Magneto-optical properties of spin-coated bismuth-substituted yttrium iron garnet films on silicon substrates at 1550-nm wavelength

Bismuth-substituted yttrium iron garnet (Bi:YIG) films were prepared by using spin coating processes with metal-organic-decomposition-method-based solutions on crystalline silicon (Si) substrates, and their magneto-optic properties at the 1550-nm wavelength region were investigated by performing various thermal treatments. The maximum Verdet constant of the Bi1Y2Fe5O12 film on the Si substrate with a middle buffer layer of Bi2Y1 Fe5 O12 was measured to be 1 072 038°/T/m at 1550-nm wavelength in the unsaturated linear magnetization region by accounting for the negative Verdet constant of the silicon substrate. The optimum thermal treatment condition was observed at the maximum annealing temperature of 700 °C and the annealing speed of 3 °C/min. These spin coating enabled processes may be included to the conventional complementary metal-oxide semiconductor fabrication processes to demonstrate integrated optical waveguide-type isolators on silicon-on-insulator wafers.Bismuth-substituted yttrium iron garnet (Bi:YIG) films were prepared by using spin coating processes with metal-organic-decomposition-method-based solutions on crystalline silicon (Si) substrates, and their magneto-optic properties at the 1550-nm wavelength region were investigated by performing various thermal treatments. The maximum Verdet constant of the Bi1Y2Fe5O12 film on the Si substrate with a middle buffer layer of Bi2Y1 Fe5 O12 was measured to be 1 072 038°/T/m at 1550-nm wavelength in the unsaturated linear magnetization region by accounting for the negative Verdet constant of the silicon substrate. The optimum thermal treatment condition was observed at the maximum annealing temperature of 700 °C and the annealing speed of 3 °C/min. These spin coating enabled processes may be included to the conventional complementary metal-oxide semiconductor fabrication processes to demonstrate integrated optical waveguide-type isolators on silicon-on-insulator wafers.


I. INTRODUCTION
A good magneto-optic (MO) material applicable to the complementary metal-oxide semiconductor (CMOS) processes is needed to demonstrate integrated optical isolators (IOIs) on silicon (Si) wafers, which are critical parts in photonic integrated circuits (PICs). Various MO materials based on organic and inorganic materials have been studied by many researchers. 1,2 The organic MO materials are good for thin-film coating, but they are limited to relatively low MO properties and low thermal budgets which are major obstacles in their applications as integrated optical isolators. The inorganic magneto-optic metal-oxides (MOMOs), such as yttrium iron garnet (YIG), orthoferrites (YFeO 3 , LaFeO 3 , and BiFeO 3 ), and nanocrystals (γ-Fe 2 O 3 and CoFe 2 O 4 ), have been recognized for their high thermal durability and good magneto-optic properties as potential materials in applications to integrated optical isolators. 3 Recently, metal-substituted YIG crystals are most frequently chosen as the magneto-optic materials for optical isolator applications because of their low optical absorption properties at the near-infrared wavelength region. 4 Bismuth-substituted yttrium iron garnet (Bi:YIG) films grown by the liquid phase epitaxy (LPE) method on gadolinium gallium garnet (GGG) substrates were used to be patterned into direct planar waveguides and to demonstrate the integrated optical waveguide-type isolator (IOWTI) with an external magnetic field applied 5 and with sputter-deposited thinfilm magnets. 6 A thin layer of cerium-substituted YIG (Ce:YIG) fabricated by the sputtering method on the GGG substrate was bonded on the top of a waveguide-type Si Mach-Zehnder interferometer (MZI) or of a waveguide-type Si microring interferometer (MRI) as an upper cladding to form the IOWTIs. [7][8][9] These approaches to IOWTI implementation using the direct Bi:YIG waveguide or the bonded Ce:YIG cladding layer are not suitable for mass production of PIC chips under the CMOS processes. A monolithic integration of the MO material layer directly on the Si waveguides has been pursued to demonstrate the IOWTI by using pulsed laser deposition (PLD). 10 This PLD method is still a challenging approach to be adapted to the CMOS process for a full wafer scale PIC production. In addition, further improvement is needed to reduce the large optical insertion loss caused by this approach.
A solution-based spin coating approach to form the MO film layer can relatively be easy to be adapted to the CMOS process. Recently, the metal-organic decomposition (MOD) method was demonstrated to form the spin-coated MO film layers directly on a substrate. 11 The spin-coated Bi:YIG films on glass substrates were prepared from the MOD solutions, and their MO properties such as Faraday rotation, magnetization, and optical absorption at the visible wavelength region were reported. [12][13][14] The MO properties of the Bi:YIG films spin-coated on glass substrates with the MOD solutions at the 1310-nm and 1550-nm wavelengths have also been reported previously. 15 However, the MO properties of the Bi:YIG films spincoated on Si substrates are very important for their applications to the IOWTI in Si-based PICs.
In this paper, we have prepared spin-coated Bi:YIG films on the Si substrates using the MOD solutions and measured the MO properties of the films by performing thermal treatments at various conditions. The maximum Verdet constant of the films at 1550nm wavelength was determined at unsaturated linear magnetization regions using a sensitive Faraday rotation measurement system based on an auto-balanced photoreceiver (ABPR) and a lock-in amplifier (LIA) under alternating magnetic fields. (100) crystal direction of the surface] using a polishing machine with sand papers and colloidal silica slurry. The averaged thickness of the polished silicon substrates was measured by an electronic micrometer with 1-μm measurement resolution, and its measured value was 280 μm. The MOD solution was spun coated on the polished side of the Si substrate for 30 s at 6000 rpm. Then, the crystallization process of the MOD films coated on the Si substrate was performed in two steps of pre-annealing and main annealing processes. For the pre-annealing process, the coated films were heated for 30 min at 120 ○ C to dry out the solvent in the films and then heated for another 30 min at 450 ○ C to decompose the organic components chemically combined with metal components in the film. The abovementioned spin coating process and the pre-annealing process were repeated 20 times to obtain a proper thickness of the main Bi:YIG film in a thickness range of 0.6-1.5 μm. A reasonable thickness (about 60-80 nm range) of the buffer layers was obtained by repeating only 3 times the above spin coating process and the pre-annealing process. The main annealing process was performed by heating, baking, and cooling the samples using a computer controlled electric furnace for various conditions of heating and cooling speeds (annealing speeds) and baking temperatures. The optimum baking temperature for the crystallization of the MOD films is reported to be around 750 ○ C. 12 A spin-coated and thermally treated Bi 2 :YIG film sample was prepared on the Si substrate and a Bi 1 :NIGG buffer layer, and its crystal structure and grain sizes were measured with an x-ray diffractometer (XRD) and an atomic force microscope (AFM), respectively, whose measured results are shown in Figs. 1(a) and 1(b), respectively. The measured XRD pattern in Fig. 1(a) shows the strong peaks corresponding to the garnet structure along with weak peaks corresponding to the partially formed orthoferrites, such as BiFeO 3 and YFeO 3 , which are intermediate products of the thermally treated Bi 2 :YIG films. Based on the measured AFM image in Fig. 1(b), the maximum size of the crystal grains in the Bi 2 :YIG film is approximately about 0.25 μm.

II. EXPERIMENTAL SETUP
The thickness of the Bi 2 :YIG film on the Si substrate was determined directly from the cross-sectional view of the scanning electron microscope (SEM) image of the film sample. The SEM image taken at the cross-sectional edge of the fabricated Bi 2 :YIG film on the Si substrate is shown in Fig. 1(c). Since the boundaries of the buffer layer were not easily distinguishable from the main Bi 2 :YIG FIG. 1. Measured data of the crystal structure, grain size, and thickness for one of the fabricated Bi:YIG films using (a) an x-ray diffractometer, (b) an atomic force microscope, and (c) a scanning electron microscope, respectively.

ARTICLE
scitation.org/journal/adv layer and the substrate layer, the thickness of the buffer layer was calculated by measuring the thickness of the Bi 2 :YIG film sample of the same material compositions with no buffer layer and with a buffer layer with a desired thickness (see Ref. 15 for details). The measured thicknesses of the films on the Si substrates were in the range of 0.642-1.517 μm depending on the material composition, and their error range was within ±0.040 μm. This thickness error was accounted to estimate the error of the measured Verdet constants of the samples and denoted as an error bar in the plotted data. In this experiment, we have fabricated the main film samples of Bi 1 :YIG and Bi 2 :YIG material compositions on the Si substrate with no buffer layer and with one of the Bi 1 :YIG, Bi 2 :YIG, and Bi 1 :NIGG buffer layers.

B. Measurement of the Verdet constants of Bi:YIG films
The Verdet constants of the fabricated Bi:YIG film samples on the Si substrates were measured by using a sensitive Faraday rotation measurement system with a lock-in amplifier (LIA) and an autobalanced photoreceiver (ABPR) under an alternating magnetic field, as described in Refs. 15 and 16. When the light beam passes through a Bi:YIG film sample, it suffers a Faraday rotation whose polarization rotation angle θ is proportional to the product of the Verdet constant V and thickness L of the sample and the applied magnetic field B, 17 θ = VBL.
(1) The total Faraday rotation angle per unit magnetic field corresponds to V total L total which is the sum of the Faraday rotation angles caused by the Bi:YIG film sample layer, the buffer layer, and the silicon substrate. It can be expressed as where pairs of V Bi:YIG , L Bi:YIG ; V Buffer , L Buffer ; and V Subs , L Subs indicate the Verdet constants and thicknesses of the Bi:YIG film, the buffer layer, and the substrate, respectively. One technical point that we have to consider is the opposite signs of the Verdet constants of the Si substrate and the YIG film layer. The crystalline silicon has a negative Verdet constant due to its diamagnetic property, while the YIG garnet has a positive Verdet constant due to its ferrimagnetic property. 18,19 The Faraday rotation angle of the incoming light beam in the sample per unit magnetic field (=θ/B = V total L total ) varies from a negative value for the Si substrate only case to a positive value for the case of a sufficiently thick Bi:YIG film deposited on the Si substrate.
With the Faraday rotation measurement setup shown in Fig. 2, the Faraday rotation angle per unit magnetic field (=θ/B = V total L total ) is determined from the measured output voltage R LIA of the LIA and the time averaged output voltage (VSM) measured at the signal monitoring mode of a single photodiode in the ABPR under the measured root mean square (rms) magnetic field BRMS as follows: 15,16 Since the LIA output R LIA only reflects the absolute value of the rms output of the ABPR depending on the polarization rotation that had taken place in the sample under the AC modulated magnetic field, it is not easy to account for the opposite Faraday rotations of the diamagnetic substrate and the ferrimagnetic main Bi:YIG and buffer layers. It is known that the silicon has a relatively large negative Verdet constant of about −1500 ○ /T/m at the 1550-nm wavelength due to its diamagnetic responses compared to the positive Verdet constant of the silica glass of 6.6 ○ /T/m. 20,21 Unlike in the case of measuring the Verdet constant of metal-substituted YIG crystal films on the silica glass substrate, 15 we must consider the opposite Faraday rotation of the light beam passing through the Si substrate of the large diamagnetic property to achieve the net Faraday effect within the main Bi:YIG and buffer layers. In order to eliminate the opposite Faraday rotation due to the Si substrate from the measured LIA output R LIA , we rotated the sample to two different angles of 0 ○ and 60 ○ with respect to the light beam path and measured the R LIA values. Then, we compared the measured R LIA values with analytically calculated R LIA values for the two optical path length cases with the known Verdet constant of the Si substrate and the known refractive indices of the main Bi 2 :YIG film, the Bi 1 :YIG buffer layer, and the Si substrate. The refractive indices of the Bi 1 :YIG, Bi 2 :YIG, and silicon are known to be 2.32, 2.44, and 3.47, respectively, at the 1.55-μm wavelength. 22,23 The refractive index of the Bi 1 :NIGG buffer layer was estimated to be similar to that of a film-type ferrite garnet [(Bi, Lu, Y) 3 (Fe, Ga)5O 12 ] whose refractive index was reported as 2.15 ± 0.1 at the 1550-nm wavelength. 24 In the calculation of the R LIA values, the direction of the applied magnetic field, the Fresnel reflections at the layer interfaces, the Faraday rotation at each layer, and the interference effects among the boundaries between layers were also considered for both the beam incidence angles at the 1550-nm wavelength.
The calculated Verdet constants (horizontal axis) corresponding to the outputs of the LIA (R LIA , vertical axis) for the cases of the Bi 2 :YIG and Bi 1 :YIG film samples on the Si substrate with the Bi 1 :YIG and Bi 2 :YIG buffer layers, respectively, are shown in Figs. 3(a) and 3(b). In Fig. 3(a), the LIA output R LIA is originally about 0.048 mV when the Verdet constant of the Bi 2 :YIG films is zero. As the Verdet constant of the Bi 2 :YIG film increases, the R LIA value decreases due to the opposite Faraday rotation of the Bi 2 :YIG film with respect to that of the Si substrate until both are the same. When the Faraday rotation angle of the Bi 2 :YIG film is larger than that of the Si substrate, the R LIA value starts to increase. If the measured R LIA value is 0.01 mV at the 0 ○ degree beam incident case, as shown in Fig. 3(a)

ARTICLE scitation.org/journal/adv
is increased during the sample rotation, it becomes V 2 . The hatched and filled areas in Fig. 3 indicate the error ranges calculated from the thickness errors of the layers, as mentioned above. The Faraday rotation angle per unit magnetic field within the samples with or without a buffer layer consists of the sum of V Bi:YIG L Bi:YIG (or V Bi:YIG L Bi:YIG + V Buffer L Buffer ) and V Subs L Subs , as shown in Eq. (2). When the sample is rotated from 0 ○ to 60 ○ , the measured R LIA value either decreases or increases depending on the Faraday rotation [V Bi:YIG L Bi:YIG (+V Buffer L Buffer )] within the Bi:YIG layer compared to that (V Subs L Subs ) within the Si substrate, as illustrated with arrows in Figs. 3(a) and 3(b). With the known V Subs and the measured L Subs and L Bi:YIG , we can determine the Verdet constant of the Bi:YIG film. For the samples with a buffer layer, the Faraday rotation within the buffer layer (V Buffer L Buffer ) was calculated by taking the average value of the Verdet constant of each buffer layer treated at each thermal condition which was obtained from the measurement of each of the Bi 1 :YIG, Bi 2 :YIG, and Bi 1 :NIGG samples without any buffer layer on the Si substrates (as shown in Fig. 4). However, there is an uncertain region where the variation of the measured R LIA value is not well noticeable during the sample rotation possibly depending on the Bi:YIG film thickness. These uncertainties with the thickness errors are marked as error bars in Fig. 4.

III. MEASURED RESULTS
The measured Verdet constants of the Bi:YIG films [Bi 2 :YIG and Bi 1 :YIG for Figs. 4(a) and 4(c), and 4(b) and 4(d), respectively] as functions of the annealing temperature corresponding to the maximum temperatures of the main annealing processes are shown in Fig. 4 for various conditions of the buffer layer and for two different cooling speeds of the main annealing process (1 ○ /min and 3 ○ /min for Figs. 4(a) and 4(b), and 4(c) and 4(d), respectively). The enhanced Verdet constants of the Bi:YIG films are measured at the annealing temperatures from 650 ○ C to 700 ○ C but observed to be dependent on the buffer layer and the annealing speed. The maximum Verdet constant of the Bi:YIG film measured in this experiment is 1 072 038 ○ /T/m for the Bi 2 :YIG film on a Bi 1 :YIG buffer layer treated at an annealing temperature of 700 ○ C and at an annealing speed of 3 ○ C/min. Compared to the same Bi:YIG film on a glass substrate fabricated by the same MOD method, the measured Verdet constant for the silicon substrate shows 15.8% improvement. This improvement may be attributed to the crystallized and periodic structure of the surface of the Si substrate and to the smaller difference in the thermal expansion coefficient of the Si substrate [∼3.5 × 10 −6 / ○ C (silicon, single crystal) 25 ] compared to that of the YIG crystal [∼10 × 10 −6 / ○ C (YIG, single crystal) 26 ] and that of the glass substrate [∼1.3 × 10 −6 / ○ C (glass, fused silica) 27 ]. 15 For the Si substrate, the Bi 1 :YIG films show relatively low Verdet constants compared to those of the Bi 2 :YIG films. The maximum Verdet constant of the Bi 1 :YIG film is measured to be only 451 853 ○ /T/m for the condition of the annealing temperature of 700 ○ C and the annealing speed of 1 ○ C/min. with no buffer layer and plotted as a black dotted line with open squares in Fig. 4(b). However, the   Fig. 4, the saturated magnetization levels M SAT of both the film samples shown in Fig. 5 are similar. This feature can be explained by the relationship between the magnetization and the Faraday rotation as follows: 28 where θ F is the angle of Faraday rotation; n 0 is the refractive index of the magneto-optic material; λ is the wavelength of the propagating beam; ε 0 is the permeability of free space; M and Msat are the projected amount of the non-saturated and saturated magnetization along the direction of the external magnetic field, respectively; and α ± are the right (+) and left (−) circular electronic polarizability of the material, respectively. The Faraday rotation angle θ F of the beam propagating through the magneto-optic material under an applied magnetic field obviously increases linearly as a function of the magnetization projection (M) along the magnetic field which corresponds to the measured magnetic moment in Fig. 5. However, M and Msat affect not only the amount of Faraday rotation but also the difference of the circular electronic polarizability (α − -α + ) which originated from the difference between the resonance energies of the electrons in the crystal structure of the Bi:YIG films for both right and left circular polarized electromagnetic waves. Thus, similar levels of saturated maximum magnetization, M SATS , of the Bi 1 :YIG and the Bi 2 :YIG films, as shown in Fig. 5, do not always mean similar levels of magneto-optic performances for both the materials but may result in a different birefringence depending on the different MO performance. The circular polarization birefringence of the Bi 2 :YIG film which is proportional to (α − -α + ) in Eq. (4) is much larger than that of the Bi 1 :YIG film for optical input beams having both circular polarization components.

IV. CONCLUSIONS
Spin-coated Bi:YIG film samples were prepared on Si wafers by a MOD method which can be considered to be a potential CMOS-compatible process, and their MO properties were investigated after various thermal treatments. The Verdet constants of the films were measured under an unsaturated linear magnetic field range when the films were formed with various buffer layer conditions and treated at various annealing temperatures and annealing speeds. The maximum Verdet constant of a Bi 2 :YIG film formed on the Si substrate with a Bi 1 :YIG buffer layer was obtained to be 1 072 038 ○ /T/m after a thermal treatment at a maximum annealing temperature of 700 ○ C and annealing speed of 3 ○ C/min. The measured result indicates that the magneto-optic characteristics of the Bi:YIG films on the silicon substrate are enhanced significantly compared to those formed on the glass substrate. The enhanced MO characteristics of the Bi:YIG films on the silicon substrates will be useful for demonstrating integrated optical waveguide-type isolators.