電子產品軟焊焊點及界面之研究-覆晶銲錫接點之熱電效應及其抗電遷移之研究

行政院國家科學委員會專題研究計畫 成果報告

覆晶銲錫接點之熱電效應及其抗電遷移之研究

計畫類別： 整合型計畫

計畫編號： NSC94-2216-E-009-021-

執行期間： 94 年 08 月 01 日至 95 年 07 月 31 日

執行單位： 國立交通大學材料科學與工程學系(所)

計畫主持人： 陳智

計畫參與人員： 邱聖翔 梁世緯 張元蔚 陳俊宏

報告類型： 精簡報告

報告附件： 出席國際會議研究心得報告及發表論文

處理方式： 本計畫可公開查詢

中 華 民 國 95 年 10 月 30 日

Չࡹଣ୯ৎࣽᏢہ঩཮ံշ஑ᚒࣴزीฝ

Ɏ ԋ ݀ ൔ ֋

ɍයύ຾ࡋൔ֋

ႝηౢࠔ೬ౌౌᗺϷࣚय़ϐࣴزɡ!

ᙟ඲᎗ᒴௗᗺϐ዗ႝਏᔈϷځלႝ

ᎂ౽ϐࣴز

!

!

ीฝᜪձǺɍ!ঁձࠠीฝ! !

Ɏ

!᏾ӝࠠीฝ!

ीฝጓဦǺNSC ! :5ɡ3327ɡF!ɡ11:ɡ132ɡ!

୺Չය໔Ǻ! :5 ԃ! 9! Д! 2! ВԿ! :6! ԃ! 8! Д! 42! В!

!

ीฝЬ࡭ΓǺഋඵ!ୋ௲௤!

ӅӕЬ࡭ΓǺ!

ीฝୖᆶΓ঩Ǻ!ߋဃ๔!ఉШጎ!஭ϡጩ!ഋߪֻ!

!

!

ԋ݀ൔ֋ᜪࠠ)٩࿶຤ਡۓమൂೕۓᛦҬ*Ǻɍᆒᙁൔ֋!!

Ɏ

ֹ᏾ൔ֋!

!

ҁԋ݀ൔ֋хࡴаΠᔈᛦҬϐߕҹǺ!

ɍॅ୯Ѧрৡ܈ࣴಞЈளൔ֋΋ҽ!

ɍॅεഌӦ୔рৡ܈ࣴಞЈளൔ֋΋ҽ!

Ɏ

рৢ୯ሞᏢೌ཮᝼Јளൔ֋Ϸว߄ϐፕЎӚ΋ҽ!

ɍ୯ሞӝբࣴزीฝ୯Ѧࣴزൔ֋ਜ΋ҽ!

!

!

ೀ౛БԄǺନౢᏢӝբࣴزीฝǵගϲౢ཰מೌϷΓω୻ػࣴزीฝǵ

ӈᆅीฝϷΠӈ௃׎ޣѦǴளҥջϦ໒ࢗ၌!

!!!!!!!!!!ɍੋϷ஑ճ܈ځдඵች଄ౢ៾Ǵɍ΋ԃɍΒԃࡕёϦ໒ࢗ၌!

!!!!!!!!!!

୺ՉൂՏǺ!

!

ύ!!!๮!!!҇!!!୯! ! ΐΜϖ! !ԃ! !Μ! !Д!!Μΐ! !В!

!

!

ኴ૞

ءઔߒ׌૞ಾኙ٥དྷᙔሩ(SnPb)ፖྤሩᔷᙔΔᙔᎬ(SnAg3.5)៿དྷᔷᙔ൷រڇሽᔢฝ෼

ွխሽੌፖᄵ৫ऱࠟጟ෼ွࠐ೚൶ಘΔઔߒխ׌૞ܓشદ؆ᒵᑷቝᏚ(IR)ࠐၦྒྷሽ՗ցٙᇙ

ऱᄵ৫᧢֏Δޓאڼࠐ൶ಘ៿དྷ࿨ዌڇ೏ሽੌയ৫ࢍՀࢬขسऱሽᑷயᚨא֗լٵ֡՚ऱ

ᔱᖄᒵኙ࣍ሽᔢฝயᚨࢍՀధᡏழၴऱᐙ᥼ΖΖ່৵٦಻ٽሽᆰᑓᚵࠐᇞנᔷᙔ൷រփऱ

ሽੌയ৫։܉֗ᄵ৫։܉Δ٦ઔߒڕ۶༼֒ᔷᙔ൷រऱݼሽᔢฝ౨ԺΔ༼֒הଚऱࠌشኂ

ࡎΖ

ءઔߒ׌૞ಾኙ٥དྷᙔሩհ៿དྷ࿨ዌڇ೏ሽੌയ৫Հၞ۩ሽᔢฝ෼ቝઔߒΖءઔߒࠌش

ࠟጟլٵ࿨ዌऱᔷᙔհ៿དྷ৞ᇘᇢׂΔรԫጟᇢׂࢬࠌشհUBM੡Ti/Cr-Cu/Cu(དྷׂጤ)ፖ

Cu/Ni(P)/Au(ഗࣨጤ)ΙรԲጟᇢׂࢬࠌشհUBM੡Ni/Cu(དྷׂጤ)ፖCu/Ni(ഗࣨጤ)Ζઔߒ᧩

قڇຏሽመ࿓խΔᔱᖄᒵਢ່׌૞ऱ࿇ᑷᄭΔਢขسྡྷۘᑷயᚨऱ່׌૞ڂైհԣΖᆖط

ሽᆰᑓᚵ࿨࣠࿇෼Δڇຏሽመ࿓խΔڇᔱᖄᒵፖᔷᙔ൷រԵՑ๠ᄎڶԫᑷរ(hot spot)ขسΔ

ᑷរऱᄵ৫ޓᄎᙟထ؆ףሽੌऱᏺףۖ༼֒Δຍଡᑷរऱژڇኙ࣍៿དྷ࿨ዌڶףຒధᡏऱ

ᐙ᥼Ζ௽ܑਢڇອᄕጤขسףຒขس௛֞ᖄી៿དྷ࿨ዌऎထ੺૿ధᡏΖ

ᔱᖄᒵऱ֡՚Ոᄎኙ៿དྷᔷᙔ൷រऱሽᔢฝధᡏழၴՈڶৰՕऱᐙ᥼Δኔ᧭࿨࣠᧩قΔ

ףᐈፖᜍ࿍ᔱᖄᒵऱ९৫ױא࢏९ᖞଡ៿དྷᔷᙔ൷រऱሽᔢฝధᡏழၴΖ

ছߢ

ڇሽ՗ցٙ᎘ᜳ࿍՛ፖפ౨ֲᄅִฆऱ᝟ႨՀΔ៿དྷ৞ᇘ(Flip chip packaging)բྥګ੡೏ၸ

ሽ՗ցٙข঴հ׌૞৞ᇘֱڤΖ෼վሽሁ๻ૠऱ૞ޣՀΔޢଡᔷᙔ෺ലႚᙁપ 0.2AհሽੌΔ

ڇլՆऱലࠐലᄎ೏۟ 0.4AΔא 50ȝmऴஉऱᔷᙔ෺ࠐૠጩࠡሽੌയ৫ല೏ሒ 10

A/cm

Δ

ڇցٙᖙ܂ᄵ৫ 100кՀ(բ၌መᔷᙔ෺ዹរ࿪ኙᄵ৫հԫתאՂ)Δሽ՗ᔢฝലኙᔷᙔ෺հ

ױᔾ৫ທګٲ୭Ζ່ڰڇ 1960 ڣז༉ၲࡨڶᔱΕᎬ८᥆ऱሽᔢฝΰelectromigration, EMα

ઔ ߒ ࿛ ࿛ [1,2,3] Ζ Pro. Tu ኘ ᤚ ࠩ ڼ ം ᠲ ױ ౨ ऱ ᣤ ૹ ࢤ ۖ ၲ ࡨ ထ ֫ ઔ ߒ

ܶ ሩ ᔷ ᙔ

Electromigration[4-8]

Ζኙ࣍ྤሩᔷᙔऱElectromigrationΔؾছբຬᥛڶઌᣂᓵ֮࿇।[9-10]Ζ

ۖڇભഏՠᄐ੺ঞڶIntel, IBM, א֗Flip Chip TechnologyԿ୮ֆ׹ၲࡨૹီڼംᠲࠀٺ۞

ڶઔߒຝ॰ڇ൶ಘڼംᠲΖ

ءઔߒಾኙ៿དྷ৞ᇘխሽ՗ᔢฝኙᔷᙔ෺հױᔾ৫ࢬທګհٲ୭ၞ۩ઔߒࠀ༼נᇞެ

հሐΔٵழބנᔷᙔޗறڶᣂհሽᔢฝ೶ᑇڕޗறऱᙇᖗΕᒵሁऱ๻ૠ…࿛Δࠐ༼ࠎՠᄐ

੺հ೶ەΖ

ኔ᧭ޡᨏ

ቹԫ੡ءઔߒհ៿དྷᇢׂ࿨ዌቹΔདྷׂጤհ UBM ։ܑ੡ CrΔphase-in Cr-CuΔፖ CuΔ

ࠡদ৫։ܑ੡ 1000ǹΔ3000ǹ ፖ 7000ǹΖഗࣨጤհ UBM ։ܑ੡ Cu : 20ȝm ΔNi: 5ȝm Δ

Au : 0.25ȝmΖ

ᔷᙔঞڇ೏࣍ࠡዹរ 30 ৫Հଈ٣ፖདྷׂጤ൷ٽ(reflow)Δ൷ထ٦ፖഗࣨጤኙᄷၞ۩รԲڻ

൷ٽ(reflow)Ζ

ቹԲ੡ءઔߒհᇢׂ 3D࿨ዌቹΔሽ՗ੌൕԲᇆbumpհདྷׂጤ 45

ߡၞԵΔ٦طഗࣨጤ

հ৵ֱੌנΔ൷ထطԫᇆbumpདྷׂጤ 45

ߡၞԵΔ٦طഗࣨጤ৵ֱ 45

ߡੌנΖ

ቹԿ੡ല៿དྷᇢׂདྷׂጤཛٻ IR ೠྒྷᕴΔIR ױאઠຘशདྷׂΔࢬאױאຘመशདྷׂᨠ

ኘࠩདྷׂࢍՀհᔱᖄᒵᒵሁ࿨ዌፖຏሽመ࿓խᄵ৫ऱ։܉Ζ

ቹ؄੡׼ԫิլٵ࿨ዌऱᔷᙔᇢׂΔདྷׂጤհ UBM ։ܑ੡ Ni ፖ CuΔࠡদ৫։ܑ੡ 3ȝmΔ

5ȝm Ζഗࣨጤհ UBM ։ܑ੡ Cu : 30ȝm ΔNi: 5ȝmΖ

੡Ա૞൶ಘᔱᖄᒵ֡՚ኙ࣍៿དྷᔷᙔ൷រڇሽᔢฝயᚨՀధᡏழၴऱᐙ᥼Ζءઔߒ๻ૠ

ԱԿጟլٵ֡՚ऱᔱᖄᒵ٦೚։࣫Ζޢ੄ᖄᒵ९৫ຟ੡ 850umΔቹնΕք੡ daisy-chain ऱ

࿨ዌࠀ׊ຑ൷ڶ 6 ឍᔷᙔסჇΔᔱᖄᒵऱ᜔९৫੡ 2550 PmΔᐈ৫։ܑ੡ 100ȝm ፖ 40ȝmΔ

দ৫ઃ੡ 1.5 ȝmΔܓشຍࠟጟ࿨ዌࠐ൶ಘᔱᖄᒵᐈ৫ऱயᚨΖ

รԿጟ࿨ዌঞڕቹԮࢬقΔਢطԿ੄ᔱᖄᒵຑ൷ڇԫದΔᐈ৫੡ 100ȝmΔࠀ׊ࢍՀڶ 4

ឍᔷᙔסჇΔ3 ੄ᔱᖄᒵ։ܑᑑಖ੡ T1ΕT2ΕT3Ι؄ឍᔷᙔסჇᑑಖ੡ B1~B4Ζݺଚױא

៶طഗࣨጤլٵۯᆜऱሽੌΔױאࠐ൶ಘլٵᔱᖄᒵ९৫ኙ࣍ڇሽᔢฝயᚨՀధᡏழၴऱ

ᐙ᥼Ζ

3-D

ሽᆰᑓᚵ։࣫

៿དྷ৞ᇘᇢׂආشᜳᓂࢍຝ८᥆ᐋऱᑓীΔߠቹ԰Δਢᙇش٥དྷᙔሩ(eutectic SnPb)ᔷ

ᙔΔདྷׂጤආشᔱᖄᒵΔᔱᖄᒵऱ֡՚੡ᐈ 34Pmፖদ 1.5PmΔഗࣨࠌشᎭᖄᒵΔᎭᖄᒵऱ

֡՚੡ᐈ 80Pmፖদ 25PmΖདྷׂጤऱࢍຝ८᥆ᐋ(UBM)ਢAl/Ni(V)/Cu 0.7PmΔࣨጤආشNi

4PmΖٵழەᐞտ८᥆֏ٽढ(IMC)ऱسګΔڇདྷׂጤ੡Cu

Sn

1.4PmΔഗࣨঞਢNi

Sn

1PmΖདྷׂጤऱ൷ᤛၲՑ(contact opening)ऴஉ੡ 85PmΔࢍຝ८᥆ᐋၲՑ(UBM opening)੡

120PmΖᔷᙔऱ೏৫੡ 144.7PmΖ

ቹ԰Ε ៿དྷ৞ᇘᇢׂڇདྷׂጤආشᜳᓂࢍຝ८᥆ᐋ Al/Ni(V)/Cu հ࿨ዌቹΖ

׼؆Δشࠐૠጩᔷᙔ൷រऱሽॴڇၦྒྷՂऱ༓۶யᚨΔࢬආشऱᑓীڕቹԼΔԫᑌᙇ

ش٥དྷᙔሩ(eutectic SnPb)ᔷᙔΔདྷׂጤආشᔱᖄᒵΔᔱᖄᒵऱ֡՚੡ᐈ 100Pmፖদ 1.5PmΔ

ഗࣨࠌشᎭᖄᒵΔᎭᖄᒵऱ֡՚੡ᐈ 100Pmፖদ 30PmΖདྷׂጤऱࢍຝ८᥆ᐋ(UBM)ਢCu

3.6PmΔࣨጤආྤሽᝳNi 4PmΖٵழەᐞտ८᥆֏ٽढ(IMC)ऱسګΔڇདྷׂጤ੡Cu

Sn

1.4PmΔഗࣨঞਢNi

Sn

1PmΖདྷׂጤऱ൷ᤛၲՑ(contact opening)ऴஉ੡ 85PmΔࢍຝ८᥆

ᐋၲՑ(UBM opening)੡ 110PmΖᔷᙔऱ೏৫੡ 75PmΖڼԫᔷᙔ࿨ዌᄎჸ಻ኔᎾၦྒྷಱሁΔ

ലᄎڇ࿨࣠ፖಘᓵխ༼נΖ

ᑓী৬مਢܓشഏ୮೏ຒሽᆰխ֨༼ࠎऱANSYSຌ᧯Δຍਢԫଡ๯ᐖऑࠌش׊ֱ࿓ڤ

೜٤ऱઝᖂૠጩຌ᧯Δࠌشցైऱጟᣊ੡SOLID69ΔຍਢԫጟԶᆏរڤऱք૿ᑷሽᓀٽց

ైΖᑓী৬مऱޡᨏࠌආشطՀ࢓Ղऱֱڤ(Bottom-up)Δ٣྽נᔷᙔऱתଳ૿૿ᗨΔඝ᠏

360

ݮګ෺᧯ΔڕቹԼԫΖ٦ᢄנᖄᒵຝٝΔ൷ထല᧯ᗨጻ௑֏(ቹԼԲ)Δਜףᢰ੺යٙΖ

ڼຝ։ܛױ೚ሽࢤᑓᚵ։࣫Ζ

ቹԼԫΕ ᔷᙔ൷រᑓᚵ᧯ᗨቹΖ ቹԼԲΕ ᔷᙔ൷រᑓᚵጻ௑֏ቹΖ

ૉਢ૞։࣫ᑷሽᓀٽߓอΔಘᓵᄵ৫։܉ൣݮΔ੡Ա಻ٽኔᎾཋᑷൣݮፖሎጩऱᄕૻΔ

ڇኔᎾᇢׂխΔೈԱࠟឍኔᎾױאሽᔢฝᇢ᧭ऱᔷᙔ෺؆ΔኙᚨࠡהᔷᙔऱຝٝආشԱք

૿᧯ऱ࠷זᔷᙔ(dummy solder)Ζ٦ലࡌ໮৞ᇘದࠐΔՂֱףՂश(Si)དྷׂΔՀֱ੡ BT ഗࣨΔ

່৵ऱᑓীڕٵቹԼԿΖ

ቹԼԿΕ ৞ᇘᇢׂᑓᚵ᧯ᗨቹΖ

।ԫ੡ᑓᚵࢬࠌشऱޗறऱᑷሽࢤᔆΔץܶᑷႚᖄএᑇ(Thermal conductivity)ፖሽॴ෷

(Resistivity)Δࠡխڂ੡ሽॴᄎᙟထᄵ৫Ղ֒ۖՂ֒ΔTCR ऱயᚨਢլױאઊװऱΔՈڂڼ

ᏺףԱᑓᚵૠጩழऱܺᣄ৫Ζ

࿨࣠ፖಘᓵ

ᔷᙔհሽᑷயᚨઔߒ

ຏሽছΔIR ٣ڇ 70 ৫܂ᄵ৫ऱீإΔطቹԼ؄(a)ױא઎ࠩઠຘशདྷׂऱᔱᖄᒵᄵ৫

։܉ઌᅝऱ݁֌Δࠀ׊ᔱᖄᒵऱᒵሁ؆ᨠױאৰ堚ᄑऱܧ෼Ζኙᖞଡ៿དྷ࿨ዌڇ 70 ৫ࢍՀ

ਜղ 0.59 ڜഛऱሽੌΔڕቹԼ؄(b)ࢬقΔሽੌֱٻ༉ڕቹխᒢᙰࢬਐقΔᔱᖄᒵፖᔱ Pad

ױאৰ堚ᄑऱᨠኘࠩΔࠟឍᔷᙔסჇۯ࣍ቹխᔱ Pad ऱإՀֱΔࢬאط IR ऱ࿨࣠᧩قᔱᖄ

ᒵڇຏሽመ࿓խᄎֺᔱ Pad ڶֺለ೏ऱᄵࣙΔڂ੡ᖞଡᔷᙔ८᥆ਢᑷऱߜᖄ᧯ࠀ׊ᚥܗᖄ

ᒵലᑷႚᖄנװΙቹխ່೏ᄵ࿇سڇᔱᖄᒵऱխ؇પ 134 ৫Δۖᔱ Pad ط࣍ᔷᙔڇՀֱऱ

ᣂএ׽ڶપ 105 ৫Ζቹխᔱ Pad փഎਢ passivation openingΔ؆എঞਢ UBM openingΖݺଚ

ڇᔱ Pad ॵ२࠷ԫය९৫੡ 75um ऱဠᒵΔڼဠᒵᄎຏመᔱᖄᒵፖᔱ Pad Δࠀڇ passivation

opening

ࡉ UBM opening ऱᢰ੺ᑑಖ AΕBΖቹԼ؄(c)੡ 75m ဠᒵऱᄵ৫։܉ڴᒵΔࠀ׊

ᨠኘࠩ passivation opening ࡉ UBM opening ऱᢰ੺ AΕB ᄵ৫։ܑ੡ 118.2 кፖ 109.7 кΖ

ଖ൓ԫ༼ऱਢݺଚ࠷ᖞଡᔱ Pad փഎ passivation opening ऱؓ݁ᄵ৫׽ڶ 105.2 кΔ໢׽ڶ

ڇֽؓጤᔱᖄᒵፖ UBM ऱ൷Ց๠ࠩᔱ Pad ׼ԫጤ༉ڶ 1700к/cm ऱᄵ৫ඪ৫Δຍਢԫଡ

ઌᅝᣤૹऱᐙ᥼Ζ

ۖڇຏሽऱመ࿓խΔᔷᙔփຝऱᄵ৫ԫऴਢݺଚࢬტᘋᔊऱΔءઔߒޓ৬م 3D ऱሽᆰ

ᑓᚵ࿨࣠Δࠀ࿇෼ࠩڇຏሽመ࿓խΔڇᔱᖄᒵፖᔷᙔ൷រԵՑ๠ᄎڶԫᑷរ(hot spot)ขسΔ

ڇ৵ᥛᄎڶݙᖞऱᔷᙔ൷រփຝऱሽፖᑷߓอऱ։࣫Ζ

ᔱᖄᒵ֡՚ኙ࣍ሽᔢฝ෼ွհઔߒ

ᔱᖄᒵᐈ৫ऱᐙ᥼

ຏሽছΔIR ٣ڇ 100 ৫܂ᄵ৫ऱீإΔطቹԼն (a)ױא઎ࠩઠຘशདྷׂऱᔱᖄᒵऱᒵሁ

؆ᨠױאৰ堚ᄑऱܧ෼ΖڕቹԼն (b)ࢬقΔຏሽছΔ઎ࠩઠຘशདྷׂऱᔱᖄᒵᄵ৫։܉ઌ

ᅝऱ݁֌Δᔱᖄᒵፖᔱ Pad ױאৰ堚ᄑऱᨠኘࠩΔኙᖞଡ៿དྷ࿨ዌڇ 100 ৫ࢍՀਜղ 0.6

ڜഛऱሽੌΔڕቹԼն (c)ࢬقΔ֗ױᨠኘࠩᇢׂڇຏሽ৵հᄵ৫։܉Ζ

ݺଚኙ࣍ቹնΕքຍࠟጟ࿨ዌਜղ 100 ৫ 0.6 ڜഛऱሽੌΔຏሽ৵࿨࣠᧩قΔᐈ৫੡ 40

ऱᔱᖄᒵڇԫᛳၴࡉᙔ൷រ༉ᔡࠩధᡏΔྥۖᐈ৫੡ 100 ऱᔱᖄᒵঞڇ 18 ଡ՛ழ৵թధ

ᡏΖ੡Ա૞൶ಘຍଡధᡏழၴլٵऱ଺ڂΔݺଚܓش IR ࠐၦྒྷᔱᖄᒵ Pad Ղ 40ȝm x 40ȝm

ऱᄵ৫ΔطቹԼք ࿨࣠᧩قΔ40ȝm ᒵᐈऱᔱᖄᒵ࿨ዌઌኙ࣍ 100ȝm ᐈ৫ऱ࿨ዌᄎڶֺለ

೏ऱᄵࣙΔઌኙऱྡྷۘᑷயᚨՈֺለᣤૹΖ

ቹԼնΕ(a)ຏሽছΔቹնհ B1 ᘿ୴ீإقრቹΔ(b) ຏሽছΔቹնհ B1 ᄵ৫ீإقრቹ (c) 0.8 A/100кհ IRᄵ৫։܉ቹΖ ቹԼքΕᐈ৫ 40ȝm ፖ 100ȝm հᔱᖄᒵሽᔢฝధᡏழၴ(daisy-chain)Ζ

ᔱᖄᒵ९৫ऱᐙ᥼

ݺଚኙ࣍ቹԮ࿨ዌၞ۩ᔱᖄᒵ९৫யᚨᐙ᥼ऱ։࣫Δຏሽᑓڤ։ܑ੡(1).ሽੌੌᆖ 3 ੄ᖄᒵ

4

ឍᔷᙔסჇ(B1+T1+B2+T2+B3+T3+B4). (2) ሽੌੌᆖ 2 ੄ᖄᒵ 3 ឍᔷᙔסჇ

(B1+T1+B2+T2+B3). (3)

ሽੌੌᆖ 1 ੄ᖄᒵ 2 ឍᔷᙔסჇ(B1+T1+B2).ኙ࣍ຍ 3 ጟᑓڤਜղ

100

৫ 1 ڜഛऱሽੌΔሽੌയ৫੡ 7.1 u 10

A/cm

Ζ࿨࣠᧩قሽੌຏመ 3 ੄ᖄᒵऱధᡏழၴ

੡ 35 ՛ழΕሽੌຏመ 2 ੄ᖄᒵऱధᡏழၴ੡ 1700 ՛ழΕሽੌຏመ 1 ੄ᖄᒵऱధᡏழၴ੡

၌መ 3000 ՛ழΖطڼ࿨࣠ױאवሐᔱᖄᒵ९৫ᐙ᥼ధᡏழၴ੷ሰΔط࣍ຍ 3 ጟլٵ९৫ऱ

ᔱᖄᒵ࿨ዌհሽੌയ৫ઃઌٵΔհࢬאᄎທګధᡏழၴڶڕڼՕऱ஁ฆڂైڇ࣍ྡྷۘᑷய

ᚨΖᆖطIRऱ࿨࣠᧩قΔڕቹԼԮࢬقΔڇຏሽऱመ࿓ᅝխΔຍ 3 ጟլٵ९৫ऱᔱᖄᒵᄵ

ࣙ։ܑ੡ 65.1 кΕ38.6 кΕ19.1 кΔۖຍᄵࣙऱ஁ฆ༉ਢທګధᡏழၴڶຍᏖՕլٵऱ׌

૞଺ڂΖ

ڇྡྷۘᑷயᚨऱֆڤխ:

R

I

P

P

੡ Joule heating powerΔ I ਢሽੌΔ R ਢሽॴΖڇ 3 ੄ᔱᖄᒵ९৫ຏሽऱመ࿓խΔ᜔ሽ

ॴ੡ 1210 m:Δᔱᖄᒵሽॴ۾ᖞଡಱሁऱ 81%ΔᔷᙔסჇ׽ڶ 5 mȍΔࠡ塒ऱሽॴਢڶഗࣨ

ጤऱᎭᖄᒵࢬ༼ࠎΔطڼױ൓वᔱᖄᒵਢڇຏሽመ࿓խ່׌૞ऱ࿇ᑷᄭΖ

ቹԼԮΕ3 ੄լٵᔱᖄᒵ९৫ 850-PmΕ1700-PmΕ2550-PmΔሽੌፖᄵ৫հᣂএቹΖ

ᑷᔢฝ෼ွհઔߒ

ݺଚڇኙ࣍ሽᔢฝயᚨխᑷᔢฝ෼ွࠐ೚ಘᓵΔݺଚኙቹԮऱ࿨ዌڇ 100 ৫Հਜղ 0.8 ڜ

ഛऱሽੌΔሽੌ׽ੌᆖ B1ΕB2 ፖԫයᖄᒵΖطቹԼԶ࿨࣠᧩قΔᔱᖄᒵխ؇(111.5 к)ط

࣍ཋᑷֺለլ࣐Δઌኙऱᄎֺࠟጤ(109.7 к) ڶለ೏ऱᄵࣙΔࠀ׊ࠟឍᔷᙔסჇۯ࣍ቹխᔱ

Pad

ऱإՀֱΔױ౨Ոਢທګڼ෼ွऱ׼ԫଡڂైΖ

ݺଚ٦ຍԫิຏሽ೶ᑇխ࿇෼ԫଡڶᔊऱ෼ွΔڇຏሽऱመ࿓ᅝխΔ޲ڶሽੌੌᆖऱᔣ

२ۯᆜՈᄎڶขسᄵ৫Ղ֒ऱ෼ွΔڕቹԼ԰(a)ࢬقΔሽੌੌᆖ B1~B4 ፖ 3 ੄ᔱᖄᒵΔխ

ၴऱ 2 ឍᔷᙔסჇᄎֺ 2 ࠟጤڶֺለ೏ԫរऱᄵࣙΔࠀ׊׽ڶ 2.7 ৫ؐ׳ऱᄵ஁Ζᅝਜղ

ઌٵऱሽੌ 0.8 ڜഛΔሽੌੌᆖ B2ΕB3 ፖԫයᔱᖄᒵΔڕቹԼ԰(b)ࢬقΔB2ΕB3 ऱᄵ৫

પ੡ 113.0 qCΔڶᔊऱਢΔலᢰ޲ڶሽੌຏመऱ B1ΕB4ΔຶྥՈၦྒྷࠩ 111.0 qC ऱᄵ৫Ζ

ຍ෼ွࠌݺଚ൓वᔣ२ۯᆜܛࠌ޲ڶሽੌᆖመΔᝫਢԫᑌᄎڶᄵࣙऱ෼ွขسΖቹԼ԰(c)

ሽੌੌᆖ B1ΕB2 ፖԫයᔱᖄᒵΔB1ΕB2 ᄵ৫੡ 112.5 qCΔலᢰ޲ڶሽੌຏመऱ B3ΕB4Δ

ઌٵऱՈၦྒྷࠩ 110.7 qC ऱᄵ৫Ζ

ቹԼ԰Εሽੌ(0.8 A)Εੌᆖլٵ९৫ᔱᖄᒵհᔱ Pad ᄵ৫ (a)ሽੌੌᆖ B1 ࠩ B4(b) ሽੌੌᆖ B2 ࠩ(c) ሽੌ ੌᆖ B1 ࠩ B2Ζ

ሽੌയ৫࿨࣠։࣫

I.

ᑑᄷᑓী

໢ԫឍ៿དྷᔷᙔ൷រऱሽੌയ৫։ؒቹڕቹԲԼԿ(a)Δሽੌයٙਢ 0.567 ڜഛΔࢬኙ

ᚨऱؓ݁ሽੌയ৫ਢ 5000 ڜഛ/ֱؓֆ։Ζױא࿇෼ቹԲԼԿ(a)խऱદۥຝ։ਢ೏ሽੌയ

৫೴Δ։ؒڇᔱᖄᒵΔࠡؓ݁ଖપ੡ 1.11 × 10

ڜഛ/ֱؓֆ։Ζ੡ԱֱঁֺለሽੌႃխயᚨΔ

ലࠡயᚨऱ࿓৫ၦ֏Δڂڼݺଚࡳᆠ”ፋႃ෷”(crowding ratio)੡ᔷᙔփຝऱሽੌയ৫່Օଖ

ೈאؓ݁ሽੌയ৫Ζࢬאᅝႃխ෷ଖ။ՕழΔ༉।قሽੌ։ؒऱլ݁֌Δֱঁ೚ֺለ։࣫Ζ

طቹԲԼԿ(a)(b)Δݺଚױא࿇෼ሽੌႃխயᚨ࿇سڇᔱᖄᒵऱԵՑ๠Ζ࠷ᑑᄷᑓীխΔᔷ

ᙔᔾ२ᔱᖄᒵԵՑ๠ऱሽੌയ৫່Օଖ੡ 1.11 × 10

ڜഛ/ֱؓֆ։Δࠡኙᚨऱፋႃ෷੡

22.2Ζ൷Հࠐ៶طޏ᧢࿨ዌࢨਢޗறࢤᔆࠐᨠኘࠡޏ᧢ኙ྇ᒷሽੌႃխயᚨऱய࣠Ζ

ቹ

ԲԼԿ

III.ޏ᧢ࢍຝ८᥆ᐋদ৫

੡Աֺለנࢍຝ८᥆ᐋদ৫ऱᣂএΔݺଚආشԱլٵদ৫ऱࢍຝ८᥆ᐋࠐᑓᚵΔץࠪ

0.5-Pm CuΕ5-Pm CuΕ10-Pm CuΕ20-Pm Cuא֗ 20-Pm electroless NiΔ։ܑࠉڻطቹԲԼ

ն(a)ࠩ(e)ΖൕቹԶऱ࿨࣠ݺଚױא࿇෼ᣤૹऱሽੌႃխயᚨࠉྥຟ࿇سڇᔱᖄᒵၞࠩᔷᙔ

ऱԵՑ๠Ζ܀ਢদ৫ለ৵ऱࢍຝ८᥆ᐋ࿨ዌױאڶயऱࠌᔷᙔऱຝٝ᎛ᠦሽੌႃխயᚨΔ

ࡳࠌࠡڇሽᔢฝऱයٙՀڶ݁֌ऱሽੌയ৫։ؒΖٺܑኙᚨऱሽੌയ৫່Օଖ։ܑ੡Κ1.17

× 10

Ε1.69 × 10

Ε4.37 × 10

Ε7.54 × 10

Εፖ 1.34 × 10

ڜഛ/ֱؓֆ։Δኙᚨࠩऱហႃ෷੡Κ

23.4Ε8.7Ε3.4Ε1.5 ፖ 2.7Ζ࿨࣠ݺଚױא࿇෼ࢍຝ८᥆ᐋऱদ৫။দΔᔷᙔᇙ૿ऱሽੌയ

৫່Օଖ။՛Δᏺףࢍຝ८᥆ᐋদ৫ۖ྇ᒷሽੌയ৫່Օଖࠡ଺ڂڇ࣍ࠌሽੌႃխऱ෼ွ

᎛ᠦᔷᙔ൷រΔڂ੡ࢍຝ८᥆ᐋڶߜړऱݼሽᔢฝࢤᔆΖ

ቹԲԼնΕ(a)ࢍຝ८᥆ᐋޏ੡ 0.7-Pm Cu ழΔऎᔱᖄᒵ࠷ᖩኲ૿հሽੌയ৫։ؒቹ;(b)ࢍຝ८᥆ᐋޏ੡ 5-Pm Cu ழΔऎᔱᖄᒵ࠷ᖩኲ૿հሽੌയ৫։ؒቹ; (c) ࢍຝ८᥆ᐋޏ੡ 10-Pm Cu ழΔऎᔱᖄᒵ࠷ᖩኲ૿հሽੌയ৫ ։ؒቹ;(d) ࢍຝ८᥆ᐋޏ੡ 20-Pm Cu ழΔऎᔱᖄᒵ࠷ᖩኲ૿հሽੌയ৫։ؒቹ;(e) ࢍຝ८᥆ᐋޏ੡ 20-Pm electroless NiழΔऎᔱᖄᒵ࠷ᖩኲ૿հሽੌയ৫։ؒቹΖ

ᅝݺଚ࠷נᔷᙔ່Ղጤऎᔱᖄᒵۯᆜऱሽੌയ৫ଖኙઌኙۯᆜஆᑑ܂ቹΔڕቹԲԼ

քΔݺଚױא࿇෼ሽੌയ৫່Օଖࣔ᧩Հ૾Δڂ੡ࢍຝ८᥆ᐋऱদ৫யᚨΔ່ۖՕଖऱۯ

ᆜપฃڇ-55Pm ๠Δڼܛ੡ᔱᖄᒵԵՑऱۯᆜΖ׼؆ݺଚՈױא࿇෼ԫᑌদ৫ऱழଢྤሽ

ᝳ᠛ய࣠լڕᎭ૞ࠐऱړΔ׌૞ਢࠐ۞࣍܅ሽॴ෷ऱ Cu ױאޓڶயऱ։ཋሽੌΖۖሽੌയ

৫ኙࢍຝ८᥆ᐋऱᣂএቹխ(ቹԲԼԮ)Δݺଚױא࿇෼ࠡᣂএપ੡ਐᑇՀ૾Ζ

ቹԲԼքΕլٵࢍຝ८᥆ᐋদ৫հሽੌയ৫ऎᔱᖄᒵኙᚨஆᑑ։ؒቹΖ ቹԲԼԮΕហႃ෷ኙࢍຝ८᥆ᐋᎭদ৫ᣂএቹΖ

IV.ޏ᧢ࢍຝ८᥆ᐋሽॴ෷

੡Ա൶ಘࢍຝ८᥆ᐋሽॴ෷ऱயᚨΔݺଚᙇشԱאᑑᄷᑓীխࢍຝ८᥆ᐋऱ10଍Ε50

଍Ε100଍ፖ500଍ࠐ܂ֺለΖࠡኙᚨऱሽॴ෷։ܑ੡Κ295Ε1477Ε2954ፖ14770P:-cmΔ

ൕቹԲԼԶױא઎נࠐࠟଡ᝟ႨΔรԫΚᔱᖄᒵຝٝદۥऱՕሽੌ೴࢓ᔱ८᥆ᒌ࢏ۼΔ।

قሽੌሁஉڂ੡ࢍՀՕሽॴऱࢍຝ८᥆ᐋۖޏ᧢Δڂ੡ሽੌྤऄႉܓऴ൷ੌઠመࢍຝ८᥆

ᐋΔࢬאڇᔱ८᥆ᒌੌᆖߩജሁஉ৵թ݁֌ऱ࢓ᔷᙔ൷រ։ཋΙรԲΚᔷᙔ൷រຝٝ଺ء

ऱሽੌയຝ։ؒط1000ࠩ10000ڜഛ/ֱؓֆ։Δ٦Օሽॴ෷ऱࢍຝ८᥆ᐋऱޏ࿳ՀΔሽੌ

യຝ։ؒՀ૾۟ط1000ࠩ3000ڜഛ/ֱؓֆ։Ζ

ቹԲԼԶΕ(a)ሽॴ෷ޏ੡ 295

P:-cm

ΓP:-cm

P:-cm

P:-cm

ᅝݺଚԫᑌ࠷נᔷᙔ່Ղጤऎᔱᖄᒵۯᆜऱሽੌയ৫ଖኙઌኙۯᆜஆᑑ܂ቹΔڕቹԲ

Լ԰Δݺଚױא࿇෼ሽੌയ৫։܉ࣔ᧩᧢ऱ݁֌Δױא٦ڻᎅࣔሽੌሁஉڂ੡ࢍՀՕሽॴ

ऱࢍຝ८᥆ᐋۖޏ᧢Δڂ੡ሽੌྤऄႉܓऴ൷ੌઠመࢍຝ८᥆ᐋΔࢬאڇᔱ८᥆ᒌੌᆖߩ

ജሁஉ৵թ݁֌ऱ࢓ᔷᙔ൷រ։ཋΖ

ᄵ৫։ؒ࿨࣠։࣫

I..ᑑᄷᑓী

ط࣍ڶદ؆ᒵᑷቝᏚױא։࣫ᔷᙔՂֱᔱᖄᒵऱᄵ৫։ؒൣݮΔڂڼΔݺଚආشኔ᧭

ኙᅃᑓᚵऱֱڤࠐଥإݺଚऱᑷᢰ੺යٙΔ່৵ݺଚאBTഗࣨ੡࿛ᄵ૿ 70

CΔᇢׂࡌ໮ፖ

৛ᄵ(25

C)ኙੌΔኙੌএᑇ੡ 10W/cm

-KΔሽੌයٙ੡ 0.15 ڜഛࠩ 0.6 ڜഛΖڇڼයٙՀΔ

ݺଚױא൓ࠩኔ᧭ፖᑓᚵ່൷२ऱ࿨࣠ΖቹԿԼ(a)Δଈ٣ݺଚ༉ױא઎ࠩᔱᖄᒵਢ׌૞ऱ

࿇ᑷᄭΔڂ੡ᔱᖄᒵਢᜳᓂ࿨ዌΔڶઌᅝՕऱሽॴΔՈ༉ኙᚨࠩֆڤΚP=I

R=j

Γ Δࢬא

V

ᄎขسৰՕऱ࿇ᑷၦΔࢬאߓอऱ່೏ᄵ࿇سڇᔱᖄᒵΔᑷط࿇ᑷऱᔱᖄᒵ࢓शདྷׂፖᔷ

ᙔཋᑷΔࠌ൓ᔷᙔփຝᄎขسԫଡᑷរΔױאطቹԿԼ(a)(b)ᨠኘࠩΔᑷរᄵ৫੡ 95.6

CΔ

ֺᔷᙔ൷រؓ݁ᄵ৫೏પ 4.5

CΔڂ੡ڶᄵ৫೏܅ᄵऱլٵ૜سנᄵ৫ඪ৫ऱംᠲΔ२ࠐ࿇

෼ᄵ৫ඪ৫ᄎᖄીᑷᔢฝऱ۩੡ࠌ൓൷រףຒధᡏΔڂڼݺଚലᄎಘᓵᄵ৫ඪ৫ፖሽੌհ

ᣂএΖ

ቹԿԼΕڇഗࣨ 70o CΔ0.6 ڜഛՀ: (a)ࠟឍኔᎾಱሁᔷᙔ൷រհᄵ৫։ؒ;(b)໢࠷ԫឍᔷᙔ൷រհᄵ৫։ؒቹ;(c) ᔷᙔ൷រऎᔱᖄᒵ࠷ᖩኲ૿հᄵ৫։ؒቹΖ

ݺଚױאൕቹԿԼ࿇෼Δឈထሽੌ။ՕΔᄵ৫ՈᙟհՂ֒Δۖᑷរፖؓ݁ᄵ৫Ո။஁

။ڍΔڇ 0.6 ڜഛ஁ࠩ 4.5

CΖՈڂڼᄵ৫ඪ৫ΔྤᓵਢֽؓٻࢨਢিऴٻΔՈຟਢሽੌ။

Օඪ৫။Օऱ᝟ႨΔױא᧩෼။೏ሽੌழΔڂ੡ᔱᖄᒵ࿇ᑷ။ᣤૹΔࠀ׊ڂ੡ሽੌႃխய

ᚨΔլ݁֌ऱሽੌ։ؒທګᔷᙔ൷រᄵ৫Ո։ؒլ݁Ζዿ৵ലᄎ๻ऄޏ࿳ᑷሽயᚨΔࠌᔷ

រኂࡎ༼֒Δᅝྥ༉൓ൕ྇ᒷሽੌႃխயᚨፖ྇֟࿇ᑷထ֫Ζ

ቹԿԼΕ(a)ᔷᙔ൷រᑷរፖؓ݁ᄵ৫ᙟሽੌՕ՛հᣂএቹ;(b)ᔷᙔ൷រֱֽؓٻᑷඪ৫ፖিऴֱٻᑷඪ৫ᙟሽ ੌՕ՛հᣂএቹΖ

II.ޏ᧢ࢍຝ८᥆ᐋদ৫

5-Pm CuΔڇഗࣨ 70

Cፖሽੌ 0.6 ڜഛՀऱයٙՀΔᄵ৫։ؒൣݮڕቹԿԼԫ(a)Δࠡᑷ

រᄵ৫੡ 89.5

CΔؓ݁ᄵ৫੡ 87.3

CΔ஁ 2.3

CΖૠጩԫՀᄵ৫ඪ৫પ੡ 157.4

C/ֆ։Ζۖ

ޏګ 25-Pm CuΔڇഗࣨ 70

Cፖሽੌ 0.6 ڜഛՀऱයٙՀΔᄵ৫։ؒൣݮڕቹԿԼԫ(b)Δࠡ

ᑷរᄵ৫੡ 88.2

CΔؓ݁ᄵ৫੡ 87.0

CΔኙᚨᄵ৫ඪ৫પ੡ 105.8

C/ֆ։Δ྇܅ᔷᙔ൷រ

ᄵ৫ऱய࣠ਢ່ړऱΖૉਢངګ 25-Pm ྤሽᝳ᠛Δڇഗࣨ 70

Cፖሽੌ 0.6 ڜഛՀऱයٙՀΔ

ᄵ৫։ؒൣݮڕቹԿԼԫ(c)Δࠡᑷរᄵ৫੡ 91.5

CΔؓ݁ᄵ৫੡ 87.6

CΔኙᚨᄵ৫ඪ৫પ

੡ 290

C/ֆ։Δܛਢদ৫ֺᎭ 5PmদՂ๺ڍΔױਢڂ੡ሽॴ෷ৰ஁ΔᑷႚՈৰ஁ऱᒴਚΔ

ࢬא޲ڶሒࠩৰړ૾܅ᖙ܂ᄵ৫ऱய࣠Ζ

ቹԿԼԫΕڇഗࣨ 70oCΔ0.6 ڜഛՀ: (a)ࢍຝ८᥆ᐋޏ੡ 5Pm CuழΔऎᔱᖄᒵ࠷ᖩኲ૿հᄵ৫ቹ;(b)ࢍຝ८᥆ ᐋޏ੡ 20-Pm CuழΔऎᔱᖄᒵ࠷ᖩኲ૿հᄵ৫։ؒቹ; (c)ࢍຝ८᥆ᐋޏ੡ 20-Pm electroless NiழΔऎᔱᖄᒵ

࠷ᖩኲ૿հᄵ৫։ؒቹΖ

ቹԿԼԲፖቹԿԼԿΔז।ᄵ৫ፖሽੌऱԿଡᣂএΖଈ٣ᑷរᄵ৫Δڂ੡ᔱᖄᒵਢ׌

૞࿇ᑷᄭΔឈྥݺଚࠌشԱদᓂ࿨ዌΔ܀ኙ࣍྇ᒷᄵ৫ऱய࣠սྥڶૻΔ੷۟ؓ݁ᄵ৫ࠡ

ኔຟ஁լԱڍ֟Ζ܀ਢᄵ৫ඪ৫থᄎ஁ฆৰՕΔ׌૞ᝫਢڂ੡ྤሽᝳ᠛ऱᑷႚய࣠լړΔ

ᖄીᄵ৫஁ฆৰՕΔڶለՕऱᄵ৫ඪ৫Ζ

ቹԿԼԲΕ(a)լٵࢍຝ८᥆দ৫ፖޗᔆΔᔷᙔխᑷរፖሽੌհᣂএቹ;(b) լٵࢍຝ८᥆দ৫ፖޗᔆΔᔷᙔխ ؓ݁ᄵ৫ፖሽੌհᣂএቹΖ ቹԿԼԿΕլٵࢍຝ८᥆দ৫ፖޗᔆΔᔷᙔխᑷඪ৫ፖሽੌհᣂএቹ

ຏൄՕ୮ᄎܓش Black’s ֱ࿓ڤࠐૠጩሽ՗ข঴ऱࠌشኂࡎΔֱࠡ࿓ڤڕՀΚ

)

k T

Q

(

e x p

j

A

MTTF

1

ࠡխ A ਢൄᑇΔj ሽੌയ৫Δn ሽੌയ৫ऱਐᑇΔQ ੡੒֏౨Δk ီं౿೷ൄᑇΔۖ T ੡࿪

ኙᄵ৫Ζ៶طڼֆڤΔݺଚױא࿇෼ࠩᆖطޏ᧢ࢍຝ८᥆ᐋऱদ৫ᚨᇠױאڶயऱ༼ࣙᔷ

រኂࡎΔڂ੡ᏺףࢍຝ८᥆ᐋদ৫լႛࠌᔷរᇙऱ່Օሽੌയ৫྇ᒷΔՈࠌ൓ᖙ܂ᄵ৫૾

܅Δڂ੡ Cu ߜړऱሽࢤፖᑷႚΖ

III.ޏ᧢ࢍຝ८᥆ᐋሽॴ෷

٣ছ༼ࠩ׼ԫଡ྇ᒷሽੌႃխயᚨऱֱऄ༉ਢޏ᧢ࢍຝ८᥆ᐋऱሽॴ෷ΔՈط࣍ᔷរ

ኂࡎፖᄵ৫ᇿሽੌയ৫ஒஒઌᣂΖ੡Աא߻༼೏ᜳᓂሽॴ෷ທګৰՕ֒ᄵΔ៶ڼݺଚ༉ࠐ

઎ࠡᄵ৫ᐙ᥼Δݺଚױא࿇෼ೈॺሽॴ෷༼೏ৰڍΔܡঞࠡኔኙᄵ৫ऱᏺףਢ޲ڶৰՕऱ

஁ܑΔڇ 0.6 ڜഛऱழଢΔፖᑑᄷᑓী׽஁પ 6.7

CΔྥۖԫ౳ᖙ܂යٙႛڇ 0.2 ڜഛΔኙ

֒ᄵᐙ᥼ޓ՛Ζ

ቹԿԼ؄Εڇഗࣨ 70o CΔ0.6 ڜഛՀ:(a)ሽॴ෷ޏ੡ 295

P:-cm

P:-cm

P:-cm

P:-cm

ᔷᙔ൷រၦྒྷሽॴհ༓۶யᚨ

੡Աᨠኘᔷᙔ൷រڇၦྒྷሽॴழऱ༓۶யᚨΔ௽چආشԫጟᒵሁΔڕቹԿԼք(a)ࢬقΖ

Ղ૿ڶ؄ឍᔷᙔ൷រΔ؆൷ᑇଡᒵሁΔࠡխၦྒྷऱքଡᒵሁᑑုڇቹՂאঁᎅࣔၦྒྷֱڤΖ

รԫଡֱऄ(ቹԿԼք(b))Δሽੌᆖط 1 ᇆፖ 2 ᇆᒵሁΔၦྒྷ 4 ᇆፖ 5 ᇆऱሽۯ஁Δ٦ૠጩ

נሽॴΖֱऄԲ(ቹԼ԰(c))Δሽੌᆖط 1 ᇆፖ 4 ᇆᒵሁΔၦྒྷ 2 ᇆፖ 5 ᇆऱሽۯ஁Δ٦ૠ

ጩנሽॴΖֱऄԿ(ቹԿԼք(d))Δሽੌᆖط 1 ᇆፖ 2 ᇆᒵሁΔၦྒྷ 3 ᇆፖ 5 ᇆऱሽۯ஁Δ

٦ૠጩנሽॴΖร؄ଡֱऄ(ቹԿԼք(e))Δሽੌᆖط 1 ᇆፖ 2 ᇆᒵሁΔၦྒྷ 5 ᇆፖ 6 ᇆऱ

ሽۯ஁Δ٦ૠጩנሽॴΖ

ቹԿԼքΕ(a)ᒵሁऱؓ૿قრቹ;ᔷᙔፖᒵሁऱم᧯ቹΔ಻ٽၦྒྷሁஉ।قቹ:(b)ֱऄԫ;(c)ֱऄԲ; (d)ֱऄԿ; (e)ֱऄ؄Ζ

ၦྒྷਢܓشሽᄭࠎᚨᕴKeithley 2400Δਜף 0.2 ڜഛΔᙟထףᑷࣨࠎ࿯ഗࣨլٵᄵ৫Δ

ൕ 25

Cࠩ 150

CΔၦྒྷ؄ጟֱڤΔࠡ࿨࣠ڕՀቹԿԼԮΔױא࿇෼ࠡሽॴᙟᄵ৫Ղ֒ऱᣂ

এઌᅝߜړΔ؄ଡլٵֱڤऱሽॴᙟᄵ৫Ղ֒ऱএᑇ੡Κ5.1 × 10

Ε4.4 × 10

Ε4.3 × 10

Ε

4.9 × 10

K

Δڂ੡ݺଚၦྒྷࠩऱਢᑇጟ८᥆ऱ᜔ࡉΔࢬאࠡ࿨࣠ਢઌᅝ൷२ቃཚΖᅝڇ৛

ᄵऱழଢΔֱऄԫၦྒྷࠩऱሽॴ੡ 0.89 mΓΔ൷Հࠐࠉݧ੡ 0.87Ε0.96 ፖ 0.94 mΓ

ቹԿԼԮΕሽॴ੡ᄵ৫ऱᣂএቹΖ

ᇨڕհছ༼נऱΔط࣍៿དྷᔷᙔਢԫଡᒵࠩסჇ(line-to-bump)ऱ࿨ዌΔڂڼڇᔷᙔփ

ຝᔾ२ᔱᖄᒵऱԵՑᄎڶሽੌႃխயᚨΔΔڂڼሽੌയ৫ऱլ݁֌։ؒԫࡳᄎᐙ᥼ሽۯፖ

ሽॴऱᣂএΖቹԿԼԶΔܛ੡ᅝሽੌ੡ 0.2 ڜഛழऱሽੌയ৫։ؒΔ಻ٽݺଚၦྒྷ࿨࣠܂

৵ᥛ։࣫Ζ

ലሽੌയ৫։ؒ᠏ང੡ሽۯ։ؒൣݮΔቹԿԼ԰(a)Δױא࿇෼ሽۯ᧢֏ຟ࿇سڇᔱᖄ

ᒵऱຝٝΔۖ׊ൕቹԿԼ԰(b)ऱᖩኲ૿ሽۯ։ؒױא࿇෼ؐᢰऱሽۯ஁ਢ׳ᢰऱ 9 ଍Δຍ

ᑌᄎທګၦྒྷՂऱ஁ฆΔՈ༉ਢլٵۯᆜऱၦྒྷរᄎڶլٵऱሽۯ஁ଖΔ൓ࠩլٵऱሽॴ

ଖΖࠉᅃ௅ኔ᧭ၦྒྷԫᑌऱֱऄΔ࠷נᑓᚵऱሽॴଖΔٺܑ੡ 0.77Ε0.76Ε0.83 ፖ 0.83 m:Ζ

ᖞ෻ګ।ԲΖ࿨࣠࿇෼Δኔ᧭ၦྒྷຟֺᑓᚵ࿨࣠೏Δ೏પ 12 ۟ 14%Δ׌૞ਢڂ੡ᑓᚵආش

ऱሽॴ෷ਢڇ 20

CΔۖኔ᧭ၦྒྷᄵ৫ਢڇ 25 ࠩ 30

CΔױߠᑓᚵ࿨࣠ৰฤٽኔ᧭ၦྒྷΔൕ

ሽॴऱ༓۶யᚨױא֘ංሽੌႃխயᚨΖ

ቹԿԼ԰Ε(a)໢ԫឍᔷᙔऱሽۯ։܉ቹ;(b)ऎᔱᖄᒵ࠷ᖩኲ૿հሽۯ։܉ቹΖ Approach (node-node) Experimental (m:) Simulation (m:) 1 (4-5) 0.89 0.77 2 (2-5) 0.87 0.76 3 (3-5) 0.96 0.83 4 (5-6) 0.94 0.83 ।ԲΕኔ᧭ፖᑓᚵሽॴհֺለ।Ζ

ྥۖኔᎾሽॴଖၦྒྷۯᆜᚨᇠޏ੡ሽੌၞࠩᔷᙔऱᖄᒵছጤԫ੄၏ᠦΔߠቹ؄ԼΔڼ

ழࡳᆠࠡ੡ֱऄնΔൕᑓᚵ൓ࠩຍٺሽॴଖ੡ 7.7 m:Δڕ࣠෻ᓵૠጩڼ࿨ዌऱሽॴપ੡ 1.0

m:Δױߠڂ੡ሽੌሁஉፖሽੌႃխயᚨᐙ᥼հՀΔᖙ܂ሽॴ੡݁֌։ؒሽੌՀሽॴऱ 7.7

଍Ζ

؄Լ

ۖᅝᔷᙔ൷រڂ੡ሽᔢฝขس़֞ழΔࠡᐙ᥼ሽੌയ৫ፖሽۯऱ࿨࣠ڕቹ؄ԼԫΖᅝ

ขسԫଡ۾ᖕࢍຝ८᥆ᐋၲՑ 18%ऱ़֞ழΔֱऄԫࠩ؄ሽॴՂ֒ 0.12m:ΔՂ֒෷પ੡

15%ΔױਢֱऄնឈྥՂ֒ 0.5m:ΔױਢࠡՂ֒෷׽ڶ 6.5%Ζߠ।ԿΖࢬאᎅڕ࣠ݺଚუ

ೠྒྷڂ੡ሽᔢฝขس़֞ۖທګሽॴՂ֒Δֱऄԫࠩ؄ຟਢԫଡլᙑऱֱڤΖ

࿨ᓵ

ءڣ৫׌૞հ࿨࣠ڕՀ:ݺଚױאܓش IR ፖ 3-D ሽᆰᑓᚵࠐ։࣫נ៿དྷ࿨ዌհྡྷۘᑷ

யᚨΔࠀ׊࿇෼ڇᔱᖄᒵፖ UBM ԵՑ٦ຏሽऱመ࿓խᄎڶԫଡᑷរ(hot spot)ขسΔࠀ׊ᄎ

ᙟထ؆ףሽੌऱ༼೏ۖڶޓ೏ऱᄵࣙΔޓ൶ಘլٵ࿨ዌኙ࣍ᔷᙔ൷រऱሽᑷயᚨհᐙ᥼Ζ

ءઔߒޓܓش້֮ᔷᙔ࿨ዌΰKelvin bump probesαࠐᨠྒྷፖྒྷၦ៿དྷᔷᙔ෺࠹ሽᔢฝழ֞

੐ᔢฝፖګ९ऱ෼ွΔઔߒᔷᙔ࠹ሽᔢฝᐙ᥼ۖขسऱధᡏΖᔱᖄᒵऱ֡՚ᐙ᥼ሽᔢฝऱ

ధᡏழၴ੷ሰΔઔߒ࿨࣠᧩قΔڇઌٵऱຏሽ೶ᑇհՀΔ။ᐈፖ။࿍ऱᔱᖄᒵ๻ૠױא࢏

९ᔷᙔ࿨ዌհሽᔢฝధᡏழၴΖڇ᠖堚ٺጟᔷᙔհధᡏᖲࠫ৵Δآࠐઔߒհૹរലထૹڇ

ڕ۶ڶயލࠫሽᔢฝࢬທګհధᡏΖ

ءઔߒᆢऱઌᣂઔߒ࿨࣠Δ࣍ 94 ڣ࿇।࣍ Applied Physics Letter ཚעᓵ֮؄ᒧΕjournal of

material research

ԫᒧΕJournal of Electronic MaterialsΕഏᎾᄎᤜᓵ֮ԿᒧΖ

6

Ε೶ە֮᣸

1.

H. B. Huntington, J. Phys. Chem. Solid, 20, p76-87, 1961.

2.

J. R. Black, IEEE Trans Electron Device, ED-16, p338, 1969.

3.

I. A. Blech, J. Appl. Phys. 40ΰ2α, p485, 1969.

4. K. N. Tu, “Electromigration in

stressed thin films,” Phys. Rev.

B45, 1409 (1992).

5. K. N. Tu, C. C. Yeh, C. Y. Liu, and

C. Chen, Appl. Phys. Lett., 76, 7

(2000).

6. S. Brandenberg and S. Yeh, Surface Mount Int. Conference and Exposition, SMI 98

Procedings, p.337 (1998)

7. C. Y. Liu, C. Chen, C. N. Liao, and K. N. Tu, Appl. Phys. Lett., 75, 58 (1999).

8. C. Y. Liu, C. Chen, and K. N. Tu, J.

Appl. Phys, 88, 5703 (2000) .

೶ף 2006 TMS Annual meeting ઔ฾֨൓

Presentation schedule for Chih Chen’s group in 2006 TMS Annual meeting

3/13, Mon

EMPMD Council Meeting

ʳ

ʳ

ʳ

1.

3/15, Wed.

2.

3.

4.

5.

6.

7

2006 TMS Annual Meeting & Exhibition

཮᝼ࣁ؂ԃ೿཮ᖐᒤޑεࠠᏢೌ཮

᝼ϐ΋ǴୖуΓኧϷፕЎኧࣣ࣬྽౲ӭǴᏢೌࣚᆶ཰ࣚ೿ࢂ࣬྽࣮ख़೭ঁࣴ૸

཮ǴᖐΥߎឦǵഏౠǵଯϩη...฻೿Ԗߚதӭޑ᝼ᚒ૸ፕǴځύόЮӧԜሦୱϐ

୯ሞޕӜᏢࣚᆶ཰ࣚ஑ৎᆶ཮Ǵᆶ཮ύࡐӭፕЎ᝼ᚒϣ৒࣬྽кჴǴӢԜᆶځ

дୖуޣ૸ፕǴ೿Ԗ࣬྽ԏᛘǶךॺ׳Ԗ۩ӧᆶύᆶύࣴଣଣγǴऍ୯ UCLA

׷਑س׹࿶ჱ௲௤૸ፕ᎗ᒴӧႝᎂ౽ਏᔈۭΠޑୢᚒǴ٠Ъ๏ךॺࡐӭᝊ຦ޑ

ཀـǶ

Ԝԛ஥ሦᏢғୖу൑ԛЬाࣁ Lead Free solder implementation: Reliability,

Alloy Development, and new Technology: Electromigration and reliability

Ǵᆶ཮ύว

౜೚ӭว߄Ԗᜢܭႝᎂ౽ख़ाЎ᝘ޑբޣǴ೿р౜ӧԜԛޑ཮᝼ύǴ׳஥ٰ೚

ӭᆒߍޑᄽᖱϣ৒Ǵзךॺε໒౳ࣚǶᆶ཮ύёаว౜ځჴӧႝᎂ౽೭ঁሦୱǴ

ϝԖ೚ӭ҂ޕޑୢᚒሡाว௚ǴΨᗋԖߚதӭςޕޑୢᚒሡाլܺǶԶՔᒿ๱

౜ϞёឫԄႝηϡҹλЁκϯޑᖿ༈Ǵᙟ඲࠾းמೌڀԖཱུ٫ޑႝ܄کၨӳޑ

ණ዗ૈΚǴԜמೌς࿶ࡐදၹޑ೏௦Ҕӧଯஏࡋႝη࠾းౢ཰ύǶՔᒿ๱ჹܭ

ႝηϡҹфૈޑሡ؃ຫٰຫଯǴӧ౜Ϟޑႝၡ೛ी΢Ǵ؂΋ঁᙟ඲с༧܌܍ၩ

ޑႝࢬཇٰຫεǴ྽᏾ঁᙟ඲с༧ᡏᑈຫٰຫλਔǴ္य़ޑϟय़ϸᔈᆶႝ዗ޑ

࣬ϕਏᔈ༈Ѹ׳уᝄख़ǴӵՖ໒วཥޑ׷਑܈ࢂ૸ፕрཥޑှ،БݤǴ೭ჹܭ

۳ࡕޑᙟ඲࠾းࣴزΞࢂќ΋ঁख़ाޑࡷᏯǶԜԛୖᆶ୯ሞ཮᝼ᕇ੻ؼӭǴҁ

ჴᡍ࠻ޑࣴزԋ݀ӧႝᎂ౽ޑሦୱύࢂӧܭሦӃޑӦՏǴԖ೚ӭޑࣴزΨЇҔ

ډךॺޑፕЎǶୖу೭ঁ཮᝼ନΑགڙډ๱Ӝޑ TMS ԃ཮౰ݩޜ߻ޑ਻ݗѦǴ

׳Ԗᐒ཮ૈ୼ᆶ୯ሞޕӜ஑ৎᏢޣ཮य़٠ှᆶځ૸ፕǴ׆ఈஒٰૈӆ஥ሦᏢғ

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1. S. H. Chiu, T. L. Shao, Chih Chen*, D. J. Yao, and C. Y. Hsu, Infrared Microscopy of Hot

Spots Induced by Joule Heating in Flip-chip SnAg Solder Joints under Accelerated

Electromigration, Appl. Phys. Lett. 88, 022110 (2006) NSC 92-2216-E-009-008. SCI.

2. S. W. Liang, T. L. Shao, Chih Chen*, Everett CC Yeh, and K. N Tu, “Relieving Current

Crowding Effect in Flip-chip Solder Joints during Current Stressing”, J. Mater. Res. Vol.

21, No. 1, 137 (2006). NSC 92-2216-E-009-008.

3. C. K. Chou, C. A. Chen , S. W. Liang, and Chih Chen*, Redistribution of Pb-rich Phase

during Electromigration in Eutectic SnPb Solder Stripes, J. of Appl. Phys. 99, 054502

ʔ(2006). NSC 92-2216-E-009-008. SCI.

4. S. W. Liang, Y. W. Chang, and Chih Chen* , Effect of Al-trace dimension on Joule heating

and current crowding in flip-chip solder joints under accelerated electromigration, Appl.

Phys. Lett. 88, 172108 (2006). NSC 94-2216-E-009-021.SCI.

5. C. C. Wei and Chih Chen*, Critical Length of Eutectic SnPb Solder Stripe, Appl. Phys.

Lett. 88, 182105 (2006). SCI.

6.Ying-Chao Hsu, Yuan-Ming Huang, Chih Chen*, and Henry Wang, Interfacial Reaction and

Shear Strength of Pb-free SnAg2.5Cu0.8Sb0.5 and SnAg3.0Cu0.5Sb0.2 Solder Bumps on

Au/Ni(P) Metallization, J. of Alloy and Compound, 417, 180-186 (2006). SCI.

7. C. Y. Hsu, D. J. Yao*, S. W. Liang and Chih Chen, Everett C. C. Yeh, Temperature and

current-density distributions in flip-chip solder joints with Cu traces, J. Electronic

Materials. 35 (5): 947-953(2006). SCI.

8. S. W. Liang, Y. W. Chang, T. L. Shao, and Chih Chen*, K. N. Tu, Effect of 3-dimensional

Current and Temperature Distribution on Void Formation and Propagation in Flip-chip

Solder Joints during Electromigration, Appl. Phys. Lett. 89, 022117 (2006).

electromigration in flip-chip solder joints using Kelvin bump probes, Appl. Phys. Lett., 89,

032103 (2006)

10. C. K. Chou, Y. C. Hsu, and Chih Chen*, Electromigration in Eutectic SnPb Solder Stripes,

J. Electronic Materials. In press. SCI.

11. S. W. Liang, Y.W. Chang, and Chih Chen*, Geometrical effect of bump resistance

measurement by Kelvin structure. J. Electronic Materials. In press. SCI.

12 S. H. Chiu, D.J. Yao, and Chih Chen*, Effect of Al-trace dimension on electromigration

failure time of flip-chip solder joints, J. Electronic Materials. In press.

13. Chih Chen*, and S. W. Liang, invited review on “Electromigration Issues in Lead-Free

Solder Joints” J. Mater. Sci. : Materials in electronics. In press.

14. K. N. Tu, Chih Chen, and Albert T. Wu, Stress analysis of spontaneous Sn whisker growth,

J. Mater. Sci.: Materials in electronics. Invited review. In press.

Effect of Al-trace dimension on Joule heating and current crowding

in flip-chip solder joints under accelerated electromigration

S. W. Liang, Y. W. Chang, and Chih Chena兲

Department of Material Science and Engineering, National Chiao Tung University, Hsin-chu, Taiwan 30050, Republic of China

共Received 31 January 2006; accepted 27 March 2006; published online 25 April 2006兲

Three-dimensional thermoelectrical simulation was conducted to investigate the influence of Al-trace dimension on Joule heating and current crowding in flip-chip solder joints. It is found that the dimension of the Al-trace effects significantly on the Joule heating, and thus directly determines the mean time to failure共MTTF兲. Simulated at a stressing current of 0.6 A at 70 °C, we estimate that the MTTF of the joints with Al traces in 100␮m width was 6.1 times longer than that of joints with Al traces in 34␮m width. Lower current crowding effect and reduced hot-spot temperature are responsible for the improved MTTF. © 2006 American Institute of Physics.

关DOI:10.1063/1.2198809兴

To meet the relentless drive for miniaturization of por-table devices, flip-chip technology has been adopted for high-density packaging due to its excellent electrical charac-teristic and superior heat dissipation capability. As the re-quired performance in microelectronics devices becomes higher, the design rule indicates that in each bump the opera-tion current is expected to attain a value of 0.2 A, with fur-ther increase to 0.4 A likely in the near future.1Loading with such a high current at the confined space of the solder bump, electromigration inevitably becomes a critical reliability issue.2 In addition, during accelerated electromigration test, the applied current may reach 2.0 A,3 rendering substantial Joule heating in the solder bumps.4The total length of the Al trace is typically few hundreds to few thousands microme-ters, which corresponds to a resistance of approximately few hundreds milliohms or few ohms. In contrast, the resistances of the solder bumps and the Cu trace in the substrate are relatively low, typically in the order of few or tens of millio-hms. Therefore, the primary contributor for Joule heating in the solder joints is the Al trace.4As a result, the temperature in the bumps during accelerated testing is likely to be much higher than that of the ambient because of the Joule heating. The other critical issue is the current crowding effect in the solder bumps. The line-to-bump geometry is believed to ren-der undesirable current crowding behavior, resulting in el-evated current density in the solder regime than the average current density.5 These two issues play substantial roles in

the mean-time-to-failure共MTTF兲 analysis, as delineated by

Black’s equation,6

MTTF = A1

jnexp

冉

kT

冊

where A is a constant, j is the current density, n is a model parameter for current density, Q is the activation energy, k is the Boltzmann constant, and T is the average bump tempera-ture. It follows that the MTTF decreases exponentially with increasing bump temperature. Wu et al.7 conducted a series of electromigration tests for SnPb solder bumps, and ob-served that the MTTF decreased from 711 to 84 h as the

testing temperature was raised from 125 to 150 ° C at a cur-rent density of 5.0⫻103A / cm2. In addition, the MTTF de-creased from 277 to 84 h as the current density was doubled from 2.5⫻103_{to 5.0⫻10}3_{A / cm}2 _{at 150 ° C. Predicted by}

Black’s equation and validated experimentally by Wu et al., the stressing temperature and the current density both play substantial role in determining the observed MTTF.

Several intrinsic material characteristics contribute to the Joule heating and current crowding effects. They include the dimension of Al trace, the thickness of under bump

metalli-zation共UBM兲, the UBM materials, the solder materials, as

well as the dimension of passivation.8Among them, the di-mension of Al trace is believed to be the critical one. How-ever, no systematic studies have been initiated to elucidate the effect of Al-trace dimension in Joule heating and current crowding of the solder joints during electromigration. This is because the solder joints are completely encapsulated by Si die, underfill, and underlying substrate. Hence, it is some-what difficult to analyze the temperature fluctuation and the current density inside the solder joints. To overcome this problem, in this study we used a three-dimensional thermo-electrical simulation to identify the temperature and the cur-rent density inside the solder bumps. This study offers a bet-ter insight on the effect of Al-trace dimension in the Joule heating and current crowding during accelerated electromi-gration of solder joints.

To proceed our simulation, four models with identical structure of solder bumps and Cu lines but with different dimensions of Al trace were constructed. Shown in Fig. 1共a兲 is a standard model, which includes two SnPb solder bumps

connected by an Al trace of 1840␮m in length, 34␮m in

width, and 1.5␮m in thickness. For the second model, as

shown in Fig. 1共b兲, the width of the Al trace was increased to 100␮m with the remaining structure unchanged. Figure 1共c兲 exhibits the third model, in which the thickness of the Al

trace was adjusted to 4.4␮m with the remaining dimension

identical to those of the first model. It is noted that the sec-ond and the third model had the same cross-sectional area of Al trace. For the fourth model, as depicted in Fig. 1共d兲, a

shorter Al trace which is 670␮m less than the standard

model was used while the remaining features identical to those in the first model. The dimension of the Si chip was a兲_{Author to whom correspondence should be addressed; electronic mail:}

[email protected]

APPLIED PHYSICS LETTERS 88, 172108共2006兲

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7.0⫻4.8 mm2_{with its thickness of 290␮m. The dimension}

of the bismaleimide triazine 共BT兲 substrate was 5.4 mm in

width, 9.0 mm in length, and 480␮m in thickness. The bot-tom of the BT substrate was maintained at 70 ° C and the convection coefficient was set to be 10 W / m2° C in a 25 ° C ambient temperature. The intrinsic parameters of materials used in this simulation can be found in our previous publication.9 Constant currents, ranging from 0.1 to 0.6 A, were applied through the two Cu lines on the BT substrate. The current crowding effect can be relieved to some ex-tent by increasing the width or the thickness of the Al trace. In this letter, we designate the crowding ratio to be the maxi-mum current density inside the solder bump divided by the average current density in the UBM opening, which was ob-tained assuming the current spreads uniformly on the UBM opening. The crowding ratio indicates the degree of nonbal-ance in the current distribution in the solder bump. It is re-alized that the current crowding would accelerate the damage caused by electromigration because of the enhanced wind force in the current crowding region. Figures 2共a兲–2共d兲 dem-onstrate the cross-sectional views for the current density dis-tribution of the four models as they were stressed at 0.6 A. As shown, the local current density inside the solder bump near the entrance of the Al trace was reduced substantially in the second and the third model. The crowding ratio for the first model reached a value of 19.8. When the cross section of the Al trace was increased by 2.9 times, the crowding ratios were reduced down to 12.0 and 11.7 for the second and the third model, respectively. Since the geometry of the Al trace near the solder bump was not varied for the fourth model, the distribution of current remained the same as the first model. From our simulation, we conclude that increas-ing the cross section of the Al trace directly reduced the crowding ratio.

Furthermore, the dimension of the Al trace exerts signifi-cant effect on Joule heating of the solder bumps. Figures 3共a兲–3共d兲 illustrate the temperature distributions in the center cross sections for the four models when they experience a stress current of 0.6 A at 70 ° C. A hot spot inside the solder bump was observed near the entrance point of the Al trace into the solder bump just beneath the passivation opening. The mean temperature was obtained by averaging the node temperatures in a 70⫻70␮m2_{area, as shown in Fig. 3共a兲.}

The temperatures in the hot spot were 102.8, 81.7, 83.6, and 90.3 ° C for the four models, respectively, whereas the aver-age temperatures were 97.9, 80.6, 82.0, and 86.1 ° C, respec-tively. It can be seen that the Joule heating effect was greatly reduced when the cross section of the Al trace was increased.

Figures 4共a兲 and 4共b兲 show the hot-spot and average

tem-peratures as a function of the applied current up to 0.6 A. Also, the trend for lower stressing current behaves the same with smaller magnitude in temperature difference as that stressed by 0.6 A. Due to the hot spot, a thermal gradient was built up across the solder bump. The thermal gradient was derived from the temperature difference between the hot-spot and the average temperature of the solder close to the BT side, divided by the bump height. It can be observed that the second model exhibits the lowest thermal gradient among the four models.

In general, the Al trace is considered to be the primary Joule heating source during accelerated electromigration test as its cross-section area is typically one to two orders of magnitude less than that of the solder bump and the Cu line. Under the same applied current, the Joule heating power is proportional to the total resistance of the stressing circuit. The resistance of the Al trace for the first model was

1331 m⍀, whereas it decreased to 530, 551, 532 m⍀ for the

rest of the three models, respectively. Therefore, the Joule heating effect was less significant for the stressing circuit configuration with smaller total resistance. In addition, for the third and fourth models, the total resistance and the cross section for heat dissipation were almost identical, yet there is still 6.7 ° C difference in hot-spot temperature. Since the av-erage current density in the Al trace for the fourth model was about three times larger than that for the third model, the local Joule heat power, which is proportional to the square of the local current density, is likely to be responsible for the temperature difference in these two models.

Furthermore, the effect of Al-trace dimension on the

MTTF could be estimated using Eq.共1兲. For the same solder

joint with different dimensions of the Al traces under the

FIG. 1. The four models constructed in this study.共a兲 The first model with a 34-␮m-wide, 1.5-␮m-thick, and 1848-␮m-long Al trace.共b兲 The second model with a wider Al trace of 100␮m.共c兲 The third model with a thick Al trace of 4.4␮m.共d兲 The fourth model with a shorter Al trace of 1178␮m.

FIG. 2. The cross-sectional views for the current-density distribution in the solder bump when they were stressed by 0.6 A.共a兲 The first model. 共b兲 The second model.共c兲 The third model. 共d兲 The fourth model.

FIG. 3. The cross-sectional views for the temperature distribution in the solder bumps when they were applied by 0.6 A at 70 ° C.共a兲 The first model.共b兲 The second model. 共c兲 The third model. 共d兲 The fourth model.

172108-2 Liang, Chang, and Chen Appl. Phys. Lett. 88, 172108共2006兲

same stressing conditions, the activation energy Q and the constant A are kept identical for the four models. Choi et al. proposed that the term j−n_{in the equation needs to be revised}

to共cj兲−nin order to include the high current crowding effect in the solder joints. In addition, the temperature factor is

modified to共T+⌬T兲 to account for considerable Joule

heat-ing effect durheat-ing the accelerated electromigration test. Bran-denburg and Yeh found that n is equal to 1.8 for the eutectic solder joints when the average current density is employed, and the activation energy they measured was 0.5 eV for the

SnPb solder with Al/ Ni共V兲/Cu UBM.10 Since voids

typi-cally form near the entrance point of the Al trace where the solder experiences the maximum current density and the hot-spot temperature, we propose that the共cj兲 term to be taken as the maximum current density and the hot-spot temperature should be adopted for the共T+⌬T兲 term. For the solder joint in the standard model, the maximum current density reached

1.05⫻105_{A / cm}2 _{and the hot-spot temperature was}

102.8 ° C. For the solder joint with Al trace in 100␮m

width, the maximum current density was 6.39⫻104_{A / cm}2

and the hot-spot temperature was reduced down to 81.7 ° C. The MTTF would be 6.1 times longer than that of the stan-dard model under 0.6 A at 70 ° C, in which the relief of current crowding contributed about 2.5 times, and the de-crease in Joule heating contributed approximately 2.5 times on the lifetime increase. For the joint with Al trace in 4.4␮m thickness, the maximum current density decreased to 6.20⫻104_{A / cm}2_{and the hot-spot temperature was reduced}

to 83.6 ° C. The estimated MTTF would be 5.9 times longer than that of the standard. For the fourth model, the MTTF is about 1.7 times longer than that of the standard model, mainly due to lower Joule heating effect. It is noteworthy that the Joule heating effect could be further reduced if the length of the Al trace is further decreased, but the current crowding effect remains the same when only the length is changed. The above estimation demonstrates that the solder joints with wider or thicker Al traces could significantly crease the electromigration resistance. In addition, it also in-dicates that the Joule heating effect needs to be taken into account during the accelerated electromigration test. Other-wise, the MTTF may be underestimated.

In conclusion, the dimension of the Al trace plays a cru-cial role in the Joule heating effect during accelerated elec-tromigration test since the Al trace is the dominant heating source. The solder joints with wider or thicker Al trace would render reduced current crowding and Joule heating effects. Therefore, the electromigration lifetime would be ex-tended significantly for the solder joints with wider or thicker Al traces under the same stressing conditions.

The authors would like to thank the National Science Council of Taiwan for the financial support through Grant No. 94-2216-E-009-021. In addition, the assistance on simulation facility from the National Center for

High-Performance Computing共NCHC兲 in Taiwan is appreciated.

1

K. N. Tu, J. Appl. Phys. 94, 5451共2003兲.

2

International Technology Roadmap for Semiconductors, Assembly and Packaging Section, Semiconductor Industry Association, San Jose, CA, 2003, pp. 4–9.

3

W. J. Choi, E. C. C. Yeh, and K. N. Tu, J. Appl. Phys. 94, 5665共2003兲.

4

T. L. Shao, S. H. Chiu, Chih Chen, D. J. Yao, and C. Y. Hsu, J. Electron. Mater. 33, 1350共2004兲.

5

Everett C.C. Yeh, W. J. Choi, and K. N. Tu, Appl. Phys. Lett. 80, 4 共2002兲.

6

J. R. Black, IEEE Trans. Electron Devices ED-16, 338共1969兲.

7

J. D. Wu, P. J. Zheng, Kelly Lee, C. T. Chiu, and J. J. Lee, Proceedings of the 52th Electronic Components and Technology Conference, IEEE Com-ponents, Packaging, and Manufacturing Technology Society, San Diego, CA, 2002共unpublished兲, p. 452.

8_{S. W. Liang, T. L. Shao, and Chih Chen, J. Mater. Res. 21, 137共2006兲.} 9

S. H. Chiu, T. L. Shao, Chih Chen, D. J. Yao, and C. Y. Hsu, Appl. Phys. Lett. 88, 022110共2006兲.

10

S. Brandenburg and S. Yeh, Proceedings of Surface Mount International Conference and Exhibition, San Jose, CA, 23–27 August 1998共SMTA, Edina, MN, 1998兲, p. 337.

FIG. 4.共a兲 The hot-spot temperature. 共b兲 The average temperature. 共c兲 The thermal gradient in the solder bump as a function of applied current up to 0.6 A at 70 ° C for the four models.

172108-3 Liang, Chang, and Chen Appl. Phys. Lett. 88, 172108共2006兲

Effect of three-dimensional current and temperature distributions

on void formation and propagation in flip-chip solder joints

during electromigration

S. W. Liang, Y. W. Chang, T. L. Shao, and Chih Chena兲

Department of Material Science and Engineering, National Chiao Tung University, Hsin-chu, 30050 Taiwan, Republic of China

K. N. Tu

Department of Materials Science and Engineering, UCLA, Los Angeles, California 90095-1595

共Received 5 February 2006; accepted 23 May 2006; published online 13 July 2006兲

Effect of three-dimensional current distribution on void formation in flip-chip solder joints during electromigration was investigated using thermoelectrical coupled modeling, in which the current and temperature redistributions were coupled and simulated at different stages of void growth. Simulation results show that a thin underbump metallization of low resistance in the periphery of the solder joint can serve as a conducting path, leading to void propagation in the periphery of the low current density region. In addition, the temperature of the solder did not rise significantly until 95% of the contact opening was eclipsed by the propagating void. © 2006 American Institute of Physics.

关DOI:10.1063/1.2220550兴

Electromigration has become a critical reliability issue

for high-density solder joints in flip-chip technology.1,2

Electromigration-induced failures and mean time to failure 共MTTF兲 of flip-chip joints have been investigated for both eutectic SnPb and Pb-free solders.3–10It was found that voids were formed inside the solder adjacent to the underbump

metallization 共UBM兲,4 and propagated along the interface

between the solder and the UBM, causing opening failure of the joints when the voids eclipsed the entire contact opening. However, the mechanism of void nucleation and growth and especially the corresponding change of current distribution in the solder joint due to void formation are unclear. In particu-lar, it is unknown why some voids are formed at the periph-ery of the UBM opening under the dielectric, where the cur-rent density is low.8,11In Blech structure of Al stripes, Tu et

al. proposed that resistive vacancy might move to the low

current density region to form voids due to the high gradient of current density, which was as high as 1010_{A / cm}3_.12

How-ever, for flip-chip solder joint, the gradient is estimated to be only 1.33⫻106A / cm3owing to its large dimension.8 There-fore, the growth of voids in the periphery of the UBM open-ing, which is located at the low current density region, may not be driven by the gradient of current density. In this letter, three-dimensional finite element method was employed to simulate the effect of void formation on redistribution of current density and temperature in a flip-chip solder joint, especially in the periphery area where a low-resistance thin-film UBM exists.

Three-dimensional 共3D兲 thermoelectrical coupled

simu-lation was carried out by finite element analysis to find out the current density and temperature redistributions in our test

samples.13The model used was a SOLID69 eight-node

hexa-hedral coupled field element withANSYSsoftware. The elec-trical and thermal resistivities of the materials as well as the boundary conditions used in this modeling followed those of

our previous study.13 In our samples, the diameters of the passivation opening and the UBM opening were 85 and 120␮m, respectively. Figure 1共a兲 shows the cross-sectional view of the current density distributions before void growth when 0.28 A was applied to the bump. The Al trace, the UBM in the chip side, and the metallization in the substrate were ignored. It was found that the current crowded into the solder bump in the passivation opening. The current crowd-ing behavior near the entrance of the Al trace can be clearly demonstrated. The maximum current density reached 5.42 ⫻104_{A / cm}2_{, which is about 22 times higher than the}

aver-age value. It is proposed that this local high current density was responsible for the initial void formation due to flux divergence.4,6Figure 1共b兲 illustrates the temperature distribu-tion before void formadistribu-tion. The maximum temperature inside the solder bump was 109.6 ° C; therefore, the increase in temperature due to Joule heating was only 9.6 ° C. The tem-perature was quite uniform inside the bulk of the solder.

In stage I, a semicylindrical void, 45.5␮m in diameter and 13.0␮m in height, was formed inside the solder near the entrance of the Al trace. The current redistributed due to void formation, and the maximum current density occurred in the solder near the upper left corner of the periphery of the UBM opening under the Al trace. As shown in Fig. 2共a兲, void

for-a兲_{Author to whom correspondence should be addressed; electronic mail:}

[email protected]

FIG. 1. 共a兲 Cross-sectional view of current density distribution in solder joint before void formation;共b兲 corresponding cross-sectional view for tem-perature distribution.

APPLIED PHYSICS LETTERS 89, 022117共2006兲

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mation resulted in redistribution of current in two ways. First, current may drift farther along the Al trace, passing the void, and entered the solder. Second, the current may drain down to the solder through the surrounding UBM/ intermetallic layer共IMC兲 layer. It is intriguing that the UBM/ IMC layers served as a current path, directing the current into the upper left corner of the periphery of the UBM open-ing. Since the UBM/IMC layers have much higher electromi-gration resistance,2 voids are formed mainly inside the sol-der. It is clear that the solder on the left of the void has higher current density than that under the passivation open-ing. Therefore, voids may propagate toward the solder in the UBM periphery. Compared with that shown in Fig. 1, the maximum current density inside the solder has been reduced

to 4.43⫻104A / cm2 due to void formation. On the other

hand, the temperature inside the solder decreased slightly to 109.5 ° C, which was 0.1 ° C lower than that before void formation, as illustrated in Fig. 2共b兲. This may be attributed to the smaller crowding effect as a result of void formation. Since the maximum current density occurred near the periphery of the UBM opening, we assume that the void propagates toward the left-hand-side periphery, as illustrated

in Fig. 3共a兲. The void depleted 50% of the UBM opening,

which is denoted as stage II. Since the UBM/IMC layers still serve as a current path, the void may be able to propagate to the edge of the solder bump. Therefore, we postulate that the growth of void in the low current density region under the periphery of the UBM opening is mainly attributed to current redistribution, not to the gradient of current density. The maximum current density inside the solder bump reduced further to 4.04⫻104_{A / cm}2 _{due to void formation. Figure}

3共b兲 shows the corresponding temperature distribution in the solder bump. The maximum temperature in the solder was 109.3 ° C, which was 0.2 ° C lower than that in stage II. Again, this may be due to the smaller crowding effect in the solder joint at this stage. Although there was a slight increase

in temperature in the Al pad, the temperature inside the sol-der did not alter much at this stage. From the results reported by Gee et al.,11the shape of the void may resemble a pan-cake shape for solder joints with thin-film UBM. In addition, due to the limitation of our simulation modeling, semicylin-drical voids were adopted in this study. However, whether it is circular, semicircular, or irregular remains unclear at this moment, and needs further experimental investigation.

The void was then assumed to propagate to fill 80.5% of

the UBM opening, as shown in Fig. 4共a兲. It is denoted as

stage III. The current entered the joints through a smaller contact area, causing an increase in maximum current den-sity. It rose to 8.70⫻104_{A / cm}2_{, and almost the whole}

pas-sivation opening experienced current density higher than 1.0⫻104A / cm2. Therefore, void propagation would expe-dite in this stage. The maximum temperature in the solder bump increased to 109.4 ° C because of the higher current crowding effect at this stage, as shown in Fig. 4共b兲. In the absence of current flowing through the solder in the left-hand side of the joint, the temperature on the right-hand side was higher than that on the left-hand side. However, there was still no obvious temperature increase in the solder close to the entrance point of the current into the solder.

The solder in the passivation opening was completely depleted at this final stage, leaving a small amount of solder near the periphery of the UBM opening, as illustrated in Fig. 5共a兲. There was approximately 4.0% of contact area left for conducting the current at this stage. With further decrease in contact area, the maximum current density became 1.69

⫻105_{A / cm}2_{. The UBM/IMC layers served as a conducting}

path to direct the current to the remaining solder. Hence, the remaining solder near the periphery of the UBM opening could be completely depleted and failure followed. Figure 5共b兲 shows the temperature distribution at this stage. The maximum temperature in the solder bump was 110.4 ° C, which was 0.8 ° C higher than that before void formation.

TABLE I. The simulated maximum current density inside the solder, the corresponding crowding ratio as well as the bump resistance at each stage.

Original

bump Stage I Stage II Stage III Stage IV

Void proportion共area%兲 0 28.8 50.0 80.5 96.0

Maximum current density inside solder

共A/cm2_{兲 5.42⫻10}4 _4.43⫻104 _4.04⫻104 _8.70⫻104 _1.69⫻105

Bump resistance共m⍀兲 11.2 14.6 19.0 25.3 42.9

Maximum temperature inside solder共°C兲 109.6 109.5 109.3 109.4 110.4 FIG. 2. 共a兲 Cross-sectional view of current density distribution in solder

joint at stage I; 共b兲 corresponding cross-sectional view for temperature distribution.

FIG. 3. 共a兲 Cross-sectional view of current density distribution in solder joint at stage II; 共b兲 corresponding cross-sectional view for temperature distribution.

022117-2 Liang et al. Appl. Phys. Lett. 89, 022117共2006兲

Our simulation also shows that bump resistance in-creased gradually in the first three stages, and then inin-creased rapidly in the final stage, as shown in Table I. Bump resis-tance was defined as the decrease in voltage between the entrance point of the Al trace into the Al pad共disk兲 and the junction point of the Cu line with the solder joint. In stage I, the bump resistance increased from 11.2 to 14.6 m⍀. It

in-creased to 19.0 and 25.3 m⍀ in stages II and III,

respec-tively. It rose to 42.9 m⍀ in stage IV. This increase in bump resistance may also enhance the local Joule heating effect. However, no significant local Joule heating was found in the thermal simulation up to stage IV. This may be attributed to the fact that the major heating source was the Al trace.14In our model, the total resistance of the Al trace was about

1800 m⍀. Consequently, the increase in bump resistance

was quite small compared with that of the Al trace. In addi-tion, the increase in bump resistance was mainly due to the following manner: owing to void formation, the current needed to drift farther in the Al pad共disk兲, and then flowed down to the solder bump. Therefore, the local Joule heating

in the Al pad 共disk兲 increased when voids were formed.

Since there was good heat dissipation in the Si side, the increase in temperature due to void formation was quite small. Nevertheless, the increase might be higher when larger current was applied, since the overall Joule heating would be significantly higher at higher stressing current.

In summary, we have employed the 3D finite element method to simulate the current and temperature redistribu-tions due to the formation and propagation of a pancake-shape void in solder joints during electromigration. It is pro-posed that current redistribution is the main reason accounting for void formation and propagation, especially the propagation into the low current density region below the contact passivation. It is found that UBM provided a con-ducting path for current to go below the passivation, and it

directed the current to the periphery of the solder joint, which is in agreement with the experimental observation of void formation in those regions. Increase in temperature due to void formation was not significant since the major heat source was the Al trace and the applied current was as low as 0.28 A.

The authors would like to thank National Science Coun-cil of Taiwan of the Republic of China for the financial sup-port through Grant No. NSC 95-2218-E-009-022. In addi-tion, the assistance on simulation facility from the National

Center for High-performance Computing共NCHC兲 in Taiwan

is highly appreciated. 1

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Mater. 33 1350共2004兲. FIG. 4. 共a兲 Cross-sectional view of current density distribution in solder

joint at stage III.;共b兲 corresponding cross-sectional view for temperature distribution.

FIG. 5. 共a兲 Cross-sectional view of current density distribution in solder joint at stage IV;共b兲 corresponding cross-sectional view for temperature distribution.

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