CN114556166A - CMOS color image sensor with metamaterial color separation - Google Patents
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Abstract
Methods of constructing multifunctional scattering structures while complying with the stringent requirements imposed by the manufacturing process are described. The described methods and apparatus perform an objective function based on etching away a network of wires embedded in a 3D structure to form voids. Optimization algorithms for designing a binarized device that meets manufacturing requirements are also disclosed.
Description
Cross Reference to Related Applications
This application relates to U.S. patent No. 16/656,156, entitled "Color And Multi-Spectral Image Sensor Based On 3D Engineered Material", filed 2019, month 10 And day 17, the contents of which are incorporated herein by reference in their entirety.
Statement of government assistance
The invention is completed under government support granted by DARPA under the number HR 0011-17-2-0035. The government has certain rights in the invention.
Technical Field
The present disclosure relates to image sensors, and more particularly, to metamaterial spectrographs (metamaterials) fabricated using CMOS fabrication techniques.
Background
Optical systems are typically designed by modular combinations of components to achieve complex functions. For example, the lens and diffractive optics may be combined for hyperspectral imaging. This approach is intuitive and flexible, and can access a wide range of functions from a limited set of elements. However, the overall size and weight of the optical system may limit its range of applications. Recent advances in nano-fabrication may alleviate this limitation by replacing the bulky elements with planar arrays of resonant nanostructures of sub-wavelength thickness. By engineering the scattering of individual elements in the array, these devices can reproduce the versatility of complex optical systems in a single element. However, efforts to combine multiple meta surfaces (metassurface) to achieve more complex functions have been hampered by a reduction in scattering efficiency, which is inversely proportional to the number of tasks performed simultaneously.
The inherent tradeoff between versatility and efficiency in these systems is due to the limited degree of freedom, which is proportional to the volume of the device and the maximum refractive index contrast. In particular, this limits the range of independent functions that can be achieved with any ultra-thin system, such as sorting light by frequency, polarization, and angle of incidence (sort). In contrast, three-dimensional scattering elements with a thickness greater than one wavelength typically encode many simultaneous functions, but are so far inefficient due to weak scattering and low index contrast.
Historically, optical designs have been modular, which provides an intuitive way to build and reconfigure optical settings. With advances in nano-fabrication technology, it has become possible to fabricate structures with sub-wavelength feature sizes, which enables multifunctional optical elements to incorporate more complex set-up functions. Examples include a toroidal lens that can separate different polarization and spectral bands. However, the degree of performance and functionality that can be achieved with super-surfaces and other planar structures is inherently limited by the number of optical modes that can be controlled.
Constructing the refractive index with high contrast on a sub-wavelength scale provides a wide optical design space that can be used to display multifunctional optical elements. To date, this has been primarily used for two-dimensional structures, or meta-curvatures. However, their performance is limited by the available optical degrees of freedom.
To highlight the benefits of the teachings of the present disclosure in the following sections, consider the example of an image sensor here. Currently, most sensors use absorption filters to record color. Fig. 1A shows a prior art image sensor where every fourth adjacent pixel has an absorptive color filter on top, two for green, one for blue and one for red. A problem with such image sensors is that the efficiency is limited to around 30% because most of the light is absorbed. Color image sensors are ubiquitous in cell phones, cameras, and various instruments. The color is detected by a simple absorption filter placed directly on top of each pixel. The absorptive nature of the filter means that light in excess of 2/3 is actually absorbed and lost, i.e., red and blue light incident on a green pixel, for example, is absorbed and only green light passes through.
Disclosure of Invention
Complex three-dimensional (3D) scattering structures are disclosed in this application that allow for separation of colors on a bayer pattern, for example, with greater efficiency. Designs that provide polarization information are also described.
The cost-effectiveness and large-scale manufacturing of such structures present significant challenges to the design process. The goal is to achieve optimal performance given the inherent limitations associated with large scale CMOS fabrication processes.
The disclosed method and device solve the described challenges and provide a practical solution to the above-mentioned problems.
In particular, the disclosed methods and apparatus teach various steps for designing 3D scattering structures using scalable manufacturing processes. Currently, the largest scale manufacturing capable of handling dimensions smaller than 100 nanometers is the CMOS foundry manufacturing process. In CMOS processes, a very complex network of copper wires can be fabricated, stacked on top of each other and embedded in silicon dioxide. An example of such a network is shown in fig. 1B, where light and dark grey represent metal and silica, respectively. However, according to embodiments of the present disclosure, the wires may be etched away using a liquid etchant, such that the final 3D scattering structure consists of voids in SiO 2. According to another embodiment of the present disclosure, the 3D scattering structures may be left as voids in SiO2, or the voids may be filled with a higher refractive index material such as TiO2 using an atomic layer deposition process.
According to a first aspect of the present disclosure, a method for constructing a three-dimensional (3D) scattering structure is disclosed, comprising forming a dielectric structure comprising a first dielectric and a network of metal wires, wherein the position, shape and size of the metal wires are selected according to one or more target functions; and etching away the metal wire from the dielectric structure, thereby forming a structure comprising a space filled with the first dielectric and voids, wherein the voids are located, shaped and sized according to one or more objective functions, wherein the 3D light scattering structure so formed is configured to receive electromagnetic waves and scatter the electromagnetic waves according to the one or more objective functions.
Other aspects of the disclosure are provided in the description, drawings, and claims of the present application.
Drawings
Fig. 1A shows a prior art image sensor.
Fig. 1B shows a prior art structure of wires that can be implemented using CMOS foundry fabrication techniques, with feature sizes below 100 nanometers.
Fig. 2A-2A' illustrate an exemplary three-dimensional (3D) scattering structure according to an embodiment of the present disclosure.
Fig. 2B-2C illustrate the wavelength separation function of the embodiment of fig. 2A and 2A'.
Fig. 3A-3C illustrate an exemplary three-dimensional (3D) scattering structure according to another embodiment of the present disclosure.
FIG. 3D illustrates various steps of an exemplary optimization algorithm in accordance with an embodiment of the present disclosure.
Fig. 4A illustrates an exemplary 3D structure made of a dielectric and including a wire network according to an embodiment of the disclosure.
Fig. 4B illustrates an exemplary process of etching away a wire mesh within a 3D structure according to another embodiment of the disclosure.
Fig. 5 shows an exemplary flow chart illustrating various steps of designing a 3D scattering structure according to the teachings of the present disclosure.
Fig. 6 shows an exemplary graph illustrating the refractive index profile in a horizontal position.
Figures 7A-7C show graphs representing the performance of a 3D scattering structure implemented in accordance with the teachings of the present disclosure.
Detailed Description
Fig. 2A shows an image sensor (200) according to an embodiment of the disclosure. The image sensor (200) comprises a three-dimensional (3D) scattering structure (201) acting as a spectral separator. The 3D scattering structure (201) includes a plurality of dielectric pillars (205) formed to scatter light in a predetermined pattern. Incident light (202) that passes through the 3D scattering structure (201) is scattered off by the dielectric pillars. By arranging the dielectric pillars (205) according to one or more target functions, the scattering pattern is tailored to perform the desired function. As an example, the 3D scattering structure (201) may be designed as a beam splitter to simultaneously sort and focus the incident light (202) into any number of wavelengths (λ)1,…,λn) Each of which is directed to a single pixel located in a focal plane (203) below the 3D scattering structure (201), as shown in fig. 2A. According to embodiments of the present disclosure, the 3D scattering structures (201) may be porous polymer cubes or clusters of dielectric or semiconductor (e.g., Si) particles embedded in a SiO2 matrix. According to further embodiments of the present disclosure, the 3D scattering structure (201) may be a porous polymer cube or a cluster of high refractive index particles embedded in a low refractive index matrix.
Those skilled in the art will appreciate that the image sensor (200) of fig. 2A does not operate based on absorption as compared to the prior art image sensor (100) of fig. 1A, and therefore, it provides a significant improvement in efficiency as compared to prior solutions. This will be quantified later using an exemplary embodiment of the present teachings. As described in more detail throughout the disclosure, the disclosed apparatus and methods provide the following additional benefits over existing solutions:
the 3D scattering structure (201) of fig. 2A can be manufactured by known and scalable photolithography processes.
The 3D scattering structure (201) of fig. 2A can be designed to act as a spectral separator for any spectral band (e.g., infrared, mid-infrared, etc.). In other words, in addition to hyperspectral imaging, thermal imaging is another potential application of the disclosed teachings.
The spectral splitting function may be combined with other desired functions such as polarization splitting.
Embodiments according to the present disclosure may also be designed to perform optical image processing, such as Gabor filtering for edge detection.
Fig. 2A 'shows an image sensor (200') according to an embodiment of the present disclosure, comprising an exemplary three-dimensional (3D) scattering structure (21) acting as a spectral filter. Incident light (22) entering from above is scattered while passing through the 3D scattering structure (21) and classified in a focal plane (23) consisting of four sub-pixels, shown as red, blue, green (x-polarization) and green (y-polarization). Also shown in fig. 2A', the red (600 nm-700 nm) and blue (400 nm-500 nm) spectral bands are sorted into opposite quadrants. In addition, the green (500 nm-600 nm) spectral bands are further separated according to linear polarization. The red and blue quadrants may be polarization independent.
According to an embodiment of the present disclosure, a 3D scattering structure (21) may be designed using an adjoint variable method (adjoint variable method) that generates a structure that optimizes a specified objective function. As an example, and referring to fig. 2A', the objective function may be selected based on the focusing efficiency of the incident light focused to one of the four target regions, depending on frequency and polarization. Starting from the empty volume (empty volume), a full-wave finite-difference time-domain (FDTD) simulation is performed to calculate the sensitivity of the figure of merit to the refractive index perturbations. The specified scattering structures are iteratively formed and updated. In other words, the optimal design is generated by iterative updates to the initial geometry, each step improving performance. The sensitivity can be calculated by only two simulations, allowing efficient optimization of the 3D device with modest resources. The sensitivity of multiple incident wavelengths in the visible spectrum can be calculated, assigning each spectral band to a different quadrant, red (600 nm-700 nm), green (500 nm-600 nm), and blue (400 nm-500 nm). The refractive index of the device can be updated using the spectrally averaged sensitivity.
Fig. 2B-2C show simulated intensities of incident light within the 3D scattering structure (21) of fig. 2A'. Intensity was analyzed along a diagonal cross-section intersecting the red and blue quadrants of fig. 2A. Each wavelength undergoes multiple scattering before being focused on its respective target region. Fig. 2C shows the intensity distribution of incident light in a diagonal cross-section through a green pixel for two orthogonal input polarizations. In both cases, a plane wave (λ ═ 550nm) incident from above is preferentially routed to the pixel corresponding to its polarization. At the same time, both polarizations are assigned the same region for the red and blue spectral bands, maintaining mirror symmetry of the objective function.
According to an embodiment of the present disclosure, the 3D scattering structure (21) of fig. 2A' classifies red, green, and blue light with efficiencies of 84%, 60%, and 87%, respectively. Throughout this disclosure, efficiency is defined as the average over the entire spectrum of the portion of the total power incident on the device that reaches the target quadrant for which the device is designed for the visible spectrum of the embodiment of fig. 2A'.
Referring to fig. 2A and 2A', those skilled in the art will appreciate that the disclosed concept provides considerable flexibility in defining the target scattering function, with independent control of any incident polarization, angle, or frequency. However, complex three-dimensional structures present significant challenges to fabrication. Large scale implementation of these devices in visible wavelength image sensors would require high manufacturing yields with resolutions below 100 nanometers. This can be achieved by multilayer lithography, where three-dimensional devices are constructed by repeated material deposition and patterning. Here, each layer consists of a series of patterned mesas (mesas) composed of high index dielectrics. The interstitial spaces are filled with a low index dielectric to form a planar surface of the substrate for subsequent layers.
To further clarify the layered manufacturing method discussed above, reference is made to fig. 3A and 3C, which show the layered design of the 3D scattering structure (31) of fig. 3C. In other words, the 3D scattering structure (31) of fig. 3C may be constructed by stacking the multiple layers (301, …, 305) of fig. 3A on top of each other. The fabrication process may be CMOS compatible, where the fabrication constraints may be directly integrated with the design algorithm. Each layer (301, …, 305) can be produced using photolithography. The 3D scattering structure (31) may be made of TiO2 and SiO2, which are transparent at visible frequencies. These layers (301, …, 305) may be 2 μm by 2 μm layers, each 400nm high. Those skilled in the art will appreciate that these are exemplary dimensions for descriptive purposes and that embodiments in accordance with the present disclosure are also contemplated and have dimensions and numbers of layers other than those described above. As shown in fig. 3B, each layer may include a set of irregular TiO2 mesas surrounded by SiO 2. Referring to fig. 3B, the photolithography process may begin by growing a thin layer of dielectric (e.g., TiO2) on top of a substrate (e.g., SiO 2). A pattern is transferred onto the layer by photolithography and the unprotected material is etched away to produce a two-dimensional dielectric structure. Finally, the surface is coated (deposited) with a low index dielectric and mechanically polished (planarized). By repeating the same process for each layer and stacking the layers, the desired 3D structure is produced. As described above, such a photolithographic process provides flexibility in material design and is compatible with industry standard CMOS fabrication processes.
Optimization algorithm
Gradient descent
Referring back to fig. 2A' -3C, as previously described, a three-dimensional dielectric junction optimized to perform a targeted optical scattering function is designed in accordance with the teachings of the present disclosureAnd (5) forming. In the case of the exemplary embodiments shown in fig. 2A' -3C, such an objective scattering function involves focusing the incident plane wave to different positions depending on frequency and polarization. Exemplary three-dimensional (3D) scattering structures (21, 31) are designed from spatially dependent refractive index profiles within a cubic design region
To be defined. This represents a wide design space capable of expressing a variety of complex optical multifunctionalities. However, determining the optimal refractive index profile for a given objective function remains a challenging inverse design problem, especially for strongly scattering devices.
To overcome this challenge, an iterative approach guided by gradient descent may be implemented in accordance with the teachings of the present disclosure, where, starting from an initial refractive index profile, full-wave simulation (FDTD) is used to calculate the sensitivity of the focusing efficiency with respect to refractive index perturbations. The sensitivity can be calculated by only two simulations, allowing efficient optimization of the three-dimensional device with modest resources. Based on the sensitivity, the initial design is modified to maximize performance while meeting manufacturing constraints. This updating process is repeated until the optimized device is able to effectively perform the target function
To further clarify the above description, reference is made to FIG. 3D, which illustrates various steps of a gradient-based optimization algorithm in accordance with an embodiment of the present disclosure. In step (81), a uniform refractive index profile is used
To initialize the algorithm, where nmaxAnd nminRepresenting the maximum and minimum values of the refractive index, respectively. The distribution is continuously updated to make the focal plane
The electromagnetic intensity at the medium target position is maximized. The objective function serves as a proxy for the focusing efficiency while simplifying the sensitivity calculations. At step 74, the steps are simulated (forward and adjoint) from two FDTDs according to the following expressionCalculating sensitivity of electromagnetic field in step (72, 73)
Wherein the content of the first and second substances,
is the electric field within the cube when illuminated with a plane wave from above (step 72),
is the electric field within the cube when illuminated from below with a point source at the target location (step 73). The phase and amplitude of the point source is given by the electric field at the target location in forward modeling (forward simulation). The sensitivity can be calculated for multiple incident wavelengths and polarizations in the visible spectrum, each spectral band being assigned to a different quadrant, red (600 nm-700 nm), green (500 nm-600 nm) and blue (400 nm-500 nm). Then, in step (74), the spectrally averaged sensitivity is used to update the refractive index of the device using the following equation:
the step size a may be fixed at a fraction (e.g., 0.001) to ensure that the change in refractive index can be treated as a perturbation in a linear range. The sensitivity is recalculated after each update. After several iterations, the algorithm converges to an optimized design, step (75), where the resulting structure focuses the incident light with the desired efficiency.
Fig. 4A shows a 3D scattering structure (410) made of a dielectric, the 3D structure (410) comprising a network of wires (415) embedded inside the scattering structure (410). The dielectric may be made of an oxide such as silicon dioxide and the wire network (415) may be made of a metal such as copper. As previously mentioned, in order to create a complex 3D scattering element performing the target function, voids may be formed within the 3D scattering structure (410) by etching away the wire network (415) originally fabricated within the 3D scattering structure (410). To do this, reference is now made to fig. 4A-4B, and according to a further embodiment of the present disclosure, vias (420) are etched in the dielectric to access the ends of the wires in the wire network (405), and then the wires are etched away using a liquid etchant to obtain voids (415').
Throughout this disclosure, the term "thread pitch" refers to the minimum spacing between two adjacent lines of a network of threads within a 3D structure. Furthermore, there is a minimum filament feature size imposed by the limitations of the manufacturing process. Thus, when voids are formed within the 3D structure by etching away the wires, the minimum wire spacing sets the minimum dielectric feature size and the minimum wire size sets the minimum void/air feature size. In the following, exemplary steps of a method of designing a 3D scattering structure (410) while taking into account manufacturing process constraints according to the teachings of the present disclosure are described.
Free, continuous optimization
Hereinafter, a 3D structure made of a dielectric in which voids are formed according to an objective function will be described. The process may start with a free optimization, as described above in relation to fig. 2A-3D, where the refractive index is allowed to vary continuously between air (n ═ 1.0) and the low refractive index material SiO2(n ═ 1.5). For example, a gradient descent algorithm may be used in which the sensitivity of the objective function to exponential changes is calculated at all points in the design area. Referring to the examples of fig. 2A' and 3C, the objective function to be optimized may be selected as the electric field strength at different foci for different bands. Such an objective function may be used when designing the wavelength separator. The design obtained by free and continuous optimization may not meet the requirements imposed by manufacturing constraints. In this context, the term "free optimization" refers to an optimization method that does not impose manufacturing constraints, and the term "continuous optimization" refers to an optimization method that cancels specific manufacturing constraints. For example, in such an optimization method, the refractive index may take any value within a set range, not just an extreme value. As described in detail in the following paragraphs, the disclosed method addresses this problem by implementing a binarization of the refractive index (binning) and then further optimizing the design using, for example, a gradient descent method, while taking into account manufacturing requirements.
Two-dimensional (2D) shape representation and binarization
In this document, the term "dualization" refers to manufacturing constraints in which only a small amount of material can be selected, thus not allowing a continuous refractive index profile. For example, CMOS technology imposes such manufacturing constraints. Considering the example of a 2D shape, an explicit representation (explicit representation) of such a shape may be a series of points in the 2D plane that define the boundaries of such a shape. In the case of a rectangle, the shape may be defined by only four points in a plane. Another way to represent a particular shape, such as a rectangle, or an arbitrary shape is to use an implicit representation (implicit representation). In this context, the term "level set function" refers to a function that is an implicit representation of a geometry. For example, in the case of a 2D shape, the level set function may be defined as a function f (x, y), or in other words, a three-dimensional surface. An outline defined by f (x, y) being a constant (e.g., constant equal to 0) defines the boundary of the two-dimensional shape.
As will be described in detail later, according to embodiments of the present disclosure, it is conceivable to represent the level set function of a feature with a geometric shape such as a rectangle instead of a free shape allowed by a free continuation optimization algorithm. As described below, such an approach would allow for an optimized design while meeting the stringent requirements imposed by the manufacturing process. Gradient information from the continuous optimization method can then be mapped to perturbations of the level set function such that the boundaries of the shape move in a manner that improves the design. When reduced to a feature having, for example, a rectangular shape (or some other parameterizable shape), the boundary perturbation may be converted to a perturbation of a feature parameter, for example in the case of a rectangle, a center point and two widths. In the following, examples of features having a rectangular shape will be used to describe the teachings of the present disclosure, bearing in mind that features having shapes other than rectangular are also contemplated.
Level set representation
According to an embodiment of the present disclosure, the design of the aforementioned 3D structure is implemented in 2D, while layering is implemented in the propagation direction of the input source. In other words, for example with reference to a rectangular feature, the position and width of the feature are the parameters that are controlled. Fig. 5 shows a flow chart (500) describing various steps of a design process in accordance with an embodiment of the present disclosure. As can be seen in the flowchart (500), an initial optimization design based on free/continuous optimization is first provided (step 510). Such a design would provide a refractive index profile in the horizontal direction substantially in each layer and there are no manufacturing limitations in creating such an initial design. Then, for each layer, the following steps are taken:
1. the program is run to identify peaks in the void index distribution (step 520). The minimum found in this way represents a void region which is not necessarily completely void according to the free/continuous optimization as described before. In other words, some regions may represent local minima.
2. The identified regions are then ranked based on their proximity to the voids (step 530). This is performed using design results based on a free/continuous optimization algorithm as described previously. In other words, the void features are preferentially placed where the free design is most needed.
3. Proceeding from the highest level to the lowest level of void features, each void is replaced by a rectangle approximating the original exponential distribution (step 540). The dimensions of the rectangle are chosen to maintain the same volume average refractive index as the original profile, thereby providing a binary index substitution. This is illustrated in fig. 6, which shows an exemplary graph representing an exponential distribution versus horizontal position.
4. Each feature needs to satisfy manufacturing (e.g., CMOS process) constraints (step 550-. In other words, the width of each feature is required to meet the minimum width requirement, which, as previously mentioned, is set by the minimum line size that can be manufactured. The distance between the centers of adjacent features is required to meet the manufacturing pitch requirements. Any features that do not meet these requirements can be ignored.
5. Using the center/width of each feature found in the previous step, a level set function is created and assigned to each feature (step 580). As will be described later, the created level function will be updated (step 580) to improve the performance of the binarized design.
Performance improvement for binarized designs
As previously described, according to embodiments of the present disclosure, and to satisfy manufacturing constraints, a 3D structure may be designed based on a particular shape, such as a rectangular bar. As with the design using free/continuous optimization, this design has provided improved overall performance over existing solutions. However, the free-form based design may still yield better overall performance than the more specific feature based design. In accordance with the teachings of the present disclosure, starting with a binarized device, the gradient information can be used to iteratively update the design to further improve overall performance. As shown in the flow chart (500) of fig. 5, step (580), the gradient information from the free/continuous optimization method may be mapped to perturbations in the width/center of all rectangular features used in the binarized design (step 580 of fig. 5). In other words, the gradient of the objective function with respect to the refractive index profile can be mapped to perturbations of the boundary by the Hamilton-Jacobi equation. This means that we can update the boundary (here the width) with the same information used to optimize the continuous graded index structure. The inventors have noted that when such an approach is adopted, and after several iterations, a significant improvement of already good performance of the binarized design will be obtained, while taking into account constraints imposed by the manufacturing process (e.g., CMOS process). Hereinafter, the performance of the described design method will be described using exemplary embodiments of the present disclosure.
Fig. 7A-7C show performance results associated with exemplary 3D scattering structures optimized for single polarization and three color focusing (e.g., red, green, and blue). The 3D structure is made of SiCOH (n ═ 1.3), where an air gap (n ═ 1) is formed using the aforementioned method. Using 8 layers (450 nm/layer), the 2D method as described before was used. Fig. 7A shows the transmission spectra associated with a design based on free/continuous optimization. Graphs (701A, 702A, 703A) show the transmission as a function of wavelength for the colors (blue, green, red), respectively. FIG. 7B shows the transmission spectra associated with the binarized design. The graphs (701B, 702B, 703B) show the transmittance versus wavelength curves for different focal regions. A decrease in performance was noted compared to the results obtained with the free optimization case. FIG. 7C shows the transmission spectra obtained after further optimization of the binarized design after gradient information from the free/continuous optimization method is mapped to perturbations in the width/center of all rectangular features used in the binarized design. The graphs (701C, 702C, 703C) show the transmission as a function of the wavelength of the colors (blue, green, red), respectively. It can be noted that the performance of the binarized design is significantly improved.
Claims (13)
1. A method for constructing a three-dimensional (3D) scattering structure, comprising:
forming a dielectric structure comprising a first dielectric and a network of metal wires, wherein the position, shape and size of the metal wires are selected according to one or more target functions; and
the metal wire is etched away from the dielectric structure, thereby forming a structure comprising a space filled with the first dielectric and voids, wherein the voids have a position, shape and size according to one or more objective functions,
wherein the 3D light scattering structure so formed is configured to receive electromagnetic waves and scatter the electromagnetic waves according to one or more objective functions.
2. The method of claim 1, further comprising filling the void with a second dielectric different from the first dielectric, thereby obtaining a 3D light scattering structure made of two different dielectrics.
3. The method according to claim 1 or 2, wherein etching is performed by creating vias in the 3D scattering structure.
4. The method of any of claims 1-3, wherein the forming is performed by a CMOS process.
5. The method of claim 2 wherein said first and second dielectric materials comprise SiCOH and TiO2, respectively.
6. The method of any of claims 1-5, wherein the forming is performed using stacked layers.
7. The method of claim 6, wherein the location and size of the voids are provided using a gradient descent based optimization method.
8. The method of claim 7, wherein voids within each layer have a geometric shape that is each represented by one or more parameters.
9. The method of claim 8, wherein each geometric shape is a rectangle and the one or more parameters include two widths and a center in a horizontal direction.
10. The method of claim 9, wherein the optimization method comprises providing an initial 3D pattern using a continuous optimization algorithm to produce a refractive index profile in a horizontal direction within each layer.
11. The method of claim 10, wherein the optimization method further comprises:
for each layer:
identifying a minimum of the refractive index profile to provide a location of the void;
rank ordering the slots based on a continuous optimization algorithm to indicate how each slot is binarized;
from highest rank to lowest rank, setting two widths and centers for each gap;
checking each void against the set size and set spacing requirement to provide a set of acceptable voids; and
perturbing the two gap widths of the set of acceptable gaps based on a continuous optimization algorithm to further optimize and improve the overall performance of the 3D scattering structure.
12. The method of claim 11, wherein the set size and spacing requirements are related to CMOS fabrication constraints.
13. An image sensor constructed based on the method of any preceding claim.
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