Article pubs.acs.org/JPCC
Band Edge Modulation and Light Emission in InGaN Nanowires Due to the Surface State and Microscopic Indium Distribution Tie-cheng Zhou,† Jun-jie Shi,*,† Min Zhang,‡ Mao Yang,† Hong-xia Zhong,† Xin-he Jiang,† and Pu Huang† †
State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, People’s Republic of China ‡ College of Physics and Electron Information, Inner Mongolia Normal University, Hohhot 010022, People’s Republic of China ABSTRACT: InGaN nanowires (NWs) show exceptional optical properties and have huge potential in applications such as light-emitting diodes, laser diodes, and solar cells. Although lots of work has focused on improving their optical performance, little is known about the influence of the In distribution and surface states on the microscopic light emission mechanism. In order to give an atomiclevel understanding, we investigate the electronic structures of the wurtzite Ga-rich InGaN NWs with different In distributions using first-principles calculations, in which both the unsaturated and saturated NWs are considered. We find that In atoms are apt to distribute on the surface of the NWs and that the short surface In−N chains can be easily formed. For the unsaturated NWs, several new bands are induced by the surface states, which can be modified by the surface In microstructures. The randomly formed surface In−N chains can highly localize the electrons/holes at the band edges and dominate the interband optical transition. For the saturated NWs, the band edges are determined by the inner N and Ga atoms. Our work is useful to improve the performance of the InGaN NW-based optoelectronic devices.
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INTRODUCTION Group-III nitride semiconductors have attracted much attention due to their huge potential in light-emitting diodes (LEDs), laser diodes (LDs), and solar cells.1−4 The InGaN ternary alloys are of great importance because their direct band gaps can be tuned continuously from 0.7 (InN) to 3.4 eV (GaN), which closely matches the visible spectrum. It is wellknown that the InGaN alloys have high light-emitting efficiency, despite of their large threading-dislocation (TD) density (109− 1010 cm−2) caused by the lattice mismatch1,5 and the strong builtin electric field (MV/cm).6 This fact clearly indicates that there are many carrier-localization centers in InGaN alloys, which are closely related to the In microstructures.7,8 Recent theoretical calculations have proven that the several-atom In−N clusters and the short In−N chains dominate the light emission in InGaN alloys.9−11 It is known that the density of the TDs and defects can be significantly reduced by synthesizing the InGaN nanostructures,12−14 which makes a great improvement for the performance of the InGaN-based optoelectronic devices. The wurtzite GaN nanostructures with hexagonal morphology have been synthesized in experiments.15 The light emission due to the surface states is observed in the GaN nanowires (NWs).16 Recently, high-quality single-crystalline InGaN NWs with some exceptional optical properties have been synthesized by lowtemperature halide chemical vapor deposition,17 in which a continuous tunability of the light emission wavelength has been realized by varying the In content. The white light emission based on the InGaN NWs has also been acquired.18 Moreover, © 2013 American Chemical Society
the InGaN-based core/shell nanostructures with different In distributions in their optical active layers are fabricated.19−21 Strong light emission from the InGaN shell is observed in the n-GaN/InGaN/p-GaN core/shell/shell NWs.19 Two optical emission peaks from the InGaN shell and InN core were obtained in the InN/InGaN core/shell NWs.20 The photoluminescence (PL) in the GaN/InGaN core/shell NWs has been observed due to the strain relaxation in the InGaN shell.21 With the In incorporation, the InGaN nanostructures also have improved performance for some optoelectronic devices, such as high electron mobility for the field effect transistors (FETs),22 enhanced PL intensity of ultraviolet−blue and −green luminescence for LEDs and LDs,23−25 and more efficient carrier collection for solar cells.26 Obviously, the In atoms play an important role in the light emission in InGaN nanostructures. To utilize the excellent optical properties of InGaN nanostructures, it is crucial to understand the light emission mechanism due to the surface states and the microscopic In distributions. In order to explore the mechanism of the light emission in GaN and InGaN nanostructures, some theoretical calculations have been carried out successively. Carter et al.27 found that the surface states have an important influence on the electronic structures of the unsaturated GaN NWs. Wang et al.28 reported that the surface states, induced by the surface three-fold-coordinated Received: April 17, 2013 Revised: July 10, 2013 Published: July 25, 2013 16231
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N and Ga atoms, are important for the multiwalled GaN nanotubes. The electronic and optical properties of core/shell InGaN nanorods were reported.29 The influence of the diameter30,31 and strains32 on the band gap of the InGaN NWs were also discussed. To the best of our knowledge, a detailed theoretical calculation for the In distributions in the InGaN NWs is rarely reported at present. The role of the In microstructures and the surface states on the light emission is still poorly understood. Our purpose here is to investigate the surface states and In distributions at an atomic level and explore
their influence on electronic and optical properties of the Garich InGaN NWs using the powerful first-principles calculations. We find that the In atoms tend to distribute on the surface of the Ga-rich InGaN NWs. The short surface In−N chains are easily formed due to their small formation energy, which can highly localize the band edge states and dominate the light emission for the unsaturated InGaN NWs. For the saturated NWs, however, the recombination centers are in the inner of the NWs and mainly determined by the inner Ga and N atoms.
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CALCULATION METHODS Our first-principles calculations are performed using SIESTA and DMol3 codes.33,34 In our SIESTA calculations, the local density approximation (LDA) and Ceperley−Alder (CA) exchange−correlation functional are adopted. The Ga (4s24p13d10), In (5s25p14d10), N (2s22p3), and H (1s1) are considered as valence electrons. The double-ζ basis plus polarization (DZP) is used for all species, in which the equivalent plane wave cutoff energy is chosen as 200 Ry. During the geometry optimization, the Monkhorst−Pack k-sampling 1 × 1 × 10 is adopted. The maximum displacement is 0.01 Å. The convergence threshold for the maximum energy difference, the maximum force, and the maximum stress are 10−5 eV, 0.05 eV/Å, and 0.05 GPa, respectively. A fine k-grid of 1 × 1 × 50 is employed to calculate the electronic structures. In the DMol3 calculations for the spatial charge distributions, the LDA-PWC exchange−correlation functional is chosen, and the double numerical atomic orbital plus polarization (DNP) basis is adopted. In the present calculations, the distance between two adjacent NWs is more than 15 Å. Convergence with respect to the cutoff energy and k-point sampling has been carefully checked.
Figure 1. Band gap of GaN NWs as a function of their diameters with (and without) the hydrogen saturation and compared with other calculations.27,30,35
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RESULTS AND DISCUSSION Our calculation results for the band gap of the GaN NWs with different diameters (9.56−28.62 Å) together with some previous theoretical results are shown in Figure 1. We can see from Figure 1 that the band gap decreases with increasing diameter for the saturated NWs. This is due to the important
Figure 2. Band gap as a linear function of 1/dx for the saturated GaN NWs with (a) LDA and (b) LDA-1/2, where d (in units of Å) is the NW diameter.
Figure 3. Total energy, band structures, and PDOS are derived from the LDA calculations for the unsaturated In6Ga90N96 NWs with the uniform In distribution. Here, (a) is the total energy difference ΔEtot with respect to the six surface In atom case, (b−h) are the band structures with the surface In atom number of 0−6, respectively, and (i) is the PDOS of the surface N, In, and Ga atoms for the six surface In atom case. The inset in (i) shows the PDOS in the vicinity of the LUMO. A comparison with the LDA-1/2 method is summarized in Figure 5. 16232
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Figure 4. Same as in Figure 3 but for the saturated In6Ga90N96 NWs. Here, (i) is the PDOS of the inner N, Ga, and surface In atoms for the six surface In atom case.
quantum confinement effect. Generally, the dependence of the + NW band gap on its diameter can be described as Eg = Ebulk g A/dx, where Ebulk is the band gap of the bulk GaN, d is the g diameter of the NW, and A and x are two fitting parameters. According to Figure 1, we find that x = 1.142 (1.373) for LAD (LDA-1/2) calculations (see Figure 2). As suggested by Nanda,36 if we regard the NW as a simple finite-depth square well, its band gap should depend linearly on 1/d2. The deviation from the 1/d2 is due to the contribution of the NW surface to the electronic properties.27 The results of Figure 2 are close to those of the previous calculations (x = 1.173427 and 1.4137). For the unsaturated NWs, several bands, induced by the surface states, are introduced in the previous band gap of the saturated NWs (see Figure 3). The effective band gap, defined as the energy difference between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), is thus reduced. We can also find from Figure 1 that the effective band gap, the gap between the edge-induced states, is insensitive to the diameter of the unsaturated NWs. This is because the surface states, only determined by the surface Ga and N atoms, are localized and weakly depend on the NW diameter. Our results are in good agreement with the previous calculations.27,28,35 Moreover, considering the underestimation of the band gap in the LDA calculations, we use the LDA-1/2 method38,39 to revise the band gaps. We find that the band gaps derived from the LDA-1/2 have an increment of 1.0−1.6 eV, which is in agreement with that of the popular Heyd−Scuseria−Ernzerhof (HSE) method.30 We can see from Figure 1 that our revised band gap from the LDA-1/2 is 4.8 eV for the saturated GaN NW (d ≈10 Å). The corresponding value from the HSE calculation is 5.1 eV.30 Our revised band gaps are also comparable with experiments.15−17,24 Considering the important surface effects,27 we chose the Garich In6Ga90N96 NWs with the diameter of 22 Å in our following calculations. In order to have a comprehensive understanding of the In distribution and its influence on the band edges, we constructed seven models with different In distributions for the unsaturated and saturated NWs and calculated their electronic structures by using the LDA method
Figure 5. Comparison of the band gap and VBW derived from the LDA with the LDA-1/2 results for the same In6Ga90N96 NWs as those in Figures 3 and 4.
(see Figures 3 and 4). We can see from Figures 3a and 4a that the total energy decreases if the surface In atom number increases for both the unsaturated and saturated NWs. The physical reason is that the strains in the NWs, caused by the large radius of the In atom, can be released by the surface In atom relaxation. We can thus understand that the In atoms are apt to distribute on the surface of the NWs. Compared with Figure 4b−h, we can see from Figure 3b−h that there are several new bands, induced by the surface atoms, in the band structures of the unsaturated NWs. This is also confirmed by the previous calculations.27,28 Furthermore, Figure 3i shows the PDOS of the surface In, Ga, and N atoms, which is related to the band structure of Figure 3h. We can find from Figure 3h and i that the HOMO (LUMO) is dominated by the surface N (In) atoms. The N-induced surface bands are weakly dispersive. This clearly indicates that the 2p orbital of the surface N atoms is highly localized. 16233
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Table 1. Our SIESTA Results for the Unsaturated and Saturated In6Ga90N96 NWs with Different Surface In Microstructuresa unsaturated
modelb
ΔEtot
Eg(LDA)
Eg(LDA-1/2)
VBW(LDA)
VBW(LDA-1/2)
c (Å)c
I II III IV
0.00 0.11 0.09 0.23 0.23 0.03 0.05 0.00 0.13 0.13
1.36 1.34 1.34 1.26 0.10 (7.5%) 2.49 2.50 2.50 2.49 0.01 (0.4%)
2.42 1.96 2.26 2.04 0.46 (21.2%) 3.91 3.90 3.90 3.89 0.02 (0.5%)
7.35 7.38 7.39 7.39 0.04 7.19 7.20 7.20 7.20 0.01
6.57 6.65 6.66 6.66 0.09 6.25 6.27 6.27 6.28 0.03
5.239 5.241 5.240 5.240 0.002 5.227 5.226 5.226 5.226 0.001
max. difference saturated
I II III IV max. difference
Here ΔEtot, Eg, and VBW denote the total energy difference, the band gap, and the VBW in units of eV, respectively. The lattice constant is indexed by c. bThe models I−IV (see Figure 6) have all In atoms distributed on the outer surface of the In6Ga90N96 NWs, and In microstructures are designed as follows: Model I is for the uniform In distribution; model II has one 2-In chain along the c direction; model III has one 2-In chain in the c plane, and model IV has one 3-In chain in the c plane. cOur lattice constant c, obtained from the geometry optimization by LDA and adopted in our present LDA and LDA-1/2 calculations,38,39 is in excellent agreement with that from the experiment (5.22 Å).17 a
Table 2. Atomic Mulliken Charge Transition in In6Ga90N96 NWsa surface atoms unsaturated saturated
inner atoms
Ga
In
N(Ga)
N(In)
Ga
In
N(Ga)
N(In)
0.656 0.437
0.836 0.643
−0.643 −0.513
−0.664 −0.541
0.624 0.626
0.830 0.840
−0.621 −0.628
−0.658 −0.665
a Here the uniform In-distribution with three-surface and three-inner In atoms is considered. The positive (negative) value means losing (acquiring) charge and N(Ga) (N(In)) represents the N atom bonded with Ga (In) atom.
Figure 6. Spatial charge distribution (ρ = 0.03 e/Å3) of the HOMO and LUMO for the unsaturated In6Ga90N96 NWs for models I−IV. Here, the red, gray, and blue balls stand for the In, Ga, and N atoms, respectively.
With the LDA-1/2 method, we recalculated the electronic structures for the saturated and unsaturated In6Ga90N96 NWs. Similar results are obtained except for the quantitative difference (see Figure 5). We find that the band gaps derived from the LDA-1/2 have an increment of 1.0−1.3 eV (see Figure 5a and b). The corresponding valence bandwidths (VBWs) have a reduction of 0.8− 1.0 eV (see Figure 5c and d). Generally, the VBWs obtained from the LDA closely match those from the experiments. For example, the VBW derived from the LDA is 7.343 (5.993) eV for GaN (InN),40 which is in good agreement with the experimental values of 7.041 (6.042) eV. We thus show the LDA results in Figures 3 and 4. As discussed above, we know that the most stable structures have all of the In atoms distributed on the surface of the
Hence, the N-induced surface bands are basically determined by the 2p orbital of the N atom. On the other hand, the Ininduced bands are strongly dispersive when the surface In atom number increases, which is due to the increasing overlap between the surface In atomic orbitals. The effective band gap is thus reduced for the unsaturated NWs. However, the band gap of the saturated NWs, dominated by the inner Ga and N atoms (refer to Figure 4i), increases gradually when more In atoms are moved to the surface (see Figure 4b−h). This is due to the inner region of the NW changes from the ternary InGaN to the binary GaN. Here, the band gap difference between the zero and six surface In atom cases is up to 0.24 eV (9.6%) for the saturated InGaN NWs with In content (6.25%). 16234
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The lattice constant (c) and the VBW have a negligible variation in models I−IV for the saturated and unsaturated NWs. Again, we find that the conclusions derived from the LDA calculations are similar to those obtained from the LDA-1/2 method. Hence, we just present our LDA results in the text below. From the above analysis, we know that the surface In microstructures have a significant influence on the band edges of the unsaturated In6Ga90N96 NWs. To give an intuitive picture of these effects, we further calculated the spatial charge distributions of the HOMO and LUMO for models I−IV using the DMol3 package. For the unsaturated NWs, we can see from Figure 6 that both the HOMO and LUMO are localized around the short surface In−N chains. Figure 7 further shows the band structure and PDOS for model III (as a representative) with a 2-In short chain in the c plane. We can see from Figure 7b that the 2p state of the surface N atoms dominates the HOMO and that the 5s and 5p states of the surface In atoms determine the LUMO. Hence, both the HOMO and LUMO are localized in the vicinity of the short surface In−N chains (see models III and IV of Figure 6). This directly leads to an increase of the optical transition probability between the LUMO and HOMO. Naturally, the short surface In−N chains, which are formed randomly in the growing process, can localize the surface excitons and dominate the light emission in the unsaturated InGaN NWs. For the saturated In6Ga90N96H48 NWs, our calculations show that both the HOMO and LUMO are confined in the inner part of the NW (see Figure 8). The inner Ga and N atoms dominate the band edge states (please refer to Figure 4i), in which the surface In microstructures have little influence. This is because the surface states are removed from the band structures due to the H-saturation, and both the HOMO and LUMO are determined by the inner N and Ga atoms. In order to understand the influence of the surface states on the charge transition, we further calculated the atomic Mulliken population of In, Ga, and N atoms. Our results are summarized in Table 2 for the uniform In6Ga90N96 NW with three surface In atoms and three inner In atoms as a representative. We can see from Table 2 that the charge transitions among the surface Ga, In, and N atoms are larger (smaller) than those for the inner atoms for the unsaturated (saturated) NW. The physical
In6Ga90N96 NWs. Let us now further investigate the influence of the surface In microstructures on electronic structures and optical properties of the NWs. For this purpose, we constructed four typical models (uniform and different short surface In−N chains) in wurtzite In6Ga90N96 NWs. The difference of the total energy (ΔEtot), the band gap (Eg), the VBW, and the lattice constant (c) for the four chosen models are listed in Table 1. We can see from Table 1 that the maximum energy difference for the four models is 0.23 (0.13) eV for the unsaturated (saturated) NWs, which is much smaller than the formation energy of the N vacancy (
