微秒脈沖電場(chǎng)下Pb0.99(Zr0.95Ti0.05)0.9?8Nb0.02O3陶瓷擊穿過(guò)程電阻變化規(guī)律

劉藝 楊佳李興 谷偉 高志鵬

(中國(guó)工程物理研究院流體物理研究所,沖擊波物理與爆轟物理重點(diǎn)實(shí)驗(yàn)室,綿陽(yáng) 621900)

微秒脈沖電場(chǎng)下Pb0.99(Zr0.95Ti0.05)0.9?8Nb0.02O3陶瓷擊穿過(guò)程電阻變化規(guī)律

劉藝 楊佳?李興 谷偉 高志鵬?

(中國(guó)工程物理研究院流體物理研究所,沖擊波物理與爆轟物理重點(diǎn)實(shí)驗(yàn)室,綿陽(yáng) 621900)

(2016年12月12日收到;2017年1月23日收到修改稿)

陶瓷作為應(yīng)用非常廣泛的一種材料,其電擊穿問(wèn)題一直是研究的重點(diǎn)和熱點(diǎn).由于擊穿過(guò)程涉及熱、光、電多場(chǎng)耦合效應(yīng),目前還沒(méi)有一個(gè)普適的模型能夠解釋陶瓷擊穿問(wèn)題.針對(duì)此問(wèn)題進(jìn)行分析,實(shí)驗(yàn)中采用脈沖高壓發(fā)生裝置擊穿陶瓷,通過(guò)對(duì)陶瓷擊穿過(guò)程中等效電阻的研究,揭示了PZT95/5陶瓷樣品體擊穿和沿面閃絡(luò)形成過(guò)程的異同.結(jié)果顯示,在兩種擊穿模式下,陶瓷樣品內(nèi)部均會(huì)在40 ns左右形成導(dǎo)電通道,陶瓷等效電阻急劇下降至105?量級(jí);然后體擊穿與沿面閃絡(luò)的導(dǎo)電通道以不同的速率繼續(xù)擴(kuò)展;電阻減小速率與導(dǎo)電通道上載流子的濃度有關(guān),二者的等效電阻以不同速率減小,直至導(dǎo)電通道達(dá)到穩(wěn)定.

Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3,脈沖高壓,擊穿,等效電阻

1 引言

陶瓷的電擊穿現(xiàn)象是在各種高電壓設(shè)備研制和應(yīng)用過(guò)程中受到廣泛關(guān)注的問(wèn)題[1?6].在高電壓陶瓷電容器、高壓變壓器、高壓脈沖電源設(shè)計(jì)中,電擊穿問(wèn)題普遍存在,并且直接影響這些高壓器件的可靠性和壽命.電擊穿過(guò)程是一個(gè)非常復(fù)雜的物理過(guò)程,針對(duì)不同的介質(zhì)特性表現(xiàn)出不同的特點(diǎn).在前人研究的基礎(chǔ)上,目前已經(jīng)建立的電擊穿理論包括雪崩擊穿理論[7]、碰撞電離擊穿理論[8]和電荷陷阱理論等[9].但是,這些理論都無(wú)法對(duì)所有擊穿過(guò)程進(jìn)行準(zhǔn)確的描述;另外,上述理論都是基于均勻介質(zhì)展開(kāi)討論,基于復(fù)雜體系擊穿過(guò)程的研究還相對(duì)較少.陶瓷材料是工業(yè)中應(yīng)用最廣泛的材料之一,內(nèi)部存在晶粒、晶界、氣孔、雜質(zhì)等[10],對(duì)陶瓷這種典型復(fù)雜體系的介電擊穿進(jìn)行研究,有利于我們未來(lái)更好地認(rèn)識(shí)相關(guān)材料,為后續(xù)的器件設(shè)計(jì)提供理論基礎(chǔ).

鐵電陶瓷PZT95/5是一種典型的功能陶瓷,由于其自身的優(yōu)良儲(chǔ)能特性和壓電性能[11],受到了研究人員和工程師的廣泛關(guān)注.極化的PZT95/5陶瓷具有較高的儲(chǔ)能密度,在應(yīng)力作用下,能夠發(fā)生從鐵電相到反鐵電相的轉(zhuǎn)變,釋放束縛電荷并形成高功率的瞬態(tài)電能輸出,因此PZT95/5鐵電陶瓷廣泛用于脈沖能源裝置中[12?14].本文選擇極化PZT95/5作為研究對(duì)象,研究其在脈沖電場(chǎng)作用下的兩種典型擊穿現(xiàn)象,觀測(cè)PZT95/5陶瓷在脈沖電場(chǎng)下電擊穿過(guò)程中的電壓波形特征,結(jié)合電路模型分析計(jì)算,得到了樣品電阻隨擊穿過(guò)程的變化規(guī)律.這對(duì)未來(lái)壓電換能(PZT)陶瓷的設(shè)計(jì)與應(yīng)用具有非常重要的意義.

2 實(shí)驗(yàn)

2.1 樣品制備

實(shí)驗(yàn)所用PZT95/5采用固相合成法制備,以Pb3O4,ZrO2,TiO2和Nb2O5的粉體為原料,按分子式Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3的化學(xué)計(jì)量比配料,濕法球磨混勻后合成PZT95/5粉體.添加質(zhì)量分?jǐn)?shù)為6%的聚乙烯醇(PVA)黏結(jié)劑至粉體中,混合均勻過(guò)篩,然后在200 MPa壓強(qiáng)下干壓成型.坯體在排塑后放入坩堝,在鉛保護(hù)氣氛中燒結(jié).燒結(jié)后樣品進(jìn)行加工、清洗,絲網(wǎng)印刷銀電極,700?C下保溫0.5 h燒銀,最后在直流電場(chǎng)下對(duì)被銀樣品進(jìn)行極化.制備好的PZT95/5陶瓷的斷面掃描電子顯微鏡(SEM)照片如圖1所示.從圖中可以看出樣品陶瓷晶粒尺寸約為3—6μm,樣品致密,無(wú)明顯孔隙.該方法制備的PZT95/5陶瓷理論密度為7.8 g/cm3,實(shí)驗(yàn)樣品的相對(duì)密度約為97%.

圖1 PZT95/5陶瓷樣品斷面的SEM照片F(xiàn)ig.1.SEM image of PZT95/5 ceramic sample.

PZT95/5陶瓷的相結(jié)構(gòu)采用日本Mark Science公司MXPAHF型X射線衍射儀進(jìn)行表征,X射線衍射(XRD)圖譜如圖2所示.與PZT95/5標(biāo)準(zhǔn)圖譜[15]對(duì)比發(fā)現(xiàn),極化后的陶瓷樣品以菱方鐵電相[16]為主,存在少量的焦綠石相.這主要是由于樣品制備過(guò)程中Nb2O5摻雜容易使溶膠-凝膠的摻雜不均勻,以致反應(yīng)不完全,形成了少量焦綠石相[17].

圖2 PZT95/5陶瓷樣品的XRD圖譜Fig.2.XRD patterns of PZT95/5 ceramic sample.

實(shí)驗(yàn)樣品的靜態(tài)電滯回線采用德國(guó)aixACCT公司的TF Analyzer 2000系統(tǒng)測(cè)試,樣品厚度為2 mm,外加電壓頻率為0.1 Hz,結(jié)果如圖3所示.圖中曲線表現(xiàn)出明顯的鐵電相電滯回線特征:當(dāng)電場(chǎng)逐漸增大時(shí),PZT95/5陶瓷極化強(qiáng)度逐漸增大,繼續(xù)增加電場(chǎng)至2 kV/mm時(shí)陶瓷達(dá)到飽和極化;當(dāng)電場(chǎng)強(qiáng)度降低時(shí),極化強(qiáng)度也逐步降低,但電場(chǎng)強(qiáng)度降為零時(shí),極化強(qiáng)度不為零,此時(shí)的極化強(qiáng)度稱為剩余極化強(qiáng)度;當(dāng)電場(chǎng)反轉(zhuǎn)后,極化強(qiáng)度為零時(shí)的反轉(zhuǎn)電場(chǎng)強(qiáng)度稱為矯頑電場(chǎng)(約1.2 kV/mm).

圖3 PZT95/5陶瓷極化樣品電滯回線Fig.3.Hysteresis loop of polarized PZT95/5 ceramic sample.

2.2 實(shí)驗(yàn)設(shè)計(jì)

大量實(shí)驗(yàn)結(jié)果表明,電擊穿發(fā)生過(guò)程會(huì)在材料內(nèi)部或表面形成一條或多條擊穿通道(又稱導(dǎo)電通道),因此人們常常通過(guò)光學(xué)方法觀測(cè)擊穿通道的動(dòng)態(tài)變化特征,以此來(lái)研究透明電介質(zhì)材料的電擊穿規(guī)律,但PZT95/5陶瓷不具有透光特性,所以很難用光學(xué)方法直接觀察其擊穿通道變化.

本文主要通過(guò)測(cè)量材料等效電阻的變化來(lái)表征擊穿通道的產(chǎn)生和發(fā)展過(guò)程.利用微秒脈沖高壓發(fā)生裝置對(duì)PZT95/5陶瓷樣品進(jìn)行脈沖電壓加載,并對(duì)加載電壓進(jìn)行監(jiān)測(cè),通過(guò)電壓曲線的特征,分析電擊穿導(dǎo)電通道在PZT95/5陶瓷內(nèi)或表面的形成過(guò)程.實(shí)驗(yàn)裝置等效電路如圖4所示.

圖4 裝置等效電路圖Fig.4.Circuit of experimental setup.

圖4中T為調(diào)壓器,D為整流二極管,R1為充電電阻,C為脈沖電容,K為觸發(fā)開(kāi)關(guān),R2為限流電阻,R3為保護(hù)電阻,Rs為負(fù)載(PZT95/5陶瓷樣品),實(shí)驗(yàn)裝置相關(guān)參數(shù)如表1所示.實(shí)驗(yàn)裝置采用25號(hào)變壓器油作為絕緣保護(hù)介質(zhì),加載到PZT95/5陶瓷樣品兩端的電壓波形如圖5所示.

表1 實(shí)驗(yàn)裝置相關(guān)參數(shù)Table 1.Experimental con fi guration parameters.

圖5 加載電壓波形Fig.5.Applied voltage curve.

3 實(shí)驗(yàn)結(jié)果與討論

3.1 實(shí)驗(yàn)結(jié)果

體擊穿和沿面閃絡(luò)樣品擊穿過(guò)程中裝置輸出電壓變化如圖6所示.從圖中可以看出體擊穿和沿面閃絡(luò)發(fā)生后加載電壓均會(huì)陡降,體擊穿樣品的電壓變化率約為60 kV·μs?1,沿面閃絡(luò)樣品的電壓變化率約為14 kV·μs?1,明顯慢于體擊穿樣品的電壓變化率.

3.2 分析

對(duì)陶瓷材料而言,電擊穿是一個(gè)十分復(fù)雜的瞬態(tài)過(guò)程,目前還沒(méi)有準(zhǔn)確的模型能夠?qū)ζ錂C(jī)理進(jìn)行解釋.一般而言,PZT95/5陶瓷材料內(nèi)部存在少量微裂紋,在外電場(chǎng)的作用下裂紋的能量為靜電能和電-彈性能之和,裂紋尖端會(huì)產(chǎn)生嚴(yán)重的局部電場(chǎng)集中,隨著外部電場(chǎng)的增強(qiáng),施加到裂紋上的能量急劇增大,當(dāng)外部靜電能和電-彈性能高于裂紋的表面能時(shí),裂紋開(kāi)裂并逐漸擴(kuò)展,形成擊穿通道.

擊穿通道形成和發(fā)展的過(guò)程可簡(jiǎn)單地用材料等效電阻的變化過(guò)程來(lái)表征.PZT95/5陶瓷樣品在發(fā)生電擊穿前相當(dāng)于陶瓷電容器,表現(xiàn)為非線性電介質(zhì);隨著擊穿過(guò)程中導(dǎo)電通道的形成,樣品的電阻特性占據(jù)主導(dǎo)作用,此時(shí)可近似作為線性電介質(zhì)分析其等效電阻的變化.根據(jù)圖4實(shí)驗(yàn)電路模型,陶瓷樣品電阻Rs、樣品兩端電壓Us和裝置輸出電壓U在擊穿過(guò)程中的變化規(guī)律可用電路方程描述為

基于脈沖高壓發(fā)生裝置設(shè)計(jì)原理,擊穿發(fā)生時(shí)外部輸出電壓U基本不變,即dU/dt=0,且U=(Rs+R2)Us/Rs.由陶瓷樣品電阻的電阻率和尺寸參數(shù)可得,擊穿前Rs值在109?量級(jí),U約等于Us,由(1)式推導(dǎo)可得Rs與Us的關(guān)系為

(2)式中R2已知,常數(shù)A可以由陶瓷擊穿前樣品兩端電壓確定,得到樣品電阻Rs隨時(shí)間的變化曲線如圖7所示.

圖6陶瓷擊穿電壓波形Fig.6.The voltage change during body-breakdown and fl ashover.

圖7 所示為PZT95/5鐵電陶瓷電阻隨時(shí)間變化的曲線,根據(jù)曲線特征,可以將樣品電阻變化過(guò)程分成三個(gè)階段.在第一階段,擊穿發(fā)生40 ns左右,體擊穿與沿面擊穿的擊穿通道產(chǎn)生,樣品電阻從4×108?迅速下降至105?量級(jí),兩者的電阻變化速率一致,約為1010?·μs?1.在第二階段,樣品電阻從105?緩慢下降至102?量級(jí),但沿面擊穿與體擊穿的過(guò)程存在較大差別.首先,體擊穿可以分為兩個(gè)小階段,第I階段是樣品內(nèi)部孔洞或者微裂紋擊穿[20,21],在外加電場(chǎng)作用下,陶瓷內(nèi)部的孔洞或裂紋尖端處由于局部電場(chǎng)集中往往率先發(fā)生擊穿.第II階段是晶粒擊穿,孔洞或微裂紋擊穿后施加在晶粒上的電場(chǎng)強(qiáng)度增大,加上載流子產(chǎn)生的熱效應(yīng)的逐漸累積,最終使得晶粒發(fā)生擊穿.而沿面擊穿只有一個(gè)階段.其次,體擊穿達(dá)到穩(wěn)定狀態(tài)所需時(shí)間明顯比沿面閃絡(luò)更短.在第三階段,體擊穿和沿面閃絡(luò)樣品的電阻值逐漸趨于穩(wěn)定,分別達(dá)到130和20 ?.

圖7 陶瓷電阻變化曲線Fig.7.The resistance change during the bodybreakdown and fl ashover.

通常來(lái)講,在電場(chǎng)作用下鐵電陶瓷發(fā)生電擊穿時(shí),首先在極短的時(shí)間內(nèi)形成導(dǎo)電通道,將陶瓷兩極貫穿,樣品電阻急劇下降,同時(shí)產(chǎn)生高溫[22],進(jìn)一步燒蝕通道周圍的介質(zhì),導(dǎo)致樣品等效電阻進(jìn)一步下降,此后隨著導(dǎo)電通道的成形,電阻值逐漸趨于穩(wěn)定.體擊穿與沿面閃絡(luò)的區(qū)別在于:導(dǎo)電通道路徑上載流子濃度不同[23,24],導(dǎo)致其等效電阻變化規(guī)律不同.對(duì)于體擊穿,在導(dǎo)電通道成長(zhǎng)階段,其附近載流子濃度更高,有利于電子傳導(dǎo),導(dǎo)致等效電阻減小速率比沿面閃絡(luò)更快,放熱效應(yīng)也更加明顯,對(duì)陶瓷的燒蝕分解更加直接,導(dǎo)電通道內(nèi)部的溫度更高,內(nèi)部等離子體擴(kuò)散系數(shù)更大[25],因此減少了達(dá)到穩(wěn)定狀態(tài)所需要的時(shí)間;而對(duì)于沿面閃絡(luò)而言,導(dǎo)電通道路徑在陶瓷與絕緣油的界面上,其載流子濃度更低[26],擊穿過(guò)程中的放熱效應(yīng)更弱,使得導(dǎo)電通道的生長(zhǎng)速率相對(duì)較慢,在擊穿后期,絕緣油擊穿產(chǎn)生的碳化物逐漸附著在沿面閃絡(luò)通道上,使得等效電阻繼續(xù)降低,所以沿面閃絡(luò)等效電阻的最終穩(wěn)定值比體擊穿更小.

圖8為沿面閃絡(luò)和體擊穿樣品擊穿通道的SEM照片.沿面閃絡(luò)通道的燒蝕程度較弱,以箭頭符號(hào)表示的燒蝕區(qū)域明顯少于未燒蝕區(qū)域;體擊穿燒蝕程度較強(qiáng),擊穿通道上形成了明顯的熔融區(qū),表明體擊穿過(guò)程的放熱效應(yīng)確實(shí)要強(qiáng)于沿面閃絡(luò)過(guò)程.

圖8 沿面閃絡(luò)和體擊穿樣品擊穿通道的SEM照片(a)沿面閃絡(luò);(b)體擊穿Fig.8.SEM images of PZT95/5 ceramic samples under fl ashover and body-breakdown:(a)Flashover;(b)body-breakdown.

4 結(jié)論

本文研究了PZT95/5陶瓷在脈沖高電壓作用下的電擊穿現(xiàn)象.根據(jù)擊穿過(guò)程中樣品上的電壓響應(yīng)變化得到了電擊穿過(guò)程中電阻隨時(shí)間的變化;基于電阻變化曲線特征,將擊穿過(guò)程劃分為三個(gè)階段,即擊穿通道產(chǎn)生階段、擊穿通道擴(kuò)展階段和擊穿通道穩(wěn)定階段;在擊穿通道擴(kuò)展階段,介質(zhì)載流子濃度的差異導(dǎo)致體擊穿的導(dǎo)電通道擴(kuò)展速率明顯快于沿面閃絡(luò)的導(dǎo)電通道擴(kuò)展速率.

[1]Farouk A M 2014 High Voltage Engineering(Boca Raton:CRC press)pp299–349

[2]Hemmert D,Holt S,Krile J 2007 Proceedings of 10th Annual Directed Energy SymposiumHuntsville,USA,November 5–8,2007 p5

[3]Matsushima H,Okino H,Mochizuki K,Yamada R 2016 J.Appl.Phys.119 154506

[4]Kim S C,Heo H,Moon C,Nam S H 2016 IEEE Trans.Plasma Sci.44 687

[5]Du J F,Liu D,Bai Z,Yu Q 2016 Jpn.J.Appl.Phys.55 054301

[6]Shkuratov S I,Talantsev E F,Menon L,Temkin H,Baird J 2004 Rev.Sci.Instrum.75 2766

[7]Forster E O 1990 J.Phys.D Appl.Phys.23 1507

[8]Whitehead S 1953 Dielectric Breakdown of Solids(Oxford:Clarendon Press)pp37–54

[9]Tu D M,Wang X S 1993 Acad.J.Xi’an Jiaotong Univ.27 33(in Chinese)[屠德民,王新生1993西安交通大學(xué)學(xué)報(bào)27 33]

[10]Qu Y F 2007 Physical Behavior of Functional Ceramics(Beijing:Chemical Industry Press)pp107–118(in Chinese)[曲遠(yuǎn)方2007功能陶瓷的物理性能(北京:化學(xué)工業(yè)出版社)第107—118頁(yè)]

[11]Wang Y L 2003 Properties and Applications of Functional Ceramics(Beijing:Science Press)pp146–154(in Chinese)[王永齡2003功能陶瓷性能與應(yīng)用(北京:科學(xué)出版社)第146—154頁(yè)]

[12]Han S M,Huh C S 2016 IEEE Trans.Plasma Sci.44 1429

[13]Hu Y H,Yao H Y,Yu Z J,Wang Y Z 2016 Rare Metal Mat.Eng.45 571

[14]Du J M,Zhang Y,Zhang F P,He H L,Wang H Y 2006 Acta Phys.Sin.55 2584(in Chinese)[杜金梅,張毅,張福平,賀紅亮,王海晏2006物理學(xué)報(bào)55 2584]

[15]Lan C F,Nie H C,Chen X F,Wang J X,Wang G S,Dong X L,Liu Y S,He H L 2013 J.Inorg.Mater.28 503(in Chinese)[蘭春鋒,聶恒昌,陳學(xué)鋒,王軍霞,王根水,董顯林,劉雨生,賀紅亮2013無(wú)機(jī)材料學(xué)報(bào)28 503]

[16]Hall D A,Evans J D S,Covey-Crump S J,Holloway R F,Oliver E C,Moria T,Withers P J 2010 Acta Mater.58 6584

[17]Wang J X,Wang J,Yang S Y,Bian L 2009 J.Lanzhou Univ.Technol.35 22(in Chinese)[王軍霞,王進(jìn),楊世源,邊亮2009蘭州理工大學(xué)學(xué)報(bào)35 22]

[18]Lysne P C 1977 J.Appl.Phys.48 4565

[19]Wen D Y,Lin Q W 1997 Detonation and Shock Waves 3 27(in Chinese)[溫殿英,林其文1997爆轟波與沖擊波3 27]

[20]Jiang Y X,Wang S Z,He H L 2014 Chin.J.High Pressure Phys.28 680(in Chinese)[蔣一萱,王省哲,賀紅亮2014高壓物理學(xué)報(bào)28 680]

[21]Zhang F P,Du J M,Liu Y S,Liu Y,Liu G M,He H L 2011 Acta Phys.Sin.60 057701(in Chinese)[張福平,杜金梅,劉雨生,劉藝,劉高旻,賀紅亮2011物理學(xué)報(bào)60 057701]

[22]Pakhotin V A,Zakrevskii V A,Sudar N T 2015 Tech.Phys.60 1149

[23]He L,Ji Y Z,Liu G C 2007 J.Changchun Univ.28 165(in Chinese)[賀莉,紀(jì)躍芝,劉國(guó)彩2007長(zhǎng)春工業(yè)大學(xué)學(xué)報(bào)28 165]

[24]Zhang F H 2008 Ph.D.Dissertation(Xi’an:Shaanxi University of Science&Technology)(in Chinese)[張方暉2008博士學(xué)位論文(西安:陜西科技大學(xué))]

[25]Lu Q M,Yang W H,Liu W D 2004 Nucl.Fusion Plasma Phys.24 33

[26]Slutsker A I,Hilyarov V L 2011 Phys.Solid State 53 1325

PACS:77.22.Jp,77.90.+kDOI:10.7498/aps.66.117701

Resistance of Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3under high voltage microsecond pulse induced breakdown?

Liu YiYang Jia?Li XingGu WeiGao Zhi-Peng?
(National Key Laboratory of Shock Wave and Detonation Physics,Institute of Fluid Physics,China Academy of Engineering Physics,Mianyang 621900,China)

12 December 2016;revised manuscript

23 January 2017)

Ferroelectric ceramics have been widely used in lots of fi elds,such as mechanical-electric transducer,ferroelectric memory,and energy storage devices.The dielectric breakdown process of ferroelectric ceramic has received much attention for years,due to the fact that this issue is critical in many electrical applications.Though great e ff orts have been made,the mechanism of dielectric breakdown is still under debate.The reason is that the electrical breakdown is a complex process related to electrical,thermal,and light e ff ects.In the present work,we investigate the breakdown process of Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3(PZT95/5)ceramic,which is a kind of typical ferroelectric ceramic working in the high voltage environments.The high voltage pulse generator is used in the breakdown experiments to apply a square pulsed voltage with an amplitude of 10 kV and a width of 7μs.The resistivity change in the breakdown process is recorded by the high-frequency oscillograph in nano-second.The results show that there are two di ff erent breakdown types for our sample,i.e.body-breakdown and fl ashover.To better understand the breakdown mechanism of the PZT95/5 ceramic,the formation of the conductive channel in ceramic in the process is investigated by comparing the resistivity development in body-breakdown and fl ashover processes.The development of the conductive channel formation can be divided into three steps in body-breakdown.In the fi rst step that lasts for the fi rst 40 ns of breakdown,the conductive channel starts forming,with the equivalent resistance sharply decreasing to about 105? in the mean time.Then,i.e.in the second step,conductive path grows into a stable one with the equivalent resistance decreasing to the magnitude of about 102?.The resistance decreases slowly to about 130 ? in the third step,which means that the conductive channel is completely formed.The channel formation of fl ashover can also be divided into three steps.The fi rst step is similar to that of body-breakdown,with the equivalent resistance decreasing to about 105? in about 40 ns.In the second step of fl ashover,the conductive path keeps growing into a stable one with the equivalent resistance decreasing to 102?,but with a di ff erent resistance changing rate from that in body-breakdown,and the resistance decreases slowly to about 20 ? in the end.Di ff erent behavior between the body-breakdown and the surface fl ashover can be explained by di ff erent carrier densities on the conductive paths in the two breakdown processes.In the body-breakdown,the carrier density in the conductive channel is higher than that in the surface fl ashover,which improves the electron transfer and reduces the resistance.This may explain the reason why the channel formation in body-breakdown is faster than in fl ashover.This study is helpful for further materials design and applications.

Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3,high voltage pulse,breakdown,equivalent resistance

10.7498/aps.66.117701

?沖擊波物理與爆轟物理國(guó)防科技重點(diǎn)實(shí)驗(yàn)室基金(批準(zhǔn)號(hào):2016Z-04)資助的課題.

?通信作者.E-mail:whuyj168@126.com

?通信作者.E-mail:z.p.gao@foxmail.com

?2017中國(guó)物理學(xué)會(huì)Chinese Physical Society

http://wulixb.iphy.ac.cn

*Project supported by the Science and Technology Foundation of National Key Laboratory of Shock Wave and Detonation Physics(Grant No.2016Z-04).

?Corresponding author.E-mail:whuyj168@126.com

?Corresponding author.E-mail:z.p.gao@foxmail.com