Mg雜質(zhì)調(diào)控高Al組分AlGaN

1、Mg雜質(zhì)調(diào)控高Al組分AlGaN光學(xué)偏振特性鄭同場(chǎng)，林偉收稿日期：2015-06-30 錄用日期：2015-10-25基金項(xiàng)目：國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃（973）項(xiàng)目（2012CBR19300），國(guó)家高技術(shù)研究發(fā)展計(jì)劃（863）（2014AA032608），國(guó)家自然科學(xué)基金（11404271、11204254），海峽聯(lián)合基金（U1405253）通信作者： HYPERLINK mailto: ; ，蔡端俊，李金釵，李書平，康俊勇*（廈門大學(xué) 物理與機(jī)電工程學(xué)院，福建省半導(dǎo)體材料及應(yīng)用重點(diǎn)實(shí)驗(yàn)室，福建 廈門 361005）摘要：高Al組分AlGaN帶邊發(fā)光以e光為主的發(fā)光特性，從根本上限制了沿c面

2、生長(zhǎng)器件的正面出光，成為光電器件發(fā)光效率急劇下降的主要原因。第一性原理模擬計(jì)算表明AlxGa1-xN混晶的晶格常數(shù)比c/a偏離理想值程度隨Al組分的增大而增大，導(dǎo)致晶體場(chǎng)分裂能cr從GaN的40 meV逐漸減小;當(dāng)組分達(dá)到0.5時(shí)呈現(xiàn)0值，Al組分繼續(xù)提升，cr進(jìn)一步下降，價(jià)帶頂排列順序翻轉(zhuǎn)，直至AlN達(dá)到最低值-197 meV。通過Mg摻雜應(yīng)變AlGaN量子結(jié)構(gòu)能帶工程調(diào)控高Al組分AlGaN的價(jià)帶結(jié)構(gòu)，反轉(zhuǎn)價(jià)帶頂能帶排序，實(shí)現(xiàn)光發(fā)射o光占主導(dǎo)，從根本上克服高Al組分AlGaN發(fā)光器件正面出光難的問題。關(guān)鍵詞：高Al組分AlGaN；發(fā)光偏振特性；Mg雜質(zhì)；能帶工程中圖分類號(hào)：O 781；O

3、469 文獻(xiàn)標(biāo)識(shí)碼：A高Al組分AlGaN基紫外發(fā)光器件在殺菌消毒、環(huán)境凈化、防偽識(shí)別、以及生化檢測(cè)等諸多領(lǐng)域有著越來越廣泛的應(yīng)用和市場(chǎng)需要，引起人們強(qiáng)烈的關(guān)注參考文獻(xiàn)： Khan A, Balakrishnan K, Katona T. Ultraviolet light-emitting diodes based on group three nitrides J. Nat Photonics, 2008, 2(2):77.- Kneissl M, Kolbe T, Chua C, et al. Advances in group III-nitride-based deep UV lig

4、ht-emitting diode technology J. Semicond Sci Tech, 2011, 26(1):014036. Shur MS, Gaska R, Member S. Deep-Ultraviolet Light-Emitting Diodes J. IEEE T Electron Dev, 2010, 57(1):12.。1998年，美國(guó)Sandia 國(guó)家實(shí)驗(yàn)室J. Han 等利用Al0.2Ga0.8N/GaN多量子阱結(jié)構(gòu)，研制出第一只波長(zhǎng)短于GaN帶隙（365 nm）的353.6 nm的紫外發(fā)光二極管（Light emitting diode, LED） Ha

5、n J, Crawford MH, Shul RJ, et al. AlGaN/GaN quantum well ultraviolet light emitting diodes J. Appl Phys Lett, 1998, 73(12):1688.。此后，波長(zhǎng)更短的紫外發(fā)光二極管和激光二極管（Laser diode, LD）相繼問世，AlGaN紫外發(fā)光器件研制取得了長(zhǎng)足的進(jìn)步 NOTEREF _Ref423442959 h 3, Allerman a. a., Crawford MH, Fischer a. J, et al. Growth and design of deep-UV

6、(240290nm) light emitting diodes using AlGaN alloys J. J Cryst Growth, 2004, 272(1-4):227.- Hu X, Deng J, Zhang JP, et al. Deep ultraviolet light-emitting diodes J. Phys Status Solidi, 2006, 203(7):1815. Hirayama H, Fujikawa S, Noguchi N, et al. 222-282 nm AlGaN and InAlGaN-based deep-UV LEDs fabric

7、ated on high-quality AlN on sapphire J. ng J, Zhang JP, et al. Deep ultraviolet light-emitting diodes J. Phys Status Solidi, 2009, 206(6):1176.。然而，相比于傳統(tǒng)InGaN基藍(lán)、綠光發(fā)光器件，AlGaN基紫外光電器件的發(fā)光效率始終有限，且隨著Al組分的增加而急劇下降 NOTEREF _Ref423442909 h 2。起初，人們普遍將效率下降歸因于AlGaN晶體質(zhì)量不高，內(nèi)量子效率低下7；p型AlGaN摻雜困難 Nam KB, Nakarmi ML, L

8、i J, et al. Mg acceptor level in AlN probed by deep ultraviolet photoluminescence J. Appl Phys Lett, 2003, 83(5):878.- Nakarmi ML, Nepal N, Lin JY, et al. Photoluminescence studies of impurity transitions in Mg-doped AlGaN alloys J. Appl Phys Lett, 2009, 94(9):091903. Li J, Yang W, Li S, et al. Enha

9、ncement of p-type conductivity by modifying the internal electric field in Mg- and Si-codoped AlxGa1-xN/AlyGa1-yN superlattices J. Appl Phys Lett, 2009, 95(15):151113. Zheng T, Lin W, Cai D, et al. High Mg effective incorporation in Al-rich Alx Ga1-xN by periodic repetition of ultimate V/III ratio c

10、onditions J. Nanoscale Res Lett, 2014, 9(1):40.，載流子注入效率低；襯底等材料具有強(qiáng)烈的紫外吸收等。近年來隨著AlGaN紫外光電器件研究的深入，人們逐漸認(rèn)識(shí)到效率下降的背后AlGaN材料本身的能帶結(jié)構(gòu)在其中扮演了重要角色 Li J, Nam KB, Nakarmi ML, et al. Band structure and fundamental optical transitions in wurtzite AlN J. Appl Phys Lett, 2003, 83(25):5163.- Nam KB, Li J, Nakarmi ML, e

11、t al. Unique optical properties of AlGaN alloys and related ultraviolet emitters J. Appl Phys Lett, 2004, 84(25):5264. Shakya J, Knabe K, Kim KH, et al. Polarization of III-nitride blue and ultraviolet light-emitting diodes J. Appl Phys Lett, 2005, 86(9): 091107. Kawanishi H, Senuma M, Nukui T. Anis

12、otropic polarization characteristics of lasing and spontaneous surface and edge emissions from deep-ultraviolet (240 nm) AlGaN multiple-quantum-well lasers J. Appl Phys Lett, 2006, 89(4):041126. Kawanishi H, Senuma M, Yamamoto M, Niikura E, Nukui T. Extremely weak surface emission from (0001) c-plan

13、e AlGaN multiple quantum well structure in deep-ultraviolet spectral region J. Appl Phys Lett, 2006, 89(8):081121. Taniyasu Y, Kasu M, Makimoto T. Radiation and polarization properties of free-exciton emission from AlN (0001) surface J. Appl Phys Lett, 2007, 90(26):261911. Sedhain a., Lin JY, Jiang

14、HX. Valence band structure of AlN probed by photoluminescence J. Appl Phys Lett, 2008, 92(4):041114. Zhang J, Zhao H, Tansu N. Effect of crystal-field split-off hole and heavy-hole bands crossover on gain characteristics of high Al-content AlGaN quantum well lasers J. Appl Phys Lett, 2010, 97(11):11

15、1105. Kolbe T, Knauer A, Chua C, et al. Optical polarization characteristics of ultraviolet (In)(Al)GaN multiple quantum well light emitting diodes J. Appl Phys Lett, 2010, 97(17):171105. Claudio de Carvalho L, Schleife A, Fuchs F, et al. Valence-band splittings in cubic and hexagonal AlN, GaN, and

16、InN J. Appl Phys Lett, 2010, 97(23):232101. Netzel C, Knauer a., Weyers M. Impact of light polarization on photoluminescence intensity and quantum efficiency in AlGaN and AlInGaN layers J. Appl Phys Lett, 2012, 101(24):242102.。隨著Al組分的增大，價(jià)帶頂按能量從高到低的能帶排序由GaN的9、7和7，逐漸轉(zhuǎn)變?yōu)锳lN的7、9、7。價(jià)帶頂能帶的差異使得在材料發(fā)光中占主導(dǎo)地位的

17、導(dǎo)帶和價(jià)帶第一子帶間的帶邊發(fā)光以電場(chǎng)與c軸垂直的o光（Ordianry Light, Ec）為主轉(zhuǎn)變?yōu)橐噪妶?chǎng)與光軸平行的e光（Extraordianry Light, Ec）為主，表現(xiàn)為正面光發(fā)射逐漸被側(cè)面光發(fā)射所取代。相較于外延層正面，狹小的側(cè)壁面積極大地限制了光抽取的效率，且側(cè)向光難以有效利用。更為不利的是，由于AlGaN材料相對(duì)于空氣為光密介質(zhì)，輻射光由材料內(nèi)部出射時(shí)易在界面上發(fā)生全反射。根據(jù)AlN和GaN折射率可推知AlGaN的全射角介于24.6 28.4之間，這意味著在高Al組分AlGaN中少量偏離側(cè)向傳播的光投射至外延層正表面時(shí)會(huì)被全反射回器件內(nèi)部而逐漸遭到吸收損耗，難以從器件中有

18、效抽取。傳統(tǒng)提高光抽取效率方法主要采用對(duì)光電器件進(jìn)行結(jié)構(gòu)優(yōu)化，如表面粗化 Windisch R, Rooman C, Meinlschmidt S, et al. Impact of texture-enhanced transmission on high-efficiency surface-textured light-emitting diodes J. Appl Phys Lett, 2001, 79(15):2315., Fujii T, Gao Y, Sharma R, et al. Increase in the extraction efficiency of GaN-bas

19、ed light-emitting diodes via surface roughening J. Appl Phys Lett, 2004, 84(6):855.、圖形化藍(lán)寶石襯底 Wuu DS, Wang WK, Shih WC, et al. Enhanced Output Power of Near-Ultraviolet InGaN-GaN LEDs Grown on Patterned Sapphire Substrates J. IEEE Photonic Tech L, 2005, 17(2):288., Huang X, Liu J, Kong J, et al. High

20、-efficiency InGaN-based LEDs grown on patterned sapphire substrates J. Opt Express, 2011;19(14):949.、布拉格反射鏡 Nakada N, Nakaji M, Ishikawa H, et al. Improved characteristics of InGaN multiple-quantum-well light-emitting diode by GaN/AlGaN distributed Bragg reflector grown on sapphire J. Appl Phys Lett

21、, 2000, 76(14):1804., Mqw HIG, Chen CH, Chang SJ, et al. High-Efficiency InGaN-GaN MQW Green Light-Emitting Diodes With CART and DBR Structures J. IEEE J Sel Top Quantum Electron, 2002, 8(2):284.、光子晶體 Oder TN, Kim KH, Lin JY, et al. III-nitride blue and ultraviolet photonic crystal light emitting di

22、odes J. Appl Phys Lett, 2004, 84(4):466., Wierer JJ, David A, Megens MM. III-nitride photonic-crystal light-emitting diodes with high extraction efficiency J. Nat Photonics, 2009, 3:163.等技術(shù)，雖然能夠從一定程度上減少因介質(zhì)折射率差異引起的全反射，但不能從根本上解決正面出光困難的局面。為了繞開這一限制因素，人們?cè)噲D將AlGaN外延生長(zhǎng)轉(zhuǎn)移到非極性面上，使得e光傳播方向恰好轉(zhuǎn)向器件正面出光方向，輻射光易于從正面出

23、射 Taniyasu Y, Kasu M. Surface 210 nm light emission from an AlN pn junction light-emitting diode enhanced by A-plane growth orientation J. Appl Phys Lett, 2010, 96(22):221110.。然而相比于沿c軸擇優(yōu)生長(zhǎng)的AlGaN晶體，非極性面晶體生長(zhǎng)較為困難，內(nèi)量子效率難以超越。采用能帶工程，對(duì)材料能帶結(jié)構(gòu)進(jìn)行適當(dāng)?shù)募舨?，以調(diào)控材料光學(xué)性質(zhì)是一種有效可行的方法 Banal R, Funato M, Kawakami Y. Optical

24、 anisotropy in 0001-oriented AlxGa1xN/AlN quantum wells (x0.69) J. Phys Rev B, 2009, 79(12):1.- Fu D, Zhang R, Wang BG, et al. Ultraviolet emission efficiencies of AlxGa1xN films pseudomorphically grown on AlyGa1yN template (xy) with various Al-content combinations. Thin Solid Films, 2011, 519(22):8

25、013. Zhang J, Zhao H, Tansu N. Large optical gain AlGaN-delta-GaN quantum wells laser active regions in mid- and deep-ultraviolet spectral regimes J. Appl Phys Lett, 98(17):26.。前期的摻雜研究表明，在生長(zhǎng)過程中，Mg雜質(zhì)源以脈沖形式而非連續(xù)同時(shí)通入反應(yīng)腔，在有效地提高M(jìn)g的摻雜效率的同時(shí)，雜質(zhì)原子由于其電負(fù)性和離子半徑大小與主晶格原子的差異，將影響AlGaN材料價(jià)帶結(jié)構(gòu)，價(jià)帶軌道的空間分布發(fā)生變化 Li J, Kang

26、J Band engineering in Al0.5Ga0.5N/GaN superlattice by modulating Mg dopant J. Appl. Phys. Lett. 2007, 91:152106.，這不僅意味著載流子的傳輸行為受到影響，電子空穴復(fù)合發(fā)光的偏振狀態(tài)也將發(fā)生改變。然而以往的研究更多地關(guān)注受主Mg摻雜的電學(xué)特性 Nakarmi ML, Kim KH, Khizar M, et al. Electrical and optical properties of Mg-doped Al0.7Ga0.3N alloysJ. Applied Physics Lett

27、ers, 2005, 86(9):092108.- Simon J, Protasenko V, Lian C, et al. Polarization-induced hole doping in wide-band-gap uniaxial semiconductor heterostructures J. Science, 2010, 327(5961):60. Aoyagi Y, Takeuchi M, Iwai S, et al. High hole carrier concentration realized by alternative co-doping technique i

28、n metal organic chemical vapor deposition J. Applied Physics Letters, 2011, 99(11):112110.，對(duì)于其影響發(fā)光偏振特性的認(rèn)識(shí)和利用還有待探索。本文采用第一性原理模擬計(jì)算Mg摻雜Al0.75Ga0.25N/AlN量子結(jié)構(gòu)價(jià)帶頂能帶結(jié)構(gòu)，提出采用Mg雜質(zhì)能帶工程調(diào)控高Al組分AlGaN的發(fā)光偏振特性，提高o光比重，進(jìn)而提高發(fā)光器件的的正面出光。1模型構(gòu)建及方法采用基于密度泛函理論的第一性原理方法模擬計(jì)算AlxGa1-xN混晶的能帶結(jié)構(gòu)。構(gòu)建2a2a2c GaN纖鋅礦超原胞結(jié)構(gòu)模型，所構(gòu)建AlxGa1-xN混晶模型

29、Al組分x分別為0.00、0.25、0.50、0.75、1.00。Al原子以替位的方式均勻地占據(jù)部分Ga原子位置，以體現(xiàn)更高的代表性。圖1（a）展示了典型的混晶模型Al0.75Ga0.25N。非摻量子結(jié)構(gòu)所構(gòu)建的結(jié)構(gòu)模型基于2a2a8c纖鋅礦超原胞，如圖1（b）所示。Mg摻雜應(yīng)變Al0.75Ga0.25N/AlN量子阱結(jié)構(gòu)通過Mg原子替代阱中單個(gè)Ga原子構(gòu)建，如圖1（c）所示。第一性原理計(jì)算采用VASP程序包 Kresse G, Furthmller J. Efficient iterative schemes for ab initio total-energy calculations u

30、sing a plane-wave basis set J. Phys Rev B, 1996, 54(16):11169.；計(jì)算過程中，Ga的3d電子當(dāng)作價(jià)電子處理，電子離子相互作用采用投影綴加波贗勢(shì)法（PAW） Blochl P. Projector augmented-wave method J. Physical Review B, 1994, 50(24):17953., Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method J. Phys Rev B,

31、1999, 59(3):11.描述；交換關(guān)聯(lián)能采用廣義梯度近似（GGA） Perdew J, Burke K, Ernzerhof M. Generalized gradient approximation made simple J. Phys Rev Lett, 1996, 77(18):3865.的PW91交換關(guān)聯(lián)函數(shù)；電子波函數(shù)采用平面波展開，平面波基組的截?cái)嗄茉O(shè)為520eV；布里淵區(qū)積分采用553的Monkhorst-Pack點(diǎn)陣 Monkhorst H, Pack J. Special points for Brillouin-zone integrations J. Phys R

32、ev B, 1976, 13(12):5188.。結(jié)構(gòu)優(yōu)化過程中，允許總能計(jì)算的誤差為10-4 eV，離子弛豫運(yùn)動(dòng)的收斂標(biāo)準(zhǔn)為10-3 eV，以保證各原子充分弛豫，使體系能量達(dá)到最低。圖1（a）Al0.75Ga0.25N混晶模型,（b）非摻和（c）Mg摻雜Al0.75Ga0.25N/AlN量子阱結(jié)構(gòu)Fig. 1 Al0. 75Ga0.25N alloy (a), structure of undoped, (b) and Mg doped (c) Al0.75Ga0.25N/AlN quantum structure.2結(jié)果與討論2.1 AlxGa1-xN混晶光學(xué)偏振特性圖2.（a）AlxGa

33、1-xN價(jià)帶頂能帶結(jié)構(gòu)，（b）晶格常數(shù)c/a比與晶體場(chǎng)分裂能cr隨Al組分變化關(guān)系Fig. 2 (a) The band structure of AlxGa1-xN at valence band maximum, (b) the c/a ratio and crystal field splitting cr as a function of Al composition.眾所周知，材料發(fā)光主要源于帶邊電子躍遷，價(jià)帶頂附近的能帶對(duì)光發(fā)射貢獻(xiàn)較大，特別是導(dǎo)帶與價(jià)帶第一子帶之間的電子躍遷在材料發(fā)光中占主導(dǎo)地位。為此我們重點(diǎn)分析價(jià)帶頂?shù)哪軒㈥P(guān)系隨Al組分的變化。在不考慮自旋軌道耦合作用的情況

34、下，原本立方對(duì)稱性閃鋅礦布里淵區(qū)中心處（k = 0）三重態(tài)15在纖鋅礦AlGaN六角對(duì)稱結(jié)構(gòu)下分裂為6雙重態(tài)和1單態(tài)，分別對(duì)應(yīng)為重空穴帶HH、輕空穴帶LH和晶體場(chǎng)分裂空穴帶CH。通常定義輕重空穴帶HH/LH與晶體場(chǎng)分裂空穴帶CH的能量差為晶體場(chǎng)分裂能cr。在無(wú)應(yīng)力狀態(tài)下，GaN中CH帶為第三子帶，位于HH和LH帶之下；隨著Al組分的增大，CH帶上移與HH和LH帶間的晶體場(chǎng)分裂能逐漸減少；當(dāng)Al組分提升至0.5時(shí)，cr減少至零，三子帶呈現(xiàn)簡(jiǎn)并；隨著Al組分進(jìn)一步增大，CH成為第一子帶，cr轉(zhuǎn)而為負(fù)。價(jià)帶頂能帶的排列順序隨著Al組分的變化而改變，如圖2（a）所示。通過對(duì)晶格常數(shù)比c/a的計(jì)算，可以

35、發(fā)現(xiàn)各模型AlGaN晶格常數(shù)比c/a偏離理想纖鋅礦結(jié)構(gòu)值1.63，c/a偏離程度隨Al組分的增大而增大，如圖2（b）所示，導(dǎo)致晶體場(chǎng)分裂能cr由GaN的40 meV逐漸減小，當(dāng)組分達(dá)到0.5時(shí)呈現(xiàn)0值。而當(dāng)Al組分繼續(xù)偏向AlN，cr呈現(xiàn)負(fù)值并逐漸減小，最終達(dá)到最小-197 meV。高Al組分與低Al組分AlxGa1-xN的價(jià)帶結(jié)構(gòu)的差異，對(duì)材料發(fā)光性質(zhì)有著決定性作用。材料發(fā)光主要來源于帶邊電子躍遷，特別是導(dǎo)帶與價(jià)帶第一子帶之間的電子躍遷在材料發(fā)光中占主導(dǎo)，第一子帶與其它子帶間的能量間距越大，其發(fā)光所占比重也越大。結(jié)合AlxGa1-xN混晶能帶結(jié)構(gòu)分析可知，低Al組分AlGaN的帶邊發(fā)光以o光

36、為主；隨著Al組分的增加，o光急劇減弱而e光迅速增強(qiáng)；高Al組分AlGaN的帶邊發(fā)光則變?yōu)閑光為主，如圖3（a）所示。光子的傳播方向與其偏振方向垂直，o光主要沿平行于c軸的方向傳播，大部分的光位于全反射角之內(nèi)，容易從外延層中逃逸，因此正面光抽取效率高。而e光主要沿垂直于c軸方向即側(cè)向傳播，正面的全反射和側(cè)面的狹小面積極大地限制了光抽取效率，如圖3（b）所示。全反射過程中大多數(shù)輻射光被材料吸收損耗，由于器件側(cè)向長(zhǎng)度尺寸遠(yuǎn)大于縱向厚度，e光在材料內(nèi)部的傳播距離比o光更為深遠(yuǎn)，增大了傳播過程中再被材料吸收的可能。由此可見，價(jià)帶頂能帶結(jié)構(gòu)對(duì)AlGaN紫外發(fā)光器件的發(fā)光效率起著關(guān)鍵作用，高Al組分AlG

37、aN價(jià)帶頂能帶帶序的反轉(zhuǎn)引起的光學(xué)偏振特性的變化，從根本上限制了器件的正面出光，導(dǎo)致器件的發(fā)光效率急劇下降。從能帶工程方面考慮，調(diào)制高Al組分的AlGaN價(jià)帶結(jié)構(gòu)，反轉(zhuǎn)輕重空穴帶至價(jià)帶頂，如此一來導(dǎo)帶和價(jià)帶第一子帶的躍遷復(fù)合輻射光易于從正面出射。圖3.（a）高Al組分AlGaN材料發(fā)光特性示意圖，（b）AlGaN LED與空氣間光的折射示意圖Fig. 3 The schematic diagram of the emitting light characteristics of high Al content AlGaN material (a) and the refraction betw

38、een AlGaN LED and air. 2.2應(yīng)變調(diào)控Al0.75Ga0.25N/AlN量子結(jié)構(gòu)發(fā)光偏振特性AlxGa1-xN/AlyGa1-yN（x y）量子結(jié)構(gòu)作為深紫外發(fā)光器件的有源層，量子阱組分往往大于0.5，不可避免的呈現(xiàn)側(cè)向發(fā)光的偏振特性。以往研究表明雙軸壓應(yīng)變能夠改變材料的價(jià)帶結(jié)構(gòu)，利用AlxGa1-xN/AlyGa1-yN（x y）中阱和壘間的失配應(yīng)變調(diào)控價(jià)帶翻轉(zhuǎn)是一種可行的解決方案 NOTEREF _Ref430420364 h 32, NOTEREF _Ref430420367 h 33。上述計(jì)算模型中，Al0.75Ga0.25N和AlN的cr均為負(fù)值，呈現(xiàn)側(cè)向發(fā)光特

39、性，本文以Al0.75Ga0.25N和AlN典型高Al組分AlGaN構(gòu)建量子結(jié)構(gòu)，Al0.75Ga0.25N阱層和AlN壘層厚度分別為4和12分子層。當(dāng)AlxGa1-xN/AlyGa1-yN（x y）量子結(jié)構(gòu)中阱與壘共格生長(zhǎng)，阱和壘的晶格常數(shù)因阱與壘間相互施加應(yīng)力而發(fā)生改變。相較于阱層，壘層厚度大，單位尺寸上所受到的應(yīng)力較小，晶格常數(shù)變化較小，而阱的晶格常數(shù)向靠近壘層晶格常數(shù)變化。模擬計(jì)算顯示當(dāng)阱壘層都弛豫至平衡晶格常數(shù)時(shí)，晶體場(chǎng)分裂能較之于Al0.75Ga0.25N混晶從-92 meV增大至-58 meV，如圖4（a）所示。考慮到實(shí)際生長(zhǎng)情況下，Al0.75Ga0.25N量子結(jié)構(gòu)通常在AlN

40、層上外延，厚度遠(yuǎn)大于量子結(jié)構(gòu)，阱層面內(nèi)晶格常數(shù)受到壘層壓縮幾近于AlN晶格常數(shù)值。有鑒于此，進(jìn)一步設(shè)定阱Al0.75Ga0.25N a和b晶格常數(shù)值固定為AlN弛豫狀態(tài)下的晶格常數(shù)值，此時(shí)Al0.75Ga0.25N的c軸晶格相應(yīng)的受拉伸而發(fā)生改變。為了確定壓應(yīng)變下的晶格常數(shù)c，根據(jù)Brich-Murnaghan Yu ZG, Gong H, Wu P. Lattice dynamics and electrical properties of wurtzite ZnO determined by a density functional theory method J. J Cryst Gro

41、wth, 2006, 287(1):199.狀態(tài)方程擬合能量晶格體積曲線，如圖4（b）所示，以預(yù)測(cè)雙軸應(yīng)變下的穩(wěn)定幾何結(jié)構(gòu)參數(shù)。圖4.（a）Al0.75Ga0.25N/AlN量子結(jié)構(gòu)平衡晶格能帶結(jié)構(gòu)（b）雙軸應(yīng)變下體系總能量與體積關(guān)系圖（c）雙軸應(yīng)變Al0.75Ga0.25N/AlN量子結(jié)構(gòu)能帶結(jié)構(gòu)Fig. 4 (a) The band structure of equilibrium Al0.75Ga0.25N/AlN quantumn structure. (b) The relation between system total energy and volume under biaxi

42、al strain. (c) the band structure of Al0.75Ga0.25N/AlN quantumn structure with biaxial strain. 纖鋅礦結(jié)構(gòu)的AlGaN的晶格常數(shù)a和c之間的應(yīng)變關(guān)系可以通過泊松比表述 Ruvimov S, Suski T, Iii JWA, et al. Strain-related phenomena in GaN thin films J. Phys Rev B Condens Matter, 1996;54(24):745753.， (1)式中和分別為沿a、c軸的應(yīng)變，為泊松比。對(duì)于在c面藍(lán)寶石上沿c軸外延生長(zhǎng)

43、的薄膜，面內(nèi)受到雙軸應(yīng)變。由彈性應(yīng)變理論（胡克定律）結(jié)合纖鋅礦AlGaN的對(duì)稱性可推導(dǎo)得出， (2)其中c13和 c33為彈性常數(shù)，a和c為受應(yīng)力的晶格常數(shù)，a0和c0為不受應(yīng)力的晶格常數(shù)。將計(jì)算優(yōu)化后阱Al0.75Ga0.25N的晶格常數(shù)a、c、a0、和c0 值代入公式（1）和（2）得到泊松比為0.256，與文獻(xiàn)報(bào)道的AlN數(shù)值0.237相近 Hu G, Ramesh KT, Cao B, et al. The compressive failure of aluminum nitride considered as a model advanced ceramic J. J Fluid M

44、ech, 2011, 59(5):1076.，表明優(yōu)化后的理論晶格常數(shù)有著合理的數(shù)值?；趦?yōu)化的平衡晶格參數(shù)，模擬計(jì)算體系能帶結(jié)構(gòu)，如圖4（c）所示，HH/LH和CH子帶能量有所偏移，對(duì)應(yīng)晶體場(chǎng)分裂能由-58 meV進(jìn)一步增大至-25 meV。量子結(jié)構(gòu)阱壘間的失配應(yīng)變能夠調(diào)制AlGaN的價(jià)帶結(jié)構(gòu)，減小了CH子帶和HH/LH子帶間的能量差距。2.3 Mg雜質(zhì)能帶工程調(diào)控Al0.75Ga0.25N/AlN量子結(jié)構(gòu)發(fā)光偏振特性一般而言，Mg摻雜往往會(huì)對(duì)價(jià)帶結(jié)構(gòu)產(chǎn)生影響，價(jià)帶頂能帶順序也有可能受到牽連，成為實(shí)現(xiàn)調(diào)控發(fā)光偏振特性的因應(yīng)方案。為此，本文采用第一性原理研究了Mg摻雜應(yīng)變Al0.75Ga0.2

45、5N/AlN量子結(jié)構(gòu)的價(jià)帶頂電子態(tài)密度分布，以深入了解Mg摻雜與光學(xué)偏振特性的直接關(guān)聯(lián)。理論上，介質(zhì)內(nèi)光子的吸收和發(fā)射過程通常包含電子從某一能態(tài)躍遷至另一能態(tài)的過程，對(duì)于從滿態(tài)的單電子布洛赫態(tài)到空態(tài)的單電子布洛赫態(tài)的躍遷，根據(jù)費(fèi)米黃金定律 Dirac P. A. M. The Quantum Theory of the Emission and Absorption of Radiation J. Proc R Soc A Math Phys Eng Sci, 1927, 114(767):243.Modulating optical polarization of Al-rich AlGaN

46、 via Mg dopantZHENG Tong-chang, LIN Wei*, CAI Duan-jun, LI Jin-chai, LI Shu-ping, Kang Jun-yong*(Key Laboratory of Semiconductors and Applications of Fujian Provinces, School of Physics and Mechanical & Elctrical Engineering，Xiamen University, Xiamen 361005,China)Abstract: The development of Al-rich

47、 AlGaN suffers from the optical polarization E/c which is unfavorable for light extraction efficiency for optoelectronic devices grown on the c-plane, especially for Al-rich AlGaN. Based on first-principles simulations, the complex physics behind the optical polarization probably stem from the fact

48、that the lattice parameter c/a ratio deviates from the ideal value for a hexagonal close-packed crystal structure. It is found that c/a ratio increases with Al content increases. The resulting crystal-field splitting energy cr varing from 40 meV to 0 meV as Al content increases from 0 to 0.5, and fi

49、nally droped down to -197 meV in AlN. The band engineering via Mg-doping strained AlGaN quantum structure allows modulation of the band structure especially at valence band maximum changing the valence band order so as to switch the emitted light polarization to ordinary light polarization，which will motivate further experimental work on improving light extraction efficiency in Al-rich AlGaN.Key words: Al-rich AlGaN; Opt