1 INTRODUCTION

Gallium nitride (GaN) is extensively studied for optoelectronic applications such as light emitters, high electron mobility transistors, and photodetectors [13" target="_self" style="display: inline;">–3]. The broadband light emitters can be constructed based on ternary compounds such as indium gallium nitride (InGaN) formed from III-V bulk semiconductors, which offer tunable band gaps from 3.4 eV (GaN) to 0.64 eV (InN) [4,5]. However, the high In content required to generate red or near-infrared light decreases the efficiency of light generation due to In segregation and a higher defect density resulting from the lattice mismatch with the substrate [6]. These problems can be overcome by developing novel 2D-3D heterostructures based on GaN interfaced with transition metal dichalcogenides (TMDs), which have a lattice constant similar to GaN [7]. The TMDs monolayers have high quantum efficiency of light emission in the red wavelength regime because their direct band gaps are significantly narrower than in GaN. The heterostructure of monolayer molybdenum disulphide (MoS2) interfaced with GaN constitutes an ideal material system for efficient light emitters over a broad wavelength range covering the lower ultraviolet to the near-infrared range. The interface in such a hybrid-layered material critically influences the electronic transport and carrier transfer. The band offset, interface phonons, the proximity of defect states of the two material system, and the interaction of excitons in the 2D semiconductor with that in the bulk III-V semiconductor are expected to modify the carrier mobility and absorption characteristics in addition to the emission properties of the materials.

MoS2 has a high exciton binding energy in the red region and has multiple excitonic states across the visible to the ultraviolet (UV) wavelength range [8,9]. GaN absorbs in the UV region, and a simultaneous interband transition of carriers can be generated with UV excitation. The extent of UV absorption in MoS2 is much higher than that in GaN and the absorption from the MoS2–GaN heterostructure in the UV-visible region is higher than that in GaN and MoS2 [10]. Furthermore, the GaN emission band lies near the Γ point of MoS2 that has a high density of states [8]. The overlap of these electronic transitions can facilitate energy transfer at the interface between the two semiconductors. The optical properties of monolayer MoS2 are significantly affected by the semiconductor substrate, and the relaxation of the excited carriers depends on the excitation energy [11,12]. The heterostructure of a 2D semiconductor with a bulk semiconductor or its hybrid structure with plasmons is extensively studied because of the potential applications due to the tunable electrical and optical properties of these materials [13–16" target="_self" style="display: inline;">–16]. The relative position of the energy levels determines the transport or the relaxation of the optically generated carriers across the interface in the MoS2–GaN heterostructure [15,17]. The excitation at the C exciton state, which is close to the Γ point, results in a charge transfer without any momentum change [11,18]. Optically dressed phonons significantly influence the dynamics of the excitonic states in MoS2- [19] or graphene- [20] based semiconductor nanostructures. In these recent works, the plasmonically induced dressed phonon states were utilized for coherent coupling of excitons and photons. Metal nanoparticles were used to drive the phonons for the enhanced light–matter interaction that resulted in coherent exciton–plasmon coupling. However, these phonon related effects can be induced by a polar dielectric surface to influence the excitonic properties of 2D materials.

GaN is a polar semiconductor widely used in optoelectronics. Its surface properties strongly depend on the termination (gallium or nitrogen) during the growth. The surface and interface phonon related processes are dominant mechanisms for the relaxation of optically generated carriers in nitrides. The drift of optically generated hot electrons in GaN produces a non-equilibrium phonon population in momentum space, so-called “hot phonons.” These phonons slow down the relaxation of optically excited carriers in GaN [21]. The interaction of phonons with electrons in a MoS2–GaN heterostructure can modulate the dynamics of the excitonic states in MoS2 [22]. The coupling of phonons with the carriers or excitons affects the charge carrier mobility and causes the broadening of the emission bands that is crucial for the development of the broadband lasers and LEDs [23].

In this study, we report the modification of the non-equilibrium absorption characteristics of MoS2 and the photoluminescence (PL) emission properties in 2D MoS2–GaN (0001) vertical heterostructure induced by the different couplings at the interface. The most stable interface of the MoS2–GaN (0001) heterostructure is calculated using density functional theory (DFT), which revealed a type I band alignment consistent with our experiments and previously reported results [15,22]. The valence band maxima and the conduction band minima are almost entirely contributed by MoS2 states. We observed the coupling of optically generated carriers with the phonon modes and transfer of energy and charge across the interface between the semiconductors. As a result, a significant change in the position, amplitude, and linewidth of the excitonic absorption state of MoS2 at the Γ point as well as significantly changed dephasing of carriers at all excitonic bands occurs. The PL emission from MoS2 is enhanced in intensity and blue-shifted, but the PL emission from GaN is reduced in intensity due to coupling of electrons with longitudinal optical (LO) phonons and reabsorption of the emitted light by MoS2.

2 THEORETICAL CALCULATIONS

We performed DFT calculations for van der Waals (vdW) heterostructures based on a MoS2 monolayer and GaN (0001) surface employing the Quantum ESPRESSO package [24,25]. We used generalized gradient approximation (GGA-PBEsol) for the exchange-correlation function along with ACBN0 [26], a novel pseudo-hybrid Hubbard density functional approach that ensured the accurate value of the GaN band gap. The ion–electron interaction was treated with the projector augmented-wave pseudopotentials [27] from the PSlibrary database [28] while the wave functions were expanded in a plane-wave basis of 80 Ry. The heterostructure was constructed by stacking the MoS2 on the Ga-terminated GaN slab containing 12 Ga-N bilayers and fixing the in-plane lattice constant to the calculated bulk value of the substrate (3.18 Å, 1 Å = 0.1 nm). The dangling bonds of nitrogen at the bottom side of the slab were passivated by pseudohydrogens. We have considered several stacking configurations and found the most stable one shown in Figs. 1(a) and 1(b) with the MoS2–GaN distance of approximately 2.32 Å in line with the previous results [10]. A semi-empirical vdW correction (DFT-D2) [29] was added in order to determine a correct interlayer distance between MoS2 and GaN in each structure. The Brillouin zone sampling at the DFT level was performed following the Monkhorst–Pack scheme using a 10×10×1k-points grid further increased to 16×16×1 in the projected density of states calculations. The electronic band-structure plots in the form of MoS2 and GaN projected density of states (k, E) maps were obtained using the GREEN package [3032" target="_self" style="display: inline;">–32] as a post-processing tool; for these reasons the structure was recalculated self-consistently with the SIESTA code [33] using similar values of all the parameters (e.g., exchange-correlation functional, k-points meshes). The optical properties were calculated employing the PAOFLOW code [34].

Fig. 1. Geometry and electronic structure of the MoS2–GaN heterostructure calculated from the first principles. (a) Top view and (b) side view of the most stable interface structure (II). The unit cell is marked as a blue dashed parallelogram in panel (a). The dashed bonds in (b) denote their mostly van der Waals character. (c) Relative band edge positions of bulk GaN and four interface structures. The bands of the isolated MoS2 monolayer are not aligned, and the panel indicates only the value of the band gap. More details are provided in Fig. 7 in Appendix A. (d) Electronic structure of the interface calculated within the semi-infinite surface model and projected on MoS2 (red) and GaN states (blue).

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3 EXPERIMENT

A bulk GaN-monolayer MoS2 vertical heterostructure is synthesized by fabricating monolayer MoS2 over the commercially available 4.5 μm thick silicon-doped GaN film on a double side polished sapphire substrate (MSE supplies) by the chemical vapor deposition (CVD) method [35]. The equilibrium absorption spectra of the individual semiconductors are measured using a spectrophotometer with a white-light source and a photomultiplier detector. Raman characteristics of the heterostructure are studied with a high-performance micro-Raman spectrometer equipped with an Olympus BX51 microscope using an optical excitation of 2.33 eV.

The non-equilibrium absorption spectrum of MoS2 and the decay kinetics were studied with optical pump-probe spectroscopy. A 100 fs Ti:sapphire oscillator seeded optical parametric amplifier laser was used as source for pump and probe pulses. Excitations at 2.33 eV and 3.54 eV are used as pump energies. The sample is first excited with the pump pulses, and the behavior of the excited sample is studied with white-light probe pulses. The difference in absorption of the probe pulses (ΔA) in the presence and absence of pump pulses is measured at different delay times by varying the distance traveled by the pump and probe pulses.

The PL emission properties of the III–V semiconductor are studied using a home-built PL setup. An ultraviolet (UV) excitation line at 3.82 eV from a He-Cd laser source is used to excite the sample. The emitted signal from the sample is collected using a pair of UV collimating lenses in a reflecting geometry. The emitted signal is filtered using a 3.76 eV edge long-pass filter and then detected using a CCD spectrometer. The emission characteristics of MoS2 are studied with a home-built micro-PL system. The setup consists of a home-built upright epifluorescent microscope fitted with 2.25 eV edge dichroic beam splitter. A laser line with an energy of 2.33 eV is focused onto the sample through a 100× microscope objective. The emitted signal from the sample is collected by the same objective lens, and separated from the reflected and the scattered excitation signal passing through a dichroic mirror. The emitted signal from the monolayer MoS2 is further filtered with a 2.10 eV edge long-pass filter and detected with an AD111 photomultiplier tube (PMT)-based spectrometer.

4 RESULTS AND DISCUSSION

The structural and electronic details of the interface determine the optical properties of the heterostructure. The theoretical model based on first principles calculations will be discussed before presenting the experimental observations. The MoS2–GaN (0001) interface is modeled assuming the lattice matching between the monolayer MoS2 and the GaN crystals. Several stacking configurations were considered as shown in Fig. 6 in Appendix A, but our calculations clearly favored the structure shown in Figs. 1(a) and 1(b) with S and Mo atoms aligned with the topmost Ga and N, respectively. The analysis of relative band-edge positions in Fig. 1(c) indicated that in all the configurations the band gap is significantly reduced with respect to GaN, in agreement with the previous studies [10,15]. The most stable structure reveals a band gap of predominantly of MoS2 origin, which is further confirmed by the electronic band structure in Fig. 1(d). Importantly, the type I band alignment is robust against the structural details; in particular, the band offsets hardly change between four different interface configurations.

The atomic force microscopy (AFM) characteristics show the MoS2 layers with lateral dimensions extending over 5 μm grown on GaN as shown in Figs. 8(a) and 8(b) in Appendix A. The Raman and the absorption spectra provide the static optical characteristics of the heterostructure formed. The Raman modes of MoS2, GaN, and the MoS2–GaN interface are shown in Figs. 2(a), 2(b), and 2(c), respectively. The active Raman modes E2g1 and A1g are observed at 384cm−1 and 404cm−1, respectively, for MoS2 on a quartz substrate. However, these modes are slightly blue-shifted, and the energy difference between these Raman modes reduced to 19cm−1 in the heterostructure. The Raman characteristics combined with the AFM characteristics demonstrate that MoS2 consists of a single atomic layer. The reduced spacing between the MoS2 Raman modes on GaN substrate illustrates that the MoS2 layer is less strained in GaN compared to the quartz substrate. The Raman modes are centered at 575cm−1 and 738cm−1 and represent, respectively, the E2 and A1 longitudinal optical (LO) phonon modes of GaN. An additional Raman mode is observed in the monolayer at 419cm−1, which has been previously reported as high-order harmonic frequency of an acoustic phonon of GaN and is not an active Raman mode [22,36,37]. This Raman mode is coupled with the transverse acoustic phonon mode (XA) of MoS2 and generates a new mode at 598cm−1 [38]. The broad Raman mode centered at 454cm−1 is the combination of the second-order longitudinal acoustic (2LA) mode and optical mode A2u [39]. Moreover, the new Raman mode at 636cm−1 is the surface optical (SO) phonon of GaN [38]. The substantially modified Raman characteristics demonstrate interlayer electron-phonon coupling. The large blue-shift of the A1 Raman mode of GaN in the heterostructure is attributed to the interaction of the LO phonon with free charge carriers and the change in carrier density due to interface coupling [40]. The broadening of the A1 Raman mode and relative increase in intensity in the interface are attributed to the overlapping with the overtone of the E2g1 Raman mode of MoS2 [41].

Fig. 2. (a), (b), (c) Raman spectrum of MoS2 on quartz, GaN, and MoS2–GaN interface, respectively, showing the active Raman modes. There are various Raman modes activated at the MoS2–GaN interface. (d) Steady-state absorption spectrum of MoS2 on quartz (black) and MoS2–GaN interface (red). (e) The imaginary part of permittivity of a freestanding MoS2 layer (black) and MoS2–GaN interface (red). The insets in (d) and (e) show the corresponding spectrum of GaN.

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The steady-state absorption spectrum of MoS2 on quartz substrate consists of A and B excitonic bands centered at 1.85 eV and 2.03 eV, respectively, and a broad band centered at 2.92 eV. In the presence of the GaN layer, the A and B excitonic bands show negligible shift; however, the C excitonic band significantly red-shifted to 2.73 eV as shown in Fig. 2(d). The C excitonic state is located near the Γ point and is identified with large density of states due to band nesting [8]. The inset shows the absorption band in GaN. The absorption spectrum obtained from the DFT simulations shown in Fig. 2(e) predicts that the imaginary part of the dielectric function of the MoS2–GaN heterostructure decreases at the GaN band edge. The calculated as well as experimentally measured spectra show the enhanced absorption in the visible region in the MoS2–GaN heterostructure consistent with reported results [10]. MoS2 has a high-energy absorption band in the UV region [8,42]. The extent of UV absorption in MoS2 is larger compared to GaN [10]. The optical pump energy at 2.33 eV induces an interband transition at the K point, and by choosing an excitation at 3.54 eV, the interband transition of carriers is generated in both semiconductors at the Γ point.

The transient absorption characteristics of MoS2 are influenced due to coupling between the interfacial phonons and carriers and the carrier transfer at the interface are shown in Figs. 3 and 4. The transient absorption spectrum of MoS2 on a quartz substrate with an optical excitation of 2.33 eV consists of A, B, and C excitonic bands centered at 1.85, 1.99, and 2.91 eV, respectively, as shown in Fig. 3(a). The dependence of the transient absorption spectrum of MoS2 on the GaN layer on the power density of the pump has been shown in Fig. 3(b). The amplitudes of the A and B excitonic bands gradually increase with increase in pump fluence. However, the C excitonic band appears when the pump fluence exceeds the threshold power density. The existence of the C excitonic band with 2.33 eV excitation has been reported to be due to many body effects in MoS2 [43–46" target="_self" style="display: inline;">–46]. Band nesting close to the Γ point contributes to the higher amplitude of the C excitonic band. The transient absorption spectrum of MoS2 is significantly modified due to the electronic states of GaN. The C excitonic band shows a large red-shift to 2.76 eV; however, there is a slight change in the position of the A and B excitonic bands. The optically excited carriers in MoS2 with the pump pulse are coupled to GaN phonons. The contribution of GaN in the band structure near the Γ point as shown in Fig. 1(d) also illustrates the coupling of GaN with the electronic transitions at the interface. The exciton–phonon coupling and the charge transfer across the interface as shown in the inset in Fig. 3(a) result in changes in the non-equilibrium absorption spectra [22]. With a pump pulse excitation at 3.54 eV, the interband transition of carriers in both MoS2 and GaN is achieved at the Γ point. In MoS2, the generated hot carriers relax to the C excitonic band at a significantly slow rate [43], which reduces the amplitude of the C excitonic band. The type I band alignment at the MoS2–GaN interface shown by the DFT calculations facilitates the transfer of the photoexcited electrons in GaN to the conduction band in MoS2 with 3.54 eV excitation. The hot phonons generated in GaN have a lifetime of about 5 ps and cause slow energy relaxation of hot carriers [21,47]. Thus, the carriers as well as the phonons in the GaN layer interact with the MoS2 layer across the interface, which also changes the transient absorption characteristics of MoS2. The A and B excitonic absorption states are slightly red-shifted, but the C excitonic band is broadened, and the peak is red-shifted to 2.68 eV. The scattering of carriers in MoS2 due to interface phonons causes the spectral broadening of the C excitonic band. The carriers transferred to the MoS2 layer relax from their Γ point to the A and B excitonic states in the presence of the interface phonons and presumably increase the exciton density in the MoS2–GaN heterostructure compared to the 2.33 eV excitation.

Fig. 3. (a) Transient absorption spectrum of MoS2 showing the effect of the GaN layer and the effect of excitation energy on excitonic absorption bands. The black, red, and blue colors represent the MoS2 on quartz with 2.33 eV pump excitation, MoS2 on GaN with 2.33 eV pump excitation, and MoS2 on GaN with 3.54 eV pump excitation, respectively. The inset shows the schematics of the interface phonon coupling and the charge transfer at the interface. (b) Power dependence of the transient absorption spectrum of MoS2 on GaN with 2.33 eV. The black, red, blue, and pink colors represent the spectrum at pump fluence of 93.75, 187.5, 281, and 375μJ/cm2, respectively.

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Fig. 4. (a) Decay kinetics showing the recovery of probe absorption at the (a) A, (b) B, and (c) C excitonic bands of MoS2 showing the effect of the GaN layer and the effect of excitation energy on excitonic absorption bands. The black, red, and blue colors represent the MoS2 on quartz with 2.33 eV pump excitation, MoS2 on GaN with 2.33 eV pump excitation, and MoS2 on GaN with 3.54 eV pump excitation, respectively.

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The comparison of the decay kinetics of the A, B, and C excitonic states for the three cases is shown in Figs. 4(a), 4(b), and 4(c), respectively. The decay kinetics are represented by the equation y=∑Ai*exp(−xti)+y0, where Ai* represents the respective amplitude of lifetime ti and y0 represents the residual absorption. For MoS2 on quartz, a biexponential decay of carriers from the excitonic states is observed with finite residual absorption in the 10 ps time window we considered. In the presence of a GaN layer, we observed an additional fast decay component with a lifetime of the order 200 fs with 2.33 eV optical excitation that results in the substantially fast recovery of probe absorption at the excitonic bands of MoS2. This fast decay component represents the carrier dephasing due to coupling of electronic transitions in MoS2 with a GaN layer, which is consistent with the reported results [22]. The residual absorption is significantly reduced due to enhanced dephasing in the presence of a GaN layer. The recovery of probe absorption gradually slows down at the B and C excitonic states compared to the A excitonic state because of slow cooling of hot carriers at a higher energy state [43]. The faster recovery of the absorption of the probe at the A excitonic band (Fig. 9 in Appendix A) at higher input pump fluence is consistent with the formation of the C excitonic band due to many body effects involving A and B excitons. However, the electrostatic screening at a high density of the optically generated carriers, charge transfer from GaN to MoS2 at the Γ point, and the slower energy relaxation due to hot interfacial phonons in GaN cause a slower recovery of the probe absorption and higher residual absorption at 3.54 eV optical excitation.

The PL emission characteristics of the heterostructure are presented in Fig. 5. Figure 5(a) shows the combined emission band of the heterostructure at room temperature (RT). The emission spectrum consists of a GaN emission band centered at 3.4 eV and a weak defect band centered at 2.25 eV measured with 3.82 eV optical excitation as well as a MoS2 emission band centered at 1.87 eV measured with 2.33 eV excitation. With an optical excitation at 2.33 eV, the carriers in MoS2 are excited at the K point [48]. The carriers tend to relax to the A and B excitonic states at the K point in MoS2. The emission characteristics from the heterostructure are significantly different compared to the corresponding emission bands of the GaN layer and MoS2 on a quartz substrate. The emission spectrum of MoS2 on a quartz substrate consists of exciton and trion recombination bands centered at 1.80 eV and 1.78 eV with contributions of 53% and 47%, respectively, as shown in Fig. 5(b). The emission spectrum from MoS2 on a GaN layer shown in Fig. 5(c) is significantly different compared to the MoS2 emission in a quartz substrate. In the presence of a GaN layer, the emission band in MoS2 is enhanced in intensity and significantly blue-shifted. The excitation energy at 2.33 eV is resonant to the defect band in GaN. The charge exchange with the GaN layer [49] causes the conversion of trions into excitons in MoS2 that results in the substantially reduced contribution of trion recombination in the PL emission process. The enhanced and blue-shifted PL emission is attributed to the increased absorption in the visible region, reduced strain on the MoS2 layer, and charge transfer across the interface in the presence of a GaN layer [9,15,49,50]. The exciton band is blue-shifted by 65 meV, whereas the trion band is blue-shifted by 21 meV in the presence of a GaN layer. The higher blue-shift of the exciton band over the trion band is attributed to the stronger dependence of emission characteristics of an exciton compared to a trion [51].

Fig. 5. PL emission spectrum. (a) The emission spectrum heterostructure showing the MoS2 and GaN emission bands. PL emission band of MoS2 on (b) quartz substrate and (c) GaN substrate. The fitted peaks represent the contribution due to trion (blue) and exciton (cyan) recombination. (d) GaN band-edge emission from the GaN (black) and MoS2–GaN (red) heterostructures. The inset shows the defect band emission after heterostructure formation. PL emission characteristics at 30 K showing the LO phonon replica of GaN in (e) GaN and (f) MoS2–GaN.

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Fig. 6. Top and side views of different stacking configurations I–IV of the MoS2–GaN heterostructure. The numbers in the bottom are the energy differences with respect to the most stable structure II.

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Fig. 7. Calculated energy band alignment diagram of 2D MoS2 and bulk GaN. The valence band levels are aligned with respect to the vacuum, and the valence band offset is calculated by choosing as a reference the most stable MoS2–GaN heterostructure (model II in Fig. 1).

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Fig. 8. (a) AFM image of MoS2 on GaN substrate. (b) Height profile of MoS2 layer along the line in (a).

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Fig. 9. Power-dependent recovery of probe absorption at the A excitonic band of MoS2 on GaN. The black, red, blue, and pink colors represent the spectrum at pump fluence of 93.75, 187.5, 281, and 375μJ/cm2, respectively.

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The optical excitation with energy greater than the bandgap of GaN causes an interband transition of carriers in both semiconductors at the Γ point. Excitation in this region enhances the charge transfer between the semiconductors without momentum change [11,18]. In the GaN layer, the optically excited carriers can relax to the GaN band edges at the Γ point and recombine to generate PL emission. In addition, electrons in the GaN layer can transfer to the conduction band of MoS2 at the Γ point. In the MoS2 layer, carriers are excited to high-energy states due to optical excitation. The excited carriers at deep levels, especially holes, have fairly low probability to be scattered to the A and B excitonic states at the K point [52]. Also, the excitation at higher energy increases the probability of intervalley scattering of carriers [51]. Thus, the radiative recombination of carriers at the K point is highly reduced. Therefore, no emission is observed in MoS2 with 3.82 eV excitation. The intensity of GaN emission bands is reduced in the heterostructure at RT. However, the GaN emission is recovered at a lower temperature of 30 K. The reduced intensity of GaN emission in MoS2–GaN at RT is assigned to increase LO phonon-induced non-radiative recombination at RT. The decrease in intensity of defect band emission in GaN is due to reabsorption by the MoS2 layer. The LO phonon modes of GaN are observed at low temperature, as shown in Figs. 5(e) and 5(f), where 0,1,2,3 represent the zeroth, first, second, and third phonon replica, respectively. The Huang–Rhys (H-R) factor is calculated using the equation Sn=(n+1)In+1In, where In represents the intensity of the nth-order phonon replica [53]. The H-R factor calculated from the zeroth and first phonon replica increases from 0.51 in the GaN sample to 0.65 in the MoS2–GaN sample, which illustrates the enhanced coupling of carriers with phonons in the heterostructure.

5 CONCLUSION

In summary, we reported the change in the transient absorption characteristics of monolayer MoS2 and the modified PL emission characteristics in a monolayer MoS2–GaN (0001) heterostructure due to the coupling of carriers with the phonon modes and the energy exchange at the interface. The origin and activation of new Raman modes in the heterostructure indicate the electron–phonon coupling between GaN and MoS2. The optical excitation with 2.33 eV causes the interband transition of carriers in MoS2. The coupling of optically excited carriers in MoS2 with phonons and the exchange of carriers with GaN across the interface at the Γ point significantly change the transient absorption characteristics in MoS2 and result in the enhanced and blue-shifted PL emission from MoS2. Optical excitation with an energy greater than the bandgap of GaN generates interband transitions in both MoS2 and GaN near the Γ point. Excitation at this energy induces the coupling of carriers in MoS2 with the hot phonons in GaN, which slows down the relaxation of carriers in MoS2 and the interlayer carrier transfer as well as the intervalley scattering in MoS2. The LO phonon-induced scattering of carriers reduces the intensity of band-edge PL emission in GaN at RT. We believe that our study will be helpful to understand the energy and carrier transfer across the interface, which is crucial to improve the device performance in optoelectronic and light-harvesting applications based on a MoS2–GaN heterostructure [54].

6 Acknowledgment

Acknowledgment. A. N. and F. D. acknowledge the funding from UNT-AMMPI. J. S., P. G., and M. B. N. acknowledge support by ONR-MURI N000141310635. A. N. acknowledges the support from the NSF-EFRI project. S. K. acknowledges the support from NSF EECCS project. Finally, we acknowledge the High Performance Computing Center at the University of North Texas and the Texas Advanced Computing Center at the University of Texas, Austin.