CURRENT LIMITATIONS OF THIN FILM CONDUCTORS

James R. BlackMotorola Semiconductor Products Sector

5005 E. McDowell RoadPhoenix, AZ 85008

(602) 244-6201

Electromigration in thin film conductors is recog-nized as a potential wear-out failure mechanism forsemiconductor devices. Design guidelines have been es-tablished limiting the maximum current densities foraluminum and aluminum alloy conductors. With the devel-opment of new lithography and etching techniques en-abling the construction of very small conductors andspacings the validity of these guidelines has beenquestioned. Utilizing known experimental data of thelifetime of Al, Al 2% Si and Al 4% Cu 2% Si conductorsnew guidelines are presented which define the maximumdesign current density as a function of the conductortemperature and the conductor current. These maximumcurrent densities established by electromigration con-siderations are further limited by the product of thethicknesses of the conductor and the underlying di-electric thickness which determine conductor tempera-ture gradients caused by the conductor rise in tempera-ture above that of the substrate. Data are presentedfor the above metal films on vitreous silica.

Introduction

The electromigration wear-out mechanism of thin filmconductors carrying high current densities at elevatedtemperatures is recognized as a factor which can leadto semiconductor device failure. Guidelines have beenestablished which limit the design maximum current den-sity for aluminum and aluminum alloy film conductors to2 x 105 and 5 x 105 A/cm2 respectivelyl. The questionhas arisen as to the validity of these guidelines. Itis the purpose of this paper to evaluate the known elec-tromigration experimental data of Al, Al/Si and Al/Cu/Sithin film conductors in order to establish maximum de-sign current densities as a function of conductor tem-perature and conductor current. A limit to the maximumcurrent densities set by temperature gradients due toJoule heating of the conductors is also attempted.Finally, the combined current density limits due toelectromigration and&temperature gradients is presented.

Electromigration Current Density Limits

Figure 1 presents an Arrhenius plot of experimentaldata obtained at our laboratory for glass passivated Al,Al 2% Si and Al 4% Cu 2% Si thin films. Al and Al 2% Sibehave similarly and the data for the silicon alloy hasbeen published previously2.

Experimentally groups of conductors are stressed atelevated current densities and temperatures. The timeof each device failure due to an open circuit is record-ed for each group and these are observed to follow a log-normal distribution. The time required for 50% of thedevices in each group to fail is plotted in Figure 1 forthe 50% failure line. Experimentally knowing the aver-age lognormal failure distribution (a) to be 0.4 for allof the sample groups stressed at various temperaturesand current densities the other failure rate plots (10%,1%, 0.1% and 0.01%) are then constructed.

The cross sectional area of the conductor (wt) ap-pears in the numerator of the empirical expression be-cause it has been experimentally determined that forconductors whose width is greater than the average metalgrain size, the median lifetime T50 is a direct functionof the conductor cross section. A small void generated

by electromigration in a small cross sectional areaconductor would be fatal while that same sized void ina larger conductor would not be significant.

The power of the current density (J) was experimen-tally obtained by plotting the log of the lifetime (50%fail) in hours of groups of identical samples stressedat the same temperature against the log of the currentdensity. The slope of this plot is slightly greaterthan 2 indicating that the power of J is close to 2.

Since Tx, the time for x percent of the group tofail in hours, is in the denominator of the empiricalexpression on this plot lifetime increases as one goesdown the ordinate.

Since the experimental data follows an Arrhenius re-lationship one can obtain an expression for the empir-ical factor to be:

wt = P exp (-¢/koK)3 Tx

where: w =t =J =

Tx =P =

k =OK=_

(1)

conductor film emitter in cmconductor film thickness in cmcurrent density (amperes/cm2)time for x percent failures (hours)a constant dependent upon percent failand film composition

activation energy in electron voltsBoltzman's constant (8.62 x 10-5 eV/OK)film absolute temperature.

It should be emphasized that the power of J and theactivation energies obtained by the above described ex-periment relate only to the failure of a thin film con-ductor of the given composition which fail due to anopen circuit by electromigration processes. At the op-erating temperatures of semicondcutor device thin filmconductors the atom flux due to electromigration takesplace mainly down grain boundaries. Also, theoretical-ly3 and experimentally4 (using methods where the con-ducting film is not failing) it has been shown that thepower of J is unity for mass transport by electromigra-tion. In a failing conductor, however, the current den-sity, the temperature and the volume resistivity of thefailing member of the conductor are not constant. Thereis no intent to imply that the activation energies andthe power of J obtained with experimental methods uti-lizing failing conductors apply to the mass transportof aluminum down grain boundaries. The activationenergies and the power of J obtained by measuring theT50 lifetime of groups of conductors are simply thoserelating to conductor lifetime which is of interesthere.

The data presented in Figure 1 and the discussionwhich follows relate only to conductor films which arewider than the average grain size of the aluminum filmfrom which they are constructed. As the conductor'swidth is reduced and approaches or becomes less thanthe average grain size, the structure begins to "bam-boo," that is, most of the grain boundaries becomenormal to the electron flow and the relationships shownin Figure 1 no longer apply.

CH1727-7/82/0000-0300$00.75 © 1982 IEEE/PROC. IRPS 300

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metal fatigue due to the disparity in thermal expan-sion coefficients between the conductor and substratecould promote conductor failure under pulsed condi-tions. It is of interest, therefore, to calculate therise in temperature of a thin film aluminum or aluminumalloy conductor over that of a silicon substrate as afunction of current density when the conductor is sup-ported by a thin vitreous silicon dioxide film.

The definition of thermal conductivity of a materialx is: watts

cm - watts (10)x= C cm oCcm

The temperature rise of a thin metal film of thicknesstm, width wm and length Im on a dielectric film ofthickness td and thermal conductivity X is:

watts tAT = l (11)

where watts is the power dissipated in the conductor.This power dissipated in the conducting film can be ex-pressed as:

watts = PJ2 lmwmtm (12)

where P = volume reistivity of the metal (ohm-cm)J = current density in the metal film (A/cm2)

Substituting equation (12) into equation (11)pd2 t t

AT = m dx

(13)

where both P and x are temperature dependent. It isof interest to note that the temperature rise of theconductor over that of the substrate is independent ofthe lateral geometry of the conductor. The temperaturerise is a direct function of the metal volume resistiv-ity, the metal thickness, the dielectric thickness andthe square of the current density. The temperaturerise also varies inversely with the thermal conductivityof the dielectric. As the conductor thickness increases(for a constant current density) the wattage dissipatedin the conductor increases. Also as the dielectricthickness increases the dielectric thermal resistanceincreases. Thus the product of the metal and dielectricthicknesses is an important factor in determining theconductor temperature.

Equation (13) ignores thermal flux spreading at theedges of the metal film in the dielectric and should bequite accurate until the width of the metal film ap-proaches or becomes less than the thickness of the di-electric film. The error is conservative since theconductor would be cooler than calculated.

The volume resistivity of pure bulk Al as a functionof temperature is5:

P = 2.42 x 10-6 (1 + 4.752 x 10-3oC) (14)

Substituting equations (14) and (15) into equation (13)and assuming that the dielectric temperature was theaverage temperature of the substrate and the metal , thisequation was solved iteratively to determine the Almetal film temperature as a function of the metal cur-rent density and the product of the thicknesses of themetal and the dielectric film with the silicon tempera-ture being 200C. This is presented in Figure 6 whereit is seen that the temperature increases rapidlywith current density.

A 1 pm thick aluminum conductor on a 1 pm thickvi reous silicon dioxide film would use the 1 x 10-8cm tmtd curve which doesn't appreciably rise in tem-perature at 5 x 105 A/cm2 but at a current density of5 x 106 A/cm2 will reach 800C. At a current density of1 x 107 A/cm2 the film would reach temperature of 500C.Note that the melting temperature of pure aluminum is660% and aluminum in contact with silicon will form aeutectic which melts at 570C. This'same low meltingeutectic is formed by the chemical reaction of Al andSiO2 above 4500C. Even if a metal was available whichis very resistant to electromigration there appears tobe a temperature barrier whi%h limi4s the maxi r,m cur-rent density to the high 100 A/cm or low 10 A/cm2range.

The thermal conductivities of other useful dielec-tric films for the semiconductor industry must be bet-ter understood. It is believed that the thermal con-ductivity of polyimide films is less than that of Sio2.The thermal conductivities of the various silicon ni-tride are of interest. Also, the use of multilayeredmetal and dielectric film structures will further com-plicate the analysis.

At the present time the effect of the magnitude ofthe rise in temperature of the conductor above the sub-strate temperature on electromigration conductor failureis not known. In an ohmic contact region where the con-ductor film typically rises up over a 1 pm thick SiO2film a temperature rise of 10C would introduce a temper-ature gradient of I x 104oC/cm. If the electron flow isin the direction of the + thermal gradient mass will beremoved from the high temperature region faster thanmass is brought to that region from the cooler conduc-tor. This introduces a site for early electromigrationfailure. Since film temperature varies as the squareof the current density it was believed conservative,using equation (13), to calculate the current densitywhich would raise the aluminum conductor film tempera-ture one degree centigrade over that of the substrateas a function of film temperature and the product ofthe thicknesses of the aluminum metal and the SiO2dielectric. These data are presented in Figure 7.The current density decreases slowly with temperaturesince the volume resistivity of the aluminum increaseswith temperature at a faster rate than does the thermalconductivity of the Si02.

For the case of 1 pm thick metal on 1 pm thick 5iO2the maximum current density which limits the conductortemperature rise to 10C varies with temperature between6 x 105 and 7 x 10i A/cm2. A temperature rise of ohehalf degree centigrade would limit the maximum currentdensity for such a film to about 3 x 105 A/cm2.

The National Bureau of Standards has published a graphof the thermal conductivity of high purity fused quartzas a function of temperature.6 An equation of a curvewhich closely fits this data is:

X = 2 x 10-8(oC)2 + 3.84 x 10-6(oC) + 1.43 x 10-2 (15)

Since the volume resistivities ofAl 4% Cu 2% Si are quite similar.rises calculated for Al were assumedal 1 oys.

Al, Al 2% Si andThe temperature

to apply for the

Combined Electromigration and TemperatureGradient Jmax Limits

Using the 1°C temperature rise data to determine302

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the maximum current densities limited by Joule heating,the associated product of the Al and SiO2 thicknesseswere plotted along with the minimum conductor crosssectional area limited by electromigration characteris-tics for Al and Al 2% Si as presented earlier in Figure2. This is shown in Figure 8. For 1 vm thick Al on1 pm thick SiO2 the region on ths grzaph above and tothe right of the tmtd = 1 x 10- cm dashed line isforbidden. Only by making the conductor thickness orthe dielectric thickness thinner (or both) can oneenter this region without generating an excessive con-ductor temperature rise.

The maximum current density limited by electromi-gration considerations for Al and Al 2% Si alloy con-ductors as presented in Figure 3 is shown in Figure 9with limits imposed by temperature rise of 10C estab-lished by the product of the thicknesses of the metaland dielectric. The region of this plot above themetal and dielectric thickness product are inaccessibledue to excessive temperature rise.

Graphs similar to those of Figures 8 and 9 are pre-sented in Figures 10 and 11 for Al 4% Cu 2% Si on SiO2.From Figure 10 it is seen that for 1 pm thick metal on1 pm thick SiO2 a conductor carrying 1 A current cannotbe narrower than 150 im (6 mils) no matter how cool thesubstrate is. Figure 11 shows that the maximum currentdensity for the above described film is limited to 6 x105 A/cm2 by the film temperature rise due to Jouleheating.

Concl usions

1. Contrary to the present maximum current density-design guidelines which establish a fixed maximum cur-rent density for Al and Al alloy conductors, it has beenshown that the maximum design current density is avariable being a function of conductor temperature andthe conductor current.

2. From present electromigration data the maximumdesign current density and the minimum conductor crosssectional area for Al, Al 2% Si and Al 4% Cu 2% Si filmconductors has been presented as a function of conductorcurrent and conductor temperature to provide 0.01% fail-ures in 1 x 105 hours operational d.c. life. These dataapply to conductors whose width exceed the metal grainsize.

3. The maximum design current densities and theminimum design conductor cross sectional areas are lim-ited by the product of conductor and dielectric thick-nesses due to temperature gradients in the conductoror the temperature rise of the conductor. Design curveshave been presented for the conductor temperature riseover the substrate being limited to 10C.

4. The maximum current densities and minimum con-ductor cross sectional areas for conductors carryingvery small currents are severely limited due to theirvery small sizes which are sensitive to the formation ofvery small voids.

5. The thermal conductivities of useful dielectricfilms such as polyimide and the various types of Si3N4as a function of temperature should be better charac-terized.

6. The sensitivity of conductor life to tempera-ture gradients during electromigration stress should bebetter understood.

Acknowl edgmentThe assistance of Mr. Jack Scannell in obtainingthe Al 4% Cu 2% Si data presented in Figure 1 is grate-fully acknowledged.

Bi bliograhy

1. Mil-Standard 38510-D, Rome Air Development Center,Griffiss Air Force Base, Rome, New York.2. J. R. Black, "Electromigration of Al-Si AlloyFilms," 16th Annual Proceedings Reliabilty Physics,1978.3. H. B. Huntington and A. R. Grone, "Current Induced

Marker Motion in Gold Wires," J. Phys. Chem. Solids,20, 76 (1961).4. I. A. Blech, "Electromigration -in Thin AluminumFilms on Titanium Nitride," J. Appl. Physics, 47,1203 (1976).5. K. R. Van Horn, Ed., "Aluminum"' American Society forMetals, Metals Park, Ohio, Vol. 1, 9 (1967).6. "Thermal Conductivity of Selected Materials," NRDS-NBS 9, U.S. Dept. of Commerce, National Bureau ofStandards, Nov. 25, 1966.

7. Multilayered conductor structures will have moresevere limits than the single layer structure presentedhere.

CONDUCTOR TEMPERATURE (°C) (°K-1 SCALE)

H4356FIGURE 1

303

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MINIMUM CONDUCTOR CROSS SECTIONAL AREAFOR GLASSED Al AND Al 2% Si FILM CONDUCTORS

10-5

Q 10-64a:

-iJ

z0

C.)U'U)U) 10-7Ur)Co0C):0C.az0

E 1°-8

10 'g

2

z2

1071 200 180 160 140 120 100 80 60 40CONDUCTOR TEMPERATURE (6C) (6K-1 SCALE)

FIGURE 2

MAXIMUM CURRENT DENSITY FOR GLASSEDAl or Al 2% Si FILM CONDUCTORS

200 180 160 140 120 100 80 60 40CONDUCTOR TEMPERATURE (6C) (K-1 SCALE)

FIGURE 3

25

25

MINIMUM CONDUCTOR CROSS SECTIONAL AREA FORGLASSED Al 4% Cu 2% Si FILM CONDUCTORS

10:

4 105 ~~~~~CONDUCTOR CURRENT6105 IS JCONTOURS(

U10~~~~~~~ 0

4~~~~~~~~~~~~~~~~10Z I7;0s61

Ct 10x10C')J(/c 2

0

0

20 6

E

10

CONDUCTOR TEMPERATURE (-C) (K -I SCALE)

FIGURE 4H4362H4364-1

MAXIMUM CURRENT DENSITY TO PROVYDE 0.01%FAILURES IN 10 HOURS FOR Al 4% Cu 2% Si

GLASSED FILM CONDUCTORS AS A FUNCTION OFCONDUCTOR CURRENT AND TEMPERATURE

106

4EU

E

105

2.0

H4359-1

10 12C6200 180 160 140 120 100 80 60 40 25II I I I I I I I I

2.2 2.4 2.6 2.8 3.0 3.2CONDUCTOR TEMPERATURE (°C) (°K-1 SCALE)

FIGURE 5

3.4

H438

304

106

IE 0E

115

I I I I I I

V

-t a I

in7.

1 U(4 - Inm -I I a -1 IIIV -

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Al FILM TEMPERATURE versus CURRENT DENSITYAND THE PRODUCT OF THE Al AND Si02 THICKNESSES.

TEMPERATURE OF SUBSTRATE = 20°C.I~~~~~~~~~~~~~~~~C

1 X10

e e e , , ,D -/ N

I1 I --

x 107

J (AIcm2)

FIGURE 6

1 x 108

H4373A-1

J versus TEMPERATURE AND THE PRODUCT OF THETHICKNESS OF THE METAL AND THE SiO2 FOR I°C

CONDUCTORTEMPERATURE RISE10Jo

107

106

J05

200 180 160 140 120 100 80 60 40

CONDUCTOR TEMPERATURE (°C) (°K-1 SCALE)

FIGURE 7

MINIMUM CONDUCTOR CROSS SECTIONAL AREAversus CURRENT WITH METAL AND SiO2 THICKNESS

LIMITATION FOR Al and Al 2% Si10 -

E10-

Ul

cc

a:

-J

4

z0

LU

10-C')

0

cc

C.)

0

a

z

0

2) 102

25

H4357-1

200 180 160 140 120 100 80 60 40CONDUCTOR TEMPERATURE (2C) (K- SCALE)

FIGURE 8

25

H4361

305

w

:I-4

ccw

CL2

-l 100cc

0

z0

10 L.1 x 105

_ 2 x 10-71 x 10-

10-7_

tmtd (cm2)

t2td(Cm2)

1 X 10-10

2 x 10-12

4 x 10-10

1 2x 10-9

24x 10-9

21x 10-1

4 x 10-

1 x to-

4 x 10-7

1 x 10-7

x2 10-7

x 10-e12x 10-

1IX 10-5

104 Jr Jr I I i 10U,_::_' : _ :V

1non

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MAXIMUM J FOR GLASSED Al AND Al 2% Si FILMCONDUCTORS WITH METAL AND Si02 FILM

THICKNESS LIMITS106

ro6~~~~~~~~~~~~~.10_

x 1l0

m~~~~~~~~~~~~~~~~~X10-7

4 'x 10 *

1,1 (CM2)

1 6 10 '

CONDUCTOR CURRENT

t-- - 6,1 (CM2)

104 J c vi i I 40 25waU IOU ]Du 14U l=U lUU so 60 40 25CONDUCTOR TEMPERATURE ('C) ('K-1 SCALE) H4356-1

FIGURE 9

MINIMUM CONDUCTOR CROSS SECTIONAL AREA FORGLASSED Al 4% Cu 2% Si FILM CONDUCTORS WITH

Si02 AND METAL THICKNESS LIMITS10-5i

CJi-U 10-4LUa:

z0:0cnco 10-

0a:

0-)

010-

2

109

FIGURE 10

MAXIMUM CURRENT DENSITY FOR PASSIVATED Al 4%Cu 2% Si FILM CONDUCTORS ON Si02 versusCONDUCTOR CURRENT AND TEMPERATURE WITHMETAL AND SiO2 THICKNESS LIMITS107

1 x 10b CONDUCTOR CURRENT

_t1,ld (cm2)

_ Z , / ~~~~~~~~~~~~x10 -9

106

< IEE

Jo'

l0~-~X 106

Xf(cm2)

1 x 10-5

104 I I I I1 I lI I _ 1 1200 180 160 140 120 100 80 60 40 25CONDUCTOR TEMPERATURE ('C) ('K - SCALE) H4355-1

FIGURE 11

H4363

306

. ..c

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