Optical device and method of fabricating thereof

Abstract

An optical device and its manufacturing method are disclosed, comprising two distinct optical paths: a first optical path including a first waveguide core and a first cladding adjacent to the first waveguide core; and a second optical path including a second waveguide core and a second cladding adjacent to the second waveguide core. The thermo-optical coefficient (TOC) of the first waveguide core and the thermo-optical coefficient of the first cladding have the same sign, for example, positive, while the sign of the thermo-optical coefficient of the second waveguide core differs from the sign of the thermo-optical coefficient of the second cladding, for example, one positive and one negative. The aforementioned optical paths can be implemented in a Mach-Zehnder interferometer (MZI).

Description

Optical devices and their manufacturing methods Optical data communication systems encode digital data patterns by modulating laser light. The modulated laser light is transmitted from the transmitting node to the receiving node via an optical data network. Upon arrival at the receiving node, the modulated laser light is demodulated to obtain the original digital data pattern. Therefore, the practice and operation of optical data communication systems depend on having reliable and efficient mechanisms for transmitting and detecting laser light at different nodes within the optical data network. In this regard, it may be necessary to convert data streams from the electrical domain to the optical domain and vice versa, and to transmit data streams between various physically distributed computing systems. In some implementations, wavelength division multiplexing (WDM) can transmit modulated data streams at different carrier wavelengths over a common optical waveguide. WDM can overcome conventional fiber congestion, a potential problem in optical modules with parallel optical transceivers (one channel per fiber). In particular, WDM simplifies optical modules by significantly reducing the number of fibers per module, thereby reducing cost and size. Furthermore, the ability to employ WDM technology on semiconductor devices (e.g., integrated circuits) using semiconductor device fabrication techniques can reduce power consumption and assembly costs. However, the implementation of semiconductor device photonics is challenging due to the sensitivity of fabricating small components. Variations in the fabrication of components can lead to challenges in providing and maintaining different carrier wavelengths. Therefore, while current approaches are suitable in some respects, improvements in the devices and methods used for their fabrication are still needed. The following disclosure provides numerous different embodiments or examples for practicing various features of the provided subject matter. Specific examples of elements and arrangements are described below to simplify this disclosure. Of course, these are merely examples and not limiting. For example, forming a first feature over or on a second feature in the following description can include embodiments in which the first and second features are formed in direct contact, and can also include embodiments in which an additional feature can be formed between the two, such that the first and second features may not be in direct contact. Furthermore, reference numerals and / or letters may be repeated in various examples of this disclosure. Such repetition is for simplicity and clarity and does not in itself prescribe relationships between the various embodiments and / or configurations discussed. For ease of description, spatially related terms such as “below,” “down,” “below,” “above,” and “up” are used in this document to describe the relationship or function of one element or feature with another, as shown in the figures. In addition to the orientations depicted in the figures, spatially related terms are intended to cover different orientations of the device in use or operation. The device may be oriented in other ways (rotated 90 degrees or in other directions), and the spatially related descriptors used herein will be interpreted accordingly. Furthermore, when using terms such as "about," "approximately," etc., to describe a number or a range of numbers, the term is intended to encompass numbers within a reasonable range, taking into account the inherent variations that occur during the manufacturing process, as understood by those skilled in the art. For example, based on known manufacturing tolerances associated with the characteristics of the manufacturing process that are associated with the number, the quantity or range of the number includes a reasonable range, which includes the described quantity, such as within ±10% of the described quantity. For example, a material layer with a thickness of "about 5 nm" can cover a size range from 4.5 nm to 5.5 nm, where the manufacturing tolerances associated with the deposited material layer are known to those skilled in the art to be ±10%. In some embodiments disclosed herein, the apparatus and methods are used in WDM applications. WDM filters can be made from interferometers, one type of interferometer-based optical filter being a Mach-Zehnder interferometer (MZI). MZI provides an optical element based on two-beam interference. Exemplary embodiments of photonic devices providing waveguide configurations for MZI are discussed herein, these waveguide configurations being designed to adjust the wavelength of the photonic device's output. Employing such devices, MZI-based devices for WDM applications, as integrated circuit-based photonic circuits, offer the advantages described above. However, such devices may also exhibit high refractive index contrast and small feature size, making them highly sensitive to minute nanoscale variations in their geometry, which can be caused by semiconductor fabrication and / or patterning techniques. For example, variations in the pattern density defined on the device can lead to variations in the ability to accurately reproduce the desired pattern. In some implementations, variations (e.g., from process, design, patterning, etc.) affect the effective refractive index of the device's waveguide, which in turn alters the phase delay between the two branches of the MZI in the mutual test filter circuit, resulting in a shift in the desired filter response. The following discussion illustrates compensation techniques for limiting and / or avoiding these undesirable shifts. This disclosure is not limited to the specifically described apparatus and / or these particular challenges. Various optical communication systems or network technologies utilize both optical elements and electronic circuitry, and exemplary embodiments of photonic devices can be implemented to improve performance. For example, exemplary photonic circuits are implemented in various optical communication systems, such as in antennas and other photonics-based field applications. As a brief overview of related technologies, an MZI element includes a waveguide for guiding light. Specifically, a waveguide is formed by a waveguide having a cladding layer surrounding the wire (e.g., silicon wire). In this document, the cladding layer is referred to as the lower cladding or under-cladding material, which extends below the wire; and the upper cladding layer is referred to as the upper cladding material, which extends above the wire. When an MZI is formed on a wafer, the waveguide is formed to provide two paths for light to pass through the element; these paths are referred to as “branches” in the discussion below. In some embodiments, one branch is a reference branch, and the other is a sensing or manipulating branch. It should be noted that the “branches” of the MZI element shown in the figures are not limited to this shape, unless specifically stated in the appended claims. MZI and waveguides are typically defined by various parameters. The refractive index (n) is the ratio of the speed of light at a given wavelength in a vacuum to the speed of light in a given bulk medium. Generally, the refractive index of a material depends on the wavelength and temperature. The effective refractive index (n) eff This takes into account the light propagating within the element (rather than the refractive index of the bulk medium). The group refractive index (ng) can be used to determine the free spectral range (FSR), which can be conceptualized as the shift of the effective refractive index with wavelength. The FSR of an MZI depends on the difference between the length (ΔL) of the branch of the MZI and the group refractive index of the waveguide. In one embodiment, the length of the branch can be a linear optical distance traveling within the branch. As one apparatus that can benefit only from aspects of this disclosure, a demultiplexer device (DMX) 100 is schematically illustrated in FIG1. ​​In one embodiment, the DMX 100 may be fabricated on a semiconductor device, such as forming a silicon photonic integrated circuit (PIC). The DMX 100 includes four Mach-Zehnder interferometers (MZIs) 102a, 102b, 102c, and 102d. The MZIs 102a, 102b, 102c, and 102d are cascaded. In one embodiment, MZIs 102a and 102b each have a branch length difference of ΔL, and MZIs 102c and 102d each have a branch length difference of 2ΔL. Input light is provided at input 104, and output regions 106 include channels / ports Ch1, Ch2, Ch3, and Ch4, respectively. Each channel / port can output a different wavelength. At point (b) in Figure 1, a transmission spectrum corresponding to an implementation of circuit 100 is provided. In one embodiment, the transmission spectrum of each MZI is a raised cosine function with a period of 2Δλ or Δλ. It should be understood that the refractive index of optical materials is not a constant parameter at all temperatures; the variation of refractive index with temperature is called the "thermo-optic coefficient" (TOC). In other words, TOC quantifies the thermal effect on an optical material. Silicon's relatively high TOC means that when used to provide waveguides, temperature drift can cause a significant change in the refractive index of the silicon wire or core. In fact, silicon is one of the materials with the highest TOC among thermo-optical materials; silicon's TOC is approximately 1.86 x 10⁻⁶ Kelvin (absolute temperature). -4 Therefore, the MZI 102a-102d of the device 100 formed from silicon core waveguides is sensitive to temperature changes. Thus, if left unaddressed, temperature variations will affect the spectral response. In some implementations, a heater structure can be positioned above each branch of the MZI 102a-102d to generate and apply heat. This heat causes temperature changes in the waveguide, thereby altering the refractive index, carrier mobility, and / or other properties. Therefore, the heater can be used to change the speed and / or phase of light passing through the corresponding element. However, the use of heaters increases the power consumption of the device and / or the assembly cost of the device (e.g., an optical transceiver). This disclosure provides practices and embodiments for manufacturing without using heaters to compensate for temperature changes or process drift. In other words, in some embodiments, no heater component is used when manufacturing MZI 102a-102d. MZI 102a-102d can be formed using the methods and structures discussed below, such that each MZI is configured to compensate for process and thermal variations. This configuration includes determining parameters of the MZI, such as branch length and width, and the relative TOC of the elements (e.g., the upper cladding and the core). In some embodiments, the upper cladding element material to the core element material is selected to provide a TOC that counteracts their effects, thereby allowing process / temperature compensation for the element region so that there is no unwanted wavelength drift. In doing so, the output shown in the transmission spectrum (b) is provided by designing the MZI 102a-102d to operate in a non-thermal component, since a heater is not required. Similarly, a controller (not shown) for monitoring the heater is also not required. Referring now to Figure 2, an optical device for design and manufacture is illustrated in method 200. Method 200 is merely an example and is not intended to limit this disclosure to what is explicitly described in method 200. Additional steps may be provided before, during, and after method 200, and some described steps may be replaced, eliminated, or moved for additional embodiments of the method. For simplicity, not all steps are described in detail herein. Method 200 allows the design or adjustment of waveguide elements to provide dispersion of output wavelengths in a manufacturing-insensitive manner. Method 200 allows the design or adjustment of waveguide elements to provide dispersion of output wavelengths in non-thermal operation. Adjustment includes designing the waveguide, including selecting the upper cladding material, the core material, and defining the dimensions of the elements, including the core and the upper cladding. Method 200 begins with block 202, which determines the element configuration. In one embodiment, the element configuration is an MZI. Figure 3 is a schematic diagram of an embodiment of the MZI 300. In one embodiment, the MZI 300 may be one element of an optical device comprising multiple MZI elements. The MZI 300 has an input region 302 and an output region 304. In one embodiment, the MZI 300 has two unequal-length “branches,” labeled 306 and 308, where branch 308 is opposite to branch 306. That is, L1 of branch 306 is different from L2 of branch 308, where L1 and L2 are the linear optical lengths of their respective branches. In another embodiment, the MZI 300 has symmetrical, opposite branches. In one embodiment, a first waveguide defining the first branch 306 of the MZI 300 and a second waveguide defining the second branch 308 of the MZI 300 branch from the input region 302 and then recombine at the output region 304, thereby providing two paths or channels through which light can pass through the MZI 300. In some embodiments, the first waveguide branch 306 may be very close to or in direct contact with the second waveguide branch 308, such that the waveguides are optically coupled. The first branch 306 has a first optical length L1 and a first width W1. The second branch 308 has a second optical length L2 and a second width W2. The first branch 306 may include a waveguide having a core layer surrounded by a cladding, the cladding including an upper cladding and a lower cladding. The second branch 308 may include a waveguide having a core layer surrounded by a cladding, the cladding including an upper cladding and a lower cladding. In some embodiments, the composition of the layers (e.g., the upper cladding and / or the core layer) may differ between the second branch 308 and the first branch 306, such that there is a thermo-optical coefficient (TOC) difference between the branches discussed in block 204 below. For example, in one embodiment, a region, such as the first branch 306, is formed with a material that allows the TOC to be completely or partially canceled out (e.g., a positive TOC core material and a negative TOC upper cladding material). In one embodiment, the width W1 of the first branch 306 is different from the width W2 of the second branch 308. In another embodiment, W1 is greater than W2. The widths (W1, W2) and / or lengths (L1, L2) can be determined using the methods discussed below. Similarly, as described above, the MZI element includes a waveguide having a core element surrounded by a cladding layer, the cladding layer comprising a lower cladding layer and an upper cladding layer, both of which are disposed on a substrate. The n of the region of the MZI element (e.g., the region being a branch) i Depending on the configuration of the waveguide, the waveguide includes the material of the waveguide layer in the corresponding region. MZI 300 is represented by the resonance formula: Where λ0 is the center wavelength, m is the interference order, and n i and L i n represents the effective refractive index and length of the corresponding MZI branch (where i = 1 and 2). 1. For example, the effective refractive index of branch 306 is obtained from the waveguide core, upper cladding, and lower cladding of branch 306. n 2. For example, the effective refractive index of branch 308 is obtained from the waveguide core, upper cladding, and lower cladding of branch 308. Considering the wavelength shift Δλ, the resonance formula is expressed as: Where ΔX is the variation of waveguide parameters (e.g., thickness, width (W), temperature). Method 200 includes block 204 for determining compensation conditions. In some embodiments, compensation conditions include addressing both manufacturing insensitivity conditions and non-thermal operating conditions. Referring to block 202 and the example of MZI, the MZI structure includes two parameters to be selected for the design: the difference between the two branches (ΔL) and the effective refractive index of the layer (n). eff In some implementations, the width (W1, W2) and / or thickness (e.g., the thickness of the core). Compensation conditions select one or more of these parameters of the element, as well as other dimensional parameters, to provide manufacturing-insensitive conditions and non-thermal operating conditions. In one embodiment, n of the first region (e.g., the first branch) i n is different from the second region (e.g., the second branch). i In one embodiment, waveguides with silicon cores are provided in two different branches of the MZI, and lower cladding with similar composition (e.g., silicon dioxide) is provided in both branches. However, in some embodiments, including as discussed below, the upper cladding may differ between the first and second branches. In other words, the upper cladding of branch 306 differs from the upper cladding of branch 308. That is, due to the effective refractive index n 1, n 2. Depending on the top cladding, there are differences in structure and effective refractive index. In some embodiments, a difference in the thermo-optical coefficient (TOC) of the top cladding is provided between the two branches. Referring to the example of MZI 300, different TOCs can be provided between branches 306 and 308. In one embodiment, block 204 includes determining and selecting the material configuration of the first and second branches of the MZI. Different TOCs can be provided by using different cladding materials with different TOCs (e.g., one branch has a negative TOC material as the cladding, while a second branch has a larger TOC material as the cladding). Furthermore, or alternatively, different TOCs between regions can be provided by different waveguide core materials between branches 306 and 308. Other configurations exist for providing different TOCs between branches 306 and 308, such as providing different waveguide core materials between branches 306 and 308. In one embodiment, a negative TOC material is positioned as the cladding on one branch of the element (e.g., branch 306), and a larger TOC material is positioned as the cladding on the other branch. In one embodiment, Figure 4D illustrates the TOC difference between a waveguide based on a negative TOC material and one using another material such as silicon oxide. The compensation conditions for block 204 can be determined by the following compensation condition formula: Compensation Equation 1: Where dn / dX = m(X), and X can be the width, thickness, or temperature of the first region (branch 306) or the second region (branch 308). And where n... i n is region i (here, 1 (branch 306) or 2 (branch 308)). eff In some implementations, L 2 can be defined relative to m(X), where X is the width (W): Compensation Equation 2, where FSR is the free spectral range, n g,i W is the effective group refractive index of region i (here, 1 (branch 306) or 2 (branch 308)). i It is the width of region i (here, 1 (branch 306) or 2 (branch 308)). In the first step of block 204, L1 can be solved for manufacturing insensitive conditions. In one embodiment, L1 is solved as width. In this embodiment, the relationship between the configurations of region 1, branch 306 and region 2, branch 308 of the MZI 300 is determined. Specifically, the relationship between width W1, length L1 and width W2, length L2 can be determined. In one embodiment, the first step solves for the length L1 in branch 306, thereby providing a width-insensitive device. The L1 solution can be applied to: Figure 4A illustrates a graphical representation of the solution for length L1 with varying widths W1 and W2. Figure 4B illustrates a graphical representation of the solution for length L2 with varying widths w1 and w2. Each solution provided in step one of block 204 achieves the performance of a width-insensitive element. It is important to note that the formula immediately following above is provided by making the variation in the resonance formula of the element have a width variation close to zero: Where n g,1 and n g,2 These are the effective group refractive indices of branch 1 and branch 2, respectively. This leads to compensation equation 1. The free spectral range (FSR) is the shift in effective refractive index relative to wavelength. In one implementation, the FSR for MZI is provided as follows: From this representation of FSR, L1 can be replaced by compensation formula 1, making FSR equal to (=). Let dn / dX = m(X), where X can be the width, thickness, or temperature considering compensation conditions. In the implementation where X is the width (W), FSR equals (=) Solving L2 yields the compensation equation 2 above. The example solution above is provided for width (W), but other configurations are possible, including applying length and temperature as variables (X) and / or compensation parameters to be considered. In some implementations, the temperature factor is solved in a subsequent step of block 204. If the temperature factor is zero or close to zero, the component configuration is considered to be temperature insensitive. This is also known as allowing non-thermal operation. The temperature factor is solved as follows: Figure 4C illustrates solutions for variations in widths W1 and W2, with a temperature factor of zero or near zero. Figure 4D illustrates a device with a negative TOC as an upper cladding layer and another upper cladding layer (e.g., SiO2). 2) The graph of TOC sensitivity versus waveguide width. Therefore, in one stage, manufacturing insensitive conditions are determined. Manufacturing insensitive configurations can be multiple solutions, where multiple solutions involve various waveguide dimensions, such as determining the upper branch waveguide width and / or upper branch waveguide length. And in the second stage, temperature insensitive configurations are determined. In some embodiments, because the MZI configuration design provides that the effective refractive index change caused by the width variation of the MZI is offset, there is no effect on the optical phase. This cancellation is due to the engineering design of the element, for example, placing the negative TOC in a region (branch 306) and / or implementing the parameters (e.g., L1, W1) solved according to the above equation. In other words, n is provided. eff Solutions for width and length. Therefore, by providing local variations in the MZI design, such as modifications to the refractive index of the device region, an adjustment is made that allows for the manufacture and / or thermal insensitivity of the resulting device. In some embodiments, implementing the device and / or methods discussed herein provides a shift in spectral response of several picometers (pm). In some embodiments, temperature sensitivity can be reduced to less than about 1 pm / K. Method 200 then proceeds to block 206, fabricating elements of blocks 202 and 204. In one embodiment, this element is an MZI formed as part of a photonic integrated circuit (PIC). Block 206 is described below with reference to Figures 5A, 5B, and 5C, which illustrate partial cross-sectional views of an MZI 300' according to an embodiment of method 200. Figure 5A shows a top view of the MZI 300' relative to the waveguide core 314. Figures 5B and 5C are cross-sectional views corresponding to sections A-A' and B-B' in Figure 5A, respectively. Figures 5A, 5B, and 5C illustrate embodiments of the MZI 300'. The MZI 300' can be substantially similar to the MZI 300 described above with reference to Figure 3. The MZI 300' includes a substrate 310. In one embodiment, the substrate 310 may be a silicon (Si) substrate. In some other embodiments, the substrate 310 may include other semiconductor materials, such as germanium (Ge), silicon germanium (SiGe), or III-V semiconductor materials. Example III-V semiconductor materials may include gallium arsenide (GaAs), indium phosphide (InP), gallium phosphide (GaP), gallium nitride (GaN), gallium arsenide phosphide (GaAsP), aluminum indium arsenide (AlInAs), aluminum gallium arsenide (AlGaAs), gallium indium phosphide (GaInP), and indium gallium arsenide (InGaAs). In one embodiment, the substrate 310 is a silicon-on-insulator (SOI) substrate. The substrate 310 may include a plurality of n-type well regions and a plurality of p-type well regions. p-type well regions can be doped with p-type dopants (i.e., boron (B)). n-type well regions can be doped with n-type dopants (i.e., phosphorus (P) or arsenic (As)). A lower cladding layer 312 is formed above the substrate 310. In one embodiment, the lower cladding layer 312 is silicon dioxide (SiO2). 2). Other exemplary dielectrics include other suitable oxides, silicon nitrides, silicon carbide, low-k dielectric materials, and / or other suitable materials. The TOC of the lower cladding layer 312 is negligible compared to the TOC of the core 314 and / or the upper cladding layer 316, as will be explained later. In one embodiment, the lower cladding layer 312 is formed by chemical vapor deposition (CVD), low-pressure plasma-enhanced chemical vapor deposition (PECVD), thermal oxidation, and / or other suitable deposition processes. In one embodiment, the lower cladding layer 312 is a BOX layer formed in the silicon substrate 310. The lower cladding layer 312 located in the second branch 308 is designated as lower cladding layer 312b, and the lower cladding layer 312 located in the first branch 306 is designated as lower cladding layer 312t. Lower cladding layer 312b and lower cladding layer 312t can be made of the same material (e.g., SiO2). 2). In some embodiments, the lower cladding 312b and lower cladding 312t may be regions of a single continuous layer (e.g., formed in a single deposition step). In some embodiments, the lower cladding 312b laterally surrounds the waveguide core 314b in the region of the second branch 308. A waveguide core element (also referred to as a conductor) 314 is formed over the lower cladding 312. In one embodiment, the core 314 is silicon. In another embodiment, the core 314 is SU-8 photoresist. In some embodiments, the core 314 and the substrate 310 comprise the same material. The core 314 can be formed by suitable semiconductor processes, such as deposition, photolithography, and etching of the core material to pattern the core material. In some embodiments, a hard mask layer is used for patterning the core 314. The core 314 in the second branch 308 represents core layer 314b, and the core 314 in the first branch 306 represents core layer 314t. In some embodiments, core layer 314t has the same composition as core layer 314b. The core 314, including core layer 314b and core layer 314t, is formed simultaneously by deposition and patterning processes. In other embodiments (see FIG12A), core layer 314t may have a different composition than core layer 314b. Cores 314t and 314b may have different dimensional characteristics. In one embodiment, core 314t has a longer length than core 314b. L1 may be greater than L2. Core 314t may have a width of W1. In one embodiment, the width W1 may be between approximately 300 nm and approximately 1000 nm. In one embodiment, the width W1 is determined based on the compensation formula discussed in block 204 of reference method 200 above. Core 314b may have a width of W2. In one embodiment, the width W2 may be between approximately 300 nm and approximately 1000 nm. In one embodiment, the width W2 is smaller than the width W1. In one embodiment, the width W2 may be approximately 5-50% smaller than the width W1. The ratio of optical length L1 to optical length L2 can be between 1 and 35, i.e., 0 ≤ L1 / L2 ≤ 35. In another embodiment, the length L1 / L2 ranges between approximately 1.25 and 3. The optical lengths L1 and L2, and the ratio between them, can be determined by the compensation formula of block 204 discussed above. To complete the waveguide, an upper cladding 316 is formed on the core 314. The upper cladding 316t is formed above the core 314t in the first branch 306. The upper cladding 316b is formed above the core 314b in the second branch 308. In one embodiment, the upper cladding 316t and upper cladding 316b are made of different materials. For example, the upper cladding 316t and upper cladding 316b have different TOCs. In other embodiments, such as the example of FIG. 12A, the upper cladding 316b and upper cladding 316t may be the same. In one embodiment, the upper cladding 316b of the second branch 308 of the MZI 300' is made of the same material as the lower cladding 312b of the second branch 308. In a further embodiment, the upper cladding 316b is silicon dioxide. In one embodiment, the upper cladding 316b laterally surrounds and covers the core 314b. The upper cladding 316b may have a thickness T2 above the core 314b. In some embodiments, the thickness T2 of the upper cladding 316b is equal to the thickness T1 of the upper cladding 316b, as described below. In one embodiment, the upper cladding 316b has the same sign (e.g., positive) as the waveguide core 314 in which it resides. The upper cladding 316t disposed on the first branch 306 of MZI 300' has a TOC (e.g., negative TOC and positive TOC) with the opposite sign to the TOC of the core material 314t in that region. In one embodiment, the upper cladding 316t is a material with a negative TOC, while the core material 314t is a material with a positive TOC. For example, the upper cladding 316t can be a negative TOC material, and the core material 314t can be silicon. Thermal optimization of the element with a silicon core is provided by the upper cladding 316t with a negative TOC, which can counteract the positive TOC of the silicon core 314t. An exemplary negative TOC material (e.g., suitable for the upper cladding 316t material) is titanium dioxide (TiO2). 2) In the form of. For example, amorphous silicon TiO2 deposited by sputtering. 2. The material provides a negative TOC material. In one embodiment, the negative TOC material is amorphous silicon TiO2. 2, including TiO 2 in the forms of rutile, brookite, and anatase. In one embodiment, a negative TOC material (e.g., TiO2) 2) The refractive index is between approximately 2.1 and 2.5. In one embodiment, the negative TOC material (e.g., amorphous silicon TiO2) 2) The temperature sensitivity is approximately -1e 4 to -2e -4 dn / dT. In some embodiments, amorphous silicon TiO2 is provided by sputtering deposition. 2. It can also provide low optical loss for waveguides. In one embodiment, such as amorphous silicon TiO The negative TOC material of 2 is deposited via a sputtering process such as RF magnetron sputtering. In some embodiments, annealing can be performed after sputtering. The flow rate, including the presence of oxygen, can determine the amorphous silicon TiO2. Form 2 (e.g., existing TiO2) (Percentage of two phases). In one embodiment, the negative TOC material is amorphous silicon TiO2. 2, comprising at least 10% of a first form and at least 10% of a second form, wherein these forms are selected from rutile, brookite, and anatase forms. In one embodiment, the negative TOC material is produced by providing a dopant to the material (e.g., TiO2 as described above). 2. SiO Formed in (e.g., 2). Exemplary dopants include phosphorus, boron, and / or other suitable dopants. The upper cladding 316t has a thickness T1 extending above the core 314t. In one embodiment, the thickness T1 is approximately 300 nm or greater (e.g., the thickness above the core 314t is greater than approximately 300 nm). In other embodiments, the thickness T1 may be equal to the thickness of the core 314t measured in the same direction. For example, the top surface of the upper cladding 316t may be coplanar or flush with the top surface of the core 314t. The region of the branch 306 with the upper cladding 316t providing a TOC sign opposite to that of the core 314t is called the TOC compensation region, which is denoted as TOC compensation region 320 (Fig. 5A). TOC compensation region 320 includes an element region that applies a material combination that balances the TOC to provide effective compensation (all or part) for the refractive index change. In one embodiment, the temperature factor of MZI 300' is provided by the following formula (discussed above). In some implementations, MZI 300' exhibits approximately -1e -3 μm / K < Temperature factor < Approximately 1e -3 μm / K. Therefore, method 200 at block 206 includes two regions of forming apparatus, wherein at least one region includes a TOC compensation region. In one embodiment, a lower cladding layer, such as a lower cladding layer 312, is formed over substrate 310. Waveguide core elements 314 are formed over the lower cladding layer 312. In some embodiments, the waveguide core elements are formed by depositing core material and patterning the material according to the element design (e.g., W1, W2, L1, L2) of block 204. In one embodiment, an upper cladding layer 316 is then formed over the patterned core elements 314b, 314t. The upper cladding 316 can be formed by depositing a first material (e.g., one of 316t and 316b), patterning the material to remove it from a region of the device (e.g., removing 316t from branch 308 or removing 316b from TOC compensation region 320), and depositing and patterning a second upper cladding material (e.g., 316t formed in TOC compensation region 320 or 316b formed outside TOC compensation region). In other words, the upper cladding material, because it is two different materials in some embodiments, can be formed in two separate, consecutive steps. Method 200 can then continue manufacturing in block 208, including providing other components of the PIC, including interconnections with the MZI 300'. In one embodiment, the MZI 300' is one of a plurality of components forming the device, such as the DMX of FIG1 and / or other suitable configurations, as discussed below. Once manufacturing is complete, the component is adapted for operation by supplying light to input 302, allowing the light to pass through either the path provided by branch 306 or branch 308. Each path has different characteristics, thus providing light output of different phases at output 304. In an embodiment, the light reconverges at output 304. For example, in the embodiment illustrated as MZI 300” in FIG. 6, an optical coupler 602 is included in the element. MZI 300” is substantially similar to MZI 300' in FIG. 5A, 5B, and 5C, and further illustrates the optical coupling elements at the input and output of MZI 300”. In one embodiment, the optical coupler is a multimode interface (MMI) coupler, an MZI coupler, and / or other suitable element. In one embodiment, coupler 602 is a 3-dB coupler. The refractive index (n) in the fabricated device should be very close to the design value so that the waveguide has the desired spectral response. High refractive index contrast and small feature size make silicon photonic circuits (e.g., the exemplary MZI 300') sensitive to nanoscale variations in geometry, which can be caused by process variations and local pattern density in the mask layout. These variations affect the effective refractive index and group refractive index of the guided waveguide modes, thereby altering the phase delay between the two branches of the interferometric filter circuit and changing the filter response. Applying method 200 and the resulting device, such as MZI 300', can mitigate this by providing a configuration that is less sensitive to manufacturing conditions (e.g., deviations from design values) and thermal conditions. In particular, embodiments of the methods and devices discussed herein form MZIs that allow for the cancellation of effective refractive index variations from waveguide width variations, thus maintaining the same optical differences required from MZI input to output. Furthermore, the methods and devices not only eliminate effective refractive index variations from waveguide variations but also reduce temperature sensitivity. Turning now to Figures 7 through 12B, several embodiments of devices that can be designed and / or manufactured and / or practiced according to method 200 of Figure 2, illustrating the device features of the MZI 300 described above. Throughout this disclosure, similar reference numerals are used to denote similar features. Referring to Figures 7A, 7B, and 7C, device 702 is illustrated. Device 702 is a three-stage MZI; in other embodiments, any number of stages of MZI is possible. Device 702 includes a first input (input 1) and a second input (input 2) extending to optocoupler 602, and a first MZI 300'A, a second MZI 300'B, and a third MZI 300'C connected in series to provide signals to a first outlet (port 1) and a second outlet (port 2). The output wavelength of port 1 is provided by a first delayed optical path (as denoted by branch A for the corresponding MZI); the output wavelength of port 2 is provided by a second delayed optical path (as denoted by branch B for the corresponding MZI). In one embodiment, the output wavelength at port 1 is approximately 1270 nm, and the output wavelength at port 2 is approximately 1330 nm. In one embodiment, the filtering effect of device 702 provides a near-sine wave output from MZI 300'A. With additional stages (here, the two additional stages are denoted as MZI 300'B and MZI 300'C), the output can be filtered to more closely approximate a square wave signal. In another embodiment, device 702 includes a single input. The first MZI 300'A, the second MZI 300'B, and the third MZI 300'C each contain a first branch labeled A and a corresponding second branch labeled B. The branches can be substantially similar to those discussed above with reference to branches 306, 308 of the MZI 300'. Each MZI has an unbalanced structure because a corresponding TOC compensation area is provided on one of the two branches of each MZI. In the illustrated embodiment, a TOC compensation area 700A is provided on the first branch A of MZI 300'A, a second TOC compensation area 700B is provided on the second branch B of MZI 300'B, and a third TOC compensation area 700C is provided on the second branch B of MZI 300'C. In one embodiment, the TOC compensation region 700A is defined by a region of a device (e.g., a waveguide) having an upper cladding material whose TOC sign is opposite to that of the waveguide core in that region. For example, the TOC compensation region 700A may include a negative TOC material as an upper cladding above the waveguide core, substantially similar to the upper cladding 316t of the MZI 300' described above with reference to Figures 5A, 5B, and 5C. In one embodiment, in the TOC modification region 700A, sputtered deposited amorphous silicon TiO2 is used. 2. The upper cladding is disposed above the silicon waveguide core. Conversely, in branch B of MZI 300'A, an upper cladding substantially similar to the upper cladding 316b of MZI 300' described above with reference to Figures 5A, 5B, and 5C is provided. In one embodiment, branch B of MZI 300'A has silicon oxide disposed above the silicon waveguide core. In branch B, there is no compensating TOC material. In one embodiment, the TOC compensation region 700B is defined by a region having an upper cladding material with a TOC sign opposite to that of the waveguide core in that region. For example, the TOC compensation region 700B may include a negative TOC material as an upper cladding above the waveguide core, substantially similar to the upper cladding 316t of the MZI 300' described above with reference to Figures 5A, 5B, and 5C. In one embodiment, in the TOC modification region 700B, sputtered-deposited amorphous silicon TiO2 is used. The upper cladding material is disposed above the silicon waveguide core. In contrast, in branch A of MZI 300'B, an upper cladding 316b of MZI 300' is provided that is substantially similar to that of the upper cladding 316b of MZI 300' described above with reference to Figures 5A, 5B, and 5C. In one embodiment, branch A of MZI 300'B has silicon oxide disposed above the silicon waveguide core. That is, in branch A of MZI 300'B, there is no compensating TOC material. In one embodiment, the TOC compensation region 700C is defined by a region having an upper cladding layer made of a material whose TOC sign is opposite to that of the waveguide core in that region. For example, the TOC compensation region 700C may include a negative TOC material as the upper cladding layer above the waveguide core, substantially similar to the upper cladding layer 316t of the MZI 300' described above with reference to Figures 5A, 5B, and 5C. In one embodiment, in the TOC modification region 700C, sputtered deposited amorphous silicon TiO2 is used. 2. The upper cladding is disposed above the silicon waveguide core. In contrast, in branch A of MZI 300'C, a cladding substantially similar to the upper cladding 316b of MZI 300' described above with reference to Figures 5A, 5B, and 5C is provided. In one embodiment, branch A of MZI 300'C has silicon oxide disposed above the silicon waveguide core. That is, in branch A of MZI 300'C, there is no compensating TOC material. Figures 7B and 7C are cross-sectional views at X-X1 and Y-Y1 in Figure 7A, respectively. Specifically, in the TOC compensation region 700A, an upper cladding 316t (e.g., a negative TOC material) covers the core 314 (e.g., silicon), and an upper cladding 316b (e.g., a higher TOC material, such as silicon oxide) covers the core 314 (e.g., silicon) along the tangent X-X' in MZI 300'B and MZI 300'C. In the tangent Y-Y' on the opposite side of the MZI, both TOC compensation regions 700B and 700C include an upper cladding 316t (e.g., a negative TOC material) covering the core 314 (e.g., silicon), and in MZI 300'A, an upper cladding 316b (e.g., a higher TOC material, such as silicon oxide) covers the core 314 (e.g., silicon). As discussed in other embodiments herein (e.g., referring to FIG. 12A), the TOC compensation regions 700A, 700B, and 700C can alternatively be provided by modifying the core material of the upper cladding relative to the relative branches of MZI 300'A, MZI 300'B, and MZI 300'C, while maintaining the same composition of the upper cladding. In each embodiment, one branch of the MZI has a TOC compensation region. In other embodiments, TOC compensation regions 700A, 700B, and 700C may be configured on branch A of MZI 300'A, branch A of MZI 300'B, and branch A of MZI 300'C, respectively, while branch B of each MZI element does not include a TOC compensation region. In other embodiments, TOC compensation regions 700A, 700B, and 700C may be configured on branch B of MZI 300'A, branch B of MZI 300'B, and branch B of MZI 300'C, while branch A of each MZI element does not include a TOC compensation region. In some implementations of these embodiments, the TOC compensation region is provided as an upper cladding layer by a negative TOC material in a single continuous layer extending across the element. Other configurations of the TOC compensation regions implemented asymmetrically with respect to the two branches of a single MZI device are possible. Referring to FIG8, an apparatus 800 comprising a plurality of MZIs connected in series is illustrated. The apparatus 800 includes a plurality of MZIs 300', which may be substantially similar to those discussed above with reference to FIGS. 5A, 5B, and 5C. Each MZI 300' in FIG8 is illustrated as including a TOC compensation region 802. The TOC compensation region 802 may be substantially similar to the TOC compensation regions 700A, 700B, 700C of FIG7 and / or the compensation region 320 of FIGS. 5A, 5B, and 5C. FIG8 illustrates exemplary relative length annotations for each MZI 300'. Note that each length is adjustable and can be selected according to the compensation method 200 discussed above. Note that each width is adjustable and can be selected according to the compensation method 200 discussed above. In one embodiment, one or more negative TOCs are omitted as an upper cladding layer. The illustrated embodiment includes an optical coupler 602 having a first input and a second input. In other embodiments, the optical coupler 602 includes a single input. The optical coupler 602 may be an MMI coupler, an MZI coupler, and / or other suitable elements. Each output port outputs a different wavelength of light. For example, in one embodiment, port 1 outputs a first wavelength, such as approximately 1270 nm. In one embodiment, port 2 outputs a second wavelength, such as approximately 1310 nm. In one embodiment, port 3 outputs a third wavelength, such as approximately 1290 nm. In one embodiment, port 4 outputs a fourth wavelength, such as approximately 1330 nm. Referring now to Figures 9A and 9B, another embodiment of the MZI, shown as MZI 900, is illustrated. Except that the TOC compensation region of the MZI 900 (e.g., including a negative TOC material as the upper cladding 316t) is limited to only one leg of the first branch 306, the MZI 900 can be substantially similar to the MZI 300' described above with reference to Figures 5A, 5B, and 5C. This is illustrated in the TOC compensation region 902 of the MZI 900. The TOC compensation region 902 can be substantially similar to the TOC compensation region 320. In one embodiment, the waveguide includes a core 314 providing a first linear leg and a second linear leg to provide the first branch 306, and the upper cladding on one linear leg differs from that on the second linear leg. For example, the upper cladding on one linear leg may be a material with a different TOC sign (e.g., a negative TOC material), while the upper cladding on the other leg has a larger TOC (e.g., SiO2). 2). Figure 9B illustrates a first upper cladding layer 316t, which may be a negative TOC material, and a second upper cladding layer 316t', which may be a higher TOC material such as silicon oxide. In one embodiment, the negative TOC material comprises sputtered deposited amorphous silicon TiO2. 2, for example, as discussed above with reference to 316t in Figures 5A, 5B, and 5C. In another embodiment, the refractive index is between about 2 and about 2.5. In a further embodiment, the TOC is about -1e. -4 Approximately -5e -4 Between / K. In one embodiment, the TOC compensation region 902 has a length L1 / 2. In one embodiment, the TOC compensation region 902 has a length between approximately 0.5*L1 / 2 and approximately 1.5*L1 / 2. In one embodiment, the TOC compensation region 902 has a width greater than W1. In one embodiment, the width of the negative TOC material is approximately 0.5*W1 to 2*W1. In one embodiment, the thickness T3 of the upper cladding material 316 is between approximately 10 nm and approximately 1000 nm. In one embodiment, a negative TOC material is formed by providing a dopant to the TOC material to reduce the refractive index change. Exemplary dopant includes phosphorus, boron, and / or other suitable dopant. In other words, in some embodiments, the TOC compensation region 902 is defined by a doped region of the upper cladding material located above branch 306. This also applies to other devices in this disclosure. Referring now to FIG. 10, an embodiment of the MZI 1000 is illustrated. The MZI 1000 element is substantially similar to the MZI 300' described above with reference to FIGS. 5A, 5B, and 5C and / or substantially similar to the MZI 900 described above with reference to FIGS. 9A and 9B. The embodiment of the MZI 1000 has a branch 306' configured with a core 314, which is configured as a “slot” MZI. The slot is configured within the core 314 in the linear leg of the branch 306' to provide a gap G. In one embodiment, in a top view, a width W1' extends between one edge of the core 314 and the other edge of the core 314. The width W1' can be between approximately 100 nm and approximately 300 nm. In one embodiment, the gap G has a horizontal dimension between approximately 50 nm and approximately 150 nm. In one embodiment, a TOC compensation region 902 is placed on one leg of the branch 306'. In other embodiments, the TOC compensation region may extend beyond the two legs of branch 306, as shown, for example, with respect to MZI 300' in Figures 5A, 5B, and 5C. Referring now to FIG11, an embodiment of the MZI 1100 is illustrated. The MZI element 1100 can be substantially similar to the MZI 300' discussed above with reference to FIGS. 5A, 5B, and 5C. The difference in the embodiment of FIG11 is that the waveguide of the MZI element 1100 has a subwavelength grating (SWG) configuration. In other words, the core 314 of the first branch 306 and / or the second branch 308 of the MZI element 1100 is configured as an SWG 314'. In one embodiment, a TOC compensation region 320 is provided in one branch, such as branch 306, which provides an upper cladding 316t formed over the core 314' with the SWG structure. The upper cladding 316t can be substantially similar to that discussed above. That is, the upper cladding 316t over the SWG core 314' can be a negative TOC material, such as sputtered amorphous silicon TiO2. 2. The SWG core 314' is silicon. In one embodiment, the MZI 1100 has a second branch, such as branch 308 opposite to the first branch 306, wherein an upper cladding 316b is formed in the SWG structure. The upper cladding 316b can be substantially similar to that discussed above. That is, the upper cladding 316b above the SWG core 314' in the second branch 308 can be, for example, SiO2. 2. Materials. As described above, the configuration of the MZI element 1100 can be determined by method 200. In the SWG waveguide configuration, the effective refractive index n of the equivalent linear waveguide is... effThe refractive index is determined by the spatial average of the waveguide core 314' (e.g., Si) and the corresponding cladding materials 312, 316. Compared to other configurations, the SWG configuration can be applied to waveguides to reduce propagation losses. The MZI 1000 including the SWG core 314' has a first branch and a second branch, the first branch having a TOC compensation region and including the SWG core 314', and the second branch not having a TOC compensation region and including the SWG core 314'. Referring now to Figures 12A and 12B, an embodiment of an MZI element, designated MZI 300”', is illustrated. The MZI element 300”' can be substantially similar to the MZI 300” discussed above with reference to Figures 5A, 5B, and 5C. The MZI element 300”' similarly includes a first branch 306 (the cross-section shown in Figure 12A) and a second branch 308 opposite the first branch 306 (the cross-section shown in Figure 12B); that is, Figure 12A shows the cross-section corresponding to A–A’ in Figure 5A, while Figure 12B shows the cross-section corresponding to B–B’ in Figure 5A. Similar to what has been discussed above with reference to Figures 5A, 5B, and 5C, the MZI element 300”' includes a substrate 310 and a lower cladding layer 312. However, the MZI element 300”' includes an upper cladding 316 having the same composition in the first branch 306 and the second branch 308. The TOC compensation region 320 is provided in the MZI 300”' by waveguide core layers with different material compositions between the two branches 306, 308 of the MZI 300”'. In one embodiment, core 314t' provides the core layer in the first branch 306 and core 314b provides the core layer in the second branch 308. Core 314t' is a first material, and core 314b is a second material different from the first material. In one embodiment, the material of core 314t' is a negative TOC material. In a further embodiment, the material of core 314b is a material with a higher TOC. In the MZI 300”' embodiment, the lower cladding 312 is silicon oxide and the upper cladding 316 is also silicon oxide. In one embodiment, the waveguide core 314b at branch 308 is silicon. In some embodiments, the waveguide core 314b is in an SWG configuration. In one embodiment, the waveguide core 314t' at branch 306 is a negative TOC material. In a further embodiment, the waveguide core 314t' is sputtered-deposited amorphous silicon TiO2. 2. The negative TOC material of the waveguide core 314t' can be substantially similar to that discussed above regarding the negative TOC material used as the upper cladding. In one embodiment, the formation of the waveguide core 314t' as a negative TOC material reduces the thermal effects of the device compared to using a higher TOC material such as silicon. While not intended to be limiting, one or more embodiments of this disclosure offer numerous benefits to optical communication systems. In the field of optical communication systems, exemplary optical structures provide wavelength filtering with a high quality factor. The embodiments described herein are merely exemplary, and other structures may also benefit from aspects of this disclosure. That is, various devices, including the MZI and devices described above, can offset the effective refractive index variation of waveguide width variations on the MZI while maintaining the same optical phase difference. In one example aspect, this disclosure relates to an optical device. The optical device includes a first optical path comprising a first waveguide core and a first cladding adjacent to the first waveguide core; and a second optical path comprising a second waveguide core and a second cladding adjacent to the second waveguide core. The thermo-optical coefficient (TOC) of the first waveguide core has the same sign as the TOC of the first cladding, while the TOC of the second waveguide core has a different sign than the TOC of the second cladding. In a further embodiment, the TOC of the second waveguide core cladding is positive, and the TOC of the second cladding is negative. In one embodiment, the TOC of the first waveguide core is positive, and the TOC of the first cladding is positive. In one embodiment, the second cladding is disposed above the second waveguide core, and the second cladding comprises a negative thermo-optical coefficient (TOC) material. In some embodiments, the negative TOC material is amorphous titanium dioxide (TiO2). 2). In one embodiment, the first cladding is disposed above the first waveguide core, and the TOC of both the first cladding and the first waveguide core are positive. In one embodiment of the optical device, a second cladding layer is disposed above a second waveguide core, and the second waveguide core comprises a material with a negative thermo-optical coefficient (TOC). In some embodiments, the first waveguide core is silicon. In the optical device, a first optical path may be a first branch of a Mach-Zehnder interferometer (MZI), and a second optical path may be a second branch of the MZI, which may be opposite to the first branch. In another example, this disclosure relates to an optical device. The optical device includes a first optical path and a second optical path. The first optical path includes a first waveguide core of a first material and a first cladding of a second material adjacent to the first waveguide core. The second optical path includes a second waveguide core of the first material and a second cladding of a third material. The second cladding may be adjacent to the second waveguide core. The second and third materials are different (e.g., in composition). For example, the third material may be amorphous titanium dioxide (TiO₂). 2), while the second material is another dielectric. In some embodiments, the second material is silicon dioxide. Amorphous silicon TiO₂ 2 can be a negative thermo-optical coefficient (TOC) material. In one embodiment, the second material is disposed below the third material and the second waveguide core in the second optical path. For example, the second material can be disposed below the first waveguide core in the first optical path. In one embodiment, the first material of the example optical device is silicon. A first cladding layer may be disposed above a first waveguide core, and a second cladding layer may be disposed above a second waveguide core. In some embodiments, a first optical path is a first branch of a Mach-Zehnder interferometer (MZI), and a second optical path is a second branch of the MZI, opposite to the first branch. The first branch of the MZI may be longer than the second branch. In yet another example embodiment, the optical device includes an input region, an output region, and a Mach-Zehnder interferometer (MZI) between the input and output regions. The MZI includes a first branch and a second branch. The first branch has a first waveguide including a lower cladding, a core layer, and an upper cladding. The second branch has a second waveguide including a lower cladding, a core layer, and an upper cladding. The upper cladding of the first branch includes a first material, and the upper cladding of the second branch includes a second material different from the first material. In some implementations, the first material is silicon oxide. And in one embodiment, the second material is titanium oxide. In one embodiment, the second material has a negative TOC while the first material has a positive TOC. In some embodiments, a second material is disposed above a first leg of the first branch, and a first material is disposed above a second leg of the first branch. In one embodiment, the length (e.g., optical length) of the second branch is greater than the length (e.g., optical length) of the first branch. Furthermore, the width of the second branch may be greater than the width of the first branch. In a further embodiment, the second branch comprises a negative TOC material. In another, more extensive embodiment, a method is provided. The method includes depositing a lower cladding layer on a substrate and providing a waveguide core layer on the lower cladding layer. A first upper cladding layer is deposited on a first region of the waveguide core layer. After depositing the first upper cladding layer, a second upper cladding layer is deposited on a second region of the waveguide core layer. The second upper cladding layer is different from the first upper cladding layer. In a further embodiment of the method, at least one of depositing the first upper cladding layer and depositing the second upper cladding layer includes a sputtering process. In some embodiments, the sputtering process can form amorphous silicon dioxide. The features of several embodiments have been summarized above to enable those skilled in the art to better understand aspects of this disclosure. Those skilled in the art should understand that they can readily use this disclosure as a basis for designing or modifying other processes and structures to achieve the same purposes and / or advantages as the embodiments described herein. Those skilled in the art should also recognize that such equivalent structures do not depart from the spirit and scope of this disclosure, and that they can make various changes, substitutions, and modifications to them without departing from the spirit and scope of this disclosure. 100: Demultiplexer (DMX) / Circuit / Device; 102a, 102b, 102c, 102d, 300, 300', 300”, 900, 1000: Mach-Zehnder Interferometer (MZI); 104: Input; 106: Output Area; 200: Method; 202, 204, 206, 208: Block; 300'A: First MZI / MZI 300'; B: Second MZI / MZI 300'; C: Third MZI / MZI 300”', 1100: MZI / MZI element; 302: Input area / Input; 304: Output area / Output; 306: Branch / First branch / First waveguide branch; 306': Branch; 308: Branch / Second branch / Second waveguide branch; 310: Substrate; 312: Lower cladding / Clamping material; 312b, 312t: Lower cladding; 314: Waveguide core / Core / Waveguide core element; 314': Subwavelength grating (SWG) / Core / SWG core / Waveguide core; 314b: Waveguide core / Core layer / Core / Core element; 314t: Waveguide core / Core layer / Core / Core material / Silicon core. Core / Core Component 316: Upper Cladding / Upper Cladding Material / Cladding Material 316b, 316t: Upper Cladding 320, 700A, 700B, 700C, 802, 902: TOC Compensation Region 602: Optical Coupler / Coupler 702, 800: Device A: Branch / First Branch B: Branch / Second Branch Ch1, Ch2, Ch3, Ch4: Channel / Port G: Gap L1: Linear Optical Length / First Optical Length / Length L2: Linear Optical Length / Second Optical Length / Length T1, T2, T3: Thickness W1: First Width / Width W2: Second Width / Width This disclosure is best understood through the following detailed description when read in conjunction with the accompanying drawings. It should be emphasized that, in accordance with industry standard practice, various features are not drawn to scale and are used for illustrative purposes only unless explicitly disclosed. In fact, the dimensions of various features may be increased or decreased arbitrarily for clarity of discussion. Figure 1 illustrates a diagram of a photonic circuit providing a demultiplexer device according to various embodiments of this disclosure. Figure 2 illustrates a method of manufacturing a photonic device according to an embodiment of this disclosure. Figure 3 illustrates a diagram of a Mach-Zehnder interferometer (MZI) according to an embodiment of this disclosure. Figures 4A, 4B, 4C, and 4D show illustrations of varying parameters of the MZI of Figure 3 according to an embodiment of this disclosure. Figure 5A shows a top view of an MZI with a thermo-optical coefficient (TOC) compensation region according to an embodiment of this disclosure; Figures 5B and 5C show corresponding cross-sectional views of an MZI with a TOC compensation region. Figure 7A shows a top view of another embodiment of a photonic device including a multi-stage MZI; Figures 7B and 7C show corresponding cross-sectional views, each according to an embodiment of this disclosure. Figure 8 illustrates a top view of another embodiment of a photonic device including a series-connected multi-stage MZI according to an embodiment of the present disclosure. Figure 9A shows a top view of another embodiment of an MZI with a TOC compensation region according to an embodiment of the present disclosure, and Figure 9B shows a corresponding cross-sectional view of the MZI. Figure 10A shows a top view of another embodiment of an MZI with a TOC compensation region according to an embodiment of the present disclosure, and Figure 10B illustrates a corresponding cross-sectional view of the MZI. Figure 11 shows a perspective view of an MZI with a subwavelength grating structure according to an embodiment of the present disclosure. Figures 12A and 12B show cross-sectional views of a first branch and a second branch of an MZI according to an embodiment of the present disclosure, respectively. 300: Mach-Zehnder Interferometer (MZI) 302: Input Area / Input 304: Output Area / Output 306: Branch / First Branch / First Waveguide Branch 308: Branch / Second Branch / Second Waveguide Branch L1: Linear optical length / First optical length / Length L2: Linear optical length / Second optical length / Length W1: First width / width W2: Second width / width

Claims

1. An optical device, comprising: The first optical path includes a first waveguide core of a first material and a first cladding of a second material adjacent to the first waveguide core; The second optical path includes a second waveguide core of the first material and a second cladding of a third material, the second cladding being adjacent to the second waveguide core. The second material and the third material are different, the third material being amorphous titanium dioxide (TiO2) and the second material being another dielectric. The amorphous titanium dioxide includes at least 10% of a first form and at least 10% of a second form, the first form and the second form being selected from rutile, brookite and anatase forms.

2. The optical device as claimed in claim 1, wherein the second material is silicon dioxide, the first material is silicon, and the amorphous titanium dioxide is a negative thermo-optical coefficient (TOC) material.

3. The optical device as claimed in claim 1, wherein the second material is disposed below the third material and the second waveguide core in the second optical path, and the second material is disposed below the first waveguide core in the first optical path.

4. The optical device as claimed in claim 1, wherein the first cladding is disposed above the first waveguide core and the second cladding is disposed above the second waveguide core.

5. The optical device as claimed in claim 1, wherein the first optical path is a first branch of a Mach-Zehnder interferometer (MZI), and the second optical path is a second branch of the Mach-Zehnder interferometer, the second branch being opposite to the first branch.

6. An optical device, comprising: Input area and output area; A Mach-Zehnder interferometer (MZI) between the input region and the output region, wherein the Mach-Zehnder interferometer includes: a first branch having a first waveguide, the first waveguide including a lower cladding layer, a core layer and an upper cladding layer, wherein the upper cladding layer includes a first material; And a second branch having a second waveguide, the second waveguide comprising a lower cladding, a core layer and an upper cladding, wherein the upper cladding comprises a second material different from the first material, and the second material is amorphous titanium dioxide, wherein the amorphous titanium dioxide comprises at least 10% of a first form and at least 10% of a second form, the first form and the second form being selected from rutile, brookite and anatase forms.

7. The optical device as claimed in claim 6, wherein the first material is silicon oxide.

8. The optical device as claimed in claim 6, wherein the second material has a negative thermo-optic coefficient and the first material has a positive thermo-optic coefficient.

9. A method for manufacturing an optical device, comprising: Deposit a cladding layer on the substrate; A waveguide core layer is provided on the lower cladding layer; A first upper cladding layer is deposited on a first region of the waveguide core layer; And after depositing the first upper cladding, a second upper cladding is deposited on the second region of the waveguide core layer, wherein the second upper cladding is different from the first upper cladding, and the material of the second upper cladding includes amorphous titanium dioxide, wherein the amorphous titanium dioxide includes at least 10% of a first form and at least 10% of a second form, the first form and the second form being selected from rutile, brookite and anatase forms.

10. A method of manufacturing an optical device as claimed in claim 9, wherein depositing at least one of the first upper cladding layer and depositing the second upper cladding layer comprises a sputtering process.

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