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Abstract
A material platform of highly c-axis oriented Zn1-xMgxO thin films is developed for nonlinear planar waveguides and electro-optic modulators on Si. Mg content in the film greatly influences the quality of film growth. The second harmonic generation measurement and Maker-fringe analysis reveal that the second-order nonlinear susceptibility tensor element χ33 of the annealed Zn0.72Mg0.28O is approximately 4.2 times larger than that of ZnO. The propagation loss of 633 nm wavelength light in the annealed air/Zn0.72Mg0.28O/SiO2 slab waveguide is 0.68 ± 0.09 dB/cm and 0.48 ± 0.03 dB/cm for the TE0 and TM0 modes, respectively. These results suggest the great potential of the c-axis oriented Zn0.72Mg0.28O nonlinear planar waveguides for applications in on-chip optical interconnects.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the continuous reduction in the feature size of integrated circuits, the data input/output access time between the central processing unit (CPU) and other on-chip parts, such as memory, limits the overall processing rate, although the computation speed of the CPU continuously increases [1]. The data communication rate of conventional copper interconnects is limited to several Gbit/s due to the long resistance-capacitance delay and high power consumption [2]. On-chip optical interconnects with high speed and low power consumption provide a solution to reduce the emerging gap between computation speed and data communication rate by replacing copper interconnects [3,4].
Planar waveguides are essential building blocks for on-chip optical interconnects [5]. The waveguides need high index contrast (HIC), low light-propagation loss, and complementary metal-oxide semiconductor (CMOS) compatibility to be large-scale integrated on Si platforms. Optical waveguides with index differences higher than 20% are called HIC optical waveguides [6]. Furthermore, waveguides with second-order nonlinear polarization (or Pockels) effect are the core of the electro-optic modulator that is responsible for electrical-to-optical signal conversion [7,8]. Currently, waveguide materials with large second-order nonlinear susceptibility (χ(2)) are urgently needed to increase the modulation efficiency and reduce the power consumption of the electro-optic modulator [9–12].
Current mainstream waveguide materials include polymers, Si and Si3N4. Table 1 exhibits some characteristics of the optical waveguides based on these materials. Polymer waveguides feature easy fabrication with low cost and large χ(2) that arises from ultrafast electronic polarization [13], but their limited range of operating temperatures (< 170 °C) hinders their use in real applications [14]. Si waveguides based on the silicon-on-insulator (SOI) platform possess the advantages of prominent HIC, small size, and mature fabrication process that is compatible with CMOS process [15]. However, it has near-zero χ(2) due to the central symmetry in the crystal structure of Si. Recently, Si3N4 waveguides have drawn increasing attention because of their stable material characteristics, ultralow light-propagation loss of less than 0.01 dB/cm [16], and excellent CMOS compatibility. However, the small χ(2) of Si3N4 limits its application in electro-optic modulators.
Table 1. Characteristics of some optical waveguides on Si platforms
LiNbO3 crystals are very famous for their excellent ferroelectric, nonlinear optical and electro-optic characteristics [17]. The advent of the lithium niobate-on-insulator (LNOI) technique, which involves crystal ion slicing and wafer bonding, drives the integration of LiNbO3 waveguides and electro-optic modulators on Si platforms [18,19]. However, this kind of integration faces challenges to be compatible with CMOS process and microelectronic elements in integrated circuits. ZnO waveguides have an HIC of 0.22 and good CMOS compatibility. The published minimum propagation loss in ZnO slab waveguides is approximately 0.1 dB/cm for 633 nm wavelength light [20], while the reported propagation loss in a ZnO channel waveguide for 1550 wavelength light is 7.3 dB/cm due to the immature etching process [21]. In particular, ZnO thin films easily show c-axis preferential orientation growth on SiO2/Si substrates. The c-axis crystallographic direction in wurtzite ZnO corresponds to the χ(2) tensor element χ33, which has the maximum value in the χ(2) tensor. |χ33| of ZnO thin films deposited with the molecular beam epitaxy method reached 83.7 pm/V [22], which exceeds that of LiNbO3 (68 pm/V) [23]. However, χ33 of ZnO thin films deposited with the magnetron sputtering method that is compatible with CMOS process is still less than 20 pm/V.
Herein, we propose low-loss nonlinear planar waveguides based on Zn1-xMgxO thin films deposited on SiO2/Si substrates. The advantage of Zn1-xMgxO materials lies in their small permittivity (8.5-11), easy growth with preferential c-axis orientation on SiO2, potential large χ(2) and good CMOS compatibility. As applied to the core layer of electro-optic modulators, the small permittivity helps to increase the modulation bandwidth, while the large χ(2) contributes to increasing the modulation efficiency. The major highlights in this paper are as follows. (1) Moderate Mg-incorporation into wurtzite ZnO improves the quality of film growth. (2) Mg incorporation into wurtzite ZnO significantly increases the χ(2) of the thin film under an optical frequency electric field. (3) The propagation loss of TM0 mode light (633 nm wavelength) in the air/Zn0.72Mg0.28O/SiO2 slab waveguide is reduced to 0.48 ± 0.03 dB/cm. In the following text, first, the effect of Mg content and annealing treatment on the structural and second-order nonlinear optical properties of Zn1-xMgxO thin films was investigated, and then the mode characteristics and propagation loss of the Zn1-xMgxO planar waveguide were studied. This work reveals the possibility of applying the c-axis oriented Zn0.72Mg0.28O thin films as the core layer of nonlinear optical waveguides and relevant devices in on-chip optical interconnects.
2. Experimental section
Zn1-xMgxO thin films were deposited on quartz glass or thermally oxidized monocrystalline Si(100) substrates by the radio-frequency (RF) magnetron sputtering method. The thickness of the SiO2 layer is approximately 2000 nm. Two kinds of Zn1-xMgxO ceramic targets made from high purity ZnO powder (99.99%) and MgO powder (99.99%) were used to form Zn0.89Mg0.11O and Zn0.72Mg0.28O thin films, respectively. The RF power density was approximately 3.3 W/cm2. Sputtering was performed in a mixture gas of 50% O2 and 50% Ar at a pressure of 1 Pa. The distance between the target and the surface of substrates was fixed at 150 mm. During deposition, the substrate temperature was kept at 200 °C, and the substrate was rotated at a low rate. The deposition time was controlled to obtain a thickness of approximately 500 nm, which was regarded as the minimal film thickness needed for guiding at least one optical mode of 1550 nm wavelength light. Then, these samples were annealed in ambient atmosphere at 450 °C for 180 min.
The Mg content defined as the Mg/(Mg + Zn) atomic ratio in the films was measured by X-ray photoelectron spectroscopy (XPS) (Thermo, Escalab-250XI) using Al Kα radiation (hν=1486.6 eV). Surface and cross-section micrographs of the samples were taken using scanning electron microscopy (SEM) (Hitachi, S-4800). The surface roughness was measured using atomic force microscopy (AFM) (Veeco, D3100). X-ray diffraction (XRD) was performed with Cu Kα radiation generated at 45 kV-100 mA (Rigaku, SmartLab). The refractive index and extinction coefficient were determined by a spectroscopic ellipsometer (J.A. Woollam, M-2000 U). The mode characteristics and propagation loss of optical waveguides were measured by a prism coupler (Metricon, model 2010).
3. Results and discussion
3.1 Structural characteristics of Zn1-xMgxO thin films
Figure 1 shows the morphology micrographs of the Zn1-xMgxO thin films deposited on SiO2/Si substrates. It can be clearly observed that Zn0.89Mg0.11O shows much larger columnar grains than Zn0.72Mg0.28O. The average grain size of Zn0.72Mg0.28O is tens of nm and nearly uniform, while that of Zn0.89Mg0.11O is approximately several hundred nm and quite nonuniform. According to the results of AFM measurement (10 µm×10 µm area), the root-mean-square surface roughness (σrms) of the as-deposited Zn0.72Mg0.28O and Zn0.89Mg0.11O thin films is 17.6 nm and 1.24 nm, respectively. With a similar thickness of approximately 500 nm, Zn0.72Mg0.28O shows a much smoother surface than Zn0.89Mg0.11O. After annealing, the surface roughness of the Zn0.89Mg0.11O and Zn0.72Mg0.28O thin films is 13.2 nm and 0.89 nm, respectively. This indicates that the annealing smoothens the surface morphology slightly.
Fig. 1. SEM micrographs of the surface and cross-section of the Zn1-xMgxO thin films deposited on SiO2/Si substrates. (a) Zn0.89Mg0.11O and (b) Zn0.72Mg0.28O. Insets are the micrographs of the cross-section of the films.
The XRD patterns of the Zn1-xMgxO thin films are shown in Fig. 2. The relevant data given by the XRD measurements are presented in Table 2. The c-axis lattice constant was calculated by using Scherrer's equation. The residual (or macro) strain in the Zn1-xMgxO thin film can be derived by comparing the c-axis lattice constant with that of a perfect wurtzite ZnO crystal (0.521 nm). In Fig. 2(a), all samples show only two peaks in the XRD diffractogram that can be indexed to the (0002) and (0004) peaks of wurtzite ZnO (JCPDS Card No. 36-1451). This indicates that all Zn1-xMgxO thin films exhibit a highly c-axis oriented ZnO hexagonal wurtzite crystal structure. Zn0.72Mg0.28O shows a slightly smaller c-axis lattice constant than Zn0.89Mg0.11O. This is in good agreement with the results in the published literature [24]. The reduction in the c-axis lattice constant is related to the occurrence of stress in the film, which results in tensile strain [25]. The absolute value of the strain increases with increasing Mg content.
Fig. 2. XRD patterns of the Zn1-xMgxO thin films deposited on SiO2/Si substrates. (a) θ-2θ scan and (b) normalized ω-scan rocking curve.
Table 2. Structural information derived from the XRD measurement
In addition, as shown in Fig. 2(b), the full width at half maximum (FWHM) value of the peak that corresponds to the (0002) plane in the ω-scan rocking curve decreases with increasing Mg content. This finding indicates that the Zn0.72Mg0.28O thin film shows better crystalline quality than the Zn0.89Mg0.11O thin film. This implies that there is a close relationship between the crystalline quality and Mg content in the film. After annealing, the FWHM value was reduced to 2.15°, which is smaller than that (2.37°) of annealed ZnO thin film deposited with the same method [25]. The (0002) FWHM value of less than 0.2° in the XRD ω-scan rocking curve of Zn1-xMgxO thin films with Mg composition of around 0.28 had been achieved by the pulsed laser deposition [24] and metalorganic vapor-phase epitaxy on sapphire (0001) substrates [26]. However, there is few published literatures in which Zn0.72Mg0.28O thin films deposited with magnetron sputtering on SiO2/Si substrates show FWHM value of less than 3° in the XRD ω-scan rocking curve. After annealing, the c-axis lattice constant decreases, resulting in a further increase in tensile strain. The above results reveal that the Mg content greatly influences the growth of Zn1-xMgxO thin films during magnetron sputtering deposition.
3.2 Second-order nonlinear optical characteristics of Zn1-xMgxO thin films
Second harmonic generation (SHG) is a typical indicator of second-order nonlinear optical properties. The SHG in the Zn1-xMgxO thin film deposited on a quartz glass substrate was measured in transmission mode [27]. The measurement setup is described in Supplement 1, Section 1. Figure 3 conveys the angular-dependent second harmonic intensity generated in the Zn1-xMgxO thin films. The polarization of the second harmonic signal is always p-polarized, regardless of whether the polarization of the fundamental beam is p-polarized or s-polarized [28,29]. For convenience of discussion, the case where the fundamental beam is p-polarized is defined as the p-p case, while the case where the fundamental beam is s-polarized is referred to as the p-s case. The Maker fringes formed in the opposite rotational direction are almost symmetrical, although the signal intensity at the incident angles with the same absolute value is slightly different. Generally, the deviation of the second harmonic intensity at the symmetric position reveals how the optical axis of the sample tilts away from the surface normal [30]. As shown in Fig. 1, the Zn1-xMgxO thin films are composed of highly c-axis oriented columnar grains. Thus, the small deviation of intensity at the symmetric position in Fig. 3 reveals that the mean direction of the optical axis of the columnar grains is almost perpendicular to the substrate plane. This confirms the structural characteristic of the highly c-axis orientation because the optical axis of the wurtzite ZnO crystal structure is parallel to its c-axis.
Fig. 3. Transmitted second harmonic intensity from the samples as a function of the incident angle of the fundamental beam. (a) The fundamental beam is p-polarized, and (b) the fundamental beam is s-polarized.
For the as-deposited samples, the SHG intensity of Zn0.72Mg0.28O is apparently stronger than that of Zn0.89Mg0.11O in the p-p case, while the former intensity is almost the same as the latter intensity in the p-s case. After annealing, in both cases, the SHG intensity of Zn0.89Mg0.11O increases significantly, while the SHG intensity of Zn0.72Mg0.28O increases slightly. Particularly, in the p-s case, Zn0.89Mg0.11O shows a stronger intensity than Zn0.72Mg0.28O. However, the p-polarized fundamental beam generates a much stronger SHG intensity than the s-polarized fundamental beam, since it results in a larger conversion efficiency [31]. In addition, the maximum intensity appears at approximately 45° [28,31]. The angle that corresponds to the maximum intensity in Fig. 3 was derived by fitting the experimental data. The derived values are exhibited in Table 3, where β and γ refer to the angle corresponding to the maximum SHG intensity in the p-p case and p-s case, respectively. The β and γ values reflect the crystallinity and microstructure of the thin films. It is regarded that small deviation of β and γ from 45° indicates good crystallinity and high c-axis orientation. For the Zn0.89Mg0.11O sample, regardless of whether it is annealed, the γ value is slightly larger than the β value. For the Zn0.72Mg0.28O sample, regardless of whether it is annealed, the γ value is very close to the β value. In the same case, Zn0.89Mg0.11O shows a larger γ value than Zn0.72Mg0.28O. Nevertheless, only annealed Zn0.72Mg0.28O displays β and γ values that approach 45°. It is reasonable to conclude that the annealed Zn0.72Mg0.28O shows the best crystallinity and highest level of c-axis orientation.
Table 3. Derived second-order susceptibility tensor matrix element values of the Zn1-xMgxO thin films
The χ(2) of the Zn1-xMgxO thin films under the optical frequency electric field can be derived utilizing the Maker-fringes technique by analyzing the angular-dependent second harmonic signal. As the fundamental beam with ω frequency strikes the sample, the electric field of the fundamental beam causes second-order nonlinear source polarizations in the sample. These second-order nonlinear source polarizations act as an excitation source that radiates the second-harmonic signal or frequency-doubled (2ω) output. This polarization arises from the interaction of the fundamental beam with the struck nonlinear optical material through the action of χ(2) [32]. The χ(2) tensor in matrix notation is usually used to describe the anisotropic characteristics determined by the crystal symmetry and microstructure of the material. The Zn1-xMgxO thin films possess a hexagonal wurtzite ZnO crystal structure, so we assume that Zn1-xMgxO thin films, as a whole, have the same form of χ(2) tensor as the ZnO bulk crystal with 6-mm point group symmetry. Hence, they have only five nonzero tensor elements (χ15, χ24, χ31, χ32, and χ33) [33]. Furthermore, the polycrystalline nature of the films indicates that the in-plane crystal orientation is randomly distributed, although the c-axis of most columnar grains within the film is aligned to the surface normal of the substrate. If we consider that the in-plane physical properties of Zn1-xMgxO thin films are isotropic, the symmetry of the thin films, as a whole, can be described by the space group C∞V[34]. Then, the χ(2) tensor of the Zn1-xMgxO thin films can be composed of two independent tensor elements (χ31 and χ33), as shown below:
Mg incorporation into wurtzite ZnO significantly increases the χ(2) under the influence of the electric field of the fundamental beam. As displayed in Table 2, the contraction of the c-axis lattice constant and the presence of residual strain demonstrate the occurrence of Mg incorporation into wurtzite ZnO. This enhancement should relate to the enhanced electronic response of the material. It was reported that Mg incorporation into wurtzite ZnO produces novel ferroelectricity with electronic origin [38]. The introduction of Mg2+ ion (1s22s22p6) influences the electronic configuration, resulting in the change in electronic distribution of the d-p hybridization [39]. Therefore, the Mg incorporation might also play a positive role in increasing the electronic contribution for the χ(2) generated by the optical frequency electric field. As shown in Fig. 4, it is reasonable to speculate that the Mg2+ ions preferentially occupy the Zn2+ lattice sites. It was reported that Mg2+ ions energetically prefer to substitute Zn2+ ions rather than occupying octahedral or tetrahedral interstitial sites in the wurtzite ZnO structure, since the Mg substitution for Zn lattice sites has the minimum formation energy according to first-principle calculations [40]. Furthermore, Zn0.72Mg0.28O exhibits a smaller c-axis lattice constant and larger residual strain than Zn0.89Mg0.11O. This reflects that the number of MgZn substitution sites in Zn0.72Mg0.28O is greater than that in Zn0.89Mg0.11O. Thus, it could be inferred that the MgZn substitution sites are closely related to the excitation sources that enhance the radiation of the second harmonic signal. Further theoretical and experimental studies are needed to reveal the influence of the location of Mg2+ ion in the ZnO and induced distortion of crystal structure on the electronic response to optical frequency electric field.
Fig. 4. Schematic representation of atomic positions in the (11-20) plane of wurtzite Zn1-xMgxO. The high-symmetry interstitial sites are indicated: O is the octahedral interstitial site and T is the tetrahedral interstitial site. The dashed line refers to the ‘‘interstitial channel’’ along the c axis [37].
3.3 Light-propagation characteristics of Zn1-xMgxO planar waveguides
The Zn1-xMgxO thin films deposited on SiO2/Si substrates form three-layer slab waveguides on Si, where air is the upper cladding layer, Zn1-xMgxO thin films are the core layers and the SiO2 is the bottom cladding layer. The waveguiding properties of the air/Zn1-xMgxO/SiO2 three-layer slab waveguides were investigated by the prism coupling technique in TE and TM polarization for different wavelengths (633 nm and 1539 nm). Figure 5 shows the mode patterns of the planar waveguides formed by annealed Zn1-xMgxO thin films. The presence of sharp reflectivity dips in each curve testifies to the excitation of guided modes. Then, the effective mode index (neff) can be calculated by using Eq. (2) [6]:
Fig. 5. TE (left) and TM (right) mode patterns of the air/Zn1-xMgxO/SiO2 slab waveguide measured at different wavelengths.
Table 4. Effective refractive index of the fundamental modes in the air/Zn1-xMgxO/SiO2 slab waveguides on Si substrates
The propagation path of 633 nm wavelength light in the air/Zn0.72Mg0.28O/SiO2 slab waveguide formed on the quartz glass substrate can be clearly observed (see Supplement 1, Section 5). The intensity of the light that propagates in the waveguide gradually decreases due to scattering, absorption and radiation loss. The attenuation coefficient (α) is widely used to evaluate the propagation loss. It can be determined by analyzing the scattering light of the propagating mode as a function of the propagation path in the waveguide. Both air/Zn0.89Mg0.11O/SiO2 and air/Zn0.72Mg0.28O/SiO2 slab waveguides on the quartz glass and the SiO2/Si substrates were measured. Light-propagation was only detected in air/Zn0.72Mg0.28O/SiO2 slab waveguides. However, even after several measurements (as-deposited and after annealing), light-propagation was not detected in the air/Zn0.89Mg0.11O/SiO2 slab waveguides, so the corresponding α values were not derived. This is probably caused by the large surface roughness of Zn0.89Mg0.11O layer (17.6 nm). The derived α of air/Zn0.72Mg0.28O/SiO2 slab waveguides is exhibited in Table 5. Before annealing, the α values of the TE0 mode and TM0 mode are 0.76 ± 0.06 dB/cm and 0.99 ± 0.18 dB/cm, respectively. After annealing, the α values of the TE0 mode and TM0 mode are decreased to 0.68 ± 0.09 dB/cm and 0.48 ± 0.03 dB/cm, respectively. Figure 6 shows how the intensity of 633 nm wavelength light changes with the propagation distance in the air/Zn0.72Mg0.28O/SiO2 slab waveguide on Si substrates. The TE0 mode α is comparable to that of the ZnO layer deposited with the same method (∼ 0.5 dB/cm) [20] and lower than that of the LiNbO3 planar waveguide based on a sputtering-deposited thin film (1.9 dB/cm) [41]. The α of the TE0 mode and TM0 mode corresponding to 1550 nm wavelength light is unavailable at the moment due to the presence of mangy strong noise signals appear on the decay curve. End-fire coupling method is suggested as a more suitable method than prism coupling technique to evaluate the propagation loss at 1550 nm wavelength. In the case of end-fire coupling method, slab waveguides need to be etched into strip optical waveguides in order to confine the mode light field at vertical and horizonal directions. We had tried to etch the air/Zn0.72Mg0.28O/SiO2 slab waveguide on the SiO2/Si substrate by Inductively Coupled Plasma-Reactive Ion Etching (ICP-RIE etching) with a mixture of HBr and Ar, but the roughness of sidewall is very large due to the immature etching process. Optimizing the ICP-RIE etching process is being conducted. Based on the measured values of extinction coefficients (Supplement 1, Fig. S3), it can be derived that the absorption coefficient of Zn0.72Mg0.28O at 1550 nm wavelength is less than that at 633 nm wavelength. Thus, the absorption loss at 1550 nm wavelength should be less than that at 633 nm wavelength. Then, the value of α at 1550 nm wavelength could be less than that at 633 nm wavelength if the scattering loss was reduced sufficiently.
Fig. 6. Intensity of 633 nm wavelength light that propagates in the air/Zn0.72Mg0.28O/SiO2 slab waveguides as a function of propagation distance. (a) TE0 mode. (b) TM0 mode. The filled scatters are experimental data, while the solid lines are fitting data.
Table 5. The attenuation coefficient of the 633 nm wavelength light modes in air/Zn0.72Mg0.28O/SiO2 slab waveguides on Si substrates
Notably, after annealing, the α of the TM0 mode is lower than that of the TE0 mode, implying low propagation loss. This is quite probably caused by the microstructure of the Zn0.72Mg0.28O thin films. As shown in Fig. 1, the Zn0.72Mg0.28O thin films are composed of slender columnar grains. This means that the TE0 mode light encounters more grain boundaries than the TM0 mode light. There are many defects at the grain boundaries. These defects absorb some of the light and cause the increase in the propagation loss. The annealing indeed improves the crystalline quality, increases the extent of c-axis orientation (reduction in FWHM value in Table 1) and reduces the surface roughness. This might significantly reduce the defects along c-axis direction and scattering loss at the surface, resulting in that TM0 mode light decays weaker than TE0 mode light in the annealed air/Zn0.72Mg0.28O/SiO2 slab. The low propagation loss of the TM0 mode in the Zn0.72Mg0.28O planar waveguide paves the way to utilize χ33 of the Zn0.72Mg0.28O thin film with c-axis perpendicular to the SiO2/Si substrate for application as a waveguide electro-optic modulator integrated on Si platforms. In this scenario, the light-matter interaction could be effectively enhanced by increasing the overlap between an external electric field applied along the c-axis of Zn0.72Mg0.28O and the TM0 mode field profile of the incident light. This is very beneficial to raise the modulation efficiency of the electro-optic modulator by increasing the electro-optic overlap coefficient [42]. The electro-optic overlap coefficient is the largest as the optical field profile and the external electric field profile overlap the most [43].
4. Conclusion
Highly c-axis oriented Zn0.72Mg0.28O thin films deposited on SiO2/Si substrates by radio-frequency magnetron sputtering form low-loss nonlinear planar optical waveguides on Si. The Mg content in the film greatly influences the quality of film growth. Zn0.72Mg0.28O shows a much smoother surface morphology and better crystalline quality than Zn0.89Mg0.11O. It has a (0002) FWHM value of 2.15° in the XRD ω-scan rocking curve and a root-mean-square surface roughness of 1.24 nm (10 µm×10 µm area). Furthermore, Mg incorporation into wurtzite ZnO significantly increases the χ(2) of the thin film generated by the optical frequency electric field. The annealed Zn0.72Mg0.28O displays a |χ33| of 100.3 ± 3.0 pm/V and a χ31 of 14.3 ± 0.4 pm/V. This value of |χ33| is approximately 4.2 times larger than that of ZnO and exceeds that of LiNbO3 thin film. The attenuation coefficient of the Zn0.72Mg0.28O planar optical waveguide is reduced to 0.68 ± 0.09 dB/cm and 0.48 ± 0.03 dB/cm for the TE0 and TM0 modes at 633 nm wavelength, respectively. The TE0 mode attenuation coefficient is lower than that of LiNbO3 planar waveguide based on the sputter-deposited thin film. This work reveals the great potential of the Zn0.72Mg0.28O thin films as the core layer in nonlinear optical waveguides and waveguide electro-optic modulators integrated on Si platforms.
Funding
National Natural Science Foundation of China (61804147, 62035012); National Key Research and Development Program of China (2018YFE0204000).
Acknowledgments
The authors sincerely thank Prof. Dongxiang Zhang at the Institute of Physics, Chinese Academy of Sciences for her assistance and discussion relevant to the measurement of second harmonic generation and the Maker-fringe technique. The authors also sincerely thank Dr. Lei Wang at the School of Physics, Shandong University for his help with the measurement and discussion relevant to the prism coupling technique.
Disclosures
The authors declare no conflicts of interest.
Supplemental document
See Supplement 1 for supporting content.
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