Band Engineering in Strained GaN/ultrathin InN/GaN Quantum Wells Wei Lin,† Dierre Benjamin,‡ Shuping Li,† Takashi Sekiguchi,‡ Shun Ito,§ and Junyong Kang*,†
CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 4 1698–1701
Fujian Key Laboratory of Semiconductor Materials and Applications, Department of Physics, Xiamen UniVersity, Xiamen, 361005, P. R. China, National Institute for Materials Science, Tsukuba 305-0047, Japan, and Institute for Materials Research, Tohoku UniVersity 980-8577, Japan ReceiVed April 14, 2008; ReVised Manuscript ReceiVed October 22, 2008
ABSTRACT: The strains of bond lengths and lattice in GaN/ultrathin InN/GaN quantum wells are modified by varying the well and barrier thickness. Inspection of position-dependent densities of state (DOS) calculated by ab initio simulations shows that this tunable strain significantly affects the electronic structures. The band gap and the band bending of the well decrease as the well width increases, whereas they are enhanced with an increase of the barrier thickness. The coherence and strain variation are realized by metalorganic chemical vapor deposition, according to the results of high resolution transmission electron microscopy and X-ray diffraction. Remarkable emission in the short wavelength region from the quantum wells is observed by cathodoluminescence to shift in the trend of the simulated band gap variation. The results show that the strained quantum wells have advantages for phase separation suppression and band structures engineering in the short wavelength region.
1. Introduction In recent years, InxGa1-xN has received considerable attention because of its wide application in optoelectronic devices1,2 emitting light from infrared (0.7-0.9 eV) to ultraviolet (3.4 eV).3 Unfortunately, due to low miscibility between InN and GaN, InGaN is severely subject to phase separation and large composition fluctuations, which would unduly induce deleterious effects on structural and electronic properties and hence further degrade the performance and reliability of devices. In spite of this disadvantage, the phase separation of InGaN has been known to be effectively suppressed by the biaxial strain of the GaN barrier.4,5 In addition, theoretical work has predicted that InxGa1-xN excluding the In composition between 5 and 80% is metastable against the phase separation.6 These results imply that the ultrathin InN/GaN layers is readily accessible and easy to control due to the advantages in the misfit strain and the composition, similar to ultrathin InAs/GaAs superlattices.7,8 This conjecture is strongly supported by the recent studies of successful growth of GaN/InN/GaN quantum well (QW) operating in the blue and near-ultraviolet spectral regions.9,10 However, fundamental physical properties, involving the strain therein and its effect on electronic structures of the QWs, have not been elucidated yet. Driven by the scientific interests and structural designs, we are one step down in probing the underlying mechanism theoretically and experimentally.
2. Theory 2.1. Simulation Details. To begin with, the theoretical model of the GaN/ultrathin InN/GaN QWs is constructed by assuming the ultrathin InN well layer is coherently strained with the GaN barrier layer and the interface being smooth and abrupt. The numbers of InN and GaN monolayers (ML) are denoted as n and m, respectively, and the QW is labeled below as n/(n+m) for the simplicity. To apply the strain, there are two feasible * Corresponding author. Tel: +86-592-2185962. Fax: +86-592-2187737. E-mail:
[email protected]. † Xiamen University. ‡ National Institute for Materials Science. § Tohoku University.
Figure 1. The simulated bond lengths of In-N and Ga-N as a function of WW for a constant BT of 22 ML (a), and of BT for a fixed WW of 2 ML (b), where the top and bottom dashed line represent the bond length of In-N and Ga-N in bulk, respectively. The calculated average strains versus n/(n+m) ratio (c).
ways: one increases well width (WW) under a fixed barrier thickness (BT), such as 2/24, 4/26, 6/28, 8/30, and so on; the other is to thicken the BT with a constant WW, 2/8, 2/16, 2/24, 2/32. The model is simulated using periodically repeated supercells consisting of 1 × 1 × n+m/2 unit cells within density functional theory similar to our previous works.11-13 The simulations are carried out by means of the Vienna ab initio simulation package.14,15 The pseudopotentials are specified using the projector augmented wave method within the generalizedgradient approximations.16,17 A plane-wave basis set with 500 eV cutoff is used to expand the electronic wave functions at special k points generated by a 8 × 8 × 8 Monkhurst-Pack scheme.18 The geometry optimization is performed by relaxing all degrees of freedom using the conjugate gradient algorithm in which total energy is converged within 1 meV. 2.2. Results and Discussion. To gain insight into a strained microscopic QW, one must be concerned with the changes of average In-N and Ga-N bond lengths. Figure 1a shows the calculated average bond lengths of In-N and Ga-N in the well and the barrier, respectively, as the number of InN well increases
10.1021/cg8003867 CCC: $40.75 2009 American Chemical Society Published on Web 02/05/2009
Band Engineering in InN/GaN Quantum Wells
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from 2 to 8 ML. It can be seen that the In-N bond length has a slight expansion as increasing the WW, albeit it has a mean contraction of about 3% from the bulk state. In the barrier, the Ga-N bond length extends more linearly from 1.97 to 2.00 Å, corresponding to 0.2-1.5% expansion relative to that in bulk. In contrast, the average bond lengths of In-N and Ga-N decrease as the number of GaN barriers increases from 6 to 30 ML, as shown in Figure 1b. The contraction of the In-N bond length varies from 2.7 to 4.0% relative to the bulk, while the expansion of the Ga-N bond length diminishes from 1.3 to 0.3%. The variation of bond length in the thicken layer tends to become gentle in both cases. Overall, there is a stress balance between the InN well layer and the GaN barrier layer. When the WW is increased, the In-N bond length will relax toward that in bulk and force the Ga-N bond length to expand to a new equilibrium tensile stress. Similarly, the contraction of the In-N bond length will be enhanced as the BT increases. On account of the thickness difference between well and barrier, the variation of In-N bond length relative to the bulk state is larger than that in GaN. In other words, the strain in the InN well is larger than that in GaN barrier. In order to evaluate the strain variation, an average strain, reflecting the overall variation of the bond length, is introduced and given by
ε)
cave - c0 c0
Figure 2. Position-dependent DOS of model 2/8 (a), 2/32 (b), 2/24 (c), and 8/30 (d) combined with model structures. The projected DOS for individual atoms are arranged along [0001] and the value of DOS is represented according to the color bar.
(1)
Here, cave is the average lattice constant c of the QW, which can be conveniently obtained from XRD measurements, and c0 is the lattice constant of bulk GaN. According to eq 1, we have calculated the average strain, using cave ) ncInN + mcGaN/n+m where cInN and cGaN are the lattice constants of InN and GaN in the QWs, respectively. It is of interest to note that the average strain ε is proportional to the n/(n+m) ratio, as illustrated in Figure 1c. This behavior is attributable to the barrier being much thicker than the well and c0 being close to cGaN, as shown in Figure 1 that the bond length of Ga-N is closer than that in bulk. Under this approach, the average strain ε is then rewritten as
ε)
n cInN - cGaN n+m c0
(2)
For this reason, it is more convenient to use the n/(n+m) ratio to describe the average strain as well as the thickness of the InN well and GaN barrier. The electronic structures are further investigated on the QWs to understand the influence of the strain. Arranging the partial densities of states (DOS) of each atomic layer along the [0001] direction in sequence, the details of electronic structures on atomic level can be illustrated by position dependences of DOS in Figure 2. As the GaN barrier is increased from 6 to 30 ML, the band gap of the InN well enlarges about 50 meV, as shown in Figure 2a,b. Similarly, for the case of thinning the InN WW from 2 to 8 ML, the band gap increases about 300 meV. By inspecting the average strain variation in Figure 1c, it can be seen that the both cases are nearly the same. Obviously, the band gap of the QW is more sensitive to the variation of the WW. These phenomena can be understood by coherent lattice in the QW. Since the thickness of the GaN barrier is larger than that of InN well, the InN well layer is forced to match the smaller lattice constant of the GaN barrier. Compared to the slight tensile strain beard in GaN barrier layer, the InN well layer is subject to considerable higher compressive strain. As a
Figure 3. (a) Typical HRTEM image of a cross-section structure. (b) The relative average strains in different QWs determined by XRD. The dotted line is a linear fit of the experiment data and the dashed line is theoretical results for comparison.
result of the volume decrease, the electrons repulsion would be enhanced and further induce a considerable increase of the band gap. Moreover, it is interesting to notice that the conduction band minimum (CBM) and the valence band maximum (VBM) are located at opposite sides of the well. The band bending is slightly enhanced as the BT increases, as shown in Figure 2a,b. On the contrary, when the WW is increased, the band bending is markedly reduced and the potential within the well tends to become flat, as illustrated in Figure 2c,d. This indicates that the band bending appears distinct in the region subjected to larger strain. The band bending makes electrons and holes confined at the opposite sides of the well, respectively. Examin-
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Figure 4. (a) Typical CL spectra of 8/31 sample detected in the QWs and GaN areas marked in the cross sectional scanning electron microscopy images shown in the inset. (b) Normalized CL spectra of different QWs. The insets show the corresponding emission intensity as a function of the average strain. (c) The corresponding emission wavelength as a function of the well and barrier thickness, respectively.
ing the squared wave function of the localized state, it is found that the overlap of electron and hole wave functions will keep on in the thin well of 2 ML except for a little deviation of the centers of electron and hole wave functions. By increasing the WW, the overlap will be remarkably decreased because the CBM and VBM are separated by a flatter region in the well while the band bending near the interface remains. The electron transition possibility from CBM to VBM is thus diminished. When the WW exceeds 6 ML, the flat region dominates throughout the well. Meanwhile, the band bending increases in GaN barrier due to its large strain and leads to appearance of other potential extrema of the CB and VB in barrier, as seen in Figure 2d. The electron and hole states at the extrema in barrier region have a great overlap with the states at VBM and CBM in the well, respectively. This would enhance the radiative recombination by the strong coupling between the well and barrier.
3. Experimental Procedures 3.1. Experimental Procedure. To realize band engineering in the QWs, two sets of samples are grown on 3 µm GaN by a metal organic chemical vapor deposition system (MOCVD, Thomas Swan 3 × 2” CCS). One keeps the InN WW at 4 ML and changes the GaN BT from 11 to 45 ML. The other varies the WW from 2 to 8 ML at a fixed BT of 23 ML. The well and barrier thickness are accomplished by controlling the flux and time of trimethylgallium, trimethylindium, and ammonia precursors. Eleven periods of InN/GaN QWs are grown at 730 °C under the pressure of 300 Torr, using a growth interruption to smooth the interface.10 3.2. Results and Discussion. The interface microstructure between well and barrier is inspected on cross section by a high resolution transmission electron microscope (HRTEM, JEOL JEM-3010), as a typical image shown in Figure 3a. The InN wells appear as dark contrast layers with distinct interfaces. Detailed examinations reveal that the interface is atomically sharp and its lattice is apparently coherent, which shows realization of the coherent growth of the QWs. The presence of smooth interface further indicates that the intermixing can be rarely met in this case. Furthermore, there is an overall consensus of opinion that the segregation effects in InGaN would give rise to the formation of self-organized In-rich regions with indium concentrations higher than
in the alloy and smooth the surface abruptness.19 This helps to concentrate In composition and keep the InN well layer from diffusion in our case. For these reasons, it is believed that the coherent InN well has been realized as expected. The ε is further evaluated by measuring the cave of the different QWs using an X-ray diffractometer (XRD, Bede QC200). From the angular separation in the ω -2θ scan pattern between the GaN diffraction peaks and satellite peaks, the cave is reliably determined and then the average strain is directly obtained by eq 1. In order to minimize the influence of the prestrain stemmed from the GaN, the change of the strain ∆ε/ εmean relative to the mean ε is estimated. Similar to the theoretical results, the relative strain change is nearly proportional to the n/(n+m) ratio, although subtle discrepancy likely arises from the influence of the prestrain of GaN and the defects in the QWs, as shown in Figure 3b. Obviously, this trend further supports that most of the QWs are grown coherently and the strain has been tuned by varying the well and barrier thickness. Spatially resolved cathodoluminescence (CL) spectra are acquired from the QWs to GaN at room temperature. The luminescence peaks centered at 420 and 362 nm occur in the QWs and GaN, respectively, as the typical results shown in Figure 4a. Interestingly, the luminescence peak of the QWs with a narrow fwhm of about 0.11 eV is stronger than that of GaN band edge emission. This behavior indicates that the QWs are substantially uniform in composition and geometry so that is favorable for the radiative recombination. The electronic structures are further investigated by a close inspection of the spectra of the grown QWs, as displayed in Figure 4b. The intensity is depicted as a function of the thickness of the well and barrier in the insets of Figure 4b. As the BT increases, the intensity exhibits a monotonic increase. This is attributable to the reduction of interwell coupling in the relative thick barrier. The intensities appear stronger in the WWs of 2 and 8 ML. The former results from the minimization of the spatial separation of the electrons and holes and the latter is caused by the strong coupling between the well and the barrier potential extrema. Accordingly, it is suggested that the thinner well has advantages of the precise control of emission intensity to free from the strong coupling caused by the larger strain in barrier. Furthermore, the wavelength shifts apparently from 386 to 420 nm as the WW increases, while blueshifts slightly from 402 to 399 nm with an increase of the BT, as shown in Figure 4c. These shifts quantitatively have the same orders of magnitude as the calculated results mentioned above. The red shift in the InxGa1-xN/GaN QWs can be simply explained by a reduction in the transition energy due to the variation of the piezoelectric field as the well width increases.20
Band Engineering in InN/GaN Quantum Wells However, it should be pointed out that the deep-seated reason for the piezoelectric field variation resides in the strain. Anyway, the band gap of the QWs has been tuned by modifying the strain.
4. Summary In summary, the ab initio simulations show that the strains of bond lengths and lattice are modified by varying the well and barrier thickness. The band gap decreases as either the WW increases or the BT decreases. Furthermore, the band bending is more distinct in the region with a larger strain. The coherence and strain variation are realized by MOCVD, according to the results of HRTEM and XRD. By the characterization of CL, the remarkable sharp emission peak from the QWs appears in the short wavelength region. The shifts of emission peaks exhibit a similar trend as the simulated band gap variation. Hence, the thin well is used to suppress phase separation and engineer band structures with tunable emission in the short wavelength region by introducing an appropriate strain. Acknowledgment. This work was supported by the “863” program, National Natural Science Foundation (60827004 and 60776066), Fujian and Xiamen projects of China.
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