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In this paper, c-plane stepped- and graded- InGaN/GaN multiple quantum wells (MQWs) are grown using plasma assisted molecular beam epitaxy (PAMBE) by in situ surface stoichiometry monitoring (i-SSM). Such a technique considerably reduces the strain build-up due to indium clustering within and across graded-MQWs; especially for QW closer to the top which results in mitigation of the quantum-confined Stark effect (QCSE). This is validated by a reduced power dependent photoluminescence blueshift of 10 meV in graded-MQWs as compared to a blueshift of 17 meV for stepped-MQWs. We further analyze microstrain within the MQWs, using Raman spectroscopy and geometrical phase analysis (GPA) on high-angle annular dark-field (HAADF)-scanning transmission electron microscope (STEM) images of stepped- and graded-MQWs, highlighting the reduction of ~1% strain in graded-MQWs over stepped-MQWs. Our analysis provides direct evidence of the advantage of graded-MQWs for the commercially viable c-plane light-emitting and laser diodes.
© 2016 Optical Society of America
1. Introduction
Due to their vital importance in electronics and optoelectronics, the field of group-III nitrides, has gone through spectacular developments ranging from material development, all the way to device fabrication. Specifically, the development of InGaN quantum well (QW) active regions for blue, green and white light-emitting-diodes (LEDs) makes III-nitrides the key driver for solid state lighting (SSL) technology [1–3]. However, the performance of InGaN based LEDs at high injection current density is limited by efficiency droop. To address this issue, it is important to understand the fundamental properties associated with the group-III nitride material system and InGaN/GaN multiple quantum wells (MQWs). Due to their wurtzite crystal structure, which lacks centrosymmetry, group-III nitrides have built-in spontaneous polarization fields. Moreover, these LEDs also suffer from piezoelectric fields induced by the heteroepitaxial growth on conventional lattice-mismatched substrates such as c-plane sapphire and silicon carbide (SiC) and the large strain gradients caused by the lattice mismatched InGaN/GaN layers within the active region [4]. These two types of built-in polarization fields cause band bending in c-plane InGaN/GaN MQWs, which is considered to have a major effect on efficiency droop [4, 5].
While growing InGaN based LEDs on c-plane [6], semipolar [7–9] or non-polar [9] bulk GaN substrates leads to improved performance, as compared to LED on sapphire, higher cost, small size (~1 x 3 cm2) and relatively poor crystal quality still warrants further investigations of InGaN based MQWs on conventional c-plane sapphire substrates [10]. For c-plane InGaN LEDs on sapphire, non-conventional shapes using InN/GaN alternate structures [11], staggered [12, 13], and compositionally graded [14, 15] active region designs in InGaN MQWs grown by metalorganic chemical vapor deposition (MOCVD) have been shown to reduce carrier separation which improves device performance.
In previous reports simulation and/or device characterization were performed to shed evidence on strain reduction within the MQWs [14–19]. In some reports, x-ray diffraction and Rutherford backscattering spectroscopy were employed to estimate the changes in indium composition within MQWs and deduce the resulting strain reduction [20]. However, direct observation of strain and compositions are largely lacking in compositionally graded structures. Geometrical phase analysis (GPA) on the other hand, is a robust and straightforward technique which can be used to measure lattice strains in high resolution transmission electron microscope (HRTEM) images [21–24]. In this report we performed geometrical phase analysis (GPA) on high-angle annular dark-field (HAADF)-scanning TEM (STEM) images of the active region to observe directly the distribution of strain and composition within the MQWs/barriers. We further demonstrated that GPA based microstrain analysis correlates well with macroscopic characterization techniques, such as Raman spectroscopy, temperature and power dependent photoluminescence (PL). In doing so, we demonstrated the mitigation of In clustering effects and therefore reduction in strain within the corresponding MQWs. Also, we showed the reduction of strain build up from bottom to top graded-MQWs as compared to stepped MQWs. Detailed microstructural, optical characteristics and strain maps of the grown samples were further examined using power and temperature dependent photoluminescence, Raman spectroscopy, HR-STEM techniques, HAADF-STEM intensity profile, and GPA.
2. Experimental
The structures with InGaN/GaN stepped- and graded-MQWs were grown using a VEECO GEN930 PAMBE. Template substrates with hydride vapor phase epitaxy (HVPE) grown GaN (~500nm) and physical vapor deposited (PVD) AlN nanocolumns on c-plane sapphire having 1°-offcut towards a-plane supplied by Kymatech. During the PAMBE growth, two different Knudsen cells for Ga (Ga1 and Ga2) and one cell for Indium (In) were utilized. Active nitrogen species were obtained using a Veeco Uni-Bub radio frequency plasma nitrogen source supplied with high purity nitrogen gas (99.9999%) after further purification using inert gas purifier. Adopted growth conditions were optimized for the active region by using in situ RHEED, atomic force microscopy and optical microscopic observations in separate experiments.
Nitrogen flow rate and RF power i.e. 0.4 sccm and 200 W respectively, were kept constant during MQW growth with expected growth rate of ~1.5 nm/min. In the subsequent description, φGa, φIn and, φN indicate incident flux for gallium, indium and active nitrogen, respectively. The growth schematic for stepped- and graded-MQWs is shown in Fig. 1(a). The Quantum barriers (QB) were grown using slightly metal-rich conditions followed by plasma exposure of the epi-surface for consumption of excess Ga. This is followed by well layer growth utilizing (φGa + φIn) > φN, φGa < φN [25].
Fig. 1 (a) Growth schematic of stepped and graded-QW. (b) Specular spot RHEED intensity variation during controllable MQWs growth by using plasma exposure technique. (c) Specular spot RHEED intensity variation during one cycle of QW growth with in situ images of RHEED diffraction patterns obtained at different stages.
Before growth of QB at a higher temperature, the wells were capped with ~3nm GaN. In between capping layer and barrier layer, the interruption was provided for ramping up the temperature for executing the low\high temperature scheme for corresponding well\barrier layers. Specifically, for stepped InGaN well layer constant φGa was used, whereas during growth of compositionally graded InGaN well layers, Ga effusion cell temperature was varied linearly. Under such linear change of Ga cell temperature, parabolic compositional grading profile is expected and verified in this work. MQWs were grown on 650 nm undoped GaN on the template substrate.
Figure 1(b) shows in situ RHEED variation during the InGaN/GaN QW growth. The well and barrier (including GaN capping) layers along with plasma exposure step are highlighted with different colors. During well layer, shutters Ga1, In, and N were open, whereas during GaN barrier, shutters Ga2, and N were open. However during plasma exposure step only the shutter of N was open. The adopted shuttering sequence is also indicated in Fig. 1(b) using arrows. The adopted i-SSM based growth scheme ensures controllability and repeatability of the growth process for MQWs, which has been demonstrated by the specular spot RHEED intensity variation during MQWs growth as shown in Fig. 1(c). In addition RHEED diffraction patterns acquired at different instances, i.e., A (before well growth), B (after well growth), C (after barrier growth) and D (after plasma exposure) are also shown in B and positions of A-D using arrows are shown in the RHEED intensity plot illustrated in Fig. 1(c). It can be observed that after each cycle of plasma exposure the behavior of RHEED intensity variation remains consistent and controllable. Brown et al. adopted in situ quadrupole mass spectroscopy and RHEED for optimization of metal free GaN epi layers [26]. In our work, we have used in situ RHEED intensity via active shuttering in modifying the growth condition to overcome excess Ga issue.
For optical characterization, grown samples were characterized using micro-PL and micro-Raman spectroscopy. Linearly polarized laser sources, emitting at 325 nm, 405 nm, and 473 nm, were utilized for executing micro-PL and micro-Raman spectroscopy experiments.
Different objective lenses such as, Thorlab LMU-40X-NUV/Numerical aperture (NA) 0.5, Olympus 100x/NA 0.9 and Leitz Wetzlar 20x/NA 0.4 were used for focusing the 325 nm, 405 nm, and 473 nm excitation lasers, respectively on the samples. The minimum achievable laser spot diameter on the samples can be evaluated by substituting wavelength λ of excitation laser source and NA of the objective lens in 1.22λ/NA. The power dependent micro-PL was done using 325 nm He-Cd laser as excitation source by varying excitation power from 8 mW to 0.008 mW with laser spot diameter of approx. ~0.8 µm. For temperature dependent PL (10 K to 300K), 0.5 mW of 405 nm excitation laser was used with laser spot diameter of about ~1.2 µm. For Raman spectroscopy, 325 nm and 473 nm excitation lasers with incident powers of 8 mW, and 6 mW respectively were used with the laser spot diameter ~0.8 µm and ~0.64 µm, respectively.
Focused ion beam (FIB) milling by using a Helios-400S was utilized for preparing cross-section specimens of MQWs samples. Then TEM of model Titan 80-300 ST was employed to complete HAADF-STEM analysis of prepared specimens. The microscope was equipped with an aberration corrector from CEOS company to decrease the spherical aberration coefficient (Cs) of the electron beam. In this way, high-resolution STEM (HRSTEM) analysis of the sample was realized. During the analysis, electron beam energy was set to 300 KV and Cs coefficient was decreased to about a 1 µm value. The camera length (CL) was configured to 115 mm to make the composition contrast dominant in the HAADF-STEM image. Further the GPA software package from HREM Research installed as a plugin in Gatan Microscope Suit (GMS) was utilized for the study of strain in the stepped- and graded-MQWs.
3. Results and discussion
3.1 Optical characterizations
Figure 2(a)-2(b) contains power dependent PL emission from stepped- and graded-MQWs, respectively. PL blueshift was reduced from 17 meV (for stepped-MQWs) to 10 meV (for graded MQWs) indicating the mitigation of QCSE in the presence of reduced strain in graded-MQWs [27, 28].
Figure 3(a)-3(b) contains PL spectra collected at increasing temperatures (from 10 K to 300 K) from stepped- and graded-MQWs. Gaussian peak fitting curves for stepped- (P1, P2, and P3) and graded-MQWs (P1 and P2) along with a cumulative peak fit for measured PL spectra at 10 K are also presented in the inset of Figs. 3(a) and 3(b). As shown in the inset of Fig. 3(a), in the case of stepped-MQWs, contributions to the cumulative peak fit (pink curve) from P1 (red curve) and P2 (blue curve) are competing with each other, whereas the P3 (green curve) contribution is relatively small and thus insignificant. However in the case of graded-MQWs, the major contribution to a cumulative peak fit is only from P2 (blue curve), whereas P1 (red curve) has an insignificant contribution towards the cumulative peak fit. Thus, the single dominant PL peak obtained at 10 K demonstrates reduced indium clustering and, therefore, less localization centers, i.e. the localized excitons, in graded-MQWs as compared to the stepped-MQWs. In the stepped-MQWs, spacing between P1 and P2 is less than the optical phonon energy (~92 meV) in the InGaN alloy. Thus, P1 is expected to originate from the radiative recombination of localized excitons in MQWs and P2 originated from radiative recombination of excitons confined in the regular MQWs [29, 30]. The comparison highlights the strength of having graded MQWs.
Fig. 3 Temperature dependent PL results of (a) stepped-MQWs (fitted curves as inset) and (b) graded-MQWs (fitted curves as inset), (c) PL spectrum peak position with respect to temperature for stepped- and graded-MQWs, (d) Temperature dependence of the integrated PL intensity for stepped- and graded-MQWs.
Peak energy obtained at different temperatures for stepped and graded-MQWs are shown in Fig. 3(c).The competition between In cluster sites is pronounced in the stepped-MQWs leading to the U-shaped trend (for temperature range from 10 K to 250 K); whereas the graded-MQWs demonstrated a sigmoid-shaped spectrum as shown in Fig. 3(c). Such behavior has been reported for InGaN alloys due to localized exciton effects [31]. For the lower range of temperature from 10 K to 140 K the samples demonstrate redshifts of 18 meV and 20 meV, for stepped- and graded-MQWs respectively. Such a redshift with increasing temperature under lower temperature ranges 10 K to 140 K is mainly attributed to the hopping of weakly localized carriers towards relatively stronger localized states and thermalization effects [32–34]. Above 140 K, for the stepped-MQWs a large blueshift of 21 meV is obtained. Such a blueshift is mainly due to the full-delocalization of carriers from the localized states [34]. However, a small peak shift is observed as Varshni’s effect in this temperature range overcomes the thermal delocalization effect for the graded-MQWs. These observations support the existence of higher strain in stepped-MQWs which causes compounding of the localization and InN-rich region clustering during growth, whereas reduced strain is expected in the case of graded-MQWs [35]. Figure 3(d) shows normalized integrated PL intensity versus temperature range of 10– 300 K. To further analyze this; the temperature-dependent PL integrated intensity was fitted using the following Arrhenius equation [36, 37]:
where, I0, and kB are integrated PL intensity at 0 K and Boltzmann’s constant respectively. The parameters C1 and C2 are two constants related to the density of non-radiative recombination centers in the samples. EA1 and EA2 are the activation energies corresponding to luminescence from thermal activation of defects (larger value) and delocalization of carriers (smaller value) respectively.
The obtained value of EA1 for stepped-MQWs (92 meV) is relatively higher than that of graded-MQWs (74 meV). This further confirms that the localization potential formed from indium clusters is deeper for the stepped-MQWs. The value of EA2 for stepped-MQWs (21 meV) is also relatively higher than that of graded-MQWs (9 meV). This indicates relatively deeper localization minima in stepped-MQWs as compared graded-MQWs, which mainly dominates in the low temperature range (up to 50 K). However, for higher temperature ranges (above 50 K) the process related to EA1 becomes dominant. Reduced thermal quenching is obtained for graded-MQWs as shown in the inset of Fig. 3(d) because its EA1 and EA2 both have relatively smaller values as compared to that of stepped-MQWs. Thus implemented graded-MQWs points toward reduced strain and thus mitigation of QCSE effect in graded-MQWs as compared to the stepped-MQWs. During the growth of ternary InGaN under the unstrained/reduced-strain conditions, indium inhomogeneity is likely to get suppressed and thus resulting in the lower degree of localization with lower activation energies. However, under strained conditions, severe inhomogeneity of indium is expected during the growth and thus higher degree of localization with high activation energies is expected [38].
To confirm the strain reduction and indium compositional distribution in graded-MQWs, we performed Raman spectroscopy. Figure 4(a) shows room temperature Raman spectra of stepped- and graded-MQWs obtained using two different excitation sources; 325 nm He-Cd (solid curves) and 473 nm (dashed curves) lasers. Both excitation sources resulted in the same value for E2 (GaN) phonon mode (570 ± 0.5 cm−1), which is similar to the previously reported value [39]. However, the obtained values for A1 (LO) phonon mode is excitation source dependent. With 473 nm excitation source A1 (LO) phonon mode is obtained at 437.4 ± 0.5 cm−1 for both stepped and graded MQWs samples. However, with 325nm excitation source A1 (LO) phonon mode positions are 730.5 ± 0.5 cm−1 and 732.8 ± 0.5 cm−1 for stepped- and graded-MQWs respectively.
Fig. 4 (a) Raman spectroscopy results of stepped-MQWs (black color curves) and graded-MQWs (red color curves) using different excitation laser sources. Raman spectra obtained using 325nm and 473nm lasers shown using solid and dashed curves respectively. (b) Raman spectra of stepped- and graded-MQWs focusing on A1 (LO) phonon mode.
The different results obtained with different excitation sources are mainly dependent on the corresponding penetration depth. For 473 nm excitation source, higher penetration depth reveals phonon modes mainly from bulk GaN, whereas the lower penetration depth (~100 nm) of 325 nm laser enables signal acquisition from the active region. Thus, the obtained A1 (LO) phonon mode positions of 730.5 ± 0.5 cm−1 and 732.8 ± 0.5 cm−1 for the stepped- and graded-MQWs, respectively, are the signatures of strain and composition in the MQWs. The FWHM of A1 (LO) peaks are 16.64 and 19.65 for stepped and graded-MQWs, respectively. The broader FWHM of A1 (LO) for graded-MQWs samples points towards the larger distribution of strain and composition at the interface of the well and barrier, i.e. reduced abruptness at the interface. Also, the A1 (LO) peak shifts toward a higher wave number in the case of graded-MQWs, indicating the presence of lower indium compositions in the graded-MQWs [40].
3.2 Geometrical phase analysis
To verify the obtained extended distribution of strain for graded-MQWs using Raman spectroscopy, GPA was applied to HR-STEM images. The images were recorded onto a HAADF attached above the projection chamber of the microscope. It should be noted that the strain fields are the derivatives of the displacement fields along the x- and y-axes and can be defined as follows;
where, exx, eyy, ux(r), uy(r), g1, g2, Pg1(r), and Pg1(r) are the in-plane biaxial strains, out-of-plane strain (along growth direction), displacement field along x, displacement field along y, reciprocal vector along x, reciprocal vector along y, and corresponding phase images respectively [24].The GPA analysis based on the above formulation was applied to several HAADF-HRSTEM images for the determination of strain fields in samples. HAADF-HRSTEM images for stepped- and graded-MQWs (Figs. 5(a) and 5(b), respectively) and their corresponding GPA results are shown in Figs. 5(c) and 5(d), respectively. It can be noticed from the results in Fig. 5(c) that significant strain build-up is observed for the top QW in stepped-MQWs. In contrast, the well layers of graded-MQWs are uniformly strained in the growth direction as in Fig. 5(d). Also, the strain in the growth direction was also quantified by generating a line profiles across the dotted areas shown in the strain maps. Figures 5(e) and (f) show strain profiles across three QWs, and it was found to match with the prediction of reduced strain in the graded-MQWs via other indirect probes such as Raman spectroscopy, power dependent PL and temperature dependent PL. In addition to this, HAADF intensity profiles were also acquired from HAADF-HRTEM images. HAADF intensity profiles for stepped- and graded-QW are shown in Fig. 5(g) and 5(h) respectively. In the intensity profile of graded-QW relatively gradual change of intensity is observed as compared to that of stepped-QW. Overall, about ~1% of strain reduction is directly measured for each of graded-QW as compared to the stepped-QW owing to the soft profiling of the graded-QW at the interface of the GaN barrier and InGaN well.
Fig. 5 (a) HAADF-HRSTEM images of: (a) stepped-MQWs, (b) graded-MQWs. Strain maps obtained using geometrical phase analysis for: (c) stepped-MQWs, (d) graded-MQWs. Strain profile of: (e) stepped-MQWs, and (f) graded-MQWs. The HAADF intensity line profiles for: (g) stepped-QW, and (h) graded-QW.
In addition, it also confirms the parabolic compositional grading profile in implemented graded-QW with the linear temperature variation of the Ga cell as described in the growth schematic of graded-QW. The reduction of strain in graded-MQWs is expected to lead to a reduction in the quantum-confined stark effect (QCSE) / polarization field. Obtained strain reduction in implemented graded-MQWs also supports efficient implementation of compositionally graded InGaN layers in graded QW design using our PAMBE technique.
4. Conclusion
In conclusion, by using in situ surface stoichiometry monitoring (i-SSM), we demonstrated PAMBE based growth of stepped- and graded-MQWs. This technique ensures no accumulation of Ga metal before the InGaN or graded-InGaN well layers for their kinetically controlled growth. The effectiveness of our growth technique has been demonstrated by the optical and microstrain analysis of stepped and graded-MQWs. The reduced blueshift in graded MQWs of 10 meV as compared to 17 meV for stepped-MQWs highlights the mitigation of QCSE in the presence of reduced polarization fields in graded MQWs. The mitigation of the polarization field effect in graded-MQWs was evident in the direct measurement of strain reduction (~1%) in graded-MQWs as compared to the stepped-MQWs, using GPA on the acquired images of HAADF-STEM. In stepped-MQWs, large strain gradients caused by the GaN/InGaN lattice mismatched due to compositional abruptness in InGaN/GaN layers. However in the graded-MQWs design, the obtained strain reduction is achieved by reducing the compositional abruptness and thus reducing lattice mismatch abruptness between the GaN and InGaN layers.
Acknowledgment
The authors acknowledge funding support from King Abdulaziz City for Science and Technology (KACST) Technology Innovation Center (TIC) for Solid State Lighting, grant no. KACST TIC R2-FP-008, and King Abdullah University of Science and Technology (KAUST) baseline funding, grant no. BAS/1/1614-01-01.
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