NASA Technical Reports Server (NTRS) 20150002117: Insulation Resistance Degradation in Ni-BaTiO3 Multilayer Ceramic Capacitors

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IEEETRANSACTIONSONCOMPONENTS,PACKAGINGANDMANUFACTURINGTECHNOLOGY 1
Insulation Resistance Degradation in Ni–BaTiO
3
Multilayer Ceramic Capacitors
Donhang (David) Liu
Abstract—Insulation resistance (IR) degradation in reducing atmosphere to avoid oxidation of the electrodes.
Ni–BaTiO3(cid:3)multilayer(cid:3)ceramic(cid:3)capacitors(cid:3)has(cid:3)been(cid:3)characterized(cid:3) Despite the reoxidation process, there is still a signifi-
by(cid:3)the(cid:3)measurement(cid:3)of(cid:3)both(cid:3)time(cid:3)to(cid:3)failure(cid:3)(TTF)(cid:3)and(cid:3)direct(cid:3)
cant amount of oxygen vacancies that are accommodated
current(cid:3) leakage(cid:3) as(cid:3) a(cid:3) function(cid:3) of(cid:3) stress(cid:3) time(cid:3) under(cid:3) highly(cid:3)
in the BaTiO dielectric layers. The failure mechanism of
accelerated(cid:3)life(cid:3)test(cid:3)conditions.(cid:3)The(cid:3)measured(cid:3)leakage(cid:3)current- 3
time(cid:3)dependence(cid:3)data(cid:3)fit(cid:3)well(cid:3)to(cid:3)an(cid:3)exponential(cid:3)form,(cid:3)and(cid:3)a(cid:3)char- BMEMLCCsisthoughttobedominatedbytheelectromigra-
acteristicgrowthtimeτSD canbedetermined.Agreatervalueof tion of oxygen vacancies through the grain boundaries in the
τSD representsaslowerIRdegradationprocess.Oxygenvacancy dielectriclayers[5]–[8].Waser[9],Waseretal.[10],[11],and
migration and localization at the grain boundary region results
Baiatu et al. [12] studied the IR degradation in ambient-fired
in the reduction of the Schottky barrier height and has been
SrTiO ceramic and acceptor-doped single-crystal SrTiO .
found to be the main reason for IR degradation in Ni–BaTiO3 3 3
capacitors. The reduction of barrier height as a function of The results showed that IR degradation begins with oxygen
timefollows an exponentialrelation of φ(t)=φ(0)e−2Kt,where vacancy electromigration toward the cathode with respect
the degradation rate constant K = K0e(−Ek/kT) is inversely to time, field, and temperature. Segregation of defects and
proportional to the mean TTF (MTTF) and can be determined dopants is found at the grain boundaries during the sintering
using an Arrhenius plot. For oxygen vacancy electromigration,
process and results in the formation of space-charge layers at
a lower barrier height φ(0) will favor a slow IR degradation
process, but a lower φ(0) will also promote electronic carrier the grain boundaries.
conductionacrossthebarrieranddecreasetheIR.Asaresult,a The formation of double Schottky depletion layers at the
moderatebarrierheightφ(0)(andthereforeamoderateIRvalue) grain boundaries of ceramic BaTiO and their impact on the
3
with a longer MTTF (smaller degradation rate constant K) properties of BaTiO ceramics was first proposed in [13] to
3
will result in a minimized IR degradation process and the most
explain the unique positive temperature coefficient of resis-
improvedreliabilityinNi–BaTiO3multilayerceramiccapacitors.
tance (PTCR) behavior around the Curie temperature, which
Index Terms—Barium titanate, ceramic capacitors, dielectric
onlyexistedindonor-dopedsemiconductingBaTiO ceramics.
3
degradation, insulation resistance (IR), reliability.
This model indicates that the depletion barriers are formed
because of the electron trapping by acceptor states at grain
I. INTRODUCTION boundaries. Jonker [14], [15] later extended the Heywang
INSULATION resistance (IR) degradation related to model, considering the influence of ferroelectric polarization
on resistivity below the Curie temperature.
oxygen vacancy migration has been considered to be the
In BaTiO -based MLCCs, the depletion layers are believed
primary cause of reliability degradationof multilayer ceramic 3
not only to be depleted of electron carriers and therefore to
capacitors (MLCCs) with base-metal electrodes (BMEs). The
be highly resistive but also to act as electrical barriersagainst
behavior is characterized by a slow increase in the leakage
oxygen vacancy electromigration and, thus, to slow down the
current under an applied direct current (dc) field stress.
degradation process [2], [10], [16]. Although high-resistance
TorevealIRdegradationinatimelymanner,MLCCsareoften
depletion layers both at grain boundaries and at electrode
degradedunderhighlyacceleratedlifetest(HALT)conditions
interfaces limit electronic conduction and the transport of
with different temperatures and applied voltages. Previous
oxygen vacancies across dielectric layers, oxygen vacancy
studies have shown that there are three possible factors
migration is either trapped near the grain boundary depletion
related to the IR degradationof BaTiO -based BME MLCCs:
3
layers or blocked by electrode interfaces, and these charged
the dielectric layer, the BaTiO grain boundaries, and the
3 oxygenvacanciesareneutralizedbythereductionofTi4+near
Ni–BaTiO internal electrode interfaces [1]–[4].
3
the cathode and the rare-earth (RE) doping in the BaTiO
Unlike traditional BaTiO -based MLCCs with precious- 3
3
dielectric. This agrees with a number of recently published
metal electrodes (PMEs), BME MLCCs are cofired in a
worksaboutfirst-principlescalculationsofREelementdoping,
Manuscript received December 5, 2013; revised July 11, 2014; accepted the local atomic configuration, and the solution energy of
November 7, 2014. Recommended for publication by Associate Editor oxygen vacancies [17]–[19].
F.G.Canavero uponevaluation ofreviewers’ comments.
Inthispaper,theIRdegradationinNi–BaTiO MLCCswas
The author is with the ASRC Federal Space and Defense, NASA 3
Goddard Space Flight Center, Greenbelt, MD 20771 USA (e-mail: investigatedforthreecommercialBMEcapacitorsqualifiedto
[email protected]). thesamereliabilitylevelbutmadebydifferentmanufacturers.
Color versions of one or more of the figures in this paper are available
This paper provides insight into the time-dependent corre-
onlineathttp://ieeexplore.ieee.org.
Digital ObjectIdentifier 10.1109/TCPMT.2014.2374576 lations among oxygen vacancy migration, vacancy trapping,
2156-3950©2014IEEE.Personaluseispermitted, butrepublication/redistribution requires IEEEpermission.
Seehttp://www.ieee.org/publications_standards/publications/rights/index.html formoreinformation.
2 IEEETRANSACTIONSONCOMPONENTS,PACKAGINGANDMANUFACTURINGTECHNOLOGY
TABLEI
SPECIFICATIONSANDCALCULATEDE(kV/mm),ANDVOLTSPERGRAIN(V/GRAIN)
and the depletion layer height. A theoretical model based were tested for each stress condition and for each capacitor
on the oxygen vacancy migration and entrapment at grain type.
boundary is proposed to show the relationship between the The traditional HALT measures only the time-to-
reliability,characterizedbymeantime to failure(MTTF),and failure (TTF) data of each capacitor at a given stress
the depletionlayerheightreductionduringthe IRdegradation condition, and then uses a statistical model to determine
in the BaTiO dielectric materials of BME capacitors. the MTTF data at this stress condition [19]–[22]. This
3
approach is based on a single failure mode assumption and
is adequate for most ceramic capacitors with precious-metal
II. EXPERIMENTALPROCEDURE
electrodes (PMEs). However, as has been previously
Three automotive-grade commercial BME capacitors, shown [26]–[29], many BME capacitors, when degraded
AA47450, AB47450, and AC47450, with the same under HALT conditions, reveal a more complicated failure
chip size, capacitance, and rated voltage, but made by mechanism with two distinct failure modes. A recently
different manufacturers, were selected for this paper. These performed failure analysis of these degraded BME capacitors
BMEcapacitorswerequalifiedperAEC-Q200,aspecification also confirmsthe existenceof two distinctfailure modes[37].
documentdevelopedbytheAutomotiveElectronicsCouncilof For this reason, the measurement of TTF data alone will not
United States for ceramic capacitors and passive components result in an accurate prediction of the reliability life of these
usedinharshautomotiveenvironments.Themicrostructuresof BME capacitors. To characterize the multiple failure modes
thethreeBMEcapacitorlotswereinvestigatedbycrosssection in BME capacitors, the leakage current was also monitored
processingof fiveunitspercapacitortypeandwere examined in situ and was measured every 1–3 s for each capacitor unit.
using a scanning electron microscope to reveal the number The reliabilitylife of a capacitoris, thus,notonlydetermined
of dielectric layers, average grain size, and average dielectric by the TTF data but also by the measured leakage current
layer thickness. data used to distinguish the failure modes. To differentiate
Table I summarizes the specifications, number of dielectric this new approach from the traditional single-failure mode
layers, corresponding electrical field (V/thickness), and volts HALT that measures TTF data only, this modified method
per grain at a given stress condition used to degrade the that has been used with multiple failure modes has been
capacitors to reveal their failure modes. The electric field can dubbed highly accelerated life stress testing (HALST) [29].
becalculatedbydividingthemeasureddielectricthicknessby The term HALST is used throughthe remainderof this paper
the applied voltage. The volts per grain (the voltage applied as appropriate.
to each individual BaTiO grain) can be calculated using the When IR degradation is accelerated under HALST condi-
3
dielectricthicknessandmeasuredaveragegrainsizedatafrom tions,a certainvalueofIRorofleakagecurrentmustbeused
the microstructure analysis. asthefailurecriterionatwhichtheTTFcanbedetermined.Per
The results in Table I show that at a given applied voltage, MIL-PRF-123,BaTiO3-basedMLCCsbuiltforhigh-reliability
the values of volts per grain are very similar among the three applications were constructed with a minimum dielectric
BME capacitor lots, indicating that these capacitors are not thickness of 25 μm for rated voltages greater than 50 V.
only manufactured and qualified to the same reliability level In this case, the leakage current level was very low, even
buttheywillalsohaveasimilarappliedelectricalstrengthdur- underHALSTconditions.TheMLCCwasconsideredafailure
ing degradation.The three BME capacitor lots were degraded whenIRatagivenstressconditionwasdegradedthreetofour
together under the same HALT temperature and applied volt- ordersbelowitsinitialvalue[20],[21].Waser etal.[10]have
age conditions, as shown in Table I. Twenty BME capacitors also defined characteristic lifetime tch at which the leakage
LIU:IRDEGRADATIONINNi–BaTiO3MLCCs 3
Fig. 1. Leakage current as a function of stress time for the three BME capacitor lots, degraded at 155 °C, 250 V. The plots were made with the same
x-axis scaletoreveal thedifference inTTFdata.
current has risen one decade above its minimum value to TABLEII
evaluatethedegradationrate.WiththeprogressinNi–BaTiO MTTFDATAOFTHETHREEBMECAPACITORLOTS
3
MLCC development, dielectric thicknesses have been signif- ATVARIOUSSTRESSCONDITIONS
icantly reduced, even below 2 μm [22]. As a result, leakage
current has increased significantly, and Ni–BaTiO MLCCs
3
are considered to have failed at a fairly low IR value. Some
reportsdefinetheTTFasthetimeatwhichIRisdegradedtoa
valueof500k(cid:2)[22],[23],1000k(cid:2)[24],or10%ofitsinitial
value [4], while others set a constant leakage current limit at
100 μA for all of the stress conditions being used [25]–[29].
After a review of most of the failure criteria that have been
reported for determining the TTF of MLCCs with BaTiO
3
dielectrics, the author decided to use a single current limit of
100 μA to determine the TTF for all stress levels and for all TheplotsinFig.1havethesamescaleonthex-axis.Itcanbe
MLCC samples, based on the following considerations. seenthatthesecapacitorlots,whendegradedatthesamestress
During HALST, each MLCC unit was connected in series condition, revealed significantly different TTF data. Further
to a current-limiting resistor with a dc power supply. The details about the characterization of the failure patterns and
voltage dropacross the series resistor was measured and used about the method to determine the acceleration factors have
to calculate the leakage current of the capacitor. Since the been discussed in [29].
voltage drop on the current-limiting resistor is dependent on A two-parameterWeibull plotcan be made when TTF data
the current value, a leakage current higher than 100 μA can at a given stress level are available. The MTTF, a statistical
resultinavoltagedroponthecurrent-limitingresistorofmore parameter that measures reliability, can be determined as
than 5% of the overall applied voltage. This is true for a MTTF=ηΓ(1+β−1) (1)
numberof BME capacitorswith thin dielectriclayersthatcan
be degraded under fairly low applied voltages. Although this where slope β is the dimensionless shape parameter whose
voltagedropcanbereducedifasmallervalueresistorisused, value is often characteristic of the particular failure mode,
the voltage value reading on a small resistor may be too low η is the scale parameter that represents the time at which
to ensure the accuracy of the IR measurement. For example, 63.2% of the population has failed, and Γ(x) is the gamma
whenanMLCCwitha100k(cid:2)resistorisacceleratedat150V, function of x.
the voltage drop will be 100 k(cid:2)·100 μA = 10 V, which Table II summarizes the calculated MTTF data using (1)
is 6.7% of the total applied voltage. For a 1 k(cid:2) resistor, the when all TTF data at a given stress level were used to
voltagedropisonly0.1Vacrosstheresistor,whichmaybetoo make a two-parameter Weibull plot. The reliability life, as
low to show the details of the leakage current changing with characterized by MTTF, was more than one magnitude of
the stress time. In this paper, the values of the resistor were difference among the capacitor lots under the same stress
chosen such that the maximum voltage drop at the current- condition.
limitingresistorwillbenomorethan3%oftheappliedvoltage 2) Characterization of Leakage Current Data for a Slow
under all HALST conditions. Degradation Failure Mode: As shown in Table I, all three
BME capacitor lots that were made for the same reliability
level revealed almost identical construction and microstruc-
III. RESULTS AND DISCUSSION
ture parameters and were also degraded under very similar
A. Characterization of Time-Dependent
stress conditions. However, the MTTF data contained in
Leakage Current and MTTF Data
TableIIshowsignificantdifferencesinreliabilitylifeforthese
1) LeakageCurrentandMTTFData: Fig.1showstheleak- BMEcapacitors.Tounderstandthemechanismthatdetermines
agecurrentagainststresstimeforthethreeBMEcapacitorlots the reliability life, the leakage current data shown in Fig. 1
atagivenstresscondition:155°C,250V(5×ratedvoltage). were replotted with a different scale in the x-axis to reveal
4 IEEETRANSACTIONSONCOMPONENTS,PACKAGINGANDMANUFACTURINGTECHNOLOGY
Fig.2. LeakagedataarereplottedfromFig.1withadifferentscaleinthex-axistorevealdetailsinthefailuremodesamongthethreeBMEcapacitorlots.
details of the differences in their failure modes. As shown
in Fig. 2, the TTF data appear to be highly dependent on the
failure mode exhibited during the HALST regimen.
As discussed in [27]–[29], two failure modes can be
identified in these BME capacitor lots: catastrophic and slow
degradation.A catastrophic failure is characterizedby a time-
accelerating increase in leakage current that is mainly due
to existing processing defects (voids, cracks, delaminations,
and so on) or to extrinsic defects. A slow degradation failure
is characterized by a near-linear increase in leakage current
against stress time; this is caused by the electromigration
of oxygen vacancies (intrinsic defects). The TTF data
shown in Fig. 2 clearly indicate that BME capacitors with
slow degradation failures exhibit the largest MTTF values
(AA47450), and those with the most catastrophic failures
Fig.3. Examplesofcurvefittingusing(2)fortwoBMEcapacitor samples
showed the smallest MTTF values (AC47450). Capacitor lot
withdifferentfailurepatterns.Bothappeartofitwelltotheexponentialform
AB47450 shows failures with both failure modes and with of(2)formostofthestresstime.
MTTFvaluesinbetweenthoseoftheothertwocapacitorlots.
As shown in Fig. 2, for a certain period of stress time,
the leakage current follows a slow degradation failure mode, data that finished with a strong catastrophic failure, to obtain
i.e., a gradual increase in leakage current against stress time. a proper value of τSD, some of the leakage data points at the
Withafurtherincreaseofstresstime,somecapacitorswillfail catastrophic failure side have to be gradually removed until a
catastrophically, while some will retain the slow degradation value of R2 ≥0.99 is reached.
failure mode until the failure criterion is reached. The meaning of τSD can be illustrated by the following
The leakage data shown in Fig. 2 have been curved-fitted example:let I1 and I2 betheleakagesatt1 andt2,respectively,
with a number of different mathematical functions (power for a slow degradation failure. If one assumes (I2/I1) = 2,
law,exponential,linear,logarithmic,andso on).Althoughthe then (2) can be rewritten as
(cid:2) (cid:3) (cid:2) (cid:3)
ltheaeksatgreesdsattiamsehomwenasinurFedig,.t2heapcpueravre-tofitbtienlginreeasrulatgsahinasvtemsohsotwonf II2 =e t2τS−Dt1 =e τ(cid:7)SDt =2
1
that the exponential form of
and
(cid:2) (cid:3)
I = I(t0)e tτ−SDt0 (2) τSD = ln(cid:7)(2t) ≈1.4427·(cid:7)t (3)
fits the leakage data better than a linear form. In (2), I is the where (cid:7)t is the time at which the leakage current doubles in
measuredleakagecurrent, I(t )is the leakagevalueatt =t , value. The greater the value of τ , the longer the timespan
0 0 SD
and τ is a characteristic exponential growth time. of a degradation failure, indicating a slower IR degradation
SD
Fig. 3 shows an example of curve fitting using (2) for two process.
capacitor samples with different failure modes. C13, with a At a given stress condition, when the τ of all 20 BME
SD
near-linear increase in leakage, fits very well to (2) when capacitors being tested was obtained using the curve-fitting
all of the measured leakage data points and a method of method described above, a two-parameter Weibull plot could
leastsquareswereused.AlthoughC7 failswithacatastrophic be made, and an average value of τ , (cid:4)τ (cid:5), was defined as
SD SD
failurecharacterizedbya rapidleakagecurrentincreaseatthe the scale parameter η of the Weibull plot.
end,themajorityoftheleakagedatafollowaslowdegradation Table III summarizes the values of (cid:4)τ (cid:5) determined for
SD
failure mode and still fit well to (2). A similar value of τ various stress conditions. The table can be used to compare
SD
to that of C13 could be obtained. For some of the leakage the corresponding MTTF data. In most cases, the value
LIU:IRDEGRADATIONINNi–BaTiO3MLCCs 5
TABLEIII where N is the donor concentration, d is the depletion layer
d
CALCULATEDMTTFDATAFROMWEIBULLPLOTSOFTTFDATAAND thickness, e is the electron charge, and ε ε is the dielectric
0 r
CALCULATED(cid:4)τSD(cid:5)FROMTHECURVE-FITTINGOFTHETHREEBME constant.Theelectroneutralityconditioninthedepletionlayer
CAPACITORLOTSATTHREEDEGRADATIONCONDITIONS satisfies the following requirement [13]:
n
d = s (4)
2N
d
where n is the concentration of trapped electrons at grain
s
boundary surface acceptor states (the number is N ) (cm−2).
s
The barrier height φ can be rewritten as
e2n2
φ = s . (5)
8ε ε N
0 r d
Equation (5) has often been used to estimate the grain
boundary barrier height in semiconducting BaTiO ceram-
3
ics[34],[38].InNi–BaTiO MLCCs, N ismainlydetermined
3 d
by the bulk concentration of ionized oxygen vacancies.
Although oxygen vacancies migrate under an applied dc
field and the weakly bonded electrons can be trapped by the
surfaceacceptorstates,thevalueofdepletionlayerthicknessd
in (4) is always in the submicrometer range, indicating that
N (cid:6) n . Therefore, one can assume that N (t) ≈ N (0),
d s d d
and one can also assume time independence. Therefore, the
time-dependentbarrier height φ can be expressed as
(cid:4) (cid:5)
dφ(t) d e2n2 e2 dn (t)
= s = s .
dt dt 8ε ε N 4ε ε N dt
0 r d 0 r d
To determine dn (t)/dt, the following facts were considered.
s
1) n (t) is trapped electrons at surface acceptor states in
s
the grain boundary regions. The negative space charge
due to trapped electrons is compensated for by the
formation of a positive space charge region near
the grain boundary, which behaves like a depletion
Fig.4. SchematicoftheformationofadoubleSchottkybarrieraroundthe
grainboundaryofaBaTiO3ceramiccapacitor,whereφisthedepletionbarrier barrier layer to electron conduction.
height; ns is the concentration of trapped electrons at the grain boundary 2) The computational analysis on the trapping of oxygen
surface acceptor states whose number is Ns (cm−2); and Es is the energy vacancies at grain boundaries with respect to local
level ofthesurfacestates fromtheconduction level ofthebulk.
atomicconfigurationandenergyshowsthatgrainbound-
aries attract oxygen vacancies and trap them at specific
of (cid:4)τ (cid:5) was greater than that of MTTF, but it was smaller sites at which local cation density is lower than that in
SD
in a few lower-stress levels where the catastrophic failure the grain interior [17].
modeisdominant.Certainly,therelationshipbetweenTTFand 3) Sinceoxygenvacanciesbehavelikedonors,theypossess
τ dependsuponthe failure criterion,and if a fixed absolute positive space chargeswhen ionized. The same positive
SD
value of leakage current is selected as the failure criterion, space charge in a barrier layer at a grain boundary will
then the relationship depends on the value chosen and on the thus act as a resistance for positively charged oxygen
initial leakage current value for the capacitors. vacancydiffusioninapolycrystallineBaTiO dielectric.
3
As a result, when an ionized oxygen vacancy migrates
under a dc field and reaches the barrier layer, it has a
B. IR Degradation Model for BME Capacitors
tendencyto become trapped there. The electroneutrality
1) Time-DependentDepletion Layer Height φ(t): Although
conditionrequiresthattheweaklybondedtwo electrons
the formation of a double Schottky barrier layer at a grain
that are moving in a conduction band now have to be
boundary,asshowninFig.4,wasinitiallyproposedtoexplain
localizedtomakethetrappedoxygenvacancyneutralize
the PTCR effect in donor-doped semiconducting BaTiO
3 and to become part of the crystalline structure.
ceramics [13]–[15], the same barrier depletion layer model
When Kröger and Vink [31] symbols are used, the process
has also been suggested to explain the IR degradation in
can be described by
Ni–BaTiO MLCCs [2], [4], [9]–[11]. The typical barrier
3
height can be expressed as V = V••+2e(cid:7). (6)
O O
φ = e2Ndd2 As reported in [4], the localized electrons that compensate
2ε ε the V•• localization can be trapped with the reduction of
0 r O
6 IEEETRANSACTIONSONCOMPONENTS,PACKAGINGANDMANUFACTURINGTECHNOLOGY
Ti ions surrounding the V•• as Ti4+ + e(cid:7) → Ti3+, and holds the high resistivity of the ceramic BaTiO . If all grain
O 3
Ti3++e(cid:7) →Ti2+ [4]. The reductionof Ti4+ will now reduce boundaries inside a dielectric layer are assumed to have a
the positive space charge in the positively charged depletion uniformbarrierheightφ(t),thetime-dependentresistivityρ(t)
layer and reduce the barrier height. Since the barrier height of an MLCC can be written as [13]
(cid:2) (cid:3)
isstatbeaslannsc(etd), bthye trheedutcrtaipopnedinebleacrrtrieornsheiinghstuwrfailcleloawcecreptthoer ρ(t)=ρ0e φk(Tt) (10)
Fermi level at grain boundary,and then will reduce the ns(t). where ρ is the resistivity of the grain interior. According
If we assume that (cid:7)nO is the electron concentration that has to (2), th0e time-dependent current density of an MLCC j(t)
been localized to make the trapped V•• neutral, (cid:7)n should
O O for a slow degradation failure mode can be expressed as
meet the following conditions: at t = 0,(cid:7)n (0) = 0, and (cid:2) (cid:3)
O
aint tth→e s∞urf,a(cid:7)cenOacc=epntos(r0s)t,ait.ees.,nal(l0t)rawppileldeevleenctturaolnlys abtetf=ull0y j(t)= j(t0)e tτ−SDt0 = ρE(t)
s
compensated for by the localized electrons that neutralize or
(cid:2) (cid:3)
athsemtroarpepeVdO•V•O•a•r.eHtorawpepveedr, awnidthnaeufturartlhizeerdi,ncthreeaseeleocftri(cid:7)canllOy ρ(t)= j(Et0)e− tτ−SDt0 (11)
negativefeature of n (t) will further retard the localization of
s where j(t )isthecurrentdensityatt =t and E istheapplied
electrons and reduce the localization rate of (cid:7)n . Therefore, 0 0
O field. Combining (10) and (11) results in
the change of (cid:7)nO as a function of t can be expressed by a (cid:4) (cid:5) (cid:4) (cid:5)
first-order reaction according to the reaction rate theory [30] φ(t) φ(0)e−2Kt
ρ(t) = ρ exp =ρ exp
0 0
d(cid:7)nO(t) = K(t)[ns(0)−(cid:7)nO(t)] E k(cid:4)T t −t (cid:5) kT
dt = exp − 0 .
j(0) τ
and SD
(cid:6) (cid:6)
(cid:7)(cid:7)nOnO(0()t) (cid:7)ndO(cid:7)(t)n−O(nt)s(0) = 0t−K(t)dt (7) At a given stress letvτ−el,t0E≈is−aφck(oT0n)seta−n2tK,ts.o (12)
where K(t) is the degradation rate constant and SD
n (0)−(cid:7)n (t)=n (t) is the trapped electron concentration Using (cid:4)τSD(cid:5), the average of τSD, to replace τSD, and
atssurfaceacOceptorstsatesattimet.If(cid:7)n (t)isonlybalanced e−x ≈1−x when x issmall, theintegrationof (12)resultsin
O (cid:6) (cid:6)
bbeysnims(pt)lifineedaratshaetiFmerem-iindleevpeeln,dKen(tt)co=nsKtan=tinKw0eh−ic(hEkE/kkTi)scthane MTTF t(cid:4)τ−t0(cid:5)dt = − MTTF φk(T0) ·e−2Ktdt
activation energy that is required for V•• in electromigration 0 SD (cid:6)0
O MTTF φ(0)
to be neutralized at a grain boundary region per (6) and k is ≈ − (1−2Kt)dt
the Boltzmann constant. Since (cid:7)n (0)=0, (7) finally yields 0 kT
O
and
ns(0)−(cid:7)nO(t) =e−Kt 1 φ(0)(cid:4) 1 (cid:5)
ns(0) ≈ K − .
2(cid:4)τ (cid:5) kT MTTF
SD
and
This gives rise to
(cid:7)n (t)=n (0)(1−e−Kt) (8)
the remaining trappOed electsrons in acceptor states can be MT1TF = K − 2φ(0k)T(cid:4)τSD(cid:5) ≈ K0e−kETk. (13)
simply expressed according to (8) as Equation (13) is the well-known Prokopowicz–Vaskas
n (0)−(cid:7)n (t)=n (0)−n (0)(1−e−Kt)=n (0)e−Kt. equationforMLCCs, whenappliedvoltageisa constant[35].
s O s s s
The degradation rate constant K can now be determined by
Combining (5) and (8) yields a time-dependentbarrier height an Arrhenius plot using the MTTF data obtained at various
temperatures and at a constant voltage.
e2[n (0)−(cid:7)n (t)]2
φ(t)= s O =φ(0)e−2Kt. (9) Using the MTTF data at different temperatures and at a
8ε ε N
0 r d given voltage (250 V) for the three BME capacitor lots, a
This relationship indicates that the barrier height will correspondingArrheniusplotaccordingto(13)canbeplotted,
exponentially decrease with time due to the oxygen vacancy asshowninFig.5.Bothactivationenergy E anddegradation
k
entrapment at grain boundaries. rate constant K can now be determined.
0
2) Determination of Degradation Rate Constant K: The Table IV lists the activation energy E and constant K
k 0
measurementof I–V characteristicsofceramicBaTiO inside at three different temperatures for the three BME capacitor
3
the grain interior and at the grain boundary has shown that lots. The calculated K values shown in Table IV were used
underanappliedfieldof100kV/cm,thecurrentdensityinside to estimate the MTTF data per (13). A comparison between
the grain and at the grain boundary can differ by several the measuredMTTFdata and the calculated data showsfairly
orders of magnitude. The difference increases significantly good agreement. All calculated MTTF values are smaller
as temperature increases [33]. It is the grain boundary that than the measured ones. For lot AA47450, the MTTF data
LIU:IRDEGRADATIONINNi–BaTiO3MLCCs 7
process unless the barrier height φ(t) is high enough to be
comparable to E . This is the case for AC47450, where
k
E = 1.11 eV is smaller than that of φ(0). Therefore, the
k
oxygen vacancies are more energetically favorable for local
entrapmentthanformigratingacrossthedepletionbarrier,and
theyresultin averysmallreliabilitylife whencomparedwith
the other two BME capacitor lots.
Finally, since N (cid:6) n per (4), only a tiny fraction of
d s
oxygen vacancies can be trapped at the grain boundariesdur-
ingtheelectromigrationacrossthedielectriclayertocauseIR
degradation.Thisindicatesthattheefforttosimplyreducethe
••
level of V in the dielectric material would not significantly
O
slow down the IR degradation. Indeed, a small value of K
0
••
indicates that the number of electromigrateable V must
O
Fig.5. Arrheniusplotsusing(13)andmeasuredMTTFdatainTableIIfor be minimized. The recent first-principles calculations based
thethreeBMEcapacitor lots. on the density function theory have shown that some kinds
of dopants in BaTiO dielectrics, such as RE and alkaline-
3
earth(AE)elements,wereeffectiveinimprovingthereliability
measured at 175 °C were excluded for the estimation of
life of Ni–BaTiO capacitors [17]–[19]. According to the IR
the degradation rate constant K because its value is much 3
degradation model proposed here, both RE and AE doping
smaller when combined with other MTTF data points to ••
would benefit from the frozen migrateable V , and thus
give rise to a good linear fitting. Since the BME capacitor O
reduce the value of K . On the other hand, some RE dop-
lot under degradation was so leaky at this temperature, the 0
ing elements, such as Dy and Er, due to their amphoteric
results of self-heating due to the leakage current could result
characteristics, will also benefit from the formation of deep
in a significant amount of temperature increase, and thus an
surface acceptable states N to result in a large value of E .
acceleration in the failure of the BME capacitors. S k
The correlationsbetween the formulationand the value ofthe
degradation rate constant for oxygen vacancy entrapment K
C. IR Degradation Mechanism Due to Oxygen as defined in this paper needs to be further investigated.
Vacancy Electromigration 2) Insulation Resistance and Reliability Life: According
1) Reliability and Oxygen Vacancy Migration: According to (12)
to (9)
φ(t)=φ(0)e−2Kt =φ(0)e−MT2tTF etτ−SDt0 ≈e−φk(T0)e−2Kt
which indicates that a slower IR degradation process,
and
characterized by a larger value of τ , would give rise to
1 = ≈K0e−kETk a smaller value of φ(0). This makesSDsense since a smaller
MTTF φ(0) will energetically be favorable to the continuous
where K = K0e(−Ek/kT) is the degradation rate constant electromigration of VO•• without being trapped at a grain
foroxygenvacancyentrapmentat grainboundaries.Although boundary to cause an IR degradation. However, this is only
K and MTTF can be related to each other per the one part of the equation;φ(0) also presents the barrier height
Prokopowicz–Vaskas equation, the physical meaning of K for the conduction band electronic carriers. A lower φ(0)
was clearly defined in the proposed model. To make will facilitate electronic conduction and will also deteriorate
Ni–BaTiO BME capacitors with improved reliability, the IR. As a result, when electron conduction and oxygen
3
the value of K must be minimized. This requires a smaller vacancy electromigration are both considered, a moderate
valueofthedegradationconstantK ,whichisthetotalnumber initial barrier height φ(0) and a smaller K are the keys for
0
of oxygen vacancies that are migrateable; and a large value slowing the IR degradation in Ni–BaTiO -based ceramic
3
••
of E , which is the activation energy required for V to capacitors, and thus improving their reliability life.
k O
be neutralized and trapped near the depletion layer at grain As an important conclusion of this model development,
boundaries.ThishasbeenprovenfromthecalculatedK values higher IR values may not always result in a larger MTTF,
shown in Table IV, where AA47450and AB47450 are shown butaslowerIRdegradationrate (smaller K)willalwayshave
to havesimilarvaluesof E buta muchsmallervaluefor K , thiseffect. Thisconclusioncan be verifiedfromthe measured
k 0
which gives rise to a significantly improved reliability life leakage data shown in Fig. 3, where sample AC47450 was
(larger MTTF) for capacitor AA47450. showntohavethehighestinitialIRvaluesandsmallestMTTF
On the other hand, since a typical barrier height value of and AA47450 had the lowest initial IR values but the largest
φ(0) ≈ 1.30 eV has been reported in [4], a large value of MTTF among the group.
E > φ(0) is necessary to slow down the V•• entrapment, A higher φ(0) generally means a higher resistance, and
k O
becausea largevalueof E also meansthattheentrapmentof therefore a higher electrical strength when a dc voltage is
k
••
V atgrainboundariesmaynotbeanenergeticallyfavorable applied. A higher dc electrical strength makes it more likely
O
8 IEEETRANSACTIONSONCOMPONENTS,PACKAGINGANDMANUFACTURINGTECHNOLOGY
TABLEIV
CALCULATEDDEGRADATIONCONSTANTK ANDMTTFDATAPERTHECURVE-FITTINGRESULTSINFIG.5AND(13)
thatathermal-relatedelectricalbreakdownwillbeexperienced A model based on the existence of depletion layers at
due to the localization of the electrical strength [9]–[11]. grain boundariesand on the entrapmentof electromigrateable
3) Oxygen Vacancy Migration and Compensation: Since oxygen vacancies was proposed to explain the MTTF
••
only a very small portion of V may be trapped at the differenceamongthese BME capacitors.The MTTFhasbeen
O
grainboundaries,themajorityof V•• willcontinuallymigrate found to be directly related to the degradation rate constant
O
and will eventually reach the dielectric layer and internal K of oxygen vacancy entrapment at grain boundaries.
Ni electrode interface, as has been shown by previously The MTTF and K were found to follow the traditional
reportedelectronenergylossspectroscopyandhigh-resolution Prokopowicz–Vaskasequation at a constant applied voltage.
transmission electron microscope observations [4]. A lower depletion layer height φ(0) is energetically favor-
Since there is no evidence to show that V•• can be able for a slower degradationrate and a longerreliability life.
O
transferred across the cathode electrode layer [4], [10] However,whenbothoxygenvacancymigrationandelectronic
most V•• capable of migration will now pile up along the conduction are considered, a φ(0) with a moderate height
O
Ni-electrodedielectricinterface.Toneutralizethesevacancies, would give rise to the best reliability performance.
a significant number of electrons is required, which can only It is the conclusion of this paper that reliability will not
be obtained from the cathode electron injection. The energy be improvedsimply by increasing the IR. Indeed, Ni–BaTiO
3
required for cathode electron injection at the dielectric- BMEcapacitorswithasmallerIRdegradationrateconstantK,
electrode interface is ∼1.25 eV [36]. If E is less than this, orasmalleramountofentrappedV•• atgrainboundaries,will
k O
most of the oxygen vacancies will be energetically favorable always give rise to a longer reliability life.
for localization, and a quick IR degradation will occur. This BothREandAEdopingmayhaveprofoundimpactsonthe
is exactly the case for lot AC47450. values of degradation rate constant K, and the impacts needs
The high concentration of localized electrons due to to be further investigated.
the compensation of the pile-up of oxygen vacancies will
not only dramatically change the local stoichiometry of
ACKNOWLEDGMENT
the BaTiO dielectric but it will also lead to a leakage
3
The authorappreciatesNASA ElectronicPartsand Packag-
current increase during IR degradation. This will cause a
ing Program’s support for this paper. The author would like
local temperature increase and will eventually lead to the
to thank NASA Goddard Space Flight Center Code 562 Parts
breakdown at the Ni–BaTiO interface. The initial failure
3
Analysis Laboratory for assistance with electrical testing.
site of the dielectric-electrode interface was clearly revealed
in a previously published failure analysis work regarding
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Donhang (David) Liu received the Ph.D. degree
capacitors usinganimprovedaccelerated lifetestandWeibullanalysis
in electronic engineering from Jiaotong University
technique,” Proc.SPIE,vol.3235,pp.362–367,Oct.1997.
from a joint Sino-USA education program among
[22] M.Randall, A.Gurav,D.Skamser,andJ.Beeson, “Lifetimemodeling
Jiaotong University, Pennsylvania State University,
of sub 2 micron dielectric thickness BME MLCC,” in Proc. CARTS,
andLehighUniversity.
Scottsdale, AZ,USA,Mar.2003,pp.134–141.
He(cid:3)was(cid:3)a(cid:3)Post-Doctoral(cid:3)Research(cid:3)Fellow(cid:3)with(cid:3)
[23] J. R. Yoon, K. M. Lee, and S. W. Lee, “Analysis the reliability
the(cid:3) Beckman(cid:3) Institute,(cid:3) University(cid:3) of(cid:3) Illinois(cid:3) at
of multilayer ceramic capacitor with inner Ni electrode under highly
accelerated lifetestconditions,” Trans.Elect.Electron.Mater.,vol.10, Urbana-Champaign,(cid:3)Champaign,(cid:3)IL,(cid:3)USA,(cid:3)for(cid:3)three(cid:3)
no.1,pp.1229–1234,Feb.2009. years.(cid:3) He(cid:3) joined(cid:3) AVX(cid:3) Corporation,(cid:3) (cid:48)(cid:92)(cid:85)(cid:87)(cid:79)(cid:72)(cid:3)
[24] M. Cozzolino, “A comparison of BME and traditional technology (cid:37)(cid:72)(cid:68)(cid:70)(cid:75),(cid:3) SC,(cid:3) USA,(cid:3) in(cid:3) 1995,(cid:3) as(cid:3) a(cid:3) Principal(cid:3)
ceramic capacitors,” in Proc. CARTS, Orlando, FL, USA, Apr. 2006, Engineer(cid:3) and(cid:3) member(cid:3) of(cid:3) technical(cid:3) staff,(cid:3) to(cid:3)
pp.385–394. develop(cid:3)processing(cid:3)(cid:87)(cid:72)(cid:70)(cid:75)(cid:81)(cid:82)(cid:79)(cid:82)(cid:74)(cid:76)(cid:72)(cid:86)(cid:3)(cid:73)(cid:82)(cid:85)(cid:3)(cid:76)(cid:81)(cid:87)(cid:72)(cid:74)(cid:85)(cid:68)(cid:87)(cid:72)(cid:71)(cid:3)
[25] T. Ashburn and D. Skamser, “Highly accelerated testing of capacitors passive(cid:3)components(cid:3)with(cid:3)an(cid:3)emphasis(cid:3)on(cid:3)integrated(cid:3)ferroelectrics.(cid:3)In(cid:3)2000,(cid:3)he(cid:3)
for medical applications,” in Proc. 5th SMTA Med. Electron. Symp., began(cid:3)to(cid:3)work(cid:3)with(cid:3)American(cid:3)Technical(cid:3)Ceramics(cid:3)as(cid:3)a(cid:3)Senior(cid:3)RF(cid:3)Engineer(cid:3)
Anaheim,CA,USA,Jan.2008,pp.124–131. for(cid:3)advanced(cid:3)products(cid:3)development.(cid:3)Since(cid:3)2003,(cid:3)he(cid:3)has(cid:3)supported(cid:3)the(cid:3)NASA(cid:3)
[26] J. L. Paulsen and E. K. Reed, “Highly accelerated lifetesting of base- Goddard(cid:3)Space(cid:3)Flight(cid:3)Center,(cid:3) Greenbelt,(cid:3) MD,(cid:3)USA,(cid:3)as(cid:3) a(cid:3) Senior(cid:3) Staff(cid:3)
metal-electrode ceramic chip capacitors,” Microelectron. Rel., vol. 42, Engineer(cid:3) and(cid:3) Senior(cid:3) Staff(cid:3) Engineer(cid:3) II,(cid:3) providing(cid:3) senior(cid:3)level(cid:3) technical(cid:3)
no.6,pp.815–820,Jun.2002. supports(cid:3) on(cid:3) space(cid:3) projects.(cid:3) He(cid:3) (cid:68)(cid:79)(cid:86)(cid:82)(cid:3) (cid:86)(cid:72)(cid:85)(cid:89)(cid:72)(cid:86)(cid:3) (cid:68)(cid:86)(cid:3) a(cid:3) Commodity(cid:3)Expert(cid:3)on(cid:3)
[27] D.LiuandM.Sampson,“Reliabilityevaluationofbase-metal-electrode capacitor(cid:3)technologies,(cid:3)which(cid:3)includes(cid:3)the(cid:3)evaluation(cid:3)of(cid:3)commercial(cid:3)BME(cid:3)
multilayerceramiccapacitors forpotentialspaceapplications,” inProc. capacitors(cid:3) for(cid:3)aerospace(cid:3)applications.(cid:3) He(cid:3)has(cid:3)authored(cid:3)over(cid:3)50(cid:3)technical(cid:3)
CARTS,Jacksonville, FL,USA,Mar.2011,pp.45–63. papers(cid:3)and(cid:3)holds(cid:3)four(cid:3)U.S.(cid:3)patents.