楊學(xué)弦，張峰，劉理軍，廖文虎，劉永輝，莫賢通，馮晶

(1.吉首大學(xué) 物理與機(jī)電工程學(xué)院，吉首　416000;2.湘潭大學(xué) 材料科學(xué)與工程學(xué)院，湘潭　411105)

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硒化鎢拉曼光譜層數(shù)效應(yīng)

楊學(xué)弦1，張峰1，劉理軍1，廖文虎1，劉永輝2，莫賢通1，馮晶1

(1.吉首大學(xué) 物理與機(jī)電工程學(xué)院，吉首416000;2.湘潭大學(xué) 材料科學(xué)與工程學(xué)院，湘潭411105)

摘要:應(yīng)用鍵弛豫理論(BOLS)對(duì)層狀硒化鎢材料的拉曼光譜進(jìn)行定量分析，得出了硒化鎢層數(shù)與鍵參數(shù)的數(shù)值函數(shù)關(guān)系。澄清了硒化鎢拉曼頻移層數(shù)效應(yīng)的內(nèi)在起因：硒化鎢層數(shù)增加時(shí)，拉曼振動(dòng)模A1g發(fā)生藍(lán)移是由于最近鄰原子的影響；成鍵原子控制著硒化鎢拉曼模和模的紅移。

關(guān)鍵詞：層數(shù)；二硒化鎢；拉曼頻移；有效配位數(shù)

1引言

二硒化鎢,由二維Se-W-Se 的層狀結(jié)構(gòu)構(gòu)成，層內(nèi)通過(guò)共價(jià)鍵結(jié)合,而層間通過(guò)范德瓦爾斯結(jié)合。大量實(shí)驗(yàn)研究表明[1-3],硒化鎢薄膜的電子和聲子性質(zhì)具有顯著的層數(shù)效應(yīng)：二維納米硒化鎢薄膜厚度減小到單層時(shí),能帶結(jié)構(gòu)會(huì)從間接帶隙過(guò)渡到直接帶隙；聲子譜將隨著層數(shù)的減少而發(fā)生紅移或藍(lán)移現(xiàn)象。由于拉曼散射實(shí)驗(yàn)(拉曼散射實(shí)驗(yàn)：不破壞樣品，無(wú)損檢測(cè)且結(jié)合計(jì)算機(jī)技術(shù)可達(dá)到實(shí)時(shí)實(shí)地的表征)能夠較精確地表征薄膜的層數(shù)與電子和聲子間的關(guān)系，因此常選擇拉曼散射實(shí)驗(yàn)對(duì)二硒化鎢的層數(shù)效應(yīng)進(jìn)行表征[4]。

2鍵弛豫理論

局域鍵平均近似[10]：對(duì)于任意樣品，無(wú)論是晶體、非晶體、完整或者有缺陷的，只要不發(fā)生相變其化學(xué)鍵性質(zhì)和總數(shù)保持不變。而當(dāng)外界環(huán)境發(fā)生變化時(shí)，樣品所有的化學(xué)鍵鍵長(zhǎng)和鍵能都會(huì)隨之產(chǎn)生響應(yīng)。因此，可通過(guò)樣品化學(xué)鍵參數(shù)與外界環(huán)境間的聯(lián)系對(duì)材料性能進(jìn)行研究。

鍵弛豫理論(BOLS)[7]：低配位原子(z)的化學(xué)鍵鍵長(zhǎng)自發(fā)收縮變短，鍵能增強(qiáng)。 BOLS理論數(shù)學(xué)表達(dá)[11-12]：

(1)

其中下標(biāo)z表示有z個(gè)最近鄰有效配位數(shù)；b表示塊體值；Cz為鍵收縮系數(shù)，僅僅是有效配位數(shù)的函數(shù)。d表示化學(xué)鍵鍵長(zhǎng)；m表示鍵性質(zhì)參數(shù)；E表示原子結(jié)合能。

3層數(shù)與拉曼光譜

通過(guò)泰勒級(jí)數(shù)對(duì)原子總能量進(jìn)行展開(kāi)，可得到[13]：

(2)

E(d，T)表示z個(gè)配位數(shù)的某原子總能量，T、d和u(r)分別是溫度、鍵長(zhǎng)和勢(shì)能，EB為零溫下原子間鍵能，約化質(zhì)量μ=m1m2/(m1+m2)，ω(0)是零溫零壓下拉曼光譜頻率。從能量的角度分析，任何外界條件都將引起原子鍵能的改變從而導(dǎo)致原子振動(dòng)頻率的變化。

Δωx(z,dz,Ez,μ)=

ωx(z,dz,Ez,μ)-ωx(1,dz,Ez,μ)=

(3)

在此可通過(guò)獲取低維層狀材料拉曼效應(yīng)不同模式的實(shí)驗(yàn)測(cè)量結(jié)果，對(duì)比其變化趨勢(shì)來(lái)證明這一假定的正確性。

合并式(1)和(3)，以塊體硒化鎢有效配位數(shù)Zg=12作為已知參數(shù)，可得到以下三種拉曼振動(dòng)模式的關(guān)系式：

配位數(shù)與相對(duì)拉曼頻移的函數(shù)關(guān)系式：

(4)

參考點(diǎn)頻率與配位數(shù)的一般表達(dá)式：

(5)

拉曼振動(dòng)頻率與配位數(shù)的函數(shù)關(guān)系式：

w(z)=wx(1)+

[wx(zg)-wx(1)]Ax(z,zg)

(6)

4結(jié)果與討論

(7)

(9)

硒化鎢拉曼頻移與配位數(shù)的函數(shù)關(guān)系式：

(10)

(11)

圖2是通過(guò)理論計(jì)算單/多層二硒化鎢拉曼頻移與配位數(shù)的結(jié)果圖a、b與已知實(shí)驗(yàn)測(cè)量的拉曼頻移與層數(shù)的關(guān)系，衍生出的配位數(shù)與層數(shù)的關(guān)系。從圖中可以發(fā)現(xiàn)，隨著層數(shù)的增加，有效原子配位數(shù)與層數(shù)之間成線性增加的關(guān)系，近似滿(mǎn)足等式：Z=1.16+2.26n(n<5)，Z代表配位數(shù)，n代表層數(shù)。

Fig.2Effective atomic coordination number of CN (z) of the relationship between the WSe2layers N and two Se.From the figure can be found,with the increase of layers,the effective atomic coordination number is increasing

5結(jié)論

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Raman Spectrum Effect of Layer-W

Se2YANG Xue-xian1,ZHANG Feng1,LIU Li-jun1,LIAO Wen-hu1,LIU Yong-hui2,MO Xian-tong1,FENG Jing1

(1.JishouUniversity,CollegeofPhysics,MechanicalandElectricalEngineering,Jishou416000;2.XiangtanUniversity，SchoolofMaterialsScienceandEngineering，Xiangtan411105)

Abstract:From the perspective of bond order-length-strength correlation and the local bond averaging approach,we have formulated the number-of-layer resolved Raman shifts of WSe2,with quantification of the referential origins from which the Raman shifts proceed and clarification of their origins.It is found that the primary mode and mode are dominated by the interaction between a specific atom and its nearest neighbors while the A1gmode by the dimer interaction,and therefore red shift happens to the phonons and blue shift to the A1gmode upon the number-of-layer is reduced.

Key words:layer; WSe2; Raman shift; effective coordination number

中圖分類(lèi)號(hào)：O433.4

文獻(xiàn)標(biāo)志碼：A

doi:10.13883/j.issn1004-5929.201601004

作者簡(jiǎn)介：楊學(xué)弦(1984-)，男，講師，主要從事聲子計(jì)量譜學(xué)等方面的研究。E-mail:yangxuexiand@163.com

基金項(xiàng)目：國(guó)家自然科學(xué)基金( 11447237)，湖南省自然科學(xué)基金(2015JJ6094) 資助項(xiàng)目

收稿日期：2015-07-01; 修改稿日期:2015-07-21

文章編號(hào)：1004-5929(2016)01-0012-04