于立軍,張春紅,張忠政,鄧永榮,閆萬珺

(1.長春師范大學(xué) 物理學(xué)院,長春 130032；2.安順學(xué)院 航空電子電氣與信息網(wǎng)絡(luò)工程中心,貴州 安順 561000)

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空位缺陷對(duì)CrSi2光電性能的影響

于立軍1,張春紅2,張忠政2,鄧永榮2,閆萬珺2

(1.長春師范大學(xué) 物理學(xué)院,長春 130032；2.安順學(xué)院 航空電子電氣與信息網(wǎng)絡(luò)工程中心,貴州 安順 561000)

采用第一性原理方法,計(jì)算含空位缺陷CrSi2的電子結(jié)構(gòu)和光學(xué)性質(zhì),并分析含Cr和Si空位缺陷的CrSi2光電性能.結(jié)果表明：Cr和Si空位均使CrSi2的晶格常數(shù)和體積變??；能帶結(jié)構(gòu)密集而平緩,且整體向上移動(dòng),Si空位缺陷形成帶隙寬度為0.35 eV的p型間接帶隙半導(dǎo)體,Cr空位缺陷在原禁帶間出現(xiàn)兩條新的能帶；含空位缺陷CrSi2的電子態(tài)密度仍主要由Cr 3d層電子貢獻(xiàn),Si空位缺陷對(duì)電子態(tài)密度的影響較小,Cr空位缺陷提高了Fermi面處的電子態(tài)密度；與CrSi2相比,含空位缺陷CrSi2的介電峰均向低能方向略有偏移且峰值降低,吸收系數(shù)明顯變小.

CrSi2；空位缺陷；光電性能；第一性原理

過渡金屬硅化物CrSi2是一種新型環(huán)境友好的半導(dǎo)體材料,在室溫下的帶隙寬度為0.35 eV[1],且與硅基底的錯(cuò)配度在CrSi2(0001)//Si(111)方向小于0.3%[2-3],有利于制備CrSi2/Si異質(zhì)結(jié).

摻雜是材料改性的主要方法之一,目前已有許多研究結(jié)果.例如:文獻(xiàn)[4]研究了摻雜CrSi2的半導(dǎo)體性質(zhì);文獻(xiàn)[5]研究了V摻雜多晶的熱電性質(zhì);文獻(xiàn)[6-7]測(cè)量了V摻雜和Al摻雜CrSi2單晶在不同溫度下的電阻率和Seebeck系數(shù);文獻(xiàn)[8]在實(shí)驗(yàn)和理論上研究了不同濃度Ti摻雜CrSi2的熱電性質(zhì);文獻(xiàn)[9]研究了塊體CrSi2的光電性能;文獻(xiàn)[10-16]研究了應(yīng)力作用于CrSi2和摻雜CrSi2的光電性能.半導(dǎo)體材料在生長過程中會(huì)產(chǎn)生缺陷,從而影響晶格結(jié)構(gòu)和晶體中原子的位置,導(dǎo)致半導(dǎo)體材料的電子結(jié)構(gòu)和光學(xué)性質(zhì)發(fā)生變化.目前,尚未見關(guān)于空位缺陷對(duì)CrSi2電子結(jié)構(gòu)和光學(xué)性質(zhì)影響的研究報(bào)道.本文采用第一性原理方法,計(jì)算含有Cr和Si兩種空位缺陷CrSi2的幾何結(jié)構(gòu)、電子結(jié)構(gòu)和光學(xué)性質(zhì),并分析空位缺陷對(duì)其光電性能的影響.

1 理論模型與計(jì)算方法

圖1 計(jì)算模型Fig.1 Calculation model

計(jì)算由從頭算量子力學(xué)程序(CASTEP)[17]軟件包完成.先用BFGS算法[18-21]將含有空位缺陷的計(jì)算模型進(jìn)行幾何結(jié)構(gòu)優(yōu)化,再計(jì)算其他性質(zhì).電子間的交換關(guān)聯(lián)能用廣義梯度近似(GGA-PBE)[22]泛函處理；離子實(shí)與電子間的相互作用采用超軟贗勢(shì)[23]處理.選取3s23p2為Si的價(jià)電子,3s23p63d54s1為Cr的價(jià)電子,平面波的截?cái)嗄芰吭O(shè)為310 eV,自洽計(jì)算收斂精度設(shè)為每個(gè)原子1.0×10-6eV,Brillouin區(qū)積分采用Monkhorst Pack形式[24]的高對(duì)稱k點(diǎn)方法.

空位缺陷的形成能表達(dá)式為

2 結(jié)果與分析

2.1幾何結(jié)構(gòu)

CrSi2的實(shí)驗(yàn)值[2]、計(jì)算值及含Cr空位和Si空位CrSi2的晶格常數(shù)和體積列于表1.由表1可見,Cr空位和Si空位缺陷均使CrSi2的晶格常數(shù)和體積減小.經(jīng)過結(jié)構(gòu)優(yōu)化的超胞可穩(wěn)定存在,表明空位濃度是適度的,原來的晶體仍起主導(dǎo)作用.

Cr空位和Si空位缺陷的形成能分別為13.84 eV和7.08 eV.可見,Cr空位和Si空位的形成能均較大,在常溫常壓下,該反應(yīng)不易自發(fā)進(jìn)行,空位缺陷較難形成,且Cr空位形成的難度大于Si空位形成的難度.但在高溫高壓下,CrSi2晶體中可形成空位缺陷.

表1 CrSi2及Cr空位和Si空位的晶格常數(shù)和體積Table 1 Lattice constants and volume of CrSi2,Cr vacancy and Si vacancy

2.2電子結(jié)構(gòu)

CrSi2及含Cr和Si空位缺陷的CrSi2在Fermi能級(jí)(EF=0)附近的能帶結(jié)構(gòu)如圖2所示.由圖2(A)可見,CrSi2為帶隙寬度0.38 eV的間接帶隙半導(dǎo)體,與文獻(xiàn)[1,25-27]的結(jié)果相符.由圖2(B)和(C)可見,Cr空位和Si空位缺陷均使電子能帶變密且整體上移,Fermi能級(jí)移入價(jià)帶中,含有空位缺陷的CrSi2變?yōu)閜型半導(dǎo)體.Si空位缺陷的價(jià)帶頂位于A點(diǎn)處,導(dǎo)帶底位于G點(diǎn)處,帶隙寬度為0.35 eV.

圖2 Fermi能級(jí)附近的能帶結(jié)構(gòu)Fig.2 Band structure near the Fermi energy

CrSi2和含Si空位缺陷CrSi2在高對(duì)稱k點(diǎn)處的價(jià)帶頂(VBM)和導(dǎo)帶底(CBM)的特征能量值列于表2.由表2可見,Si空位缺陷使CrSi2的帶隙寬度略減小.Cr空位缺陷使原價(jià)帶頂和導(dǎo)帶底之間出現(xiàn)兩條新能帶,原VBM和CBM以及兩條新能帶在高對(duì)稱點(diǎn)的特征能量值列于表3.

表2 CrSi2和含Si空位缺陷CrSi2的VBM和CBM在高對(duì)稱k點(diǎn)處的特征能量值及帶隙值Eg(eV)Table 2 Eigenvalues of VBM and CBM for CrSi2 and CrSi2 with Si-vacancy at high symmetry k point and band gap Eg (eV)

表3 含Cr空位缺陷CrSi2的能帶1～4在高對(duì)稱k點(diǎn)處的特征能量值(eV)Table 3 Eigenvalues (eV)of CrSi2 with Cr-vacancy from band 1 to 4 at high symmetry k point

由表3可見:含Cr空位缺陷CrSi2中能帶1的頂部在A點(diǎn),能帶2的底部在K點(diǎn),其帶隙差為-0.078 eV；能帶2與能帶3在G和A間發(fā)生交疊；能帶3的頂部在P點(diǎn)(0.633 0 eV),能帶4的底部在G點(diǎn),其帶隙差為0.048 eV.

CrSi2及含Cr和Si空位缺陷CrSi2在Fermi能級(jí)附近的總能態(tài)密度(DOS)與Cr和Si的分波態(tài)密度(PDOS)如圖3所示.由圖3(A)～(C)可見:Cr空位缺陷使價(jià)帶頂與導(dǎo)帶底之間出現(xiàn)新的電子態(tài)密度峰,與圖2(B)中出現(xiàn)的兩條新能級(jí)對(duì)應(yīng)；Si空位缺陷使電子態(tài)密度整體向高能方向移動(dòng),Fermi能級(jí)嵌入價(jià)帶中,與圖2(C)對(duì)應(yīng).由圖3(D)～(I)可見,Fermi能級(jí)附近CrSi2的電子能態(tài)密度主要由Cr 3d層電子貢獻(xiàn).Cr空位缺陷導(dǎo)致Fermi能級(jí)處Cr 3d層和Si 3p層電子的分波態(tài)密度值變大,表明兩條新能級(jí)是由Cr 3d層和Si 3p層電子貢獻(xiàn)所致,新能帶位于Fermi面與導(dǎo)帶之間,這是由于Cr空位缺陷影響了其他電子散射與導(dǎo)帶之間分裂的強(qiáng)相互作用[28],從而形成了兩條新的能帶.由于CrSi2中Si空位缺陷對(duì)總態(tài)密度的影響較小,因此,在含Si空位缺陷的CrSi2中未形成新能級(jí),但總的價(jià)電子數(shù)減少,使得含Si空位缺陷的CrSi2變?yōu)橐钥昭檩d流子的p型半導(dǎo)體.

圖3 CrSi2及含Cr和Si空位缺陷的總能態(tài)密度(A)～(C)與Cr和Si的分波態(tài)密度(D)～(I)Fig.3 Total densities (A)—(C)of states and partial density (D)—(I)of states ofCrSi2,CrSi2 with Cr-vacancy and CrSi2 with Si-vacancy

2.3Mulliken布居分析

與空位缺陷相鄰原子的Mulliken布居分析和與空位缺陷相鄰鍵的Mulliken布居分析分別列于表4和表5.

表4 與空位缺陷相鄰原子的Mulliken布居分析Table 4 Mulliken population analysis of atoms around the Cr-vacancy and Si-vacancy

表5 與空位缺陷相鄰鍵的Mulliken布居分析Table 5 Mulliken population analysis of bonds around the Cr-vacancy and Si-vacancy

由表4可見,與Cr空位相鄰Si原子的電荷為0.18e,明顯低于0.42e,這是由于空位處缺少Cr原子,減少了對(duì)Si原子的吸引作用,從而使Si原子失去的電子數(shù)減少所致.由表5可見:與Cr空位和Si空位相鄰的Si—Cr Ⅰ鍵(圖1(C)中藍(lán)色鍵)的布居數(shù)減小,共價(jià)性減弱,鍵長變短；Si—Cr Ⅱ鍵(圖1(C)中紫色鍵)的布居數(shù)增大,共價(jià)性增強(qiáng),鍵長變長；與Cr空位相鄰的Si—Si鍵布居數(shù)增大,共價(jià)性增強(qiáng),鍵長變長；與Si空位相鄰的Si—Si鍵布居數(shù)減小,共價(jià)性變?nèi)?鍵長變短.

2.4差分電荷密度分析

含Cr空位和Si空位的差分電荷密度如圖4所示,其中紅色和藍(lán)色區(qū)域分別表示電荷得與失的空間分布.由圖4可見：空位缺陷周圍的電荷分布發(fā)生了變化,Cr空位處的電荷數(shù)明顯減少,與Cr空位相鄰的Si1原子失去的電子增多,對(duì)應(yīng)Si—CrⅠ鍵布居數(shù)減小,Si2原子得到的電子增多,對(duì)應(yīng)Si—CrⅡ鍵布居數(shù)增大；Si空位處的電荷數(shù)略有增加,與Si空位相鄰的Cr1原子得到的電子增多,對(duì)應(yīng)Si—CrⅡ鍵布居數(shù)增大,與Si空位相鄰的Cr2和Cr3原子得到的電子減少,對(duì)應(yīng)Si—CrⅠ鍵布居數(shù)減小.差分電荷密度結(jié)果與布居數(shù)的分析結(jié)果相符.

圖4 含Cr空位和Si空位的差分電荷密度Fig.4 Electron density difference of Cr-vacancy and Si-vacancy

2.5光學(xué)性質(zhì)

CrSi2及含Cr和Si空位缺陷CrSi2的復(fù)介電函數(shù)ε1(A)與ε2(B)隨能量的變化關(guān)系如圖5所示.

圖5 復(fù)介電函數(shù)ε1和ε2隨能量的變化關(guān)系Fig.5 Variation relationship of the complex dielectric function ε1 and ε2 with the energy

圖6 吸收系數(shù)隨能量的變化關(guān)系Fig.6 Variation relationship of the absorptioncoefficient with the energy

由圖5(A)可見,CrSi2及含Cr和Si空位缺陷CrSi2的靜態(tài)介電常數(shù)ε1(0)分別為29.1,36.9,56.5,即空位缺陷可提高CrSi2的靜態(tài)介電常數(shù).由圖5(B)可見:在0～10 eV內(nèi),CrSi2介電函數(shù)虛部ε2(ω)在1.63 eV處出現(xiàn)介電峰,對(duì)應(yīng)CrSi2價(jià)帶Cr 3d的t2g軌道至eg軌道的d-d電子躍遷,在4.53 eV處的介電峰對(duì)應(yīng)價(jià)帶中部Si 3p態(tài)電子至導(dǎo)帶Cr 3d態(tài)的躍遷;含Cr空位缺陷CrSi2的介電峰位于1.25 eV處；含Si空位缺陷的CrSi2存在兩個(gè)介電峰,分別位于0.27 eV和1.44 eV處.即含空位缺陷CrSi2的介電峰均向低能方向偏移且峰值降低.由圖2和圖3可見,在含空位缺陷的CrSi2中,由于Fermi能級(jí)穿過價(jià)帶,因此在光子能量為0處也存在電子躍遷.

CrSi2及含Cr和Si空位缺陷CrSi2的吸收系數(shù)隨能量的變化關(guān)系如圖6所示.由圖6可見:在0～15 eV內(nèi),CrSi2的吸收系數(shù)在6.06 eV處取得峰值4.02×105cm-1；含Cr和Si空位缺陷CrSi2的吸收系數(shù)均向低能方向偏移,且吸收峰明顯降低,其中Cr空位缺陷CrSi2在4.50 eV附近取得最大吸收峰1.56×105cm-1；Si空位缺陷CrSi2在4.23 eV附近取得最大吸收峰1.34×105cm-1.

綜上,本文采用第一性原理方法對(duì)含Cr和Si空位缺陷CrSi2的幾何結(jié)構(gòu)、電子結(jié)構(gòu)、復(fù)介電函數(shù)和吸收系數(shù)進(jìn)行了計(jì)算,并分析了含空位缺陷CrSi2的光電特性.結(jié)果表明：含空位缺陷CrSi2的晶格常數(shù)a,b,c均減小,體積變?。缓琒i空位缺陷的CrSi2變?yōu)閜型半導(dǎo)體,帶隙寬度由0.38 eV變?yōu)?.35 eV,Cr空位缺陷CrSi2的原禁帶中出現(xiàn)兩條新的能帶；價(jià)帶頂和導(dǎo)帶底的態(tài)密度主要由Cr 3d層電子貢獻(xiàn)；與CrSi2相比,含空位缺陷CrSi2的介電峰均向低能方向略有偏移且峰值降低,吸收系數(shù)明顯變小.

感謝貴州大學(xué)云計(jì)算平臺(tái)提供的計(jì)算支持.

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(責(zé)任編輯：王 健)

Optical-ElectricalCharacteristicsofCrSi2withVacancyDefect

YU Lijun1,ZHANG Chunhong2,ZHANG Zhongzheng2,DENG Yongrong2,YAN Wanjun2

(1.CollegeofPhysics,ChangchunNormalUniversity,Changchun130032,China;2.EngineeringCenterofAvionicsElectricalandInformationNetwork,AnshunUniversity,Anshun561000,GuizhouProvince,China)

The electronic structure and optical properties of CrSi2with vacancy defect were calculated based on the first principles method,and the photoelectric properties of CrSi2with Cr or Si vacancy defect were analyzed.The results show that the lattice constants and volume are all decreased with Cr or Si vacancy defect.The band structure becomes intensive and gentle,and moves upward.The band structure of CrSi2with Si vacancy defect is p type indirect semiconductor with a band gap of 0.35 eV;while two new energy levels are induced in the forbidden band with Cr-vacancy defect.Density of states of the valence band top and conduction band bottom are mainly composed of Cr 3d.Si-vacancy defect has a little effect on the density of states;Cr-vacancy defect improves the density of states of the Fermi energy.Compared with that of pure CrSi2,the dielectric peak slightly moves to the lower energy and decreases with vacancy defect,and the absorption index obviously decreases.

CrSi2；vacancy defect；photoelectric properties；the first principle

10.13413/j.cnki.jdxblxb.2015.03.39

2015-02-10.

于立軍(1958—),男,漢族,副教授,從事光電半導(dǎo)體材料的研究,E-mail:ccyulw6908@163.com.通信作者:閆萬珺(1978—),女,漢族,博士,副教授,從事電子功能材料模擬和計(jì)算的研究,E-mail:yanwanjun7817@163.com.

國家自然科學(xué)基金(批準(zhǔn)號(hào):61404010)和貴州省自然科學(xué)基金(批準(zhǔn)號(hào):黔科合J字(2010)2001;黔教科KY(2012)056號(hào)).

O474

：A

：1671-5489(2015)03-0561-07