行政院國家科學委員會專題研究計畫 成果報告
氮化鎵奈米線的電子結構及線與線間的交互作用
計畫類別： 個別型計畫 計畫編號： NSC93-2112-M-110-015- 執行期間： 93 年 08 月 01 日至 94 年 07 月 31 日 執行單位： 國立中山大學物理學系(所) 計畫主持人： 蔡民雄 計畫參與人員： 唐毓慧 報告類型： 精簡報告 報告附件： 出席國際會議研究心得報告及發表論文 處理方式： 本計畫可公開查詢中 華 民 國 94 年 10 月 17 日
行政院國家科學委員會專題研究計畫成果報告
氮化鎵奈米線的電子結構及線與線間的交互作用
The electronic structure of GaN nanowires and the interaction
between these wires
計畫編號：NSC 93-2112-M-110-015
執行期限：92 年 8 月 1 日至 93 年 7 月 31 日
主持人：蔡民雄
國立中山大學物理系
計畫參與人員：唐毓慧
國立中山大學物理系
一、 中文摘要 氮化鎵是重要的藍綠色光源材料。因此在 奈米科技發展中，是重要的研究對象。氮 化鎵可以成長成奈米尺寸直徑的線狀結 構，也可以成長成柱狀結構突出於薄膜表 面。柱狀結構及的基底相對於薄膜表面是 凹陷的。奈米柱狀結構及奈米線狀結構的 一種可能的解釋是柱與基底及線與線間存 在有排斥位能，此位能防止線聚合成薄膜 或三度空間結構。另一個有趣的實驗發現 是氮化鎵奈米柱／線輻射的光的藍移現 象。用半徑約為 5.5Å 及 6.4Å 以[1010]及 ] 0 2 11 [ 為表面的無限長氮化鎵奈米線的模 型，能量極小化的計算顯示表面能，也即 是表面張力，造成平均氮–鎵鍵長隨著線 半徑的減小而減小。此傾向亦應存在於輻 射光的測量所用的較粗的樣品上。由於能 帶間隙隨著氮–鎵鍵長的減小而增加，本 研究的結果可解釋藍移現象。氮化鎵奈米 柱交互作用的計算使用規則排列的奈米盤 模型。本研究發現奈米盤存在由串聯的 鎵–氮雙層電偶極層產生的固有電偶極。 當奈米盤間的距離減小時，我們發現鄰近 的奈米盤的電偶極建立的電場會感應沿 ] 1 000 [ 方向的電子電荷移動。此電荷移動 產生的電偶極與固有電偶極的方向相反， 因此總電偶極減弱了。從電偶極在奈米盤 的強化現象可預期當奈米柱足夠長以後， 奈米柱間將存在有排斥力。 關鍵詞：氮化鎵、奈米線、電子結構、交 互作用 AbstractGaN is an important material for blue/green light sources, so that it is an important subject of researches in the development of nanoscience and nanotechnology. GaN can
be grown into nanowires. It can also be grown into rod structures protruding out of GaN thin films. The bases of the rod structures are found to sink down below the surface of the film. A plausible interpretation of nanorods and nanowires is the existence of a repulsive potential
between them, which prevents
nanowires/rods from aggregating into a film or three-dimensional structure. Another interesting experimental finding is the blue shift of emission of GaN nanowires. Using models of infinitely long nm-size-GaN wires with [1010] and [1120] side surfaces and radii of about 5.5Å and 6.4Å, respectively, energy minimization calculations show that the average Ga-N bond lengths decreases with the decrease of the radius of the nanowire due to surface energy, i.e. surface tension. This trend can be extended to larger nanowires used in photoemission measurements. Since the band gap increases with the decrease of the bond length, our result explains the observed blue shift. The interaction of GaN nanorods is studied by using the model of an array of nanodisks. The present study finds that the nanorod has an intrinsic dipole moment associated with the array of the dipolar Ga-N bi-layers along the c-axis. When the distance between nanorods is decreased, an electronic charge transfer along the [0001]direction induced by the electric field of dipoles of neighboring nanorods is found. This charge transfer gives rise to an induced dipole that counters the intrinsic one, so that the net dipole moment is reduced. The enhancement of the dipole moment in nanorod implied that
when rods are long enough, they have repulsive interaction between them.
Keywords: GaN, nanowire, electronic structure, interaction
二、 緣由與目的
GaN is an important material for blue/green light sources, so that it is an important subject of researches in the
development of nanoscience and
nanotechnology. GaN can be grown into wires with nanometer scale diameters [1][2]. The electronic structures of nanowires have been measured by x-ray near-edge absorption spectroscopy (XANES), which showed that the electronic structures of nanowires are different from that of thin films [3]. Since the applications of GaN nanowires concern their electronic structures, the first-principles calculations of the electronic structures of GaN nanowires will be important and useful. Recently Tu et al. using plasma assisted molecular beam epitaxy (MBE) to grow GaN thin films and found hexagonal rod structures protruding out of the GaN films [4]. The bases of these rods sink down below the surface of the films. The depletion of the base region suggests the existence of a repulsive potential between the surface of the rod and the surrounding film surface. The existence of repulsive potential between surfaces may also stabilize nanowires to prevent these nanowires from attracting one another to aggregate into two- or three-dimensional structures. What is the origin of this repulsive potential? The growth of GaN films have been well known to be accompanied by hexagonal hollow core screw dislocations with diameters as large as several m extending across the thickness of the films. The protruding rods seem to be the inverse of the hollow core screw dislocations.TheFrank’sdislocation theory based on and the surface energy obtained by first-principles calculation [5]
has been used to explain the screw dislocations in GaN and other high-ionicity nitride films without success. The predicted radius of the screw dislocation was one order smaller than the observed ones. Since the GaN nanorods and nanowires are grown along the c-axis, the side surfaces are
] 0 1 10
[ and [1120] oriented nonpolar surfaces. Tsai et al. have calculated the surface structures and electronic structures of these surfaces and found that relaxation/reconstruction of the surface gives rise to a surface dipole layer [6]. Both surface dipoles and the interior dipole associated with the array of the polar Ga-N bi-layers can give rise to repulsive interaction between nanorods or nanowires, which may be responsible for the separation of nanowires and the depletion at the bases of the nanorods. Whether this is the case can be elucidated by calculating the total energies and dipole moments of an array of nanorods with [1010] and [1120]oriented side surfaces as a function of the inter-rod distance.
三、研究報告內容
1. Ga-N bond length dependence on the radius of the nanowire:
(1) Structural models:
GaN nanowires are modeled by a hexagonal array of infinitely long wires. The separation between the centers of adjacent nanowires is chosen as 15.6Å, which is estimated to be large enough to have negligible coupling among nanowires. Two types of nanowires are considered, namely nanowire (I), which has [1120] side surfaces and a radius of 5.53Å and nanowire (II), which has [1010]surfaces and a radius of 6.4Å. In both types, atomic positions are optimized by energy minimization calculations using the first-principles molecular-dynamics method.
(2) Comparison of bond lengths and angles Average bond lengths and bond angles of surface atoms are given in Tables 1 and 2 for nanowires (I) and (II), respectively. The
N-Ga-N (Ga-N-Ga) bond angles of the Ga (N) surface atoms in nanowires shown in tables 1 and 2 are larger (smaller) than the ideal tetrahedral angle of 109.5o, which is due to the tilt of Ga-N surface bonds [6]. The Ga-N average bond lengths are shown in Table 3. The Ga-N average bond length along the bilayer for Nanowire (I) are shorter than that for Nanowire (II). The total Ga-N average bond length for Nanowire (I) are also shorter than that for Nanowire (II). Thus, the present bond length calculation shows that the Ga-N bond length decreases with the decrease of the nanowire radius. This trend can be
expected to be the same for the
experimentally grown nanowires with radii from several nanometers to hundreds of nanometer [7] because the physical origin, namely the surface tension associated with the surface energy, which drives this contraction, is the same. It is well known that the decrease of the cation-anion bond length increases the energy gap. Thus, the energy of emitted light will increase with the decrease of GaN nanowire or nanorod radius, which explains the experimentally observed blue shift of the CL emission [7][8].
Table I. Bond lengths and angles of surface atoms in nanowire (I)
Surface atoms Corner atoms Bond length(S) 1.813Å 1.69Å Bond length(I) 1.902Å 1.87Å N-Ga-N angle 113.49o 128.24o Ga-N-Ga angle 108.25o 102.17o
Table II. Bond lengths and angles of surface atoms in nanowire (II)
Surface atoms Corner atoms Bond length(S) 1.785Å 1.76Å Bond length(I) 1.925Å 1.91Å N-Ga-N angle 118.00o 119.84o
Ga-N-Ga angle 106.49o 106.60o
Table III. Comparison of average bond lengths in nanowires (I) and (II). The lattice constant c=5.189 Å
Nanowire (I) Nanowire (II) Along bi-layer 1.932Å 1.950Å Along c-axis 0.364c 0.357c Overall 1.917Å 1.931Å
(3) Electronic structures:
The energy bands of nanowire (I) are shown in Fig. 1. The electronic structures of these nanowires are very different from those
of bulk and films. Due to the large ratio of the numbers of surface/corner atoms and interior atoms, there are a large number of surface/dangling-bond bands in the vicinity of the Fermi-level, EF. EFis about -8.674 eV
and the surface/dangling-bond bands are ranged from about -11 to -5 eV. The highest occupied band is contributed dominantly by N corner-atom states. The lowest unoccupied band is contributed dominantly by hybridized states of Ga and N corner/surface atoms. There is an energy gap of about 0.14 eV between these two bands. Because interior atoms are relatively few, the valence-band width is about 7.29 eV. The energy gap of about 5.18 eV between occupied and unoccupied bands of interior atoms don’t resemble those of bulk GaN solid, which has an experimental energy gap of 3.34 eV [9]. Since LDA has a tendency to underestimate the energy gap, the present calculation indicates that energy gap of interior atoms of the GaN nanowires is much greater than that of the GaN bulk band gap.
2. Interaction between nanorods: (1) Strutural mdel:
The structural model considered in this
study is a hexagonal array of
four-atomic-layer thick nanodisks. A single disk is a hexagonal cylinder with the axis lying along the c-axis. It has six [1120] side surfaces. The radius and thickness of the nanodisk are 4.785Å and 7.656 Å, respectively. The disk contains two Ga-N bilayers with 50 atoms. The first, second, third and fourth layers contain 12 Ga, 13 N, 13 Ga and 12 N atoms, respectively. The atomic positions have been transported directly from the optimized ones using the molecular-dynamics calculation method and the infinite-long-wire model stated in 1. (1). (2) Dependence of the dipole and the total energy on the inter-rod distance.
The dipole moment, p, and the relative total energy, E, per disk with respect to the distance, d, between the centers of neighboring disks are given in Table IV. Table IV.
d(Ǻ) p(Debye) E(eV)
12.59 12.77 -46.51
17.19 20.60 -9.11
19.19 21.55 -7.22
21.19 21.92 -1.90
23.19 21.91 0.0
The dipole moments point in the
] 0001
[ direction. The GaN nanodisk contains two Ga-N bi-layers. Since Ga and N have positive and negative effective charges, respectively, with a magnitude of about 2.6e, each bi-layer is a dipole layer. Thus the GaN nanodisk considered in this study has an intrinsic dipole moment, pintrinsic, formed by two dipole layers. The magnitude of pintrinsic
is the saturated dipole moment of about 21.93Debyes. Table IV shows that the dipole moment decreases with the decrease of d, which can be attributed to the charge transfer effect induced by the electric fields associated with the dipoles in neighboring disks. This charge transfer gives rise to a dipole moment in opposite direction to the intrinsic dipole, so that the net dipole per disk decreases when disks are drawn closer. Table IV shows that the total energy per disk increases monotonically, which does not show repulsive interactions among disks. The lack of a repulsive force can be attributed to the charge transfer effect, which greatly reduces the net dipole moment of the disk and consequently the repulsive dipole-dipole interactions among them. Since the external electric field is proportional to d-3, the energy associated with the charge transfer effect is proportional to d-6, which drops off rapidly. Thus, one expects that if a better structural model, which has a large length to diameter ratio and a large dipole moment, and larger inter-rod distances are considered, the total energy calculation will be able to show repulsion between nanorods, i.e. the total energy will reach a maximum and then decreases with d-3. 四、計畫成果自評 此研究計畫的目的在於了解為什麼氮化 鎵可以長成奈米尺寸直徑的線狀結構，也 可以成長成柱狀結構突出於薄膜表面，以 及其輻射光的波長隨著奈米線/柱的直徑的 減小而減小，即藍移，的現象。本研究所 發現的奈米線的鎵-氮鍵長因表面張力的 關係隨著其直徑的減小而減小，可以解釋 輻射光藍移現象。本研究用奈米盤模型對 於奈米柱電偶極的計算發現奈米柱存在由 鎵-氮電偶極層累積成的固有電偶極。當奈 米盤彼此接近時所彼此感應的電偶極矩與 固有電偶極矩方向相反，因此淨電偶極矩 減弱了。以致沒有發現奈米盤間有排斥現 象。但此研究結果亦顯示，當我們用較大 的長/直徑比例的奈米柱模型就可得到預期 的奈米柱的排斥現象。 五、參考文獻
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Mater. 2003, 15, NO.3
[9] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 73rd edn., Boca Raton, Ann Arbor, Lodon, Tokyo, 1992-1993.
Fig. 1 The band structure of nanowire (I), in which A, L, M,, H, and K high symmetry points in the unit of 2a are (0,0,1.500), (0.5,0.289,1.500), (0.5,0.289,0),
(0,0,0), (0.667,0,1.500) and (0.667,0,0), respectively. All the bands shown by brown curves are the surface/dangling-bond bands. Black curves are energy bands of interior atoms.
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