Wafer-scale monolithic integration of Ce:YIG films and magneto-optical isolators on silicon

Silicon integrated cerium doped yttrium iron garnet (Ce:YIG) thin films are promising candidates for integrated nonreciprocal photonic devices, cryogenic photonic modulators and optical computing applications. However, previously reported Ce:YIG thin film on silicon is limited to milimeter sizes. Wafer-scale integration and non-destructive characterization of high quality Ce:YIG thin films on silicon has been elusive. Here, we report growth of 4-inch wafer-scale Ce:YIG thin films on silicon substrates by radio-frequency magnetron sputtering. Strong Faraday effect of 2318±102 deg/cm, low propagation loss of 80±11 dB/cm and excellent thickness uniformity of 3.5% is demonstrated across the 4-inch silicon wafer. Furthermore, a custom designed wafer-scale, non-destructive magneto-ellipsometry was established to characterize the film thickness, optical constants and magneto-optical constants across the wafer. Wafer-scale integration of ring resonator type magneto-optical isolators are also demonstrated. Our work demonstrates a step forward toward wafer-scale heterogeneous integration and characterization of magneto-optical thin films on silicon, providing material candidates for non-reciprocal photonic device arrays, magneto-optical in-memory computing networks and integrated magneto-optic magnetometers.

Using a two-step deposition method, an approximately 60 nm thick YIG layer was first deposited on a 4-inch silicon wafer by radio-frequency magnetron sputtering and then crystallized by rapid thermal annealing to serve as the seed layer for the Ce:YIG film. Subsequently, a Ce:YIG layer with a thickness of approximately 120 nm was deposited on the YIG seed layer using the same method, followed by crystallization via rapid thermal annealing. To ensure the uniform thickness of the deposited film on the wafer, the wafer undergoes continuous rotation at a constant speed of 30 rpm during the sputtering process. Rapid thermal annealing was performed at 850 °C in oxygen to crystallized YIG. The resulting film, denoted as Ce:YIG/YIG/Si, then underwent rapid thermal annealing at 950 °C under an oxygen partial pressure of 1.5 Torr for 100 seconds to crystallize Ce:YIG.

The crystal structure was characterized using an X-ray diffractometer. XRD patterns were collected over a 2θ range of 25°–40° with a step size of 0.02°, and the lattice constant of the Ce:YIG thin film was determined by fitting the XRD data. X-ray photoelectron spectroscopy (XPS) was measured on a Physical Electronics PHI Quantera Scanning X-ray Microprobe using mono-chromatic Al Ka radiation. The crystallized fraction was measured using an Oxford Instruments EBSD detector. Room temperature (300 K) magnetic hysteresis loops were measured using a vibrating sample magnetometry (VSM) model equipped with a superconducting magnet.

SiN ring resonators were manufactured in a silicon photonics foundry. The SiN waveguides were formed on a SiO2 lower cladding layer using LPCVD. After deposition of the upper SiO2 cladding, CMP was applied to achieve planarization, and reactive ion etching (RIE) was then performed in the MO waveguide region to expose the SiN core. 6 SiN ring resonator type MO isolators were fabricated by placing the devices from the wafer center to the edge followed by MO thin films deposition. The transmission spectra were characterized using a polarization-maintaining, fiber butt-coupled measurement setup.

We characterized the magneto-optical properties of the thin films across the wafer using a spectroscopic ellipsometer. Two permanent magnets were suspended above the measurement spot to apply a magnetic field to the films. During the measurements, the sample stage was translated to characterize the films at different positions across the wafer. A total of 54 test points was chosen, and a scanning path was defined to sequentially measure the Muller matrix elements of the MO thin film at each test point, following a spiral pattern from the center towards the outer edge. The Muller matrix elements were measured under positive and negative magnetic field orientations. The ellipsometric parameters, ψ and Δ, were measured in reflection mode over a spectral range of 210 nm to 1690 nm (0.7eV to 5.9eV) at an incident angle of 70°. Applying of a transverse magnetic field, we measured the Mueller matrix of the MO thin film under different magnetic field directions. After each spectrum measurement the orientation of the magnetization was reversed. To reduce the effect of random noise or increase measurement sensitivity, we repeated the measurement five times. The permittivity tensor of Ce:YIG was then obtained by model fitting and the transfer-matrix method.

For an air/magneto-optical film/substrate structure, a linearly polarized light beam was obliquely incident on the film surface at a certain angle. An external magnetic field was applied parallel to the film surface and perpendicular to the plane of incidence. Under these conditions, the dielectric tensor of the magneto-optical material was expressed as follows:

ε = [[ε1, 0, -i·ε2], [0, ε1, 0], [i·ε2, 0, ε3]]

For linear magneto-optic effects, ε3 = ε1. ε1 and ε2 are:

ε1 = ε1r - i·ε1i

ε2 = ε2r - i·ε2i

ε1 is first measured under 0 applied magnetic field. The ellipsometry data is fitted by the Tauc-Lorentz model, which defines the imaginary part of diagonal permittivity tensor elements as:

ε1i,TL(E) = (1/E) * (AmpE0Br(E - Eg) 2) / ((E squared - E0 2) squared + Br 2E 2), for E > Eg

ε1i,TL(E) = 0, for E ≤ Eg

The real part of diagonal permittivity tensor elements can be obtained using analytical integration of K-K relation.

For ellipsometry measurements, we can obtain the ellipsometry parameters ψ, Δ and the 4×4 Mueller matrix, which can be used to describe the polarization changes of light reflected from the surface of a general sample. In the case of an isotropic material, the normalized reflection Mueller matrix is given in the block-diagonal form:

M = [[1, -N, 0, 0], [-N, 1, 0, 0], [0, 0, C, S], [0, 0, -S, C]]

The Mueller matrix was scaled by M11, which represented the overall reflected intensity under completely unpolarized illumination. For a nondepolarizing optical system, the parameters N, C and S were expressed in terms of the conventional ellipsometric angles Ψ and Δ:

N = cos2Ψ, C = sin2Ψ sinΔ, S = sin2Ψ cosΔ

The transfer matrix of the magneto-optical thin-film system was denoted by Q=D1-1D2P2D2-1D3, from which the reflectances of s- and p-polarized components were calculated:

rss = (Q21Q33 - Q23Q31) / (Q11Q33 - Q13Q31)

rsp = (Q41Q33 - Q43Q31) / (Q11Q33 - Q13Q31)

rps = (Q11Q23 - Q21Q13) / (Q11Q33 - Q13Q31)

rpp = (Q11Q43 - Q41Q13) / (Q11Q33 - Q13Q31)

Meanwhile, the 4×4 Mueller matrix elements measured by the ellipsometer were also related to the reflectances, and their transformation relationship was expressed as follows:

M = [[1/2(rpp squared + rsp squared + rps squared + rss 2), 1/2(rpp squared - rsp squared + rps squared - rss 2), Re(rpp rps* + rsp rss*), -Im(rpp rps* + rsp rss*)],

[1/2(rpp squared + rsp squared - rps squared - rss 2), 1/2(rpp squared - rsp squared - rps squared + rss 2), Re(rpp rps* - rsp rss*), -Im(rpp rps* - rsp rss*)],

[Re(rpp rsp* + rps rss*), Re(rpp rsp* - rps rss*), Re(rpp rss* + rps rsp*), -Im(rpp rss* - rps rsp*)],

[Im(rpp rsp* + rps rss*), Im(rpp rsp* - rps rss*), Im(rpp rss* - rps rsp*), Re(rpp rss* + rps rsp*)]]

Accordingly, the off-diagonal Mueller matrix elements were fitted using the transfer-matrix method.

Figure 1A depicted the schematic representation of the confocal magnetron radio frequency sputtering system used for YIG and Ce:YIG deposition, showcasing the sputtering source, a 3-inch target, and the 4-inch silicon wafer within the growth chamber. The off-axis configuration allowed homogeneous deposition of Ce:YIG thin films on a 4-inch silicon wafer. The confocal setup also allowed YIG/Ce:YIG bilayer deposition.

Figure 1B showed a 4-inch magneto-optical thin film wafer. Detailed structural characterization was conducted to investigate the solubility of Ce in the YIG lattice. Figure 1C was the X-ray diffraction patterns of Ce:YIG thin film, showing well-crystallized diffraction peaks of the polycrystalline garnet phase. Due to the larger ionic radius of Ce3+ (1.15 Å) compared to Y3+ (1.02 Å), the lattice constant of Ce:YIG was larger than that of YIG. The XRD diffraction peaks of Ce:YIG showed no obvious shift from the center to the edge of the wafer, indicating that the variation in lattice constant is negligible. The calculated lattice constant was shown in Figure 1D. A bright-field TEM cross-sectional image of Ce:YIG/YIG film on Si(100) was shown in Figure 1E. While the Ce:YIG film maintains a homogeneous garnet phase in most area of the film, localized precipitation of CeO2 nanocrystals with average diameters of 10.8 nm± 2.1 nm were observed. Figure 1F presented the high resolution lattice image and Fourier transform pattern of the Ce:YIG thin film along the [011] zone axis. The Fourier transform pattern reveals diffraction spots corresponding to the garnet crystal structure, with measured interplanar spacings of d022 = 4.39 Å and d211 = 5.07 Å, corresponding to lattice constant of 12.42 Å, a good match with XRD results.

To verify the uniformity of the 4-inch wafer-scale Ce:YIG thin film, a series of characterization were conducted at selected points along the radial direction of the wafer. Owing to the use of rotational deposition during the film growth process, sampling along the radial direction can, to a certain extent, serve as a representative approximation of the overall thin-film properties across the entire wafer. To quantitatively study the Ce valence states, XPS characterization was carried out. Figure 2A shows the XPS Ce 3d spectra of the Ce:YIG thin film at the center of the wafer. The C1s peak arised from hydrocarbon on the film surface at 284.8 eV was used as a reference for absolute binding energy calibration. The peaks assigned for Ce4+ located at v (882.2 eV), v'' (888.7 eV), v''' (898.1 eV), u (900.5 eV), u'' (906.8 eV), u''' (916.5 eV) were attributed to Ce4+. The v' (884.6 eV) and u' (902.3 eV) originate from the 3d5/2 and 3d3/2 peaks of the Ce3+ ions. Figure 2B showed the Ce3+ content at different positions along the wafer radius, indicating that the Ce3+ content remains around 20% across the wafer. Figures 2C and 2D showed the EBSD map at the wafer center and the crystallized fraction of Ce:YIG along the wafer radius, respectively. Ce:YIG films maintained a high crystallization fraction of over 93% at different locations across the wafer, indicating the film was predominately garnet phase.

As shown in Figure 2E and 2F, we measured the room-temperature magnetic hysteresis loops of Ce:YIG thin films at different positions on the wafer. The saturation magnetization values of the Ce:YIG films at different positions were all within 143.5 ± 1.5 emu/cm3, which was consistent with values reported in other literature. Considering the volume error in the measured films, the saturation magnetization of the Ce:YIG films at different positions on the wafer were almost identical. All these films exhibited easy plane magnetic anisotropy. The in-plane saturation magnetic field was approximately 525 Oe, with a coercivity of 9.5±0.7 Oe, while the out-of-plane saturation magnetic field was around 2250 Oe, with a coercivity of 16.6±0.9 Oe.

To measure the thickness of wafer-scale YIG and Ce:YIG thin films, an automatic scanning program was set up across the whole wafer. Figure 3A showed the scanning trajectory of the ellipsometery measurement across the wafer. The squares in the schematic represented the probing locations on the wafer. By fitting the data, the thicknesses of the YIG and Ce:YIG films can be obtained. As depicted in Figure 3B and 3C, the thickness of the Ce:YIG layer was determined to be approximately 120 nm with a variation ratio of around 3.5% across the wafer. Meanwhile, the thickness of the YIG layer is approximately 60 nm, with a variation ratio of about 3.3% across the wafer. Additionally, both the Ce:YIG layer and YIG layer films exhibited a radial downward trend in thickness from the center to the edge, which can be attributed to the inevitable error produced by magnetron sputtering when processing large-area wafers. For confocal sputtering, it was relatively difficult to deposit thin films with in-plane thickness uniformity over large-area substrates.

In order to characterize the optical and MO properties of this film, we measured the Mueller matrix of the magneto-optical thin films using spectroscopic ellipsometry. Meanwhile, we used the transfer matrix method to calculate the real and imaginary parts of the off-diagonal elements of the Ce:YIG thin film.

Figure 4A showed the derived spectra of optical constants n and k of the YIG layer and Ce:YIG layer. Owing to the incorporation of Ce dopants, the refractive index of Ce:YIG is generally higher than that of YIG thin films over the entire wavelength range. In contrast, the extinction coefficient of the Ce:YIG thin film exhibited an absorption peak around 832 nm. This absorption arised from the intra-ionic electrical dipole transitions of the Ce3+ ions. Figure 4B exhibited the real and imaginary parts of off-diagonal permittivity tensor elements in the MO thin film Ce:YIG, which were obtained by transfer matrix method. For the real part of off-diagonal permittivity tensor elements, we observed global maxima at 800 nm. This is the result of the 4f-5d transition in Ce3+ ions at 800 nm. At the wavelength of 1550 nm, the real part of off-diagonal permittivity tensor elements of the Ce:YIG MO film was determined to be approximately 0.0046, with a variation ratio of around 13% across the wafer. The error may be caused by jitter-induced noise from the light source. In the future, we can further reduce the noise by increasing the light-source intensity. For the imaginary part of off-diagonal permittivity tensor elements, we observed global maxima at 880 nm, which is also related to an intra-ionic electrical dipole transition of Ce3+. At the wavelength of 1550 nm, the imaginary part of off-diagonal permittivity tensor elements was also found to be negligibly small and can be regarded as effectively zero.

For the 4-inch wafer, as shown in Figure 4C, the refractive index of Ce:YIG exhibits a distribution characterized by higher values at the center and lower values toward the edge. In contrast, the extinction coefficient showed the opposite trend, with lower values at the center and higher values near the edge. The refractive index n of the YIG MO film was determined to be approximately 2.218 ±0.006, with a variation ratio of around 0.25% across the wafer. Additionally, the refractive index n of the Ce:YIG MO film was determined to be 2.258±0.007, with a variation ratio of around 0.30% across the wafer. This behavior was likely attributed to subtle variations in processing conditions across the wafer during the sputtering deposition and annealing processes. Figure 4D showed the wafer-scale distribution of the extinction coefficient k of the top Ce:YIG film at a wavelength of 1550 nm. The maximum k value of the Ce:YIG film was only 1.63×10-4, while the minimum was as low as 2.20×10−5. In the wavelength of 1550 nm, where optical absorption was extremely weak, the reliability of the fitting results was relatively low, as the measurement has approached the limit of the instrument’s accuracy. Additional experimental verification was therefore needed to obtain more reasonable and accurate results. Figures 4E and 4F showed the wafer-scale distributions of the off-diagonal elements of the permittivity tensor of the Ce:YIG film. At the wavelength of 1550 nm, both the real and imaginary parts of the off-diagonal dielectric tensor elements of the Ce:YIG film were relatively small, making the measurements more susceptible to intensity noise of the ellipsometer light source. As a result, the measured overall wafer-scale variation is slightly higher, at approximately 9%. The relatively large wafer-scale variation in the off-diagonal elements of the Ce:YIG dielectric tensor may arise not only from the strong influence of measurement noise, but also from the stepwise amplification of differences in lattice constant, valence state, and optical constants during the transfer-matri…

Improvements to AI Systems Based on This Paper:

1. Wafer-Scale Process Optimization AI

• Train a generative or reinforcement-learning model on the sputtering parameters (e.g., target-substrate distance, rotation speed, oxygen partial pressure, annealing temperature) to predict optimal deposition conditions for uniform thickness and minimal CeO2 precipitation across large-area substrates.

• The improved AI can automatically tune deposition recipes for any target wafer size, reducing trial-and-error and improving yield in magneto-optical thin-film manufacturing.

2. Non-Destructive Metrology AI

• Develop a deep-learning model that takes raw Mueller matrix ellipsometry data (54-point spiral scans) and directly predicts film thickness, optical constants (n, k), and off-diagonal permittivity tensor elements (ε2) without needing manual transfer-matrix fitting.

• The AI can perform real-time, wafer-scale quality control, flagging spatial non-uniformities (e.g., >3.5% thickness variation) and predicting device performance (Faraday rotation, loss) from optical data alone.

3. Magneto-Optical Device Design Co-Optimization

• Use a physics-informed neural network (PINN) that couples the measured permittivity tensor (ε1, ε2) with waveguide geometry (SiN ring radius, coupling gap, Ce:YIG/YIG thickness) to predict isolation ratio, insertion loss, and bandwidth.

• The AI can automatically design isolator arrays across a wafer, compensating for local film variations (e.g., 13% ε2 variation) by adjusting ring dimensions per device, enabling uniform performance across the entire chip.

4. Defect Mitigation and Material Synthesis AI

• Train a classifier on XRD, XPS, and TEM data to identify CeO2 precipitates and grain-boundary defects, correlating them with processing conditions (e.g., oxygen partial pressure, annealing time).

• The AI can propose alternative dopant concentrations or annealing profiles to suppress Ce4+ formation (currently 20% Ce3+) and increase Faraday rotation beyond 2318 deg/cm, targeting >3000 deg/cm for high-efficiency isolators.

5. Predictive Modeling for Cryogenic and Optical Computing

• Build a surrogate model that predicts the temperature-dependent magneto-optical response (Faraday rotation, loss) from the room-temperature permittivity tensor, enabling design of cryogenic photonic modulators and nonreciprocal switches for quantum computing.

• The AI can simulate large-scale nonreciprocal routing networks (e.g., 4-inch wafer with hundreds of isolators) to optimize signal routing and minimize insertion loss for optical computing architectures.

6. Automated Wafer-Scale Characterization and Feedback Loop

• Implement an AI-driven closed-loop system where the magneto-ellipsometry scanner automatically adjusts measurement points (e.g., denser sampling near edges) based on initial thickness maps, reducing measurement time while maintaining accuracy.

• The AI can also trigger re-annealing or localized laser treatment if it detects high-loss regions, enabling in-situ repair of defective areas during fabrication.

7. Transfer Learning for Other Magneto-Optical Materials

• Use the Ce:YIG dataset (thickness, ε1, ε2, Faraday rotation) as a pretraining corpus for AI models that predict properties of other garnet films (e.g., Bi:YIG, Tb:YIG) or alternative MO materials, accelerating discovery of new compositions with lower loss and higher figure of merit.

• The improved AI can suggest novel dopant combinations (e.g., Ce+Bi co-doping) to achieve both high Faraday rotation and low propagation loss (<50 dB/cm) at telecom wavelengths.

What the Improved AI System Can Do:

• Design and fabricate wafer-scale magneto-optical photonic circuits with >95% device yield and uniform isolation ratios (±2 dB) across a 4-inch wafer.

• Provide real-time, non-destructive metrology for industrial production, reducing characterization time from hours to minutes.

• Enable rapid prototyping of cryogenic nonreciprocal devices for quantum networks, with predicted performance within 5% of experimental values.

• Automatically discover new garnet compositions and annealing recipes that push Faraday rotation beyond 3000 deg/cm and loss below 50 dB/cm, enabling next-generation optical isolators for data centers and AI accelerators.