1、JEDEC STANDARD Standard Method for Measuring and Using the Temperature Coefficient of Resistance to Determine the Temperature of a Metallization Line JESD33B (Revision of JESD33-A) FEBRUARY 2004 (Reaffirmed: October 2012) JEDEC SOLID STATE TECHNOLOGY ASSOCIATION NOTICE JEDEC standards and publicatio
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9、t be reproduced without permission. For information, contact: JEDEC Solid State Technology Association 3103 North 10th Street Suite 240 South Arlington, VA 22201-2107 or refer to www.jedec.org under Standards-Documents/Copyright Information. JEDEC Standard No. 33B -i- Standard Method for Measuring a
10、nd Using the Temperature Coefficient of Resistance to Determine the Temperature of a Metallization Line Contents Page l Scope 1 2 Introduction: significance and use 1 3 Terms and definitions 3 4 Summary of method 4.1 Assumptions 3 4.2 Relations used 5 4.3 Summary of procedures 6 4.4 Parameters to be
11、 selected 8 5 Precautions and measurement interferences 5.1 Linear dependence 8 5.2 Stability of resistance 9 5.3 Test current 9 5.4 Wafer-level measurements 9 5.5 Package-level measurements 10 5.6 Thermal equilibrium 10 5.7 Mean temperature of test line 11 5.8 Peak temperature of test line 11 5.9 A
12、ccurate voltage measurements 12 5.10 Probe cleanliness 12 5.11 Dew point 12 5.12 Temperature sensors 12 5.13 Concurrent testing 12 5.14 Low-k dielectrics 12 5.15 Dependence of TCR(T) on test structure design and processing 13 6 Test apparatus 6.1 Current supply 13 6.2 Voltmeter 13 7 Ambient temperat
13、ure controller 7.1 Wafer-level measurements 14 7.2 Package-level measurements 14 8 Procedure for TCR(Tref) measurement 8.1 Adjust ambient temperature 14 8.2 Determine ambient temperature 14 8.3 Measure resistance of test line at temperature T114 8.4 Determine resistance of test line at other tempera
14、tures 15 8.5 Analyze resistance data 15 8.6 Calculate TCR(Tref) 16 JEDEC Standard No. 33B -ii- Standard Method for Measuring and Using the Temperature Coefficient of Resistance to Determine the Temperature of a Metallization Line Contents Page 9 Procedure for measuring test-line temperature due to J
15、oule heating 9.1 Determine ambient temperature of test line 16 9.2 Measure resistance of test line at ambient temperature 16 9.3 Calculate resistance of test line at reference temperature 17 9.4 Measure resistance of test line during Joule heating 17 9.5 Calculate mean temperature of test line 17 10
16、 Procedure for measuring ambient temperature with test line 10.1 Apply measurement current 18 10.2 Calculate resistance of test line 18 10.3 Reverse measurement current 18 10.4 Calculate resistance mean of test line 18 10.5 Calculate ambient temperature of test line 18 11 Measurement of bias and pre
17、cision 11.1 Summary 19 11.2 Within-laboratory precision 20 11.3 Between-laboratory precision and bias 20 12 Required reporting 12.1 TCR(Tref) 22 12.2 Tref22 13 Additional, optional information to report 13.1 Results of TCR(T) measurements 23 13.2 Results of Joule heating measurements 23 13.3 Results
18、 of test-line temperature measurements 24 14 References 24 Annex A Use of TCR(T) in the nonlinear regime to estimate high temperature A.1 For aluminum 25 A.2 For copper 26 Annex B (informative) Differences between JESD33-B and JESD33-A 29 JEDEC Standard No. 33B Page 1 Standard Method for Measuring a
19、nd Using the Temperature Coefficient of Resistance to Determine the Temperature of a Metallization Line (From JEDEC BoD Ballot JCB-03-64, formulated under the cognizance of the JC-14.2 Subcommittee on Wafer-Level Reliability.) 1 Scope This method is intended for determining the temperature coefficie
20、nt of resistance (at a given temperature) of aluminum- and copper-based thin-film metallizations that are used in microelectronic circuits and devices. This method is intended for estimating a mean temperature of a metallization line stressed in an accelerated electromigration stress test before any
21、 irreversible change in resistivity occurs due to the current-density and temperature stresses imposed. This method is intended for using a metallization test line as an ambient-temperature sensor. It uses the predetermined values for the temperature coefficient of resistance of the metallization an
22、d the resistance of the test line at a reference temperature. This method is designed for use under conditions where the metallization resistivity is linearly dependent on temperature and where it does not suffer any irreversible changes. For aluminum metallizations, a linear dependence appears to h
23、old until approximately 420 C, considerably above anticipated stress temperatures. For copper metallizations, a departure from a linear dependence becomes evident at temperatures as low as 200 C. A correcting function is used for copper to correct for departures from linearity at these higher temper
24、atures This method is applicable to metallization test lines with or without vias, and with oxide or low-k dielectrics. While the method is designed for use with aluminum- and copper-based metallizations, it may also be used with other metals and alloys for conditions that satisfy the linear depende
25、nce and stability stipulations in the previous paragraphs. The metallization structure used in the method may be measured while on a wafer or a part therefrom, or as part of a test chip bonded to a package and electrically accessible via package terminals. 2 Introduction: significance and use The te
26、mperature increase of a test line due to Joule heating can be an important parameter in accelerated stress tests used to characterize the susceptibility of a metallization test line to electromigration failure at a given temperature and current density l, 2, 3. A measure of this susceptibility is th
27、e median-time-to-failure of test lines in such tests. Accurate knowledge about the metallization temperature during the test is important because the median-time-to-failure is exponentially dependent on the reciprocal of the metallization stress temperature, in kelvin. For example, an error of five
28、degrees in stress temperature introduces a 25% error in the sample estimate for t50 at a line temperature of 150 C and when the activation energy is 0.7 eV)1. JEDEC Standard No. 33B Page 2 2 Introduction: significance and use (contd) Electromigration is a metallization failure mechanism that is of g
29、reat concern, especially for the reliability assessment of very large scale integrated (VLSI) microelectronic devices. The linear dependence of the resistance of the metallization on temperature permits a test line to be used as a temperature sensor as long as the environmental conditions do not cau
30、se irreversible changes in the resistivity of the metallization. By using the temperature dependence of the resistivity of pure, bulk copper, it is possible to make temperature determinations beyond the linear range for copper. This done by using a correction factor, which is a function of the tempe
31、rature that is calculated when a linear dependence is nevertheless assumed to exist. Metals such as aluminum and copper obey Matthiessens rule 4 to a good approximation. In this case, the resistivity of the metal is the sum of the resistivity of the pure, bulk form of the metal, (T)PB, and a tempera
32、ture-independent residual resistivity, (c)r. This residual component is due to impurities and to other departures from the structural order that contributes to electron scattering. The greater the residual resistivity, the smaller will be the value of the temperature coefficient of resistance, as ca
33、n be seen in the following equations. PBrPBPBPBrPBTcdTTdTdTTdcTdTdRRTTCR)()(11)()(1)()()(11)(+=+=or .)()(11)()(PBrPBTcTTCRTTCR+=The maximum value for TCR(T) at any given temperature will therefore occur when the residual resistivity is zero. Hence, for example, one can expect that the TCR(T = 30 C)
34、for aluminum and copper will be no larger than approximately 0.00414 C-1and 0.00389 C-1, respectively. (See reference 5 and Annex A.) The magnitude of the residual resistivity, relative to the resistivity of the pure, bulk metal, is obtained from 1)()()()(=TTCRTTCRTcPBPBr. JEDEC Standard No. 33B Pag
35、e 3 3 Terms and definitions 3.1 metallization: A thin-film conductive material used to electrically connect microelectronic elements. 3.2 temperature coefficient of resistance: The fractional change in resistance of a test line per unit change in temperature at temperature T, (),C1-)R(1= )TCR( TRx T
36、T(1) where R(T) is the resistance of the test line at temperature T (see 4.2.3). NOTE For aluminum-based metallizations, the change in resistance of the test line with temperature is approximately constant from room temperature to about 420 C (see Annex A). For copper-based metallizations, a change
37、in R/T becomes evident at temperatures as low as 230 C. Hence, if TCR(T) is to be used to calculate the temperature of copper test lines at such higher temperatures, a correction function, Fcorr, will be required (see Annex A). 3.3 test line: A metallization line of specified dimensions, whose lengt
38、h is defined by the locations of two voltage taps used to make Kelvin-like resistance measurements of the test line when two other terminals force a current through the line. 3.4 test structure: A passive metallization structure, including a test line, that is fabricated on a semiconductor wafer by
39、procedures used to manufacture microelectronic integrated devices. (See 4.4.1, 13.1c, 13.2b, 13.3a.) 4 Summary of method 4.1 Assumptions The method is based on two assumptions: 4.1.1 Assumption 1 The resistance of the metallization test line is a linear function of the metallization temperature. Hen
40、ce, the resistance at a temperature T can be given by: ,T S+ )R( = R(T) 0(2) where S is the slope of the resistance-versus-temperature line and R(0) is the resistance of the test line at an ambient temperature of 0 C, as illustrated in Figure 1. (See 5.1.) Another assumption will be used to permit m
41、easurements of copper test structures at high temperatures where linearity no longer holds. (See Annex A.2. JEDEC Standard No. 33B Page 4 4.1 Assumptions (contd) 4.1.1 Assumption 1 (contd) Figure 1 Illustration of terms used in text on a plot of resistance versus temperature. Temperature (C)Resistan
42、ce () R(0) R(To) R(T) 0 RTR(T) = R(0) + S T or R(T) = R(To) + S (T - To) or R(T) = R(To) 1 + TCR(To) (T - To) ToTS = R/T = R(T) TCR(T) = R(To) TCR(To)JEDEC Standard No. 33B Page 5 4.1 Assumptions (contd) 4.1.2 Assumption 2 The resistivity of the metallization does not suffer any irreversible changes
43、 when subjected to the temperatures and currents of the test, thereby permitting repeatable resistance measurements at any temperature and current used with the method. (See 5.2.) 4.2 Relations used The method uses a number of relations: 4.2.1 Resistance of test line From the definition for TCR(T) (
44、see 3) and assumption 1 (see 4.1.1), the resistance of the test line at temperature T0is related to the resistance at another temperature, T, by the temperature coefficient of resistance of the test line for temperature T0: () ()( ). TTTTCR + 1TR = R(T)000(3) 4.2.2 Intercept and slope Equation 3 can
45、 be rewritten in the linear form of equation 2: () ()( ) () ()TTTCRTR + TTTCRTR = R(T) 000001(4a) where the intercept at T = 0 C is () ()()0001 TTTCRTR = R(0) (4b) and where the slope is () (). TTCRTR = S00(4c) Because the slope is constant (4.1.1) and T0is an arbitrary temperature, () (). TTCRTR =
46、TCR(T)R(T) = S00(4d) The purpose of equation 4d is to emphasize that the product of the temperature coefficient of resistance and test-line resistance at one temperature, T, is equal to that product at another temperature, T0. 4.2.3 Temperature coefficient of resistance Using equation 4c, the temper
47、ature coefficient of resistance at temperature T can be expressed in terms of the slope S and the test-line resistance at temperature T: . R(T)S= TCR(T)(5) Equation 5 demonstrates that the temperature coefficient of resistance is not a constant; it decreases with increasing temperature because metal
48、lization resistance increases with temperature while S remains constant. Therefore, the temperature coefficient of resistance must always be referenced to a specific temperature. JEDEC Standard No. 33B Page 6 4.2 Relations used (contd) 4.2.4 Converting TCR(T0) to TCR(T) The temperature coefficient o
49、f resistance at one temperature, T0, is related to that at another temperature, T, by: ()()( ). TTTTCR + 1TTCR= TCR(T)000(6) 4.3 Summary of procedures The method consists of procedures to determine: 1) the temperature coefficient of resistance of a metallization at a specified temperature (i.e., 4.3.1), 2) the mean temperature of the test line due to Joule heating (i.e., 4.3.2), and 3) the ambient temperature of the test line, which is inferred from a measurement of the test-line temperatur
