郭春生 丁嫣 姜舶洋 廖之恒 蘇雅 馮士維

(北京工業(yè)大學(xué)信息學(xué)部電子科學(xué)與技術(shù)學(xué)院,北京 100124)

高效在線(xiàn)測(cè)量加速實(shí)驗(yàn)中雙極晶體管結(jié)溫方法的研究?

郭春生?丁嫣 姜舶洋 廖之恒 蘇雅 馮士維

(北京工業(yè)大學(xué)信息學(xué)部電子科學(xué)與技術(shù)學(xué)院,北京 100124)

(2017年2月23日收到;2017年8月20日收到修改稿)

針對(duì)晶體管在加速壽命實(shí)驗(yàn)和老煉實(shí)驗(yàn)等實(shí)際工程中結(jié)溫的在線(xiàn)測(cè)控問(wèn)題,本文基于大電流電學(xué)測(cè)溫方法研究了型號(hào)為2N3055的雙極大功率晶體管在恒定的集電極電壓Vce和集電極電流Ice條件下發(fā)射結(jié)電壓Vbe隨著溫度T變化的對(duì)應(yīng)關(guān)系.研究結(jié)果表明,溫度在40—140?C范圍內(nèi)時(shí),在集電極加載大功率電流電壓的條件下,發(fā)射結(jié)電壓隨溫度上升而線(xiàn)性減小,基極電流隨溫度變化不超過(guò)4%.通過(guò)理論推導(dǎo)恒定功率下發(fā)射結(jié)電壓與溫度的數(shù)學(xué)模型,證明了當(dāng)基極電流數(shù)值隨溫度變化不超過(guò)4%時(shí),Vbe-T關(guān)系曲線(xiàn)呈線(xiàn)性且理論上引起的溫度誤差不超過(guò)0.5?C,以此為基礎(chǔ)推導(dǎo)出一種新的在線(xiàn)測(cè)量加速實(shí)驗(yàn)中結(jié)溫測(cè)試公式.最后利用Phase11進(jìn)行對(duì)比驗(yàn)證實(shí)驗(yàn),證明了該方法的正確性.

功率器件,結(jié)溫,電學(xué)法,在線(xiàn)監(jiān)控

1 引 言

隨著半導(dǎo)體器件在軍事、航天、工業(yè)等方面的廣泛應(yīng)用,對(duì)半導(dǎo)體器件的可靠性要求越來(lái)越高.在實(shí)際應(yīng)用中,加速壽命實(shí)驗(yàn)和老煉實(shí)驗(yàn)是常用的預(yù)測(cè)器件壽命和檢測(cè)器件優(yōu)劣的實(shí)驗(yàn)方法,在國(guó)內(nèi)外具有廣泛的應(yīng)用[1?3].現(xiàn)行實(shí)驗(yàn)過(guò)程中,結(jié)溫通常利用線(xiàn)下測(cè)溫法獲得,即通過(guò)測(cè)量的恒定熱阻計(jì)算得到加速實(shí)驗(yàn)中的結(jié)溫.然而,該線(xiàn)下法測(cè)量結(jié)溫會(huì)引入較大誤差:1)熱阻是溫度的函數(shù),材料熱導(dǎo)率變化100?C時(shí)引入的熱阻變化達(dá)到20%[4];2)線(xiàn)下測(cè)溫方法中器件與散熱器之間的接觸熱阻并未考慮,而接觸熱阻通常是不可忽略的[5].并且,李霽紅等[6]提出,由于器件生產(chǎn)工藝等因素的限制,實(shí)驗(yàn)過(guò)程中結(jié)溫往往并不恒定.根據(jù)阿倫尼斯模型推斷,溫度每上升10?C,器件壽命就下降約一半,所以結(jié)溫的準(zhǔn)確與否直接關(guān)乎預(yù)測(cè)結(jié)果的準(zhǔn)確度.

為解決線(xiàn)下測(cè)溫的問(wèn)題,通常利用在線(xiàn)測(cè)溫法.現(xiàn)行的在線(xiàn)測(cè)溫法通常利用溫度敏感參數(shù)與結(jié)溫的對(duì)應(yīng)關(guān)系[7],通過(guò)測(cè)量校溫曲線(xiàn)的方式構(gòu)建校溫曲線(xiàn)庫(kù),從而做到對(duì)結(jié)溫的在線(xiàn)測(cè)量[8?12].Baker等[13]對(duì)絕緣柵雙極型晶體管器件利用峰值柵電流和溫度的對(duì)應(yīng)關(guān)系構(gòu)建校溫曲線(xiàn),從而達(dá)到測(cè)量結(jié)溫的目的.Munk-Nielsen等對(duì)金屬氧化物半導(dǎo)體器件的峰值電流和溫度的對(duì)應(yīng)關(guān)系進(jìn)行了研究,做出了相應(yīng)的校溫曲線(xiàn)以完成對(duì)結(jié)溫的測(cè)量[14].國(guó)內(nèi)有朱陽(yáng)軍等[15]利用校溫曲線(xiàn)對(duì)雙極晶體管的結(jié)溫進(jìn)行了在線(xiàn)測(cè)量的研究.

以上研究均對(duì)結(jié)溫的在線(xiàn)測(cè)溫問(wèn)題做出了有益的探索,但是現(xiàn)有方法中均需要先測(cè)量得到校溫曲線(xiàn)庫(kù),校溫曲線(xiàn)庫(kù)通常包括十幾條校溫曲線(xiàn),一條校溫曲線(xiàn)往往需要測(cè)量數(shù)個(gè)甚至十?dāng)?shù)個(gè)參考點(diǎn)才可以得到,并且需要利用軟件進(jìn)行擬合繪制,校溫曲線(xiàn)的測(cè)量需要專(zhuān)門(mén)的設(shè)備,成本高且嚴(yán)重影響效率,不利于工程上的實(shí)際應(yīng)用.針對(duì)加速實(shí)驗(yàn)和老煉實(shí)驗(yàn)等工程上的實(shí)際應(yīng)用,為簡(jiǎn)化校溫曲線(xiàn)的測(cè)量過(guò)程,避免復(fù)雜的數(shù)據(jù)處理及擬合繪制過(guò)程,本文以雙極型晶體管為例,在電壓Vce和電流Ice恒定的條件下對(duì)結(jié)電壓Vbe隨著溫度T的變化關(guān)系進(jìn)行了研究;分析發(fā)現(xiàn)以室溫下Ibe的數(shù)值為參考點(diǎn),當(dāng)Ibe的數(shù)值隨溫度變化不超過(guò)4%時(shí),理論上引起的溫度誤差不超過(guò)0.5?C.在此理論基礎(chǔ)上推導(dǎo)得到的Vbe-T的數(shù)學(xué)模型,證明Vbe-T曲線(xiàn)存在線(xiàn)性關(guān)系,并通過(guò)校溫實(shí)驗(yàn)證明了線(xiàn)性關(guān)系的準(zhǔn)確性.

由Vbe-T的數(shù)學(xué)模型提出了一個(gè)新的測(cè)試公式:在電壓Vce和電流Ice恒定的條件下測(cè)量得到一個(gè)參考點(diǎn)的基礎(chǔ)上,只需在線(xiàn)測(cè)量出結(jié)電壓Vbe,代入公式即可快速計(jì)算出結(jié)溫.該方法簡(jiǎn)化了復(fù)雜的數(shù)據(jù)處理過(guò)程和繪圖制表步驟,一條校溫曲線(xiàn)只需測(cè)量任意一參考點(diǎn)即可得到,提高了工程應(yīng)用的效率,實(shí)現(xiàn)了對(duì)結(jié)溫在線(xiàn)監(jiān)控的目的.

2 實(shí)驗(yàn)及校溫曲線(xiàn)

2.1 實(shí)驗(yàn)及所得數(shù)據(jù)圖像

為了方便利于加速壽命實(shí)驗(yàn)和老煉實(shí)驗(yàn)等某些實(shí)際工程上的應(yīng)用,本文基于電學(xué)測(cè)溫方法測(cè)量并給出了集電極電壓Vce和集電極電流Ice恒定時(shí)發(fā)射結(jié)電壓Vbe和溫度T的關(guān)系曲線(xiàn).

將型號(hào)為2N3055的雙極大功率晶體管放在溫箱里,引腳外接半導(dǎo)體精密測(cè)試儀AgilentB 1500 A,分別設(shè)定溫度為40,60,80,100,120,140?C,待溫度穩(wěn)定后,可認(rèn)為此時(shí)結(jié)溫即為溫箱設(shè)定溫度.實(shí)驗(yàn)中晶體管采用共射極接法:集電極加20 V電壓,發(fā)射極接地,基極分別加脈沖電流50μA— 13.15 mA,電流步長(zhǎng)50μA,脈寬500μs,周期1 ms,以避免自升溫對(duì)實(shí)驗(yàn)的影響.測(cè)量相同電流Ice條件下基極電流Ibe結(jié)果如表1所列,發(fā)射結(jié)電壓Vbe如圖1所示.

表1 基極電流Ibe數(shù)值與溫度對(duì)應(yīng)關(guān)系Table 1.Base current Ibevalue and temperature correspondence.

圖1 (網(wǎng)刊彩色)Vce=20 V時(shí)擬合的校溫曲線(xiàn)Fig.1.(color online)Vce=20 V,the fitting calibration curve.

從測(cè)量得到的實(shí)驗(yàn)數(shù)據(jù)可以發(fā)現(xiàn):在晶體管的實(shí)際工作中,當(dāng)電壓Vce和電流Ice恒定時(shí),基極電流Ibe會(huì)隨著溫度的變化而改變.

2.2 校溫曲線(xiàn)的擬合曲線(xiàn)

對(duì)實(shí)驗(yàn)測(cè)量得到的數(shù)據(jù)進(jìn)行線(xiàn)性擬合,得到Vce=20 V時(shí)不同電流Ice條件下對(duì)應(yīng)的擬合校溫曲線(xiàn),見(jiàn)圖1.擬合公式為Vbe=a+bT.

從圖1中可以看出擬合曲線(xiàn)和試驗(yàn)點(diǎn)基本重疊,符合較好.以Ice=50 mA為例,擬合公式中的常數(shù)為:a=0.72861,b=?0.00204,不同的Ice對(duì)應(yīng)的擬合公式中的常數(shù)見(jiàn)表2.

表2 不同的Ice對(duì)應(yīng)的擬合常數(shù)Table 2.Di ff erent Icecorresponding fitting constants.

由擬合校溫曲線(xiàn)和擬合公式可以得知:在電壓Vce和電流Ice恒定條件下發(fā)射結(jié)電壓Vbe和溫度T呈良好的線(xiàn)性關(guān)系.

3 理論推導(dǎo)

由半導(dǎo)體器件物理[16]可知,以npn為例,集電極電壓Vce會(huì)抽取(BE)結(jié)的電子擴(kuò)散電流,而對(duì)BE結(jié)的空穴擴(kuò)散電流沒(méi)有影響.因此,Vce對(duì)輸入特性曲線(xiàn)的影響在Vce＞1 V后,基本不變,表現(xiàn)為當(dāng)Vce＞1 V時(shí),輸入特性曲線(xiàn)不變.即BE結(jié)仍可用PN結(jié)電流電壓關(guān)系.由半導(dǎo)體物理中的PN知識(shí)可知[17]:由理想PN結(jié)(,其正)向電流IF和壓降VF存在關(guān)系可推知,發(fā)射結(jié)壓降Vbe和電流Ibe的關(guān)系

q為電子電荷,k為玻爾茲曼常數(shù),T為絕對(duì)溫度,IS為反向飽和電流中空穴電流,

C是與結(jié)面積和摻雜濃度有關(guān)的常數(shù),r也為常數(shù)(r的數(shù)值取決于少數(shù)載流子遷移率對(duì)溫度的關(guān)系).將(2)式代入(1)式兩邊取對(duì)數(shù)得,的影響.令I(lǐng)be為常數(shù),當(dāng)溫度從T1變?yōu)門(mén),發(fā)射結(jié)壓降Vbe1變?yōu)閂be時(shí),

下面討論非線(xiàn)性項(xiàng)

(3)式和(4)式聯(lián)立得

理想線(xiàn)性溫度相應(yīng)Vbe應(yīng)取如下形式:

將(7)式代入(6)式得

理想線(xiàn)性響應(yīng)和實(shí)際響應(yīng)相比較,理論偏差為

取r=3.4[18],T1=300 K,T=310 K,代入(9)式得?=0.048 mV,相應(yīng)Vbe的改變量約為20 mV,相比之下誤差為0.2%.所以可以忽略非線(xiàn)性項(xiàng)的影響,(3)式可寫(xiě)為

將溫度T1、電壓Vbe1、電流Ibe1代入(10)式得出,將lnC代入(10)式得

即晶體管從溫度T1對(duì)應(yīng)的發(fā)射結(jié)電壓Vbe1和基極電流Ibe1變化到溫度為T(mén)對(duì)應(yīng)的發(fā)射結(jié)電壓Vbe和基極電流Ibe的關(guān)系表達(dá)式.(11)式存在一個(gè)非線(xiàn)性項(xiàng)根據(jù)文獻(xiàn)中所述:結(jié)溫每上升1?C結(jié)電壓Vbe就會(huì)下降2 mV,即結(jié)電壓Vbe的偏差在毫伏量級(jí)以下時(shí)對(duì)結(jié)溫預(yù)測(cè)的影響小于0.5?C,可以忽略.所以,當(dāng)此非線(xiàn)性項(xiàng)的數(shù)值大小在10?3數(shù)量級(jí)以下時(shí),基本可以認(rèn)為該項(xiàng)對(duì)結(jié)電壓的數(shù)值影響不足以對(duì)結(jié)溫的預(yù)測(cè)造成影響.即當(dāng)時(shí),該項(xiàng)可以忽略.以室溫為參考點(diǎn),取T=300 K,Ibe1為室溫下基極電流大小,則當(dāng)即以室溫下基極電流數(shù)值為參考點(diǎn),基極電流數(shù)值Ibe隨溫度變化不超過(guò)4%時(shí),基極電流的變化的影響可以忽略不計(jì).

從表1中可以看出:晶體管正常工作條件下基極電流Ibe隨溫度的變化在3%—4%;根據(jù)表1中基極電流的數(shù)據(jù)計(jì)算非線(xiàn)性項(xiàng)T大概在10?3—10?4數(shù)量級(jí),相比結(jié)電壓Vbe幾百毫伏的數(shù)量級(jí)可以忽略不計(jì),且不對(duì)校溫曲線(xiàn)的精度造成影響.表3中列出了40?C條件下和140?C條件下該非線(xiàn)性項(xiàng)的大小,表4則列出了40?C條件下和60?C條件下該非線(xiàn)性項(xiàng)的大小.的數(shù)值都在10?3—10?4左右,可以忽略;即在晶體管的正常工作條件下,基極電流Ibe隨溫度的變化在4%以?xún)?nèi),對(duì)電流Ice恒定條件下Vbe-T的線(xiàn)性關(guān)系沒(méi)有影響.

由表3和表4的數(shù)值可以看出非線(xiàn)性項(xiàng)

表3 40?C條件下和140?C條件下非線(xiàn)性項(xiàng)的大小Table 3.The size of the nonlinear term at 40?C and 140?C.

表4 40?C條件下和60?C條件下非線(xiàn)性項(xiàng)的大小Table 4.The size of the nonlinear term at 40?C and 60?C.

4 結(jié)溫在線(xiàn)測(cè)量的方法的提出及驗(yàn)證

對(duì)實(shí)驗(yàn)測(cè)量得到的校溫曲線(xiàn)進(jìn)行擬合,證明了線(xiàn)性關(guān)系的真實(shí)存在,通過(guò)理論推導(dǎo)得到了(12)式,并與實(shí)驗(yàn)數(shù)據(jù)對(duì)比證明了公式的準(zhǔn)確性.該公式的提出簡(jiǎn)化了傳統(tǒng)電學(xué)測(cè)溫方法中復(fù)雜的測(cè)量工作和數(shù)據(jù)處理校準(zhǔn)工作,極大地提高了工程效率.在實(shí)際應(yīng)用過(guò)程中,只需要確定參考點(diǎn),即給定已知參數(shù)Vbe1和T1,無(wú)需關(guān)注電流Ibe的情況而在線(xiàn)測(cè)量出結(jié)電壓值Vbe即可迅速計(jì)算出該時(shí)刻的結(jié)溫.與傳統(tǒng)電學(xué)法測(cè)量結(jié)溫時(shí)需測(cè)量校溫曲線(xiàn)相比,該方法極大地減小了測(cè)量過(guò)程和測(cè)量時(shí)間,并避免了校溫曲線(xiàn)的繪制和擬合過(guò)程.在加速壽命實(shí)驗(yàn)和老煉實(shí)驗(yàn)等實(shí)際工程中可以利用此方法對(duì)結(jié)溫進(jìn)行在線(xiàn)監(jiān)控,確保結(jié)論的準(zhǔn)確性,在半導(dǎo)體可靠性領(lǐng)域有廣泛的應(yīng)用.

用美國(guó)Phase11分別測(cè)量雙極晶體管型號(hào)為2N3055的上表殼熱阻對(duì)應(yīng)的結(jié)溫和2SD1047的下表殼熱阻對(duì)應(yīng)的結(jié)溫,與用測(cè)試公式計(jì)算的結(jié)溫進(jìn)行了對(duì)比.型號(hào)2SD1047晶體管的校溫曲線(xiàn)見(jiàn)圖2,對(duì)比結(jié)果見(jiàn)表5和表6.

圖2 (網(wǎng)刊彩色)型號(hào)2SD1047晶體管的校溫曲線(xiàn)Fig.2.(color online)Model 2SD1047 transistor temperature calibration curve.

表5 晶體管型號(hào)2N3055的對(duì)比實(shí)驗(yàn)結(jié)果Table 5.Comparison of the transistor model 2N3055 experimental results.

從表中的數(shù)據(jù)可以清晰地看到:利用本方法所得到的結(jié)溫值略大于Phase11的測(cè)量值,誤差在0.7%以?xún)?nèi),與真實(shí)情況相符.所以,通過(guò)對(duì)比實(shí)驗(yàn)可以證明本文提出的新方法可以準(zhǔn)確快速地對(duì)晶體管的結(jié)溫進(jìn)行在線(xiàn)監(jiān)控測(cè)量.

表6 晶體管型號(hào)2SD1047的實(shí)驗(yàn)結(jié)果對(duì)比Table 6.Comparison of the transistor model 2SD1047 experimental results.

5 結(jié) 論

在電壓Vce恒定的條件下,通過(guò)對(duì)不同電流Ice條件下的校溫曲線(xiàn)的研究發(fā)現(xiàn):以室溫下基極電流數(shù)值為參考點(diǎn),當(dāng)基極電流數(shù)值隨溫度變化不超過(guò)4%時(shí),Vbe-T關(guān)系曲線(xiàn)具有良好線(xiàn)性關(guān)系,且理論上引起的溫度誤差在0.5?C以?xún)?nèi).對(duì)校溫曲線(xiàn)進(jìn)行線(xiàn)性擬合,發(fā)現(xiàn)實(shí)驗(yàn)數(shù)據(jù)和擬合曲線(xiàn)基本重疊,證實(shí)了線(xiàn)性關(guān)系的真實(shí)存在.基于理論公式推導(dǎo),提出了(12)式:在電壓Vce和電流Ice恒定的條件下,測(cè)量得到參考點(diǎn)的Vbe1和T1,實(shí)時(shí)測(cè)出Vbe,代入公式中就可實(shí)時(shí)計(jì)算出結(jié)溫.通過(guò)對(duì)比實(shí)驗(yàn)證明了該方法的準(zhǔn)確性和運(yùn)用此方法計(jì)算結(jié)溫的可行性.該方法的提出簡(jiǎn)化了傳統(tǒng)電學(xué)測(cè)量方法中復(fù)雜的實(shí)驗(yàn)過(guò)程和制圖步驟,極大地提高了效率,解決了在加速壽命實(shí)驗(yàn)和老煉實(shí)驗(yàn)等實(shí)際工程中對(duì)結(jié)溫快速在線(xiàn)監(jiān)控的問(wèn)題,確保了實(shí)驗(yàn)數(shù)據(jù)的可靠度,在器件可靠性研究領(lǐng)域有廣泛應(yīng)用.

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PACS:47.80.Fg,85.30.Pq,85.30.–z,84.37.+qDOI:10.7498/aps.66.224703

*ProjectsupportedbytheBeijingMunicipalCommissionoftheEducationFoundationofChina(GrantNo.KM201510005008).

?Corresponding author.E-mail:guocs@bjut.edu.cn

High-efficiency on-line measurement of junction temperature based on bipolar transistors in accelerated experiment?

Guo Chun-Sheng?Ding Yan Jiang Bo-Yang Liao Zhi-Heng Su Ya Feng Shi-Wei

(Deputy Dean,College of Electronic Science and Technology,Faculty of Information Technology,Beijing University of Technology,Beijing 100124,China)

23 February 2017;revised manuscript

20 August 2017)

Junction temperature is an important factor a ff ecting the reliabilities of semiconductor devices.Usually,the method of measuring the junction temperature is not tested on-line.However,due to the fact that neither contact thermal resistance nor thermal resistance varying with temperature is taken into account,there exists an error in the o ff-line measurement.A way to solve the problem of o ff-line measurement is to measure the junction temperature on-line.In this paper,we propose an electrical method of measuring the temperature rise of high-power bipolar transistor in the working condition.The measurement method is based on a good linear relationship between base-emitter voltage(Vbe)and temperature during the steady-state.Taking the model 2N3055 of bipolar high power transistor for example,in this paper we study the relationship between base-emitter voltage(Vbe)and temperature under the conditions of constant collector-emitter voltage(Vce)and collector-current(Ice).During the experiment,the device is placed in a thermostat.A voltage is applied to the device collector,a current is applied to the base,and the emitter is earthed.Before the device is measured,we set di ff erent temperatures and make sure that the equipment is in a steady state.In order to avoid the e ff ect of self-heating,the pulse current is used in the experiment.The pulse width and the period are 500μs and 1 ms,respectively.

The research result shows that the base-emitter voltage(Vbe)decreases linearly with temperature increasing and the base-emitter current is changed below 4%when the temperature is in a range of 40?C–140?C.In this paper we also deduce the mathematical expressions for base-emitter voltage(Vbe)and temperature under a steady state.It is proved that theVbe-temperatrue curve is linear and temperature error is less than 0.5?C when the changes of base current value does not exceed 4%.Therefore,in this paper we deduce a new method of testing the junction temperature in the speeding up measurement experiment.By measuring any of the reference points on the calibration curve under certain experimental conditions,the junction temperature can be calculated quickly according to the proposed formula.

Finally,the phase 11 is used to verify the proposed method.We measure the thermal resistance upper the case for the junction of model 2N3055 and the thermal resistance under the case for the junction of model 2SD1047.The measurement results of phase11are compared with the junction temperature calculated using the test formula.The results show that the error of junction temperature between the two methods is less than 0.7%,which is corresponding with the needs of practical application.It proves the correctness and feasibility of the method.

power device,junction temperature,electrical method,on-line monitoring

10.7498/aps.66.224703

?北京市教委基金(批準(zhǔn)號(hào):KM201510005008)資助的課題.

?通信作者.E-mail:guocs@bjut.edu.cn