or chip (see 4.4). - S
36、TD*EIA JESDb3-ENGL 1778 W 3234b00 0592080 23T JEDEC Standard No. 63 Page 3 3 Summary of method (contd) 3.2 Assumptions 3.2.1 The method assumes that the set of tm or tf values can be modeled by Blacks equation: where: 3 is the current density in the metal test lines (A/cm*), n is the model parameter
37、 for current density, EA is the model parameter for temperature, i.e. activation energy (eV), T is the temperature of the metai test lines (K), k is Boltzmanns constant (8.617 x 10 eV/K), and A is a constant. 3.2.2 When dealing with failure-time data, tf, to determine n or EA, it is assumed in 5.2,6
38、.2, and 7.2 that there is no censoring of these data. If there is data censoring in some or all of the tests, the tf data from all tests must be used to obtain sample estimates of tm in the manner described in section 8. These sample estimates of tm are then used to obtain sample estimates of n, EA,
39、 or both as described in 5.1,6.1, and 7.1, respectively. NOTE - Using tso data rather than the failure-time (tf) data to obtain sample estimates of n, EA, or both, results in an increase in the length of the confidence interval for these estimates. The reason for the increase is that the level of in
40、formation from the individual tf values is reduced in the process of subsuming them in the tso data. But, the larger the number of experiments involved in calculating the sample estimates, the less significant will be this increase. The expected value for the ratio of the confidence interval (10) fr
41、om tso data to the interval (If) from tf data can be estimated from: where: N is the number of stress tests (tO values), NS is the sum of the numbers of test structures in the N stress tests, 1-cc is the confidence coefficient for the confidence interval, and p = 2 when either J or T is varied among
42、 the tests to obtain sample estimates of n or EA, and p = 3 when both J and T are varied to obtain sample estimates for both n and EA. See examples described in Annex A, paragraphs A.2.2 and A.4.3. JEDEC Standard No. 63 Page 4 3 Summary of method (contd) 3.3 Sample estimates for n or EA are obtained
43、 from a linear regression analysis for one independent variable (sections 5 and 6). The analysis requires failure-time data from several electromigration stress tests when these tests are conducted at different levels of current-density or temperature stress, respectively. When both current density
44、and temperature are varied, sample estimates are obtained from a multiple linear regression for two independent variables (section 7). 3.3.1 If the current density is varied while the stress temperature of the metai test lines is kept constant in a number of electromigration stress tests, then ta wi
45、ll be proportional to 1/J“ and hence or lntso = - n In J + B, In tso = Sln J + B, (3.3a) (3.3b) where B is a constant involving A and EA. A plot of In tm versus In J will display data points aligned generally along a straight line. This is illustrated in figure 1A. A linear regression analysis of th
46、e In tN - In J data pairs will yield a least-squares, sample estimate of the slope, S, of the best-straight-line fit to the data and the confidence interval for this slope. The sample estimate for n, the model parameter for the current density, is obtained from the relation S = -n. The method depend
47、s critically on the assumption of linearity (see 4.1,4.2, and 9.). A very useful tool in assessing the validity of the assumption is a visual inspection of the plotted data (see 9.2). =S Figure 1A - Plot of In tso versus In J to illustrate the behavior of eq. 33b and the best-straight-line fit to th
48、e data from which the value of n can be obtained and the linearity of the dependence may be judged STD-EIA JESDb3-ENGL 1998 W 323Yb00 0592082 OU2 W JEDEC Standard No. 63 Page 5 3 Summary of method (contd) 3.3.2 If the temperature of the test lines is changed while the current-density stress is kept
49、constant in a number of different stress tests, then tw will be proportional to exp(EN-2) is the 1-d2 percentile of the t distribution for N - 2 degrees of freedom. The degrees of freedom is a parameter of the distribution and is related to the amount of information in the data for estimating variability. NOTE - The number of experiments, N, must be at least three. This is because the degrees of freedom for the 1-d2 percentile of the t distribution in eq. 5.3 is N - 2. An N of four is preferable because of the significant penalty on the size
