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Electronic Structures and Optical Properties of Ga-Rich InxGa1-xN Nanotubes Mao Yang,† Jun-jie Shi,*,† and Min Zhang†,‡ State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking UniVersity, Beijing 100871, People’s Republic of China, and College of Physics and Electron Information, Inner Mongolia Normal UniVersity, Hohhot 010022, People’s Republic of China ReceiVed: June 29, 2010; ReVised Manuscript ReceiVed: September 24, 2010
The electronic structures and optical properties of single-walled Ga-rich zigzag InxGa1-xN nanotubes (NTs) are investigated using first-principles calculations. We find that In atoms substitute Ga atoms randomly in InxGa1-xN NTs, in which some typical In-N clusters, chains, and rings are embedded by chance. Both the electronic structures and optical properties insensitively depends on In distribution. A spiculate density of states (DOS) peak appears in the vicinity of the valence band maximum (VBM) and conduction band minimum. The imaginary part ε2 of the complex dielectric function has also a sharp peak related to the band edge absorption. The In doping can effectively adjust the band gap and enhance the peak of the band edge absorption and DOS. Unlike bulk InxGa1-xN alloys, the electron states at the VBM become extended for the NTs with various In distributions. Introduction In 1991, the carbon nanotubes (NTs) were successfully synthesized in experiments for the first time.1 Compared with bulk materials, many marvelous physical properties have been found in one-dimensional (1D) NTs due to their small size, strong quantum confinement, and surface effects.2 This stimulated extensive research interest in 1D nanostructures in the last two decades because they are believed to be one of the most important materials to the next generation of electronic and optical devices. Recently, some important 1D compound nanostructures, such as BN,3 BC2N,4 AlN,5 SiC NTs,6 and GaN NTs7 and nanowires,8 have been synthesized and investigated. It is well-known that InxGa1-xN alloy is one of the most important members in group III nitride family, acting as core components in high efficiency light emitting diodes (LEDs), laser diodes (LDs), and solar cells.9,10 Compared with the bulk alloy, 1D InxGa1-xN nanostructures are of great interest due to their extraordinary electronic structures and optical properties, which have lots of advantages in LEDs, LDs, field-effect transistors, and photovoltaics.9 Naturally, the synthesis of 1D InxGa1-xN nanostructures becomes a key issue in recent years. Kuykendall et al.12 synthesized single-crystalline InxGa1-xN (0 e x e 1) nanowires for the first time by low-temperature halide chemical vapor deposition. A core-shell structure InGaN nanowire13 with potential photonic applications was also produced. The GaN/InxGa1-xN coaxial NT microarrys14 were successfully fabricated as green LEDs. The photovoltaic devices are realized by coaxial group III nitride nanowires.15 The InxGa1-xN nanowires exhibit the exceptional optical properties and can overcome the so-called “valley of death” drop off in photoluminescence efficiency for high In concentration samples.12,16 It has been found that the efficiency of light output in InxGa1-xN nanostructure is much higher than in bulk materials.17,18 There exists a novel strong ultraviolet photoluminescence spectrum in Al-doped GaN nanowires.19 The light emission of InGaN/GaN nanocolumn20 * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +86-10-62757594. Fax: +86-10-62751615. † Peking University. ‡ Inner Mongolia Normal University.
can also be changed from blue to red with increasing the diameter of nanocolumns. On the basis of first-principles calculations, the stability and electronic structures of single-walled GaN and InN NTs have been studied.21,22 Compared with bulk materials, some novel physical properties have been found. For example, the calculations of exciton states in GaN NTs show that the excitation energies can be reduced by decreasing dimension.23 InxGa1-xN nanowires have a better band gap tunability than the bulk alloy,24 which has been confirmed by the screened exchange hybrid density functional theory (DFT) calculations. Band gap engineering can also be easily realized by changing the composition of AlN/GaN NT superlattices.25 The electronic structures and optical properties of the important bulk InxGa1-xN alloys have been studied in depth by experiments26 and theoretical calculations.27-30 It has been known that both the electronic structures and carrier localization sensitively depend on the In distribution in the bulk alloy, such as In-N clusters and chains.28-30 To the best of our knowledge, for the valued 1D InxGa1-xN nanostructures in the solid-state lighting and photovoltaics, the influence of In atoms on electronic structures, carrier localization, and optical properties is still poorly understood. We will devote to study this fundamental problem in 1D InxGa1-xN NTs as a representative of 1D nanostructures in the present paper. We investigate the electronic structures and optical properties of Ga-rich zigzag InxGa1-xN NTs based on powerful firstprinciples calculations. We find that In doping can obviously adjust the band gap of NTs and enhance the peak of the total density of states (DOS) at the valence band maximum (VBM) and enlarge the imaginary part ε2 of the complex dielectric function, which exists a sharp peak associated with the strong band edge absorption. The electronic structures of InxGa1-xN NTs are insensitive to the microscopic In distribution. Different from bulk alloys, the electron states at the VBM are extended for the InxGa1-xN NTs with various In arrangements, which is quite useful for solar cells.
10.1021/jp105986g 2010 American Chemical Society Published on Web 11/30/2010
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TABLE 1: Comparison of the Band Gap (Eg), Vertical and Horizontal Bond Length (av and ah), Length of a Unit Cell along Tube Axis (L), Tube Diameter (d) with Previous Theoretical Results for (5,0) GaN and InN NTs material GaN InN
Eg (eV) av (Å) other calculations this work other calculations this work
TABLE 2: Total Energy (Etot) and Band Gap (Eg) of (5,0) In3Ga17N20 NTs for Models I-VIa
ah (Å) L (Å) d (Å)
5.4439 1.81639 1.72 1.865 1.885 5.48 0.7222 2.06540 2.06540 0.68 2.108 2.126 6.12
5.3139 5.35 623 6.06 a
In distribution
Etot (eV)
Eg (eV)
Model I Model II Model III Model IV Model V Model VI
-45995.4595 -45995.4482 -45995.2720 -45995.3676 -45995.3956 -45995.3948
1.409 1.434 1.448 1.442 1.454 1.406
Please refer to Figure 1.
Calculation Method Our first-principles calculations are based on the CASTEP code,31 which can give accurate valence band structures and ground-state properties of semiconductors.32 We adopt a 1 × 1 × 2 supercell of Ga-rich zigzag InxGa1-xN NTs and use a planewave basis set with a cutoff energy of 350 eV and ultrasoft pseudopotentials.33 The size of the supercell is adjusted to make the interactions between adjacent NTs negligible (∼12 Å vacuum from surface to surface). The Monkhorst-Pack34,35 k-point grid is chosen as 1 × 1 × 11. The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof’s (PBE) exchange-correlation potential37 is adopted. The Ga (3d104s24p1), In (4d105s25p1), and N (2s22p3) are treated as the valence electrons. Convergence with respect to the plane wave cutoff energy and k-point sampling has been carefully checked. Our calculations for the local distortions resulting from different covalent radii of Ga and In atoms are based on reducing the magnitude of calculated forces and stresses until they become smaller than the chosen convergence tolerances. The structures of InxGa1-xN NTs have been optimized here by minimization of the total energy and the Hellmann-Feynmann forces with respect to atomic coordinates for a given distribution of In atoms in the NTs. In our following calculations, the total energy is converged to less than 10-6 eV/atom. The maximum force is less than 0.03 eV/Å. The maximum stress is less than 0.05 GPa. The maximum displacement is less than 0.001 Å. Since the optical property calculations require a dense k-point grid, we thus use a 1 × 1 × 49 k-point grid and a Gaussian smearing width of 0.1 eV. Because nonlocal potentials are adopted in CASTEP, we correct the transition matrix elements according to the formula of Read and Needs.37 Results and Discussion We know from our calculations that the zigzag GaN (InN) NT has a direct band gap at Γ point. For the (5,0) GaN (InN) NT, our calculation results for the band gap (Eg), vertical and horizontal bond length (av and ah), the length of a unit cell along tube axis (L), and tube diameter (d) together with the previous theoretical results are summarized in Table 1. The good
agreement with the previous theoretical calculations indicates that the present first-principles calculations are accurate and believable. To investigate the influence of In doping on electronic structures and optical properties of Ga-rich InxGa1-xN NTs, we adopt several (5,0) InxGa1-xN NTs with different In concentrations under the Ga-rich condition, such as In1Ga19N20 and In3Ga17N20. Six types of In distributions for In3Ga17N20 NTs (see Figure 1) are used to explore the relationship between electronic structures and In distribution. By comparison of the total DOS and imaginary part ε2 of the complex dielectric function among these InxGa1-xN NTs, we can clarify the effects of In doping in GaN NTs. First, we optimize the geometrical structure of (5,0) In3Ga17N20 NTs and calculate their total energy (Etot) for a unit cell with six different In distributions (Figure 1). By comparison of their total energy, we can outline the microstructure of In3Ga17N20 NTs. Our results are given in Table 2. The maximum difference of Etot is of 0.19 eV among Models I-VI, which indicates the substitution of In atoms with Ga atoms is randomly in the InxGa1-xN NTs. Hence we conclude that the spacial distribution of In atoms is random in In3Ga17N20 NTs, in which some typical In-N clusters, chains, and rings can be easily formed by chance. Moreover, we can also find from 1 that the band gap (Eg) of In3Ga17N20 NTs insensitively depends on In distribution. Our results for the total DOS of (5,0) GaN, InxGa1-xN, and InN NTs are shown in Figure 2. Considering the importance of the VBM and conduction band minimum (CBM) states in the photoluminescence process of semiconductors, we will only focus on the VBM and CBM states. We can see from Figure 2 that the band gap (Eg) of InxGa1-xN NTs decreases when the In concentration increases. It is more interesting to note that a spiculate DOS peak appears in the vicinity of the VBM and CBM for all these NTs. This is a typical character of 1D nanostructures. The physical reason is because the effects of the dimensionality and quantum confinements have a significant influence on electron motion. The electron DOS is quite different between 1D (∝ E-1/2) and 3D (∝ E1/2). It is the spiculate electron
Figure 1. The (5,0) In3Ga17N20 NTs with six different In distributions. (a) Three In atoms distributing uniformly (Model I), (b) three In atoms forming a clustered structure (Model II), (c) In-N chain perpendicular to the tube axis (Model III), (d) sloping In-N chain (Model IV), (e) In-N chain parallel to the tube axis (Model V), and (f) three In atoms forming a ring (Model VI). Here the gray, blue, and red spheres represent the Ga, N, and In atoms, respectively.
Structures and Properties of Ga-Rich InxGa1-xN NTs
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Figure 2. Total DOS of (5,0) GaN, In1Ga19N20, In3Ga17N20 (Model I of Figure 1), and InN NTs. We find that the DOS is insensitive to the In distribution in In3Ga17N20 NTs and thus choose the uniform In distribution here. The inset shows the magnified image of the electron DOS in the vicinity of the VBM.
Figure 3. Imaginary part ε2 of the complex dielectric function of (5,0) GaN, In1Ga19N20, In3Ga17N20 (Model I of Figure 1), and InN NTs. We find that ε2 is insensitive to the In distribution in In3Ga17N20 NTs and thus choose the uniform In distribution here.
TABLE 3: Electron Effective Mass (m*) e at the CBM, the Hole Effective Mass (m*) h at the VBM and the Optical Effective Mass (m*opt) of (5,0) GaN, In1Ga19N20, In3Ga17N20 (Models I-VI of Figure 1) and InN NTsa
a
material
m*/m e 0
m*/m h 0
m*opt/m0
GaN In1Ga19N20 Model I Model II Model III Model IV Model V Model VI InN
0.213 0.215 0.220 0.226 0.216 0.215 0.228 0.223 0.198
3.571 3.659 4.178 4.163 4.257 4.174 4.134 4.198 6.250
0.201 0.203 0.208 0.214 0.204 0.203 0.216 0.211 0.192
m0 denotes the free electron mass.
DOS peak of the 1D nanomaterials at the VBM and CBM that determines why they have more advantageous than 3D bulk materials in improving the performance of the light emitting and photovoltaic devices. We find from our numerical calculations that, in the vicinity of the VBM, the GaN NT has the smallest DOS; the DOS becomes large when the In concentration increases. The DOS peak of the InN NT is of 49.3 electrons/ eV, which is the largest among these InxGa1-xN NTs. On the contrary, the DOSs in the vicinity of the CBM are similar among these InxGa1-xN NTs. The DOSs of In3Ga17N20 NTs with different In distributions are also almost similar. Generally, the electron DOS of 1D nanomaterials in the vicinity of the VBM is directly proportional to -1/2 m*1/2 h (EV - E)
Figure 4. Imaginary part ε2 of the complex dielectric function of (7,0) GaN, In1Ga13N14, and In3Ga11N14 NTs. The uniform In distribution is chosen for the In3Ga11N14 NT.
(1)
Similarly, the DOS in the vicinity of the CBM is proportional
Figure 5. Imaginary part ε2 of the complex dielectric function of (10,0) GaN, In2Ga18N20, and In4Ga16N20 NTs with the uniform In distribution.
to
m*1/2 e (E
-1/2
- EC)
(2)
In eq 1 and eq 2, EV (EC) is the electron energy eigenvalue in the VBM (CBM) state, and m*e (m*) h is the electron (hole) effective mass at the CBM (VBM). To understand our above numerical results for the electron DOS (Figure 2), we further calculate m*e and m*h (please refer to Table 3). We can see from Table 3 that the hole effective mass of the InN (GaN) NT is the largest (smallest) among all these NTs. The m*h becomes
large if In concentration is increased. On the contrary, m*e is insensitive to In fraction in the NTs. This directly leads to the difference of the DOS peak in the VBM state shown in Figure 2. Our calculations further show that both m*e and m*h are insensitive to the In distribution in (5,0) In3Ga17N20 NTs. This indicates that the electronic structures in the vicinity of the VBM (CBM) are almost the same for the In3Ga17N20 NTs with different In distributions. Equations 1 and 2 show that the DOS of 1D nanomaterials approaches infinity at the VBM (CBM). This is extremely desirable for some typical light emitting and photovoltaic device application.
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Figure 6. Isosurface charge density plot (F ) 0.02 e/Å3) of the VBM state in In1Ga19N20 NT (a) and In3Ga17N20 NTs in (b-g) for Models I-VI of Figure 1. Here the gray, blue, and red spheres represent the Ga, N, and In atoms, respectively. Similar results can also be obtained for the CBM state.
Let us now further investigate imaginary part ε2 of the complex dielectric function for the zigzag InxGa1-xN NTs with different radii and In concentrations in order to find out the relationship between optical properties and In fraction x. Figure 3 clearly shows that, for the (5,0) InxGa1-xN NTs, the first peak of ε2 (M0-type Van Hove singularity) closely relates to the band edge transition between the VBM and CBM states. The peak is increased and its position is shifted to a lower energy due to reducing of the InxGa1-xN NT band gap if the In concentration is increased. We further calculate ε2 of (7,0) and (10,0) InxGa1-xN NTs. Figures 4 and 5 indicate that the results of the (7,0) and (10,0) NTs are similar to the (5,0) NTs. Therefore, In doping can adjust the band gap and enhance the band edge transition probability of GaN NTs. This paves a new way to increase the light emitting efficiency of LEDs and LDs and improve the energy conversion efficiency of solar cells.38 The first peak of ε2, which describes the band edge transition probability between the VBM and CBM states, is related to the optical effective mass and the momentum matrix element and is given by *1/2 ε2(ω) ∝ mopt |PCV |2(pω - Eg)-1/2
(3)
where PCV is the momentum matrix element related to the optical transition with photon energy pω and m*opt is the optical effective *-1 ) m*-1 + mh*-1. Our calculation results mass defined by mopt e of m*opt are summarized in Table 3. We can see from Table 3 that the optical effective mass m*opt insensitively depends on In concentration and distribution in InxGa1-xN NTs. This is because . mh*-1 and m*e has a negligible variation for different In m*-1 e contents and distributions. We can thus infer from Figure 3 that PCV is sensitive to the In fraction in InxGa1-x N NTs. To study the spacial distribution of electrons in the vicinity of the VBM (CBM), we further calculate the charge density of the VBM (CBM) state. Figure 6 shows the results of the charge density of the VBM state with different In concentrations and distributions. We can see from Figure 6 that the VBM state has a special π -bond behavior around the N atoms due to their large electronegativity. Unlike InxGa1-xN bulk alloys, the VBM state becomes almost like a delocalized Bloch-like state in In3Ga17N20 NTs with different In distributions. This is owing to the π -bond behavior of the VBM state, which is different from the InxGa1-xN bulk alloys. We thus have the following conclusions. The In doping does not induce any electron localization of the VBM state in GaN NTs. Charge density distribution is insensitive to the In distribution in InxGa1-xN NTs. This suggests that InxGa1-xN NTs have potential application in solar cells. Conclusions In this paper, we perform first-principles calculations of the electronic structures and optical properties of single-walled Ga-
rich zigzag InxGa1-xN NTs. Our calculations show that In atoms are distributed randomly in NTs, in which some typical In-N clusters, chains, and rings are embedded by chance. We find that a spiculate DOS peak appears in the vicinity of the VBM and CBM. In the vicinity of the VBM, the DOS peak becomes large if the In concentration increases. The DOS values in the vicinity of the CBM have no obvious variation for different InxGa1-xN NTs. The imaginary part ε2 of the complex dielectric function exists a sharp peak, which corresponds to the band edge transition. The In doping can effectively adjust the band gap and enhance the peak of the band edge absorption and DOS of GaN NTs. The momentum matrix element PCV is sensitive to the In fraction. Different from InxGa1-xN bulk alloys, the VBM state becomes almost delocalized Bloch-like state in InxGa1-xN NTs with different In distributions. Both electronic structures and optical properties are insensitive to the In distribution in InxGa1-xN NTs. Our calculations clearly indicate that the 1D NTs have marvelous advantages (spiculate DOS peak at the VBM and CBM and sharp ε2 peak related to the band edge transition) and are much better than 3D bulk materials in improving the characters of the light emitting and photovoltaic devices. This paper thus provides a theoretical foundation to increase the internal quantum efficiency of LEDs and LDs and improve the energy conversion efficiency and performance of solar cells. Acknowledgment. This work was supported jointly by the National Natural Science Foundation of China (51072007, 91021017, 60890193), the National Basic Research Program of China (2006CB921607), the Beijing Natural Science Foundation (1092007), and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (2010BS0101). Supporting Information Available: Our all geometrical structure files (1-15.cif). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Iijima, S. Nature 1991, 354, 56–58. (2) Charlier, J.-C.; Blase, X.; Roche, S. ReV. Mod. Phys. 2007, 79, 677–732. (3) Chopra, N. G.; Luyken, R. J.; Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettl, A. Science 1995, 269, 966–967. (4) Pan, H.; Feng, Y. P.; Lin, J. Phys. ReV. B 2006, 74, 045409. (5) Zhao, M.; Xia, Y.; Zhang, D.; Mei, L. Phys. ReV. B 2003, 68, 235415. (6) Szabo´, A.; Gali, A. Phys. ReV. B 2009, 80, 075425. (7) Goldberger, J.; He, R.; Zhang, Y.; Lee, S.; Yan, H.; Choi, H.-J.; Yang, P. Nature 2003, 422, 599–602. (8) Yilmaz, H.; Weiner, B. R.; Morell, G. Phys. ReV. B 2010, 81, 041312. (9) Wu, J. J. Appl. Phys. 2009, 106, 011101. (10) Chen, X.; Mathews, K. D.; Hao, D.; Schaff, W. J.; Eastman, L. F. Phys. Status Solidi A 2008, 205, 1103–1105. (11) Neufeld, C. J.; Toledo, N. G.; Cruz, S. C.; Iza, M.; DenBaars, S. P.; Mishra, U. K. Appl. Phys. Lett. 2008, 93, 143502.
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