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A novel type of GaN-based LED with a highly polarized output using an integrated multi-layer subwavelength grating structure is proposed. Characteristics of both optical transmission and polarization extinction ratio of the polarized GaN-based LED with three different multi-layer subwavelength structures are investigated. It is found that both TM transmission (TTM) and the extinction ratio(ER) of the LED output can be effectively enhanced by incorporating a dielectric transition layer between the metal grating and GaN substrate with a lower refractive index than that of the GaN substrate. Flat sensitivity of the TTM on the period, duty cycle of the metallic grating, and the wide range of operating wavelength have been achieved in contrast to the conventional sensitive behavior in single-layer metallic grating. Up to 0.75 high duty cycle of the metallic grating can be employed to achieve >60dB ER while TTM maintains higher than ~90%, which breaks the conventional limit of TTM and ER being always a pair of trade-off parameters. Typical optimized multilayer structures in terms of material, thickness, grating periods and duty cycle using MgF2 and ZnS, respectively, as the transition layers are obtained. The results provide guidance in designing, optimizing and fabricating the novel integrated GaN-based and polarized photonic devices.
©2010 Optical Society of America
1. Introduction
Gallium nitride (GaN) based semiconductors have attracted much attentions in recent years as a next generation light source [1–4], which has a variety of applications in digital-imaging systems, light management in DVD/HD-DVD optical drivers, modulation for ultra-high-density optical disks, flat panel displays, and optical interconnects in computers. Researches on the GaN based LEDs are mainly emphasized on enhancement of the light emitting efficiency in both internal quantum efficiency, which has been approaching to limit of the material, and external light extracting efficiency limited by the total internal reflection of the generated light due to the very high refractive index of GaN substrate. Several micro-structures have been proposed and integrated on the emitting surface of GaN based LEDs for increasing the light extraction efficiency and enhancing the radiated intensity [5, 6], in which either surface lattice arrays, nanoparticles or peripheral microhole arrays [7, 8] are incorporated. With the increasing applications of the GaN based LEDs, multi-functional GaN LEDs, such as LEDs with polarized light emitting are in great demands in optoelectric industry, e.g., backlighting system in flat panel LCDs, which, however, has not been seen so far in both academic and industrial fields. Nanostructure subwavelength metal grating [9–13] has shown its excellent polarization behavior and the capability of integration, compatibleness of lithograph process with techniques in semiconductor industry. Such a subwavelength metal grating strongly reflects TE polarization and allows most of the TM polarization through, functioning as a linear polarizer rather than as a diffraction grating. The figure of merit of the metal grating polarizers are TM transmission(TTM) and extinction ratio (ER), which is defined as TM transmission divided by TE transmission. In conventional metal grating polarizers, TTM and ER are inheritly a pair of trade-off parameters because achieving higher ER requires more metal volume, which leads to more absorption and thus lower TTM and both TTM and ER are sensitive functions of grating structure, such as the period, duty cycle and the operating wavelength of the grating [11]. The performance of wiregrid micropolarizers with metal wires on substrates such as BK7 glass or fused silica(with refractive index ~1.5), have been explored for polarizing beam splitters and imaging polarimetry [11, 12, 14, 15] within the limit of the inherit trade-off behavior of TTM and ER. Much efforts have been made in enhancing the TM transmission by introducing either multi-layer anti-reflection coating(ARC) stacks on both sides or a templating layer while maintaining the ER as high as possible in the near or mid infrared region [12,13]. Very recently, Zhang et al [16] demonstrated a surface emitting linearly polarized InGaN/GaN light emitting diode ‖LED) using a subwavelength metallic nanograting with a polarization ratio of 7:1, which provides experimental evidence for the feasibility of fabricating integrated polarizing GaN LEDs. The structure in Ref [16]. is essentially a single-layer system with metal grating directly on the protected GaN substrate. All these investigations laid the groundwork from which both theoretical calculation tools and the experimental verifications are demonstrated. In this paper, we propose and investigate the feasibility of an integrated GaN LED with a highly polarized output by integrating a multi-layer subwavelength grating structure onto the GaN substrate of a high refractive index (n=2.5@470nm). Characteristics of both optical transmission and polarization extinction ratio of the polarized device with three different multi-layer structures are investigated and compared. It is found that both transmission and the extinction ratio of the LED output can be effectively enhanced by incorporating a dielectric templating layer between the metal grating and the GaN substrate with a lower refractive index than that of the GaN substrate. Flat sensitivity of the TTM on the period, duty cycle of the metallic grating, and the wide range of operating wavelength have been achieved in contrast to the conventional sensitive behavior in single-layer metallic grating. The optimized multilayer structures in terms of material, thickness, grating periods and duty cycle using MgF2 and ZnS, respectively, as the transition layers are obtained. The results are of significance in designing, optimizing and fabricating the novel integrated GaN-based and polarized photonic devices.
2. Description of the devices
The polarized GaN based LEDs with three different integrated multi-layer subwavelength structures are illustrated in Fig. 1 . The GaN-based LED consists of an InGaN/GaN quantum wells (QW) wafer grown on the sapphire substrate. The QW heterosturcture consists of a GaN buffer layer, an InGaN/GaN QW (about 3nm) and a GaN cap layer (100nm). The photoluminescence (PL) peak wavelength of the wafers is designed at a typical wavelength of 470nm. A nanostructured metal polarization grating is integrated onto the emitting surface of the GaN substrate. Three types of the polarization structures are investigated: Fig. 1(a) shows an aluminum metal grating directly deposited on GaN substrate, labeled as Type-I; Fig. 1(b) shows an aluminum metal grating on a transition dielectric thin layer deposited on GaN substrate, Type-II; and Fig. 1(c) shows a two-layer grating structure in which an aluminum grating is on a dielectric grating of the same period and same duty cycle, Type-III. The difference between Type-II and Type-III is the structure of the dielectric transition layer in which type II has a continuous dielectric thin layer while type III has a dielectric transition grating. To investigate the effect of the transition layer, three dielectric materials with different refractive indices, which represent those with refractive index being lower than, close to (but still lower than) and higher than that of the GaN substrate, respectively, are chosen for the dielectric layer. For GaN LED, light waves are excited from InGaN/GaN quantum well(QW), pass through the GaN cap layer(including transition layer or transition grating when applicable) and impinge to the metal grating at normal incidence. The incident plane waves are specified with wavelength and propagation direction, in Fig. 1, z-axis is the opposite direction of light transmission, x-axis and y-axis is defined as p-polarized (TM) and s-polarized (TE) direction, respectively, i.e., the vector of electric field is parallel or perpendicular to the plane of the grating vector (that is incidence plane) for p-polarized (TM) or s-polarized (TE) state, respectively. Nanostructured polarizer is a high spatial frequency metal grating with a period smaller than the wavelength of incident light from QW. With an appropriate structural design, such a subwavelength metal grating can strongly reflects the TE polarization and allows TM polarization through, exhibiting excellent polarization behavior. Two parameters are employed to characterize the performance of the polarized GaN LEDs: TM transmittance (TTM) and transmission extinction ratio (ER). TTM and TTE is separately the power transmission coefficient for p-polarized and s-polarized light, and ER is defined as:
Fig. 1 Diagram of polarized GaN-based LEDs with integrated subwavelength metallic grating structures. (a) Type-I: metallic grating directly on GaN substrate; (b) Type-II: metallic grating on a dielectric transition layer of GaN substrate; (c) Type-III: metallic grating and a dielectric grating on GaN substrate.
3. Simulation results and discussions
In this section, polarization characteristics of the three structures shown in Fig. 1 are investigated and compared with each other. Three different materials, i.e., MgF2 (refractive index n1=1.38@0.24μm ~ 9μm, lower than that of GaN), ZnS (n2=2.44@0.35μm ~ 14.5μm), close to, but still lower than that of GaN), and a hypothetic optical solid (n3 = 2.8, higher than that of GaN), are employed as the transition layer in Type-II or transition grating in Type-III. The purpose of the introduction of a hypothetic optical solid (n3=2.8) is trying to see the effect of different refractive indices of the transition layer(with a full coverage from lower to higher than that of GaN substrate) on the performance of the transmission and the extinction ratio. The characteristics of the polarized GaN LED are investigated under different designing parameters, i.e., metallic grating period (p), metallic grating height (h), metallic grating duty cycle (dc) and thickness of the transition layer (or transition grating). Rigorous coupled-wave analysis (RCWA) [17–19] is used to simulate the GaN LED with subwavelength metallic grating structures. The design goal for the device is to achieve as high TM transmission and the extinction ratio as possible. In the present work, the polarization behaviors of the proposed structures are characterized by using the Gsolver software, in which the RCWA method is based.
3.1 Effect of thickness of the transition layer of different materials on the performance of the devices
To compare the performance of the three different structures, i.e., Type-I, Type-II, and Type-III shown in Fig. 1, we first look into the effect of thickness of the transition layer of different materials on the performance of the device. Figure 2 shows the properties of TM transmission and polarized extinction ratio of three different materials of transition layer (i.e., MgF2 with refractive index n 1=1.38, ZnS with refractive index n 2=2.44 and an assumed high refractive index material with n 3=2.8) for Type-II and Type-III versus the thicknesses of the transition dielectric layer. When the thickness of the transition layer is zero, both Type-II and Type-III reduce to Type-I. The top metallic grating is assumed to be aluminum grating with the same parameters of p=130nm; h=120nm and dc=0.5 for both Type-II and Type-III. It is seen that different transition materials with different thicknesses greatly affect the properties of the subwavelength GaN device in both transmission and extinction ratio. In both Type-II and Type-III, higher ER and TM transmission than those of Type-I (i.e., when layer thickness is zero in Fig. 2 (a) and (b)) can be achieved under certain thicknesses of the transition layer of all three different materials, among which Type-II and III with MgF2 layer(n=1.38) shows significant enhancement in both TTM and ER over a wide range of thickness of the transition layer with a relative flat sensitivity while those with ZnS and the assumed high-refractive-index layer show the enhancement in TTM and ER over only a certain small range of thickness, e.g., ~30-80nm for ZnS layer and ~30-50nm for high-refractive-index layer and with a fluctuating sensitivity. The higher the refractive index of the transition layer, the worse the performance of the device in terms of the enhancement of both TTM and ER as well as the sensitivity with thickness of the transition layer. When Type-II and Type-III is compared, the sensitivity of type-III on the thickness of the transition layer is much flatter than that of Type-II, which suggests that the tolerance on the thickness of the transition layer in type-III can be less strict than that of type-II.
Fig. 2 Polarization properties (TM transmission and ER) versus thickness of the transition dielectric layer: (a) Type-II; (b) Type-III.
The characteristics of the polarization behavior shown in Fig. 2(a) and (b) also implies more design flexibility than that in type-I (no transition layer) in addition to the enhancement of TTM and ER. Either high TTM or high ER or a trade-off of both can be tuned by different thicknesses of the transition layer depending on the specific requirement of the device.
The physical mechanism behind the enhancement of the transmission and ER can be understood from interference phenomena that happens within the 3-layer structure of GaN/transition layer/effective metal grating layer, and the Effective Medium Theory (EMT) of the sub-wavelength metallic nanograting(SMNG) in which the SMNG could be equivalently modeled as a uniaxial homogeneous birefringent layer with ordinary and extraordinary refractive indices no and ne [20,21]. The oscillating behavior of TM transmission shown in Fig. 2(a) clearly shows the interference effect from the 3-layer structure. Constructive interference happens when the refractive index of transition layer is lower than that of GaN substrate, i.e., MgF2 or ZnS layer, while destructive interference happens when the refractive index of transition layer is higher than that of GaN substrate in most of the thickness region. The lower the refractive index of the transition layer, the slower the oscillating with the layer thickness. Moreover, the equivalent ordinary and extraordinary refractive indices no and ne of a SMNG, which determines the polarizing performance of the grating, are a function of the refractive indices of the grating metal ribs, the space material between the ribs, and the duty cycle of the grating. The introduction of a transition dielectric grating in Type-III (or a dielectric layer in Type-II, a special case when duty cycle of dielectric grating in Type-III is increased to 1) indeed changes the effective refractive indices no and ne of the compound metal and dielectric grating, which subsequently results in the changes in transmission of the TM and TE components, and hence the ER. Analyses based on the EMT show that the introduction of a dielectric layer, e.g., MgF2, can result in increasing in TM transmission and decreasing in TE transmission, and hence increasing in ER, which can be seen in Fig. 2 and also in the following sections.
3.2 Effect of period of metallic grating on the performance of three different structures
In the following, the polarizing properties with different periods of metallic grating are investigated. Figure 3 and Fig. 4 show the comparison results of TTM and ER as a function of metallic grating period between type-II and type-I as well as type-III and type-I, respectively. The metallic grating is assumed to be aluminum grating with the same parameters (i.e., same grating height, h = 120nm and duty cycle dc = 0.5) for all the three structures, type-I, II, and III.
Fig. 3 TM transmission and ER versus aluminum grating period for Type-I and Type-II: (a) TTM; (b) ER. The height and duty cycle of Al grating is 120nm and 0.5, respectively.
Fig. 4 TM transmission and ER versus aluminum grating period for Type-I and Type-III: (a) TM transmission; (b) ER. The height and duty cycle of Al grating is 150nm and 0.5, respectively.
In Fig. 3, the thickness of MgF2 or ZnS transition layer is chosen at 40nm and 50nm, respectively, for type-II based on Fig. 2(a) in which both TTM and ER are enhanced when compared with type-I. It is not surprising that both TTM and ER decreases with the increased period of the Al grating [18] in the case of single Al grating directly on GaN substrate, type-I. By introducing a transition layer on GaN substrate, the device exhibits different behaviors of TTM and ER with the Al grating period. Within the period of aluminum grating up to >200nm, the structure of type-II with MgF2 transition layer shows better and flatter TTM (higher than 96%) with a good extinction ratio (>21dB) than that with no transition layer or with ZnS layer, as seen in Fig. 3(a) by the rapid fluctuating in the cases of no layer or ZnS layer when the Al grating period changes.
In Fig. 4, the thickness of MgF2 or ZnS transition grating is chosen at 30nm and 40nm, respectively, for type-III based on Fig. 2(b). The dielectric layer grating is assumed to have the same period and duty cycle as the aluminum grating in type-III. From Fig. 4, it is seen that higher and flatter TM transmission with higher ER can also be achieved with type-III structure within a certain range of Al grating period, which is similar to (or even better than) those in Fig. 3, i.e., up to >200nm for MgF2 layer or 160nm for ZnS layer. The most pronounced improvement of type-III in comparison to type-II (Fig. 3) is the much enhanced ER and the improved flatness of the TTM with ZnS layer. Within the range of the Al grating period from 100nm to 150nm, type-III with MgF2 grating layer shows TTM higher than 96% with ER higher than 36dB and that with ZnS grating layer shows TTM higher than 83% with ER higher than 38dB, both of which are much higher than that of the structure of type-I.
3.3 Effect of duty cycle of the metallic grating on the performance of three different structures
Section 3.1 and 3.2 clearly show the dependences of the TTM and ER of the three different structures on the transition layer and the metallic grating period. The behavior of the devices of different structures on the duty cycle of the metallic grating can be further characterized based on the optimized transition layer and the period of the metallic grating from the above sections.
Figure 5 and Fig. 6 show the characteristics and the corresponding comparison with type-I of the TTM and ER of type-II and type-III, respectively. For type-II in Fig. 5, the thickness of the transition layer of MgF2, ZnS and the material assumed with high refractive index n3(=2.8) is separately set as 40nm, 50nm and 37nm according to the results of Fig. 2(a). The period and the height of Al grating are fixed at 130nm and 120nm, respectively, according to Fig. 3. As expected, the TTM decreases and the ER increases as the duty cycle of the Al grating increases in the case of type-I with no transition layer, which is understandable due to the increased optical absorption and the polarization effect when the duty cycle of the metallic grating increases. The trade-off behavior, however, can be significantly improved by the introduction of the transition layer, in which much higher TTM and ER than type-I can be obtained over a wide range of duty cycle from 0.2 to 0.8 for MgF2 layer, for example, while ER still maintains the same pattern of increasing with the duty cycle as type-I.
Fig. 5 TM transmission and ER versus duty cycle of Al grating of Type-II and Type-I: (a) TM transmission; (b) ER. The period and height of Al grating are 130nm and 120nm, respectively.
Fig. 6 TM transmission and ER versus duty cycle of Al grating of Type-III and Type-I: (a) TM transmission; (b) ER. The period and height of Al grating are both 150nm.
The performance of type-III, shown in Fig. 6, is even better than type-II in Fig. 5. In the calculation of Fig. 6, the same three materials of different refractive index i.e., MgF2, ZnS and an assumed high refractive index material of n3=2.8, as that in Fig. 5 are used for the transition dielectric grating, and the thickness of the three dielectric grating is set as 30nm, 40nm and 30nm, respectively, according to the similar performance of Fig. 2 (b). The period and the height of Al grating are both fixed at 150nm, according to Fig. 4. The period and the duty cycle of the dielectric transition grating is exactly the same as Al grating. It is seen that much flatter and higher TTM and ER can be achieved over a wide range of duty cycle of Al grating than that with type-II structure in Fig. 5. For MgF2 transition layer grating, as high as 90% flat TTM and ~60dB ER can be obtained with as large as 0.75 duty cycle of the metallic grating. This is a significant progress in achieving both high TTM and high ER simultaneously, since TTM and ER are always a pair of trade-off parameters in conventional subwavelength metallic gratings [11], also witnessed by type-I structure seen in both Fig. 5 and 6.
3.4 Effect of metallic grating height on the performance of three different structures
Figure 7 and Fig. 8 shows the polarization properties versus the height of aluminum grating for type-II and type-III structure, respectively. The period of Al grating used in the calculation is separately fixed at 130nm and 150nm for type-II and type-III, and the duty cycle is 0.5 for both. For type-I, the parameters of Al grating are the same as type-II or type-III. The thickness of transition layer for type-II and type-III are the same as those in section 3.3.
Fig. 7 TM transmission and ER versus height of Al grating of Type-II and Type-I: (a) TM transmission; (b) ER. The period and the duty cycle of Al grating are separately 130nm and 0.5.
Fig. 8 TM transmission and ER versus height of Al grating of Type-III and Type-I: (a) TM transmission; (b) ER. The period and the duty cycle of Al grating are separately 150nm and 0.5.
Both Fig. 7 and 8 show that much higher TM transmission and ER can be achieved with type-II or type-III structure than that with type-I with either MgF2 or ZnS layer. While the ER increases with the height of the Al grating, or the ratio of height-to-period, the TTM takes on a periodically oscillation behavior as the height of grating varies, which is probably due to the partially optical interference that happens within the effective layer of the metallic grating. The results shown in Fig. 7 and 8 suggest that the Al grating height can be optimized within ~100nm range. The thicker the Al grating, the higher the ER, but the more difficult the fabrication. When the effects of the Al grating height on the performance of type-II and type-III are compared, Fig. 7 and 8 show the more or less the same behavior.
3.5 Wavelength dependence of the performance of different structures
In the above simulation, the wavelength of the incident light is set to 470nm. The typical wavelength of a GaN-based LED, however, could be ranging from 440nm to 520nm. The sensitivity of the structural parameters of the device on the operating wavelength is therefore important in terms of the working stability and the tolerance of the structure.
Figure 9 and Fig. 10 show the comparison results of TTM and ER between type-II, type-III and type-I, respectively, across the possible operating wavelength range from 440nm to 520nm. The period and height of Al grating used in the calculation is fixed at 130nm and 120nm for type-II, respectively, and both are fixed at 150nm for type-III. The parameters of type-I are the same as those in type-II or type-III. The duty cycle is 0.5 for all the three structures. The transition layer thickness is the same as that in section 3.3 and 3.4.
Fig. 9 TM transmission and ER versus operating wavelength of Type-II and Type-I: (a) TM transmission; (b) ER. The Al grating period and thickness are separately 130nm and 120nm.
Fig. 10 TM transmission and ER versus operating wavelength of Type-III and Type-I: (a) TM transmission; (b) ER. The period and the height of the Al grating are both150nm.
In both Fig. 9 and 10, it is seen that the TTM and ER of type-I of a given structure is a sensitive function of the operating wavelength. With the introduction of either a dielectric transition layer or a transition grating, both type-II and type-III show the much improved performance in which both TTM and ER become a flat function over the whole possible operating wavelength range in addition to the much enhanced TTM and ER level. Again, the performance of type-III seems to be better than type-II with either MgF2 or ZnS transition layer. The assumed material with high refractive index (n=2.8) does not show much improvement to type-I.
3.6 Angular effect on the performance of transmission and ER
The QW active layer of the LED emits lights to all directions. The effect of different incident angles on the TTM transmission and ER are shown in Fig. 11 . The inset of Fig. 11 is the angular coordinates system. Dependence of the TTM transmission and ER on incident angle θ (−90°<θ<90°) at different azimuthal angles Φ (−180°≤Φ≤180°) represents the angular effect on the performance of the device. Figure 11 shows the typical dependence of TTM and ER on the incident angle θ at an azimuthal angle Φ = 0° for the three types of structures, in which type-II and type-III respectively with MgF2 layer are plotted and compared with type-I. It is seen that with the introduction of either a dielectric transition layer or a transition grating, both Type-II and Type-III show a flat response over a wide range (~ ±60° from normal) of incident angle, which shows a much improvement when compared with type-I (i.e., without a transition layer). This result is consistent with the experimental result shown in Ref [12]. in which a flat response within the incident angle range of ±20° was obtained. More importantly, the ER does not show decreasing with the increasing incident angle, which means that the decreasing rate of the TE component is faster than that of TM component with the increasing incident angle. The similar performance of TTM and ER at other azimuthal angles can also be obtained. Considering further the geometry of the GaN-based LEDs and the relative small angle of total internal reflection (~23° for n GaN=2.5) of GaN substrate, the performance of TTM and ER under normal incidence should be well remained.
Fig. 11 TM transmission and ER versus incident angle θ of Type-I, Type-II and Type-III at azimuthal angle Φ=0°: (a) TM transmission; (b) ER. The period and the height of the Al grating are separately 130nm and 120nm.
3.7 Typical optimized results of type-II and type-III
The proposed multi-layer structures discussed above exhibit not only the much enhanced performance but also the more flexibility in design. Different structural parameters for different type of devices can be obtained based on different requirement in which either high TTM or ER or both are specifically defined or emphasized. To show some concrete examples, Table 1 gives some typical structural parameters and the performance for type-II and type-III, respectively.
Table 1. Simulation results of the polarization performance for type-II and type-III
In Table 1, for type II, if the period of the two structures with MgF2 and ZnS is respectively shrunk to 80nm and 110nm (other parameters remain unchanged), the TTMs and ERs are enhanced to 92% and 56dB, 88.5% and 44.6dB, respectively. For type-III, if the metallic grating parameters are changed to dc=0.6,h=150nm, p=120nm (thickness of transition grating remains unchanged) for both MgF2 film and ZnS film, TTM=95.4%, ER=51.7dB and TTM=92.5%, ER=50.3dB can be achieved respectively.
4. Conclusions
In summary, a novel type of GaN-based LED with a highly polarized output using an integrated multi-layer subwavelength grating structure is proposed. Characteristics of both optical transmission and polarization extinction ratio of the polarized GaN-based LED with three different multi-layer subwavelength structures are investigated. It is found that both TM transmission and the extinction ratio of the LED output can be significantly enhanced by incorporating a dielectric transition layer between the metal grating and the GaN substrate with a lower refractive index than that of the GaN substrate. Flat sensitivity of the TM transmission on the period of metallic grating, duty cycle of the metallic grating, and the operating wavelength have been achieved in addition to the much enhanced ER when compared with the conventional single metallic grating on a substrate. Very high duty cycle of the metallic grating (up to 0.75) can be employed to achieve >60dB ER while TTM maintains higher than ~90%, which is in significant contrast to the conventional limit of TTM and ER being always a pair of trade-off parameters. The flat sensitivity of the device also implies that the multilayer structures can be more sustainable than that of single metallic grating to large variations of the key structural parameters (i.e., period and duty cycle, etc) of the grating without loss penalty of TTM and ER, thus significantly loosen the fabrication difficulty. The proposed multilayer structures are also adaptive to a full range of the typical operating wavelength of GaN-LED from 440nm to 520nm. When the performance of the structure with a transition layer (type-II) and that with a transition grating (type-III) are compared, type-III seems to be better than type-II but more fabrication task may be needed due to the higher depth-to-width ratio in type-III. Some typical optimized multilayer structures using MgF2 and ZnS, respectively, as the transition layers are also given. The results open a new way in designing, optimizing and fabricating the novel integrated GaN-based and polarized photonic devices of high performance.
Acknowledgements
The work is supported in part by University Scientific Research Foundation of Jiangsu Province (09KJA140004), the National Scientific Foundation of China (60776065), Suzhou High-Tech Research Program (ZXG0712) and Pre-research Project of Soochow University.
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