RU2567016C1 - Method for assessment of electromigration parameters in metal conductors - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: invention is referred to the area of microelectronics and may be used for assessment and control of metallization reliability, namely to metal layout, at manufacture of integrated microcircuits in order to optimize production process and to increase information content. The method consists in testing of metal conductors in integrated circuits at three different temperatures T₁, T₂ and T₃ due to self-heating by passing current with further calculation of electromigration parameters: energy of activation

,

exponent index $$n=\{\ln \left(t_{{50}_1}/t_{{50}_2}\right)-E_a\cdot \left(1/T_1-1/T_2\right)/k\}/\ln \left(j_2/j_1\right)$$

and electromigration constant for metal conductors $$A=t_{{50}_1}\cdot j_1^n/\exp \left(E_a/\left(k\cdot T_1\right)\right)$$

, where $$\left(t_{{50}_1};{\sout{j}}_1\right)$$

, $$\left(t_{{50}_2};{\sout{j}}_2\right)$$

, $$\left(t_{{50}_3};{\sout{j}}_3\right)$$

is median time between failures of metal conductors and median value of current density that heats up the above conductors up to testing temperature T₁, T₂, T₃ respectively.

EFFECT: reduced time of testing for test structures in order to obtain electromigration parameters.

8 dwg, 6 tbl

Description

The invention relates to the field of microelectronics and can be used to assess and control the reliability of metallization, namely metal wiring, in the production of integrated circuits to optimize the production process and increase information content.

The reliability of metal conductors of integrated circuits is predicted based on the activation energy E _a and exponent n in accordance with Black's formula (1), and the determination of these parameters is a priority in the development of highly reliable metal conductors.

A known method for calculating the parameters E _a and n from the patent (EP 1978371 A, G01R 31/28, 2008). The method is based on the fact that the value of activation energy affects the value of the median time to failure during electromigration. The calculation of the values of E _a and n is carried out after an accelerated electromigration test of metal conductors, consisting of three stages, each of which differs in the value of the elevated temperature and / or electric current density. The value of the activation energy is found from the slope of the line on the Arrhenius plot. The disadvantages of this technique are: firstly, the complexity of the transient processes when switching from one measurement mode to another, secondly, the use of heating furnaces to maintain a constant elevated temperature of the samples, and thirdly, the long test duration (> 120 h).

There is also a methodology presented in the EIA / JEDEC JESD61 standard, which includes accelerated electromigration tests at a constant temperature in the regime of constant power of the flowing current, while heating is only due to the flow of current. The criterion for failure and termination of measurements is an increase in the resistance of the metal conductor relative to the initial value obtained at the beginning of the measurements (recommended values are an increase from 5% to 20%) (US 20030080761 A1, G01R 31/26, 2003). The disadvantage of this method is that we get only the median failure time of metal conductors at a constant temperature, without determining the electromigration parameters.

Closest to the claimed method is the technique presented in the EIA / JEDEC JESD63 standard, where the mean time to failure (t ₅₀ ) is determined for calculating the activation energy at least at three different temperatures when a constant current density is maintained. In this case, the value of E _{a is} found from the slope of the line, where ln (t ₅₀ ) is plotted along the ordinate axis, and 1 / T is plotted along the abscissa axis (T is temperature). To calculate the index of the degree of current density n, in turn, the values of the mean time between failures (t ₅₀ ) are determined at least at three different values of the current density when a constant temperature is maintained. In this case, the value of n is found from the slope of the line, where ln (t ₅₀ ) is plotted along the ordinate axis, and ln (J) is plotted along the abscissa axis (J is the electric current density). The disadvantages of this technique are: firstly, the use of heating furnaces to maintain a constant elevated temperature of the samples, and secondly, currents of relatively low density (<2 MA / cm ² ) are passed through the test structures to avoid the effect of self-heating, which, therefore, leads to a significant increase in test time (> 2-4 weeks).

The basis of the invention is the task of developing an express method that makes it possible to determine electromigration parameters — activation energy E _a and exponent of current density n, which are necessary in assessing the reliability of metal conductors.

The essence of the technique is as follows. Electromigration parameters are determined based on the empirically derived Black equation (J.R.Black):

where t ₅₀ is the median time between failures (median-time-to-failure) (sec), A is a constant, j is the current density (A / cm ² ), n is a measure of the degree of current density, E _a is the activation energy ( eV), k is the Boltzmann constant (eV / K); T is the temperature (K).

To determine the values of t ₅₀ conduct electromigration tests at a constant temperature, in which the samples are heated by self-heating by the flowing current. In Fig. Figure 1 shows the characteristic dependence of the resistance of a conductor on time during testing, consisting of 3 areas: access to the test mode, measurements, failure of the conductor.

Due to the fact that during testing, the value of the conductor temperature (T) is set using self-heating by the flowing current (j), then a change in the temperature value will lead to a change in the value of j, therefore, to determine the remaining parameters (A, n, E _a ) it is enough use three conditions for measurements: (j ₁ ; T ₁ ), (j ₂ ; T ₂ ), (j ₃ ; T ₃ ). As a result, we obtain a system of equations with three unknowns:

Dividing the first equation in the system by the second, and taking the natural logarithm of both parts, we get the expressions for n:

Dividing the first equation by the third in the system (2) and substituting the obtained expression for n (3) into it, having previously taken the natural logarithm of both parts, we obtain the expression for E _a .

The value of coefficient A can be determined from any equation of system (2) using the found values of n and E _a , for example:

The current density j ₁ (i = 1,2,3) for each value of t _50i is defined as the median of the set values of current densities for each temperature value T _i .

An example of using the technique

In the developed methodology, reliability tests (electromigration tests) were carried out on metal conductors with a passivating SiO ₂ layer 0.9 μm thick. The type of test structure is shown in Fig. 2. Electromigration tests were carried out on a group of three plates. The total number of samples was divided into three parts, for each of which the value of the effective test temperature was established (Table 1).

Table 1 Initial measurement data. Structure Topological length (L), microns Topological width (W), microns Thickness (N), microns Temperature ° C TiN / AlSi / TiN 800 1.2 0.7 270/300/350

The constant temperature value was selected so that the test time was less than 40 minutes. During testing, we used a measuring bench based on the Agilent 4156C precision semiconductor parameter analyzer (Fig. 3). The criterion for failure and completion of measurements was a 0.5 increase in resistance.

The current density for a metal conductor is calculated by the formula

where j is the current density (mA / μm ² ), I is the electric current (mA), S is the cross section of the conductor (μm ² ), W is the width of the conductor (μm), N is the height of the conductor (μm). The values of W and H are taken from table 1.

To obtain reliable data, in the calculations it is necessary to take into account the deviation of the geometric dimensions of the metal conductor from the nominal value that occurs during the process of its formation.

In this case, the deviation of the width of the metal conductor was taken into account (Fig. 4), therefore, formula (6) for calculating the current density can be rewritten in the following form

where j is the current density (mA / μm), I is the magnitude of the electric current (mA), S _offset is the cross section of the conductor taking into account the deviation in width (μm ² ), W is the nominal width of the conductor (μm), W _offset is the deviation of the width conductor from the nominal value (μm), N is the height of the conductor (μm).

The surface resistance of the conductor is determined by the formula

where R is the electrical resistance (Ω), W is the width of the conductor (μm), W _offset is the deviation of the width of the conductor from the nominal value (μm), L is the length of the conductor (μm).

To calculate W _offset , two test structures with sizes W ₁ , L ₁ and W ₂ , L _{2 are used} to calculate W _offset and resistances R ₁ , R ₂ . Then for two structures in one metallization layer we have

From formula (9) we obtain the deviation of the width of the conductor from the nominal value

In this case, the deviation of the width Wo _{ffset was} directly determined on the structure used for testing (see Table 2).

table 2 The topological dimensions of the conductors to determine the deviation of their width from the nominal value. Structure L, μm W, μm Test 1 800 1.2 Test 2 800 3.6

To determine the values of electromigration parameters, the following algorithm was used:

1) Conducting a series of electromigration tests at a constant temperature for a group of samples (Fig. 5) with fixing the measurement time and the value of electrical resistance at certain time intervals (Δt = 200-300 ms). Tests are carried out at least at three different temperatures - T _test = (T ₁ ; T ₂ ; T ₃ ).

, $$\left(t_{{50}_2};{\sout{j}}_2\right)$$

, $$\left(t_{{50}_3};{\sout{j}}_3\right)$$

.2) Determination of the value of 150 and the median of the current density j (Formula 7) for each of the values of the selected temperatures - $$\left(t_{{\mathrm{fifty}}_{\mathrm{one}}};{\sout{j}}_{\mathrm{one}}\right)$$

, $$\left(t_{{\mathrm{fifty}}_2};{\sout{j}}_2\right)$$

, $$\left(t_{{\mathrm{fifty}}_3};{\sout{j}}_3\right)$$

.

3) Calculation of E _a (Formula 4).

4) Calculation of n (Formula 3).

5) Calculation of coefficient A (Formula 5).

Figure 6-8 shows the distribution of the measured MTBFs for each test temperature. A linear extrapolation of the results was carried out using the least squares method. The horizontal axis X shows the failure times of structures on a logarithmic scale (sec), the vertical axis Y-p is the fraction of the number of failures. The extrapolation line has the expression Z = (ln t-ln t ₅₀ )) / S, where Z is a quantity satisfying the equation F ₀ (Z) = p, where F ₀ is the standard normalized normal distribution function. For practical calculations, MS Excel has a built-in function NORMSINV that calculates the value Z in the equation F ₀ (Z) = p from the value p.

It should be noted that at p = 0.5 (the number of failures is 50%), the function F ₀ (Z = 0) is 0.5. Also, the intersection of the extrapolation line with the horizontal axis X is the median failure time 150.

Tables 3-5 show the values of electric currents (I), the deviation of the width from the nominal value (W _offset ) for each conductor, and also the calculated value of the current density (j) (according to formula 7). The value of W _{offset was} determined by electrical measurements on the structures formed nearby.

Table 3 Data of electromigration measurements, Т = 270 ° С. I mA W _offset , microns j, mA / μm ² 86.65 0.122 114.83 90.75 0.059 113.62 85.84 0.089 110.38 89.67 0.016 108.19 89.82 0.036 110.24 88.84 0.036 109.03 91.44 0.057 114.29 85.29 0.107 111.48 87.51 0.059 109.57 86.87 0.122 115.12 86.28 0.036 105.89 86.19 0.096 111.53 89.05 0.061 111.69 90.17 0.016 108.80 88.28 0.025 107.33 89.94 0.024 109.26 87.72 0.061 110.02 87.01 0.114 114.46 85.13 0.096 110.16 85.63 0.024 104.02 90.74 0.025 110.32 88.25 0.057 110.30 88.47 0.036 108.58 84.40 0.12 111.64 84.34 0.14 113.67

Table 4 Data of electromigration measurements, T = 300 ° C. I mA W _offset , microns j, mA / μm ² 95.01 0.045 117.51 94.62 0.058 118.36 88.67 0.13 118.38 88.98 0.138 119.69

86.44 0.138 116.28 93.25 0.048 115.64 84.69 0.168 117.23 87.33 0.082 111.59 96.66 0.008 115.84 85.71 0.134 114.86 92.73 0.014 111.70 91.76 0.058 114.79 88.12 0.082 112.60 87.93 0.074 111.56 90.11 0.071 114.02 94.40 0.074 119.77 87.93 0.116 115.88 87.87 0.071 111.19 89.44 0.048 110.91 87.46 0.151 119.11 90.21 0.082 115.27 84.22 0.14 113.50

Table 5 Data of electromigration measurements, T = 350 ° C. I mA W _offset , microns j, mA / μm ² 99.02 0.075 125.74 93.13 0.045 115.19 91.38 0.111 119.87 89.76 0.176 125.22 92.68 0.119 122.48 92.79 0.146 125.77 88.05 0.129 117.45 97.77 0.061 122.63 98.40 0.074 124.84 96.61 0.019 116.86 95.73 0.074 121.45 90.39 0.114 118.90 87.23 0.087 111.96 92.00 0.165 126.98 93.87 0.075 119.20 95.43 0.061 119.69 89.94 0.131 120.19 89.46 0.193 126.91 90.9 0.198 129.60 90.49 0.086 116.04 94.34 0.143 127.50 89.81 0.082 114.76

92.06 0.082 117.63 85.36 0.114 112.29 97.42 0.019 117.84 97.39 0.05 120.98 95.92 0.143 129.64 93.86 0.142 126.74

Table 6 Summary of electromigration test data for three test temperatures. Test parameter T = 270 ° C T = 300 ° C T = 350 ° C median test time t ₅₀ sec 223.5 114.3 45.82 median values of current densities j during testing, mA / μm ² 110.3 115.45 120.59

From formulas (7) - (9) we obtain: Е _а = 0.492 eV, n = 2.6385, А = 1.338 · 10 ²³ h.

The observed operating time to failure of metal conductors during accelerated testing is much shorter than the duration of their operation under operating conditions. The lifetimes of conductors in real conditions are estimated with knowledge of the operating temperature and current of their operation on the basis of formula (1) with knowledge of the obtained parameters: activation energy E a _and current density index n. The results obtained in this paper can be used both for constructing theoretical models and for determining the electromigration parameters of conductors with various properties.

Application:

The temperature coefficient of resistance of the TCS of the metal conductor is determined, which is equal to 0.00351 ° C ^-1 . The TCS coefficient is calculated on the basis of a linear dependence of the resistance of a metal conductor on R (T) of temperature T in the range of 30 ° C, 45 ° C, 60 ° C, 90 ° C, 110 ° C:

where R ₀ is the resistance of the conductor at room temperature T ₀ = 25 ° C. The supplied current for measuring the resistance was small (20 μA) to prevent thermal self-heating due to the flow of current.

Standards:

JESD63 "Standard method for calculating the electromigration model parameters for current density and temperature", EIA / JEDEC Standard, February 1998.

JESD61 "Isothermal electromigration test procedure", EIA / JEDEC Standard, April 1997.

JESD33B "Standard method for measuring and using the temperature coefficient of resistance to determine the temperature of a metallization line", EIA / JEDEC Standard, 2004.

Articles:

Black, J.R. "Electromigration - A brief survey and some recent results", IEEE Transactions on electron devices ", ED-16, 4, April 1969.

Black, J. R., Current Limitations of Thin Film Conductors, Proceedings of the International Reliability Physics Symposium, 1982, pp. 300-306. IEEE Catalog No. 82CH17227-7.

Oates A. S. "Current density dependence of electromigration failure of submicron width, multilayer Al alloy conductors", Appl. Phys. Lett. 66, 1475 (1995).

Kononenko O.V., Matveev V.N., Field D.P., “The Energy of Activation of Electromigration in Aluminum Conductors Tested by the Drift-Velocity Method, Russian Microelectronics, Vol. 29, No. 5, 2000, pp. 316-323.

Patents:

Patent EP 1978371A, class G01R 31/28, "Electromigration testing and evaluation apparatus and methods", 2008.

US 2003/0080761 A1, class G01R 31/26, "Method and apparatus for accelerated determination of electromigration characteristics of semiconductor wiring", 2003.

US patent 6,350,626 B1, class H01L 21/66, "Method of testing electromigration lifetime", 2002.

US patent 7,660,693 B2, class G06F 3/01, "Activation energy measurement method", 2010.

Claims (1)

A method for evaluating electromigration parameters, consisting of testing metal conductors of integrated circuits at three different temperatures T ₁ , T ₂ and T ₃ , characterized in that in order to reduce test time and increase information content, heating of metal conductors is carried out only by self-heating by flowing electric current with the subsequent calculation of electromigration parameters: activation energies

current density indicator $$n=\{\ln \left(t_{{\mathrm{fifty}}_{\mathrm{one}}}/t_{{\mathrm{fifty}}_2}\right)-E_a\cdot \left(\mathrm{one}/T_{\mathrm{one}}-\mathrm{one}/T_2\right)/k\}/\ln \left(j_2/j_{\mathrm{one}}\right)$$

and
electromigration constant of metal conductors $$A=t_{{\mathrm{fifty}}_{\mathrm{one}}}\cdot j_{\mathrm{one}}^n/\exp \left(E_a/\left(k\cdot T_{\mathrm{one}}\right)\right)$$

where $$\left(t_{{\mathrm{fifty}}_{\mathrm{one}}};{\sout{j}}_{\mathrm{one}}\right)$$

, $$\left(t_{{\mathrm{fifty}}_2};{\sout{j}}_2\right)$$

, $$\left(t_{{\mathrm{fifty}}_3};{\sout{j}}_3\right)$$

- the median MTBF of the metal conductors and the median values of the current densities that heat the conductors to the test temperature T ₁ , T ₂ , T _3, respectively.

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