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ZnO的能带工程是当前ZnO研究的热点之一. 通过等价阳离子如Cd，Be，Mg等部分取代Zn形成CdZnO，BeZnO，MgZnO等合金来调控ZnO带隙的研究已广泛开展. 其中，Cd的掺杂可以减小ZnO的禁带宽度，使CdZnO合金在紫外-可见光波段光电器件中具有潜在的应用价值. 本文利用第一性原理计算结合集团展开法，通过研究纤锌矿（WZ）和岩盐矿（RS）型CdxZn1-xO合金不同Cd掺杂含量下各种构型的形成能，发现了纤锌矿结构的两种亚稳相Cd1/3Zn2/3O，Cd2/3Zn1/3O；对其晶格常数、键长、键角和电子结构的分析表明，随着Cd掺杂量的增大，晶格常数a，c均逐渐增大，而c/a值逐渐减小，O-Zn（Cd）-O键角及合金禁带宽度均逐渐减小. 通过对CdxZn1-xO合金的有效集团交互系数的分析得出，两个原子组成的集团中其有效集团交互系数最大，表明两原子集团对用集团展开法计算的形成能贡献最大. 通过比较第一性原理计算的形成能和集团展开法拟合计算得到的形成能，发现两者相差很小，表明采用集团展开法拟合计算CdxZn1-xO合金的形成能准确、可靠. 通过对大量CdxZn1-xO合金的形成能分析发现，大部分CdxZn1-xO的形成能比同组分的ZnO 与CdO混合相的能量高，表明ZnO和CdO互溶时会形成固溶度间隙，低温下难以实现全组分固溶. 在此基础上，我们计算了WZ-和RS-CdxZn1-xO随机合金的形成能并得到了相图. 对于纤锌矿结构，其临界温度为1000 K；对于岩盐矿结构，其临界温度为2250 K. 更高的临界温度表明CdxZn1-xO难以形成岩盐矿结构的合金. 进一步计算获得WZ-和RS-CdxZn1-xO的两相相图，发现Cd较易固溶于WZ-ZnO中，而Zn较难固溶于RS-CdO中.
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关键词:
- CdxZn1-xO合金 /
- 第一性原理计算 /
- 集团展开法 /
- 形成能
Bandgap engineering is one of the keys to practical applications of ZnO. Using ternary ZnMeO (Me=Be, Mg, Cd, etc.) alloys to regulate the bandgap of ZnO has been widely studied. Alloying ZnO with CdO to form CdxZn1-xO is an effective way to narrow down the bandgap of ZnO. With its narrower bandgap, CdxZn1-xO is a promising candidate for fabricating optoelectronic devices operable in the UV-visible wavelength region. In this work, we study the thermodynamic properties of CdxZn1-xO alloys of both wurtzite (WZ) and rock salt (RS) structures by first-principles calculations based on density functional theory (DFT) combined with the cluster expansion approach. The effective cluster interactions (ECIs) fitted formation energies agree well with the DFT-calculated formation energies for different compositions and structures correspondingly, validating the cluster expansion approach in calculations of the formation energy for CdxZn1-xO alloys. It is found that, for both WZ-CdxZn1-xO and RS-CdxZn1-xO alloys, the ECIs involve pair, triplet and quadruplet interactions: the pair interactions are dominant and contribute mostly to the formation energy. The first-and second-neighbor pair interaction parameters of WZ-CdxZn1-xO are positive, which indicates a tendency of ordering in WZ-CdxZn1-xO. For RS-CdxZn1-xO alloys, the nearest-neighbor pair interaction is negative, indicating a tendency to phase separation. The dominant positive second-neighbor pair interaction, however, appears to favor the ordering tendency. For both the WZ-CdxZn1-xO and RS-CdxZn1-xO alloys, the calculated formation energy of most structures is positive in the whole composition range, except for WZ-CdxZn1-xO with Cd concentrations of 1/3 and 2/3. Then, the crystal and electronic band structures of the metastable WZ-Cd1/3Zn2/3O and WZ-Cd2/3Zn1/3O are calculated. It turns out that both lattice constants a and c increase while the value of c/a and the bond angle of OZn(Cd)O decrease with increasing Cd concentration in the WZ-CdxZn1-xO alloys. Analyses of the band structures, densities of states (DOSs) and partial densities of states of WZ-CdxZn1-xO alloys reveal that the valence band maximum (VBM) is determined by O-2 p states and the conduction band minimum (CBM) stems from the hybrid Cd-5 s and Zn-4 s orbital. The VBM rises while the CBM declines, leading to the decrease of the bandgap of WZ-CdxZn1-xO with increasing Cd concentration. At finite temperatures, the thermal stability of the solid-state system is determined by Gibbs free energy. The bimodal curve, which indicates the equilibrium solubility limits as a function of temperature, can be calculated by the common tangent approach from the Gibbs free energy. The critical temperatures, above which complete miscibility is possible for some concentrations, are 1000 and 2250 K for WZ and RS phases, respectively. The higher critical temperature implies that it is more difficult to form RS-CdxZn1-xO than to form WZ-CdxZn1-xO. Finally, the phase diagrams of WZ-CdxZn1-xO and RS-CdxZn1-xO are derived based on calculations of the Gibbs free energy. At 1600 K, the solubility of Cd in WZ-ZnO amounts to 0.13, while the solubility of Zn in RS-CdO limits to only 0.01, indicating that it is much easier to incorporate Cd into WZ-ZnO than to incorporate Zn into RS-CdO.[1] Yang W F, Chen R, Liu B, Wong L M, Wang S J, Sun H D 2011 J. Appl. Phys. 109 113521
[2] Sadofev S, Blumstengel S, Cui J, Puls J, Rogaschewski S, Schaefer P, Henneberger F 2006 Appl. Phys. Lett. 89 201907
[3] Tsukazaki A, Ohtomo A, Onuma T, Ohtani M, Makino T, Sumiya M, Ohtani K, Chichibu S F, Fuke S, Segawa Y, Ohno H, Koinuma H, Kawasaki M {2005 Nat. Mater. 4 42
[4] Chung K, Lee C, Yi G C 2010 Science 330 655
[5] Ma X Y, Chen P L, Zhang R J, Yang D R 2011 J. Alloys. Compd. 509 6599
[6] Makino T, Segawa Y, Kawasaki M, Ohtomo A, Shiroki R, Tamura K, Yasuda T, Koinuma H 2001 Appl. Phys. Lett. 78 1237
[7] Bertram F, Giemsch S, Forster D, Christen J, Kling R, Kirchner C, Waag A 2006 Appl. Phys. Lett. 88 061915
[8] Sakurai K, Takagi T, Kubo T, Kajita D, Tanabe T, Takasu H, Fujita S, Fujita S 2002 J. Cryst. Growth 237-239 514
[9] Miloua R, Miloua F, Arbaoui A, Kebbab Z, Benramdane N, 2007 Solid State Commun. 144 5
[10] Tang X, L H F, Ma C Y, Zhao J J, Zhang Q Y 2008 Acta Phys. Sin. 57 1066 (in Chinese) [唐鑫, 吕海峰, 马春雨, 赵纪军, 张庆瑜 2008 物理学报 57 1066]
[11] Fan X F, Sun H D, Shen Z X, Kuo J L, Lu Y M 2008 J. Phys.: Condens. Matter 20 235221
[12] Ravi C, Sahu H K, Valsakumar M C, van de Walle A 2010 Phys. Rev. B 81 104111
[13] Hohenberg P, Kohn W {1964 Phys. Rev. B 136 B864
[14] Giannozzi P, Baroni S, Bonini N, Calandra M 2009 J. Phys.: Condens. Matter 21 395502
[15] Kohn W, Sham L J 1965 Phys. Rev. A 140 1133
[16] Vanderbilt D 1990 Phys. Rev. B 41 7892
[17] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[18] Van de Walle A, Asta M, Ceder G 2002 CALPHAD 26 539
[19] Yin W J, Dai L L, Zhang L, Yang R, Li L W, Guo T, Yan Y F 2014 J. Appl. Phys. 115 023707
[20] Yong D Y, He H Y, Su L X, Zhu Y, Tang Z K, Zeng X C, Pan B C 2015 Nanoscale 7 9852
[21] Pu C Y, Tang X, L H F, Zhang Q Y 2011 Acta Phys. Sin. 60 037101 (in Chinese) [濮春英, 唐鑫, 吕海峰, 张庆瑜 2011 物理学报 60 037101]
[22] Ravi C, Panigrahi B K, Valsakumar M C, van de Walle A 2012 Phys. Rev. B 85 054202
[23] Decremps F, Datchi F, Saitta A M, Polian A 2003 Phys. Rev. B 68 104101
[24] Schleife A, Fuchs F, Furthmuller J, Bechstedt F 2006 Phys. Rev. B 73 245212
[25] Jaffe J, Snyder J, Lin Z, Hess A {2000 Phys. Rev. B 62 1660
[26] Guerrero-Moreno R J, Takeuchi N 2002 Phys. Rev. B 66 205205
[27] Mortensen J J, Hansen L B, Jacobsen K W 2005 Phys. Rev. B 71 035109
[28] Kuisma M, Ojanen J, Enkovaara J, Rantalal T T 2010 Phys. Rev. B 82 115106
[29] Sun H Q, Ding S F, Wang Y T, Deng B, Fan G H 2008 Acta Phys.-Chim. Sin. 24 1233 (in Chinese) [孙慧卿, 丁少锋, 王雨田, 邓贝, 范广涵 2008 物理化学学报 24 1233]
[30] Powell R A, Spicer W E, McMenamin J C 1971 Phys. Rev. Lett. 27 97
[31] Kang H S, Lim S H, Kim J W, Chang H W, Kim G H, Kim J H, Lee S Y, Li Y, Lee J S, Lee J K, Nastasi M A, Crooker S A, Jia Q X 2006 J. Cryst. Growth 287 70
[32] Liu J Z, Van de Walle A, Ghosh G, Asta M 2005 Phys. Rev. B 72 144109
[33] Gan C K, Fan X F, Kuo J L 2010 Comp. Mater. Sci. 49 S29
[34] Madelung O M 2004 Semiconductors: Data Handbook (Berlin: Springer) pp173-241
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[1] Yang W F, Chen R, Liu B, Wong L M, Wang S J, Sun H D 2011 J. Appl. Phys. 109 113521
[2] Sadofev S, Blumstengel S, Cui J, Puls J, Rogaschewski S, Schaefer P, Henneberger F 2006 Appl. Phys. Lett. 89 201907
[3] Tsukazaki A, Ohtomo A, Onuma T, Ohtani M, Makino T, Sumiya M, Ohtani K, Chichibu S F, Fuke S, Segawa Y, Ohno H, Koinuma H, Kawasaki M {2005 Nat. Mater. 4 42
[4] Chung K, Lee C, Yi G C 2010 Science 330 655
[5] Ma X Y, Chen P L, Zhang R J, Yang D R 2011 J. Alloys. Compd. 509 6599
[6] Makino T, Segawa Y, Kawasaki M, Ohtomo A, Shiroki R, Tamura K, Yasuda T, Koinuma H 2001 Appl. Phys. Lett. 78 1237
[7] Bertram F, Giemsch S, Forster D, Christen J, Kling R, Kirchner C, Waag A 2006 Appl. Phys. Lett. 88 061915
[8] Sakurai K, Takagi T, Kubo T, Kajita D, Tanabe T, Takasu H, Fujita S, Fujita S 2002 J. Cryst. Growth 237-239 514
[9] Miloua R, Miloua F, Arbaoui A, Kebbab Z, Benramdane N, 2007 Solid State Commun. 144 5
[10] Tang X, L H F, Ma C Y, Zhao J J, Zhang Q Y 2008 Acta Phys. Sin. 57 1066 (in Chinese) [唐鑫, 吕海峰, 马春雨, 赵纪军, 张庆瑜 2008 物理学报 57 1066]
[11] Fan X F, Sun H D, Shen Z X, Kuo J L, Lu Y M 2008 J. Phys.: Condens. Matter 20 235221
[12] Ravi C, Sahu H K, Valsakumar M C, van de Walle A 2010 Phys. Rev. B 81 104111
[13] Hohenberg P, Kohn W {1964 Phys. Rev. B 136 B864
[14] Giannozzi P, Baroni S, Bonini N, Calandra M 2009 J. Phys.: Condens. Matter 21 395502
[15] Kohn W, Sham L J 1965 Phys. Rev. A 140 1133
[16] Vanderbilt D 1990 Phys. Rev. B 41 7892
[17] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[18] Van de Walle A, Asta M, Ceder G 2002 CALPHAD 26 539
[19] Yin W J, Dai L L, Zhang L, Yang R, Li L W, Guo T, Yan Y F 2014 J. Appl. Phys. 115 023707
[20] Yong D Y, He H Y, Su L X, Zhu Y, Tang Z K, Zeng X C, Pan B C 2015 Nanoscale 7 9852
[21] Pu C Y, Tang X, L H F, Zhang Q Y 2011 Acta Phys. Sin. 60 037101 (in Chinese) [濮春英, 唐鑫, 吕海峰, 张庆瑜 2011 物理学报 60 037101]
[22] Ravi C, Panigrahi B K, Valsakumar M C, van de Walle A 2012 Phys. Rev. B 85 054202
[23] Decremps F, Datchi F, Saitta A M, Polian A 2003 Phys. Rev. B 68 104101
[24] Schleife A, Fuchs F, Furthmuller J, Bechstedt F 2006 Phys. Rev. B 73 245212
[25] Jaffe J, Snyder J, Lin Z, Hess A {2000 Phys. Rev. B 62 1660
[26] Guerrero-Moreno R J, Takeuchi N 2002 Phys. Rev. B 66 205205
[27] Mortensen J J, Hansen L B, Jacobsen K W 2005 Phys. Rev. B 71 035109
[28] Kuisma M, Ojanen J, Enkovaara J, Rantalal T T 2010 Phys. Rev. B 82 115106
[29] Sun H Q, Ding S F, Wang Y T, Deng B, Fan G H 2008 Acta Phys.-Chim. Sin. 24 1233 (in Chinese) [孙慧卿, 丁少锋, 王雨田, 邓贝, 范广涵 2008 物理化学学报 24 1233]
[30] Powell R A, Spicer W E, McMenamin J C 1971 Phys. Rev. Lett. 27 97
[31] Kang H S, Lim S H, Kim J W, Chang H W, Kim G H, Kim J H, Lee S Y, Li Y, Lee J S, Lee J K, Nastasi M A, Crooker S A, Jia Q X 2006 J. Cryst. Growth 287 70
[32] Liu J Z, Van de Walle A, Ghosh G, Asta M 2005 Phys. Rev. B 72 144109
[33] Gan C K, Fan X F, Kuo J L 2010 Comp. Mater. Sci. 49 S29
[34] Madelung O M 2004 Semiconductors: Data Handbook (Berlin: Springer) pp173-241
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