Pore Corrosion Model for Gold-Plated Copper Contacts

796 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 4, DECEMBER 2007

Pore Corrosion Model for Gold-PlatedCopper Contacts

Amy C. Sun, Henry K. Moffat, David G. Enos, and Carly S. George

Abstract—The goal of this study is to model the electrical re-sponse of gold plated copper electrical contacts exposed to a mixedflowing gas stream consisting of air containing 10 ppb H2S at 30 Cand a relative humidity of 70%. This environment accelerates theattack normally observed in a light industrial environment (es-sentially a simplified version of the Battelle class 2 environment).Corrosion rates were quantified by measuring the corrosion sitedensity, size distribution, and the macroscopic electrical resistanceof the aged surface as a function of exposure time. A pore corrosionnumerical model was used to predict both the growth of coppersulfide corrosion product which blooms through defects in the goldlayer and the resulting electrical contact resistance of the agedsurface. Assumptions about the distribution of defects in the noblemetal plating and the mechanism for how corrosion blooms affectelectrical contact resistance were needed to close the numericalmodel. Comparisons are made to the experimentally observednumber density of corrosion sites, the size distribution of corrosionproduct blooms, and the cumulative probability distribution ofthe electrical contact resistance. Experimentally, the bloom sitedensity increases as a function of time, whereas the bloom sizedistribution remains relatively independent of time. These twoeffects are included in the numerical model by adding a corrosioninitiation probability proportional to the surface area along witha probability for bloom-growth extinction proportional to thecorrosion product bloom volume. The cumulative probabilitydistribution of electrical resistance becomes skewed as exposuretime increases. While the electrical contact resistance increasesas a function of time for a fraction of the bloom population, themedian value remains relatively unchanged. In order to modelthis behavior, the resistance calculated for large blooms has beenweighted more heavily.

Index Terms—Contact resistance, copper, corrosion, modeling.

I. INTRODUCTION

ATMOSPHERIC corrosion of intermittently-mated elec-trical connectors can lead to increased contact resistance

and reduced reliability of the devices that contain them. Typicalmeasures taken to protect such devices include an electroplatedlayer of nickel followed by an electroplated layer of gold. Theprimary purpose of these cover layers is to provide increasedresistance to environmental degradation while maintaining a

Manuscript received November 11, 2005; revised March 21, 2006. This workwas supported by Sandia Corporation (a Lockheed Martin Company) for theUnited States Department of Energy’s National Nuclear Security Administra-tion under Contract DE-AC04-94AL85000. This work was recommended forpublication by Associate Editor J. McBride upon evaluation of the reviewerscomments.

The authors are with Sandia National Laboratories, Albuquerque, NM 87185USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCAPT.2007.906340

low contact resistance, thereby enhancing the long-term relia-bility of the connector. If the electroplated layers are thin, theycan be porous, resulting in exposure of the underlying coppersubstrate. Thus, it is possible for the underlying copper to beexposed to atmospheric contaminants. The nature and extent ofthe porosity varies with the deposition conditions and thicknessof the gold and nickel layers. If extensive enough, the resultingcorrosion product may degrade the electrical performance ofthe connector.

The primary goals of this research are to characterize thedegradation mechanisms of gold-plated copper, as used in mi-croelectronic connectors, and to construct an appropriate mathe-matical model encompassing the key physical phenomena. Thismodel, once calibrated via experimental data, can be used topredict degradation of a noble metal plated copper surface asa function of time. The calibrated corrosion model may thenbe utilized to predict the electrical contact resistance of actualdevices, such as electrical connectors, and then linked with asystem-level electrical model to assess the impact which the cor-rosion process will have on system performance.

In this paper, we build upon our earlier work on understandingthe kinetics of the sulfidation process for pure copper coupons inan H S containing environment with a moving-boundary modelfor pore growth in an effort to understand the corrosion of gold-plated copper [1]–[4]. While the kinetics is expected to be sim-ilar microscopically, there is at least one significant differencewhen comparing the sulfidation of bare copper to that of metal-plated copper. A longer induction period is observed on themetal-plated surface. The induction period for the initiation ofcorrosion at a given defect site varies significantly from site tosite, and is a strong function of the geometric nature of eachdefect site. This variation in induction time is manifested exper-imentally in this study by the continuous nucleation of corrosionproduct blooms through exposure times (multiple months).

Once the model has been assembled, the resulting predictionsof the corrosion process provide the basic inputs for a macro-scopic electrical contact resistance model. To our knowledge,such a complete corrosion-to-electrical resistance model has notbeen cited in other works. Sun et al. have attempted to modelthe growth of corrosion product blooms in over Au/Ni/Cu in theBattelle Class II, mixed flowing gas (MFG) environment [5].While they used a 1-D diffusion equation in Cartesian and cylin-drical coordinates, they did not use a moving boundary approachto locate the extent of the solid corrosion product.

II. EXPERIMENTAL PROCEDURES

Oxygen-free copper coupons (UNS C10100) were electro-plated with ASTM B488 type I, grade C bright gold. Prior to

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SUN et al.: PORE CORROSION MODEL 797

plating, all samples were mechanically polished to a 600 gritfinish using silicon carbide based polishing media (resultingsurface roughness— of 262 nm), cleaned and degreased.Electroplating was conducted at a commercial plating lab usingindustry standard plating procedures. Two different gold layerthicknesses, 1.18 m and 2.49 m, were deposited. In theresults reported here, no Ni underplating was used. Further-more, for conciseness, we will focus on 1.18 m samplesin this paper.

Once prepared, each sample was exposed to a mixed flowinggas stream consisting of air containing 10 ppb H S at 30 Cand a relative humidity of 70%. Samples were monitored peri-odically to document the size distribution of the observed cor-rosion product blooms, the number density of corrosion sites,and the electrical contact resistance of the aged surface. Resis-tance data was acquired utilizing 3-mm diameter hemisphericalgold plated copper probe. Resistance measurements were madeat 30 random sites within a predetermined region of each sampleutilizing an applied load of 30 g. A single set of measurementswas obtained from each area.

III. COPPER SULFIDATION KINETICS

The sulfidation of atmospherically exposed copper occursthrough a chemical reaction between metallic copper and theH S in the gas stream. Previous experimental data measuringthe growth of the copper sulfide layer as a function of exposuretime at different H S concentrations and at different relativehumidity concluded that the growth consisted of two stages,as illustrated schematically in Fig. 1. In stage I, the kineticsof copper sulfide formation is either gas phase mass transportor surface reaction controlled. With time, the growth modetransitions to stage II, where the growth rate is now controlledby diffusion through the bulk sulfide layer and through grainboundaries with the sulfide layer. While the kinetics of thesulfidation reaction in stage I and II have been found to beeffectively independent of relative humidity, the transitionto stage II is impacted by the relative humidity [14], [15].Higher humidity promotes the transition to stage II. Studiesof the initial nucleation of Cu S on bare copper coupons haveshown that the relative humidity has a large effect on the initialstructure of the Cu S formed. Under conditions of high RH, thesulfide film is initially patchy with numerous nodular sulfidenuclei, while at low RH initial film formation is more uniformacross the surface. Cross-sectional TEM images of the resultingsulfide layers indicate that the grain structure also varies as afunction of RH. When formed at low RH, the resulting Cu Slayer is composed of large grains that span the thickness of thefilm, while films formed at high RH consist of small grainswith high porosity between the grains. As such, it is possiblethat the transition to stage II may be related to the evolvinggrain structure of the product layer. Another study where barecopper coupons were exposed at one relative humidity and thenanother shows once the transition to stage II occurs, the filmnever recovers to stage I growth no matter how low the RH isset [6]. To date, the exact mechanism of how the RH changesproduct morphology remains unknown. Given this complicatedtransport mechanism, we have chosen to model diffusion

Fig. 1. Schematic representation of the Cu S growth rate on bare coppercoupons exposed to an H S containing atmosphere. In Stage I, the growth rateis controlled by either gas phase mass transport or surface reaction, while forStage II, the kinetics are dominated by diffusional transport through the bulkCu S layer and grain boundaries within the Cu S layer.

Fig. 2. Schematic of 1-D copper sulfidation corrosion model.

within this system using an engineering-level approximationbased on a single experimentally-fitted effective bulk diffusioncoefficient.

The kinetic model for copper sulfidation used in this work issimilar to the one described by Larson [1]. A one dimensionalschematic of the sulfidation process indicating material domainswhere reactions occur is illustrated in Fig. 2. The model used todescribe the kinetics consists of three parts: the gas-solid surfacereaction which produces copper sulfide, the diffusion of coppervacancies through the Cu S layer, and a solid-solid surface reac-tion involving the injection of a copper atom into the Cu S layerfrom the copper metal causing the annihilation of the copper va-cancy in the Cu S layer.

The H S reacts with copper to form copper sulfide. At

(1)

refers to the reaction rate for copper sulfidation on theair-Cu S interface (mol cm s ). C is the concentrationof hydrogen sulfide in units of mol cm . is the concen-tration of copper vacancies on copper lattice sites within thecopper sulfide. There is a linear dependency on the H S concen-tration to yield stage I growth initially. As copper vacancy buildsup within the corrosion layer, the rate of growth slows, mod-eling slower growth in stage II. Each of the forward and back-ward kinetic parameters in (1) has an Arrhenius-like pre-factor.The units of pre-exponential factors are cm s for and cmmol s for .


The kinetic rate at the interface between the corrosion productand pure copper is defined by . At

(2)

Dissociation of copper vacancies into charged vacancies andelectron holes, as well as the electromigration effect of an in-duced electric potential are ignored in this model. The existenceof an aqueous interfacial phase (i.e., partial or complete mono-layer of water) at the gas-Cu S interface is also ignored. Asmentioned above, the effects of relative humidity can be large,but the exact mechanism is still unknown. This model does notaccount for changes in growth rate due to changes in the relativehumidity. Because the experimental data have been collectedunder a constant relative humidity, the sensitivity to RH is notaccounted for in the model. Diffusion of uncharged species istreated, assuming electroneutrality throughout. A single experi-mentally-fitted effective bulk diffusion coefficient is used to rep-resent the complex transport mechanism in the product layer.

The diffusion of uncharged copper vacancies through theCu S layer is written as a pure diffusion equation

(3)

Equation (3) and its corresponding boundary conditions at thegas-solid and solid-solid interfaces define the concentration dis-tribution of vacancies within Cu S. Due to the volumetric in-crease of the Cu S as the corrosion process progresses, the lo-cation is an unknown. Boundary conditions for (3) incor-porating the reaction kinetics are summarized. At x=X

(4)

and

(5)

At

(6)

and

(7)

where is the concentration flux of copper vacancies (mol cmsec ) based on a moving frame of reference, and is

the mesh velocity, or . Constants andare the stoichiometric coefficients for copper vacancies in thesurface reactions at either end of the domain, which is two at thegas-solid interface and negative one at the solid-solid interface.C is the molar concentration of the copper sulfide lattice,consisting of both vacancies and regularly filled lattice sites, as-sumed to be equal to 3.52 10 mol cm , the value for chal-cocite. At 0, a constant copper vacancy concentration in asmall but finite film thickness is assumed. The initial concen-tration and thickness values, and , have been chosen tominimize the sensitivities to the growth. They are 10 molcm and 1 m, respectively. Because there is no mesh move-ment on the Cu S-Cu interface, the mesh velocity is set to zero

at . Vacancy diffusion coefficient and rate constantsfor the gas-surface reaction were obtained by fitting solutionsof (3)–(7) to a series of growth experiments conducted on flatcopper coupons. Again, the effect of RH was intentionally leftout of this engineering level depiction of Cu S growth duringparameter estimation.

Equations (3) through (7) are applied to a 1-D growth do-main and discretized into multiple control volumes. The controlvolumes exchange copper vacancies via the diffusional flux ex-pression and the movement of the node positions, . All of themesh positions move as a fixed function of the top mesh po-sition, , which is moved according to kinematic boundarycondition due to the growth of the copper sulfide layer. An in-tegral balance is carried out over each control volume in boththe physical and time coordinate in order to form the differenceequations, which are then solved by a predictor-corrector back-ward Euler method.

IV. PORE CORROSION MODEL

A. Addition of Pore Resistance

Mechanistically, we assume that corrosion of gold-platedcopper initially occurs in defects in the gold layer that allowcontaminants to reach the copper surface. Corrosion productsgrow up through these openings and possibly create stressfields that cause blistering or rupturing of the gold layer leadingto greater susceptibility to corrosive attacks. For the H Ssystem we have mostly observed the growth, with little or noblistering of the gold. Therefore, we model the system as beingone which corrosion products grow up via pores. Sphericalflowerlet growth on top of a pore can be modeled as two 1-Dproblems. Fig. 3 provides a schematic. Initially the Cu S willgrow up through the cylindrical pore in 1-D geometry until itspills out on top of the plating into corrosion product bloomgrowth. Then, it can be modeled as 1-D hemispherical growth.At the intersection between the two coordinate systems, thecopper vacancy fluxes must be equated. The boundary condi-tions on the inner sphere must be adjusted to take into accountof the diffusion resistance of copper vacancies through thepore. Diffusion through the pore is modeled via a simple onedimensional film theory model

(8)

The variable is the cross-sectional area of the pore,is the diffusive flux, is the radius of the pore, is

the concentration of vacancies at the bottom of the pore, i.e.,copper–copper sulfide interface. is the concentration ofcopper vacancies at the top of the pore, and also at the surfaceof the spherical shell of the spherical domain. The total vacancyflux must be equal to the diffusive flux into the spherical domainas well as the flux at the bottom of the pore; or (6)

(9)


Fig. 3. Schematic of Cu S growth through a pore.

Through mathematical manipulation of (6)–(9), may beeliminated in order to form a boundary condition for the spher-ical grey region illustrated in Fig. 3

(10)

(11)

Da is defined as the dimensionless Damkhöler number whichcharacterizes the relative importance between reaction rate anddiffusion

(12)

Modeling the corrosion product growth through the two regions(i.e., filling the pore followed by growth of the corrosion productbloom) can be combined into a single simulation if two calcu-lations are run consecutively. In the first calculation, we use aone-dimensional geometry to grow a column of Cu S to a dis-tance equal to the sum of the plating thickness and 2/3 the poreradius. The “2/3 pore radius” number is obtained by equatingthe volume of a cylindrical column with the volume of a hemi-sphere of the same radius. Then, we switch over to a sphericalsimulation, which starts from a thin shell whose radius is equalto the radius of the pore.

Fig. 4 shows a representative growth curve as a function oftime at different pore radii. Each curve shows two regimes as thefirst describes growth through cylindrical pore before it switchesto a spherical growth. The growth rates scale as roughly forcolumn growth versus for spherical growth. After the Cu Scorrosion product layer fills the pore and transitions to a spher-ical structure, the rate of vertical growth of the corrosion productdecreases dramatically. This reduction in rate is the result of sev-eral effects. The first is simply the spherical nature of the corro-sion product bloom; an incremental increase in the height (andhence radius) of the spherical bloom results in a larger increasein volume when compared to growth within pore. Furthermore,

Fig. 4. Representative growth curves as a function of time and pore radius Theplating thickness is one micron. This is an intermediate step in the pore corrosionmodel. Note that the height above the plate is equivalent to the bloom radius.

the copper needed to create that additional volume of corrosionproduct has to diffuse through a pore of fixed cross-sectionalarea. As the pore radius decreases, the mass transport resistanceincreases.

The model thus provides a complete solution to the sourceterm for the formation of corrosion product through an unloadedprecious metal coated copper contact for the H S controlledcopper sulfidation process.

B. Distribution of Susceptible Defects in the Gold Layer

While the corrosion kinetics has been approximated by a de-terministic model, other factors, such as the distribution of de-fects (e.g., pores) in the gold layer susceptible to atmosphericcorrosion, have been addressed by a statistical approach. Givenan initial pore density (number cm ), upper and lowerlimits of pore radii, i.e., and , and a normalized probabilitydistribution , we carry out multiple single-pore growthcalculations to achieve a statistical population of corrosion prod-ucts. In the absence of experimental discovery, we have assumedthat the distribution of pore radii is a logarithmically distributedhat function, where is the normalization constant

number of pores between and (13)

(14)

whereand

Assuming no cross-correlation, the probability of there beingpores within a given area on the surface, defined as ,

follows a Poisson distribution:

(15)

and the probability of there being one or more pores within anarea, , is equal to

(16)


Fig. 5. Recorded site density as a function of time.

C. Corrosion Initiation

An induction mechanism was added to the model in responseto experimental observations that the bloom density increases asa function of time. This is illustrated in Fig. 5, which presents theexperimentally observed number density of corrosion productblooms as a function of time. The time-dependency of site den-sity indicates an induction period for the growth. Longer induc-tion period on gold-plated copper is observed compare to thosereported for bare copper coupons [14]. This increased induc-tion period is the combined effect of the hindered mass transferthrough the various defects in the gold layer, as well as theneed to break down the native copper oxide layer before sulfidegrowth can occur on top. We assume that the onset of growthof Cu S occurs with a finite areal probability, . has units ofcm s . Thus, the onset of growth within the pore is greatlyretarded for smaller pores due to an initialization rate propor-tional to the surface area.

Let be the probability of a pore of size beinguninitialized at time

(17)

(18)

is an adjustable parameter which dictates the time constantsfor the onset of growth. is the rate of initialization ofpore corrosion in pores of cross sectional area, .

Because of initiation, even though the pores of same sizegrow at the same rate, their starting times may be different. Let

be the number of pores with initial area, , havinga height at time . Let be the initial number of pores withcross-sectional area binned around . is a combination heightcoordinate. It spans the two calculations that comprise the poregrowth model. The first calculation is based on 1-D Cartesiancoordinates, while the second calculation is based on 1-D spher-ically symmetric coordinates. is a continuous coordinate rep-resenting the height of the corrosion product above the platingmaterial. Below the plating surface, is equal to the heightof the corrosion product layer in the pore. Above the surfaceof the plating layer, transforms into the radius of the bloom

product when the volume of a hemisphere of radius is equal tothe volume of a cylindrical plug of radius and height(i.e., 2 3 ). In this way, the volumes are matchedwhen transforming the growth model from 1-D Cartesian to 1-Dspherically symmetric coordinates. (19) and (20) describe therelationship between and for the spherical problem,and between and for the initial 1-D problem

for (19)

for (20)

Let be the time-independent growth rate of the cor-rosion product. It is a function of the initial area of the pore, ,and the height of the layer L at time . We assume the ambientgas above the pore remains constant with time, and there are no“loading effects” in the reactor. The equation for the evolutionof the distribution, , and its initial conditions may bedescribed by (21) and (22). These two equations are combinedwith a source term for passivation and solved via the method ofcharacteristics [7]

(21)

and (22)

D. Corrosion Site Passivation

While the number density of corrosion product blooms is ob-served to increase with time, the size-distribution of bloomsremains relatively constant. This is illustrated in Fig. 6 whichshows the corrosion product bloom size distribution at six dis-crete times. Note that the overall average bloom radius does notincrease with time. This, combined with direct experimental ob-servation (not presented here) indicates that a given corrosionsite does not grow indefinitely. While the specific mechanismresponsible for this phenomenon is unclear, there are several po-tential plausible explanations. One such explanation is that thecoalescence of Kirkendall voids at the copper/copper sulfide in-terface has effectively cut off the bare copper surface within acorrosion site from the hydrogen sulfide in the gas phase, re-sulting in the cessation of copper sulfide formation, and hencethe “death” of the corrosion site. This is supported in part via ex-perimental observation of what appears to be void coalescenceat the copper-copper sulfide interface, as illustrated in Fig. 7.Another plausible explanation is that the mode of copper sul-fide formation has transitioned from stage I to stage II growthas observed experimentally for bare copper surfaces (illustratedschematically in Fig. 1), resulting in a dramatic reduction in re-action rate at corrosion site which would appear experimentallyas though the corrosion site had “died.”

In order to capture this phenomenon (i.e., corrosion sitedeath) within the model, a probability-for-passivation sourceterm is added to the time evolution equation, (21). The variable

is redefined to be equal to the concentration of currentlyactive pores

(23)


Fig. 6. Normalized size distribution of bloom sizes of 1.18 �m-plated copper.The bins are in units of microns.

Fig. 7. FIB cross section of a single corrosion site and associated copper sulfidebloom (courtesy of Rob Sorensen, SNL).

We assume that there is a finite probability of passivation thatis proportional to the total volume of copper removed from theunderlying substrate, or proportional to the volume of coppersulfide created in the product layer, divided by the radius of thepore

(24)

is the proportionality parameter. is the volumeof copper sulfide created in the corrosion product layer.

is the number distribution of pores withproduct volume, , at time , that has an initial area . It isrelated to by a change of variables

(25)

We again use method of characteristics to solve for and ,to yield

(26)

where and

.

Fig. 8. Normalized binned distribution of bloom from numerical model. Thebins are in units of microns.

Fig. 9. Predicted bloom distribution function at day 45. The number distribu-tion of actively growing and “dead” corrosion site distributions is shown.

Fig. 8 displays the resulting number distribution binned asper the experimental data. While the addition of the passivationterm has allowed the numerical model to generate the time-in-variability of the bloom-size distribution seen in Fig. 6, sev-eral features of numerical model Fig. 8 are not in agreementwith experiment. The numerical model demonstrates an inordi-nately high percentage of middle sized blooms compared to ex-periment. Both extremely large blooms and a sufficiently highnumber of small blooms do not show up in the numerical model.This may have to do with the simplistic treatment of the phe-nomena used in (24).

Fig. 9 gives more detail about the bloom distribution pre-dicted at day 45. With the exception of small corrosion productblooms (i.e., below 5 m), the population is dominated by deadcorrosion sites, i.e., corrosion sites that have ceased growing. Asthe corrosion product volume at a single corrosion site increases,the probability of corrosion site death also increases, leading tosharp decrease in the number of corrosion product blooms over20 m. Additionally, a small number of pores (relative to theexperimental data) die at the small sizes due to the their smallvolumes. No attempt however has been made to tweak the de-pendence of (24) on , due to the speculative nature of em-ploying these formulations.


V. CONTACT RESISTANCE MODEL

A. Malucci’s Contact Resistance Model

In the previous section, an evolution model for the growth ofcopper sulfide blooms is created and simulated to compare withthe experimental measurements of bloom morphology. Never-theless, it must be linked to a contact resistance model such thatthe impact of corroded surface topology can be coupled to a sim-pler measurable quantity.

There are numerous theories on electrical contact resistance.In particular, Greenwood’s work on electrical contact theoryspawned numerous theoretical developments [8]. The key el-ement of Greenwood’s work is the recognition that there existtwo levels of constriction when two rough metal surfaces makecontact—the first level being the superficial contact area and thesecond level being the contacts through micron-sized asperities.Our approach follows much of Malucci’s extension of Green-wood’s formalism to aging surfaces. [9]–[12]. With the incor-poration of a third-level constriction, the two contributions thatmake up the total electrical contact resistance , namely theapparent contact resistance and the resistance due to asper-ities have the following forms:

(27a)

(27b)

(27c)

, the resistance due to apparent contacting area, is basedon Holm’s formula for contact resistance [11]. is the resistivityof copper. is the diameter of the th contacting asperity. isthe total number of asperities. is a numeric constant set to

. The fractions of exposed metal on both sides of the thasperity are defined as and . is the diameter of theoverall cluster of asperities, and is obtained from the Hertz stressformula for the actual diameter of contact between a sphere anda plate under elastic deformation; i.e.

(28)

is the force applied on contact. is the elastic modulusof contacting metal, and the radius of contacting probe.Malucci provides much of derivations for andwhich we also utilize in our model and will not be repeated here[9], [11].

B. Monte Carlo Simulations of Contact

In order to derive the contact resistance model, we first dividethe calculated bloom distribution into small and large blooms.The total volume of small blooms is assumed to comprise auniform surface corrosion product layer and is used as input toMalucci’s model. If a bloom occupies an area larger than a frac-tion, , of the Hertzian contact area, then the effect of the bloomis treated in a different manner. The bloom fraction cut off, , isan adjustable parameter in the model and set to 0.01. This choiceof reflects bloom population in a subset of “small” and all of

“medium and above” categories. If the bloom area exceeds ,then parts of the Hertzian contact area will be unavailable fordirect contact due to steric hindrance.

Once the contact resistance model and bloom distributions areknown, we apply a Monte Carlo approach to randomly samplethe surface to calculate the resistance of our aging coupons.When the probe lands on a large bloom, heuristic rules are ap-plied to quantify its impact to the overall electrical contact re-sistance. Blooms exceeding the surface roughness criterion afterapplied load will exclude part of the contact area. Additionally,each “large” bloom excludes an area equal to a factor of fourtimes its own area from forming an electrical connection; thisadded correction, an effect which we attribute to the creep cor-rosion around each bloom, i.e., the halo effect, was needed tofit experimental data. We add in conduction through the largebloom in parallel to conduction through the asperities, using theapproximation

(29)

(30)

is the resistance of current due to conduction throughthe bloom, treated as if the bloom were a separate material.

VI. RESULTS

The experiment provides validation data for the pore corro-sion model. Fig. 10 shows the experimentally observed elec-trical resistance data for the tested coupons. For each obser-vation, 30 random resistance measurements are taken on eachsample. As shown in the figure, there is an appreciable tail as-sociated with each cumulative probability distribution after thefirst week, indicating that the few large-size blooms contributeto the most resistance increase in the population. The medianresistance value remains relatively unchanged throughout thisstudy. While notable increase is observed in bloom density, asshown in Fig. 5, the tail in the distribution does not increase be-yond five weeks. We suspect this is due to a break-up of filmstructures from excessive probing.

The simulation results are overlaid upon the experimentaldata in Figs. 5 and 10. Table I summarizes the constants used forthe simulations. The details of the verification and parameter es-timation studies which were performed have been omitted here.Due to the large number of constants in this model, we havecombined some from the literature and some determined by fit-ting the modeling results to our earlier experimental studies.From this comparison study, there are several key points re-garding modeling sensitivities. In order to match the bloom sitedensity in Fig. 5, the total pore site density is adjusted to obtainthe trend observed in the experiments. The upper and lower poresize limits determine the final distribution of electrical contactresistances. The two limits differ by a factor of 43. More im-portantly, we have found that the film contribution from smallblooms raises ECR distribution in the entire population as thecoupon ages, which is not what we observe in the current ex-periment. Hence, we may have overstated the contribution ofsmall blooms in our simulations even though the bloom cut off


Fig. 10. Electrical contact resistance for 1.18 �m coupons.

TABLE IKEY MODEL PARAMETERS USED FOR THE CALCULATIONS

fraction is only set at 0.01. In addition, to reproduce the largetail in the CPD electrical contact resistance, we have had to in-crease the effective geometric interaction area of large bloomsby adding in the presence of “halos” in the blooms. These haloshave been shown to increase electrical contact resistances [13].

Comparing the results from the simulation with experimentaldata, it can be seen that the model roughly predicts the ECRfor the first week. Beyond that time, the increase in resistancedue to growth of the corrosion product film and blooms sur-passes the experiments, yielding distributions higher than ob-served quantities. It is unclear whether the experimental mea-surements are accurately tracking the impact of the increasingbloom density; further investigations are underway due to the

manner with which the electrical measurements were made. Ad-ditional experimentation is in progress to address this issue.

One point worth noting is the verification of the contact as-perity model presented in (27) and (28) is needed. We haveused Malucci’s formulations for finding the number of asper-ities and the degree of metal–metal contact induced by load andload under wipe conditions. In light of our data, the surface con-tact model should be verified against experiments that vary thecontact load, in order to test the validity of the contact asperitymodel.

VII. CONCLUSION

A model describing corrosion of gold plated copper and itseffects on the resulting electrical contact resistance has been de-veloped to study the aging of Au-plated copper electrical con-tacts. Experimentally, Au-plated copper coupons with two dif-ferent thicknesses have been exposed to H S contaminated airand monitored for corrosion products. Site density, site distri-bution, and resistance data were taken over twelve weeks. Thegrowth kinetics is based on earlier work of Larson et al. Wehave included pore-site initiation to account for an increase ofobserved bloom sites as a function of time and have includedbloom passivation to account for relatively time-independentbloom distributions. Simulation results show that the model pre-dicts the experimentally observed electrical resistance data atearly times and over-predicts beyond the first week. This is dueto the continual growth of corrosion film and blooms in thesimulations, whereas the experimental data show little increasein electrical contact resistance as the coupons age. Finally, thedistribution of experimental ECR is particularly biased towardslarge blooms, and the model only partially succeeds at accom-modating this skewness by increasing the contact resistance forlarge blooms. A greater contribution to the ECR due to halofilms around the blooms may be needed to extend the tails inthe ECR distribution found in this set of experimental data.

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Amy C. Sun received the B.S. degree from the University of California atBerkeley and the M.S. and Ph.D. degrees from the University of Pennsylvania,Philadelphia, all in chemical engineering.

She has worked at Sandia National Laboratories, Albuquerque, NM, since1998 on various modeling problems ranging from multiphase fluid flow, pa-rameter estimation and uncertainty analysis, and material models for polymerdecomposition. She is currently with the Geohydrology Department developingdynamic models for sustainable water resources.

Harry K. Moffat received the B.A. degrees in math and physics from the Uni-versity of Pennsylvania, Philadelphia and the Ph.D. degree in chemical engi-neering from the University of Minnesota, Minneapolis, in 1992.

He has worked at Sandia National Laboratories, Albuquerque, NM, on var-ious projects involving the development of unstructured finite element codes tobe used on massively parallel computers for reactive flows, the developmentand application of CVD chemistry mechanisms, the development of sectionalmethods for tracking particle growth, and the development of models for theprediction of corrosion events in electronic devices.

Dr. Moffat is a member of the MRS, AIChE, SIAM, and NACE.

David G. Enos received the B.S. degree in materials engineering from Rensse-laer Polytechnic Institute, Troy, NY, in 1991, and the M.S. and Ph.D. degreesin materials science and engineering from the University of Virginia, Char-lottesville, in 1997.

He joined Sandia National Laboratories, Albuquerque, in 2001, where he ispresently a Principal Member of the Technical Staff in the Materials ReliabilityDepartment. His present research activities are in the areas of aqueous and at-mospheric corrosion.

Carly S. George received the B.S. degree in biology from the University ofNew Mexico, Albuquerque, in 2003 and is currently pursuing the M.S. degreein environmental management at Arizona State University, Tempe.

She has worked at Sandia National Laboratories, Albuquerque, since 1997where she is currently a Senior Technologist in the Materials Reliability De-partment.

Documents

Pore Corrosion Model for Gold-Plated Copper Contacts