房 慧, 阮興祥, 毛春瑜, 梁 程, 黃翠萍, 白小花

(1. 廣西民族師范學(xué)院 物理與電子工程學(xué)院, 廣西 崇左 532200;2. 北京工業(yè)大學(xué) 新型功能材料教育部重點(diǎn)實(shí)驗(yàn)室, 北京 100124)

雜化效應(yīng)誘導(dǎo)壓縮應(yīng)變碳納米管能帶結(jié)構(gòu)研究

房 慧1,2, 阮興祥1, 毛春瑜1, 梁 程1, 黃翠萍1, 白小花1

(1. 廣西民族師范學(xué)院 物理與電子工程學(xué)院, 廣西 崇左 532200;2. 北京工業(yè)大學(xué) 新型功能材料教育部重點(diǎn)實(shí)驗(yàn)室, 北京 100124)

采用第一性原理對(duì)壓縮應(yīng)變下超小口徑碳納米管的帶隙和能帶結(jié)構(gòu)展開研究?？偰芮€顯示(3,0)～(8,0)單壁碳納米管在小于10%的小應(yīng)變區(qū)展現(xiàn)彈性行為。能帶結(jié)構(gòu)的計(jì)算結(jié)果顯示,超小口徑的(3,0)、(4,0)、(5,0)、(6,0)碳納米管能在較大的壓縮應(yīng)變(<10%)下較好地保持金屬性,而管徑相對(duì)較大的(7,0)、(8,0)碳納米管實(shí)現(xiàn)了半導(dǎo)體性到金屬性的轉(zhuǎn)變,表明超小口徑碳納米管在壓縮應(yīng)變下不同常規(guī)的大口徑碳管的電學(xué)行為。進(jìn)一步的分析表明,超小口徑碳納米管帶隙的變化行為與傳統(tǒng)大口徑碳納米管的不同結(jié)果主要來源于嚴(yán)重卷曲引發(fā)的σ-π雜化效應(yīng)對(duì)費(fèi)米能級(jí)附近帶態(tài)的能量和性質(zhì)產(chǎn)生劇烈的影響,進(jìn)而說明基于傳統(tǒng)碳納米管的規(guī)律已不適用于超小口徑碳納米管。

單壁碳納米管; 壓縮; 應(yīng)變; 電子結(jié)構(gòu); 第一性原理

0 引 言

碳納米管因其獨(dú)特的力學(xué)[1]和電學(xué)[2]特性成為電子學(xué)、光學(xué)和應(yīng)力傳感納米器件相關(guān)科學(xué)研究中的明星材料。理想的單壁碳納米管可以看成由石墨烯片卷曲而成的無縫中空管狀結(jié)構(gòu),其電學(xué)特性與其自身的原子幾何排列結(jié)構(gòu)尤其是它的石墨烯片的卷曲矢量(手性參數(shù))[3]密切相關(guān)。單壁碳納米管分為3類:鋸齒型(n,0)、扶手椅型(n,n)和手性管(n,m)。對(duì)于較大管徑的單壁碳納米管而言,通過它們的帶隙可以分為金屬性管和半導(dǎo)體性管。利用扭轉(zhuǎn)、軸向拉伸和彎曲等形變施加的機(jī)械載荷是誘發(fā)帶隙的變化或金屬性致半導(dǎo)體性轉(zhuǎn)變 (MST)的一種有效手段。由于應(yīng)變能使費(fèi)米點(diǎn)在電子子態(tài)所形成的分立平行線間移動(dòng),因此大多數(shù)的單壁碳納米管展現(xiàn)出鋸齒型的MST模式[4]。對(duì)于鋸齒型(n,0)管[5],其帶隙在拉伸應(yīng)變下隨應(yīng)變量而變化。MST發(fā)生時(shí)所對(duì)應(yīng)的應(yīng)變量隨直徑的減小而增加。然而,至今為止大多數(shù)的研究僅僅集中在直徑大于5埃的碳納米管。近來,直徑小于5埃的超小口徑單壁碳納米管的手性結(jié)構(gòu)已經(jīng)能夠能過透射電子顯微技術(shù)確定[6]。相關(guān)研究顯示這些超小口徑單壁碳納米管的許多性質(zhì)將不同于通常研究的大口徑碳納米管。例如,Bogár等[7]提出小口徑的鋸齒型單壁碳納米管能在小形變過程中很好的保持其金屬性,許多相關(guān)的研究也證實(shí)了這一結(jié)論[8-11]。由于嚴(yán)重卷曲引起σ和π態(tài)雜化, 超小口徑單壁碳納米管趨向于展現(xiàn)與螺旋手性無關(guān)的金屬性[8,12-13]。這一結(jié)果意味著傳統(tǒng)碳納米管分類準(zhǔn)則將不再適合于這些超小口徑的碳納米管。本論文對(duì)較大壓縮應(yīng)變下超小口徑單壁碳納米管能帶結(jié)構(gòu)的理論研究顯示這些碳納米管能在大的壓縮形變下較好的保持金屬屬性,進(jìn)而說明σ-π雜化對(duì)超小口徑單壁碳納米管的電學(xué)特性產(chǎn)生重要的影響。

1 理論模型和計(jì)算方法

1.1 理論模型

采用手性參數(shù)(n,m)確定的理想結(jié)構(gòu)對(duì)超小口徑單壁碳納米管建立計(jì)算模型,碳-碳鍵長采用1.42 ?的實(shí)驗(yàn)測定的鍵長值。理論模擬中所采用的模型如圖1所示。對(duì)于獨(dú)立單壁碳納米管采用1.0 nm的真空層以去除相鄰結(jié)構(gòu)的相互作用。計(jì)算流程上,首先對(duì)所有Zigzag單壁碳納米管初始結(jié)構(gòu)進(jìn)行弛豫使每個(gè)碳原子的受力小于0.01 eV/?以獲取穩(wěn)定的平衡結(jié)構(gòu)。通過在管軸方向施加拉伸應(yīng)變?chǔ)?(L-L0)/L(L0為未施加應(yīng)變的單壁碳納米管單胞Z軸向的基矢長度,L則是施加拉伸應(yīng)變后管軸方向單胞基矢長度)后進(jìn)行結(jié)構(gòu)弛豫來獲取應(yīng)力應(yīng)變下的平衡構(gòu)型。

圖1 (8,0)單壁碳納米管結(jié)構(gòu)示意圖Fig.1 The schematic view of (8,0) SWCNT

之前的相關(guān)研究結(jié)果提出鋸齒型小口徑單壁碳納米管的電學(xué)特性極有可能在應(yīng)變下發(fā)生劇烈的變化[14],因?yàn)檫@類碳納米管有平行于管軸方向的碳碳鍵。此外相關(guān)的第一性原理計(jì)算提出對(duì)于(n,0)鋸齒型碳納米管(n<10),強(qiáng)烈的卷曲效應(yīng)對(duì)能帶帶隙產(chǎn)生最為重要的影響[15]。因此之前對(duì)拉伸應(yīng)變在超小口徑鋸齒型單壁碳納米管上的影響展開了研究[16],研究結(jié)果表明在大于20%的拉伸形變下這些超小口徑的單壁碳納米管發(fā)生了金屬性至半導(dǎo)體性的轉(zhuǎn)變。這里將對(duì)壓縮應(yīng)變下的能帶結(jié)構(gòu)進(jìn)行進(jìn)一步的探討。

1.2 計(jì)算方法

第一性原理計(jì)算采用維也納量子化學(xué)模擬軟件包(VASP,Vienna ab initio simulation package)進(jìn)行[7-19]。交換關(guān)聯(lián)能采用廣義梯度近似(GGA)處理[25]。價(jià)電子與芯電子相互作用能采用擴(kuò)充投影平面波(PAW,projector augmented wave)來處理[20-21]。平面波截?cái)嗄苓x為Ecut=300 eV。對(duì)于全自洽計(jì)算的K點(diǎn)網(wǎng)格采用Monkhorst-Pack[22]1×1×30來設(shè)置。而非自洽的電子結(jié)構(gòu)計(jì)算則沿單壁碳納米管軸方向(z軸)采用更高的、包括Γ點(diǎn)的61個(gè)線性K點(diǎn)采樣。

2 計(jì)算結(jié)果與討論

通過對(duì)Zigzag超小口徑碳納米管(3,0)～(8,0)未施加壓縮應(yīng)變下的第一性原理電子結(jié)構(gòu)的計(jì)算得到與相關(guān)文獻(xiàn)[23-24]一致的結(jié)果(見圖2)。對(duì)于口徑較大的單壁碳納米管只有當(dāng)n是3的整數(shù)倍時(shí)Zigzag碳納米管(n,0)才顯現(xiàn)出金屬性特征,于是在(3,0)、(4,0)、(5,0)、(6,0)、(7,0)和(8,0)Zigzag碳納米管中應(yīng)該只有(3,0)管和(6,0)管展現(xiàn)出金屬性,然而計(jì)算結(jié)果表明由于σ-π雜化作用超小管徑碳納米管(3,0)、(4,0)、(5,0)及(6,0)全都展現(xiàn)出金屬性,而超小管徑碳納米管(7,0)和(8,0)不受σ-π雜化作用的影響仍然保持半導(dǎo)體性。

圖2 未施加壓縮應(yīng)變的(3,0)～(8,0)超小口徑碳納米管能帶圖

(4,0)～(8,0)管總能隨拉伸應(yīng)變的變化與(3,0)相似。圖3為(3,0)管總能在壓縮應(yīng)變小于10%范圍內(nèi)隨應(yīng)變的變化關(guān)系,總能隨應(yīng)變的拋物線型增長說明(3,0)～(8,0)管在小于10%的小應(yīng)變區(qū)展現(xiàn)彈性行為[23]。

能帶結(jié)構(gòu)的計(jì)算結(jié)果顯示,壓縮應(yīng)力應(yīng)變下管徑較小的(3,0)、(4,0)、(5,0)、(6,0)碳納米管仍然保持良好的金屬性,而管徑相對(duì)較大的(7,0)、(8,0)碳納米管實(shí)現(xiàn)了半導(dǎo)體性到金屬性的轉(zhuǎn)變。圖4為鋸齒型(7,0)和(8,0)碳納米管帶隙隨著壓縮應(yīng)變的變化關(guān)系,從圖中可以看到(7,0)碳納米管帶隙一開始隨壓縮應(yīng)變的增加而逐漸減小,壓縮應(yīng)變?yōu)?%時(shí)帶隙減為0 eV,說明隨著壓縮應(yīng)變碳納米管實(shí)現(xiàn)了從半導(dǎo)體性到金屬性的轉(zhuǎn)變。另外,鋸齒型碳納米管(8,0)應(yīng)變帶隙一開始隨壓縮應(yīng)變增加而后減小,在壓縮到10%時(shí)帶隙為0 eV,實(shí)現(xiàn)了類似于(7,0)碳納米管的從半導(dǎo)體性到金屬性的轉(zhuǎn)變行為。超小口徑碳納米管帶隙時(shí)的變化行為不同于傳統(tǒng)大口徑碳納米管的結(jié)果,說明基于傳統(tǒng)碳納米管的規(guī)律已不適用于超小口徑碳納米管。

圖3 (3,0)碳納米管總能隨壓縮應(yīng)變的變化曲線

圖4 (7,0)和(8,0)碳納米管帶隙隨壓縮應(yīng)變的變化曲線

圖5所示為(4,0)管能帶結(jié)構(gòu)在壓縮應(yīng)變下的變化。如圖所示,未施加拉伸應(yīng)變時(shí),(4,0)管由于σ和π雜化的原因并未展現(xiàn)帶隙,這類似于Iyakutti等[24]和Mohammadizadeh[25]的研究結(jié)果。而依據(jù)傳統(tǒng)對(duì)碳納米管的分類,(4,0)管應(yīng)該是半導(dǎo)體性碳納米管。(4,0)管在壓縮應(yīng)變下依然保持金屬性的原因是拉伸應(yīng)變難以改變強(qiáng)烈的σ-π鍵的雜化作用。源自于大的卷曲效應(yīng)引發(fā)“α” and “β”這2條能帶在壓縮應(yīng)變的作用下發(fā)生移動(dòng)。α帶來自于下降的反鍵π帶[9], 它的下移并與費(fèi)米能級(jí)相交而使形變前的(4,0)碳納米管展現(xiàn)金屬性行為而非半導(dǎo)體性。β帶來自于通常在鋸齒型(n,0)碳納米管(n為偶數(shù))中出現(xiàn)的簡并π帶。隨著壓縮應(yīng)變的增加,原來半滿的α帶和全滿的β帶分別上移和下移,以至于α帶成為空帶而β成為滿帶,但是在10%的壓縮應(yīng)變下并未發(fā)現(xiàn)帶隙的打開。費(fèi)米能級(jí)附近相類似的隨壓縮應(yīng)變引發(fā)的能帶變化在(3,0)、 (5,0)和(6,0)碳納米管的能帶圖中依然能夠發(fā)現(xiàn),但在這些管同樣沒能在10%的壓縮變化下打開帶隙。

圖5 (4,0)碳納米管壓縮應(yīng)變下能帶結(jié)構(gòu)的變化

3 結(jié) 論

采用第一性原理對(duì)壓縮應(yīng)變下(3,0)～(8,0)鋸齒型單壁碳納米管帶隙和能帶結(jié)構(gòu)展開研究。結(jié)果顯示壓縮應(yīng)力應(yīng)變下管徑較小的(3,0)、(4,0)、(5,0)、(6,0)碳納米管仍然保持良好的金屬性,而管徑相對(duì)較大的(7,0)、(8,0)碳納米管實(shí)現(xiàn)了半導(dǎo)體性到金屬性的轉(zhuǎn)變。超小口徑碳納米管在壓縮應(yīng)變下顯示了不同常規(guī)的大口徑碳納米管的電學(xué)行為。超小口徑的碳納米管能在較大的壓縮應(yīng)變下較好地保持金屬性,這源于嚴(yán)重卷曲效應(yīng)引發(fā)的σ-π雜化效應(yīng)。

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Hybridization effect induced band structure changes in single-wall carbon nanotubes under compression strain

FANGHui1,2,RUANXingxiang1,MAOChunyu1,LIANGCheng1,HUANGCuiping1,BAIXiaohua1

(1. College of Physics and Electronic Engineering, Guangxi Normal University of Nationalities, Chongzuo 532200, China; 2. National Key Laboratory of Advanced Functional Materials, Chinese Ministry of Education, Beijing University of Technology, Beijing 100124, China)

The band structure and band gap of ultra-small diameter single-wall carbon nanotubes (SWCNTs) under compression strain is investigated by means of first-principles method. The curve of total energy suggests that the SWCNTs with chiral comparameter in the range of (3,0)～(8,0) exhibit elastic behavior within a small strain region (<10%), among which . the band structures of (3,0)、(4,0)、(5,0)、(6,0) SWCNTs show that the ultra-small SWCNTs can maintain its metallic property by applying 10% compression strain, and the larger (7,0) and (8,0) SWCNTs realize a semiconductor to metal transition. It implies that the electronic behavior of ultra-small SWCNTs is distinctly inconsistent with conventional larger SWCNTs. The results shows that the different electronic bebavior of the ultra-small SWCNTs are mainly derived from theσ-πhybridization resulting from severe curvature effect. This hybridization effects can dramatically change the energy and characteristics of electron states near Fermi level. It suggests that the perception based on larger SWCNTs is no longer applicable to the ultra-small SWCNTs.

Single-wall carbon nanotubes(SWCNTs); compression; strain; electronic structure; first-pinciples

2016-09-30。

廣西科技廳自然科學(xué)基金資助項(xiàng)目(2015GXNSFBA139014); 廣西教育廳高等學(xué)?？茖W(xué)技術(shù)研究重點(diǎn)項(xiàng)目(KY 2015ZD135)。

房 慧(1980-),男,廣西桂林人,廣西民族師范學(xué)院副教授,博士。

1673-5862(2017)01-0034-05

O469

A

10.3969/ j.issn.1673-5862.2017.01.006