KR20220083736A - CMOS Color Image Sensors with Metamaterial Color Segmentation - Google Patents

Abstract

Methods are described for building multifunctional scattering structures while complying with stringent requirements imposed by the manufacturing process. The methods and devices described are based on etching wire networks embedded in 3D structures to form voids to perform a target function. An optimization algorithm for designing binarized devices to meet manufacturing requirements is also disclosed.

Description

CMOS Color Image Sensors with Metamaterial Color Segmentation

[01] This application relates to U.S. Patent Application Serial No. 16/656,156, filed on October 17, 2019 and entitled "Color and Multi-Spectral Image Sensor Based on 3D Engineered Materials" (Attachment No. P2404-US) As such, the contents of this patent application are incorporated herein by reference in their entirety.

[02] This invention was made with government support under Grant No. HR0011-17-2-0035 awarded by DARPA. The government has certain rights in this invention.

[03] FIELD OF THE INVENTION The present invention relates to image sensors, and more particularly to metamaterial spectrum splitters fabricated using CMOS fabrication technology.

[04] Optical systems are typically designed through modular combinations of elements to achieve complex functions. For example, to perform hyperspectral imaging, lenses and diffractive optics are combined. This approach is intuitive and flexible, providing access to a wide range of functions from a limited set of elements. However, the overall size and weight of the optical system may limit its scope of application. Recent advances in nanofabrication can alleviate this constraint by replacing bulky elements with metasurfaces, which are planar arrays of resonant nanostructures with sub-wavelength thicknesses. By engineering the scattering of individual elements in the array, these devices can reproduce the multi-functionality of complex optical systems in a single element. However, efforts to combine multiple metasurfaces for more complex functionality have been hampered by reduced scattering efficiency that scales inversely with the number of simultaneous operations.

[05] The inherent trade-off between multi-functionality and efficiency in these systems is due to a finite number of degrees of freedom that scale according to the device's volume and maximum refractive index contrast. In particular, this limits the range of independent functions achievable by any ultrathin system, such as classifying light according to frequency, polarization, and angle of incidence. In contrast, three-dimensional scattering elements with a thickness greater than the wavelength, although generally encoding many simultaneous functions, have hitherto been ineffective due to weak scattering and low refractive index contrast.

[06] Historically, optical design has been modular, a paradigm that provides an intuitive way to build and reconfigure optical settings. Advances in nanofabrication techniques have made it possible to fabricate structures at sub-wavelength feature sizes that enable multi-functional optical elements that combine the functionality of more complex settings. Examples of these include metasurface lenses capable of splitting different polarization and spectral bands. However, the degree of performance and functionality that can be achieved with metasurfaces and other planar structures is inherently limited by the number of optical modes that can be controlled.

[07] Structuring the refractive index with high contrast at the sub-wavelength scale provides a broad optical design space that can be utilized to demonstrate multi-functional optical elements. So far, it has been mainly used in 2D structures or metasurfaces. However, its performance is limited by the available optical degrees of freedom.

[08] In order to highlight the advantages of the teachings of the present invention in the following sections, an example of image sensors is considered herein. Currently, most sensors use absorption filters to record color. 1A shows a prior art image sensor, each of four adjacent pixels having an absorptive color filter thereon; Two of them are for green, one for blue, and one for red. The problem with these image sensors is that their efficiency is limited to about 30% because most of their light is absorbed. Color image sensors are ubiquitous in cell phones, cameras, and devices of all kinds. Color is detected by simple absorption filters placed directly on top of each pixel. The absorptive nature of the filters means that more than two-thirds of the light is actually lost by absorption, ie red and blue light incident on a green pixel, for example, is absorbed, and only green passes through.

[09] For example, complex three-dimensional (3D) scattering structures are disclosed herein that allow color division on a Bayer pattern with higher efficiency. Designs that provide polarization information are also described.

[010] The cost-effective and large-scale manufacturing of such structures poses significant challenges to the design process. The goal is to achieve the best performance given the inherent constraints associated with high-volume CMOS manufacturing processes.

[011] The disclosed methods and devices solve the described difficulties, and provide practical solutions to the aforementioned problems.

[012] In particular, the disclosed methods and devices teach various steps for designing 3D scattering structures using a scalable manufacturing process. The most scalable fabrication currently capable of handling dimensions smaller than 100 nm is the CMOS foundry fabrication process. In the CMOS process, it is possible to fabricate very complex networks of copper wires stacked on top of each other and embedded in SiO2. Figure 1b shows an example of such networks, where light gray and dark gray represent metal and SiO2, respectively. However, according to an embodiment of the present invention, the wires can be etched using liquid etchants such that the final 3D scattering structure consists of voids in SiO2. According to another embodiment of the present invention, the 3D scattering structure may be left as voids in SiO2, or the voids may be filled with high refractive index materials such as TiO2 using atomic layer deposition processes.

[013] According to a first aspect of the present invention, a method for building a three-dimensional (3D) scattering structure is described, the method comprising: forming a dielectric structure comprising a first dielectric and a network of metal wires - the locations of the metal wires , shape, and size selected according to one or more target functions; and etching away the metal wires from the dielectric structure to form a structure comprising voids and spaces filled with the first dielectric, the location, shape, and size of the voids according to one or more target functions. wherein the 3D light scattering structure thus formed is configured to receive and scatter electromagnetic waves in accordance with one or more target functions.

[014] Additional aspects of the invention are provided in the description, drawings, and claims of the present application.

1A shows a prior art image sensor.
1B shows the structure of prior art wires that can be realized using CMOS foundry fabrication techniques, with feature sizes of less than 100 nm.
[017] Figures 2a-2aa show exemplary three-dimensional (3D) scattering structures in accordance with an embodiment of the present invention.
[018] Figures 2b-2c illustrate the wavelength division functionality of the embodiment of Figures 2a and 2aa.
3A-3C show exemplary three-dimensional (3D) scattering structures in accordance with another embodiment of the present invention.
3D illustrates multiple steps of an exemplary optimization algorithm according to an embodiment of the present invention.
4A shows an exemplary 3D structure made of a dielectric and comprising wire networks in accordance with an embodiment of the present invention.
4B shows an exemplary process for etching a wire network in a 3D structure, in accordance with a further embodiment of the present invention.
[023] Figure 5 shows an exemplary flow diagram representing the various steps of designing a 3D scattering structure in accordance with the teachings of the present invention.
6 shows an exemplary graph showing a refractive index distribution along a horizontal position.
7A-7C show graphs representing the performance of a 3D scattering structure implemented in accordance with the teachings of the present invention.

2A shows an image sensor 200 according to an embodiment of the present invention. The image sensor 200 includes a three-dimensional (3D) scattering structure 201 that functions as a spectral divider. The 3D scattering structure 201 includes a plurality of dielectric pillars 205 formed to scatter light in a predetermined pattern. Incident light 202 that has passed through the 3D scattering structure 201 is scattered from the dielectric pillars. Through arrangements of dielectric pillars 205 according to one or more target functions, the scattering pattern is adjusted to perform a desired function. As an example, the 3D scattering structure 201 may be designed as a spectral divider to simultaneously classify and focus the incident light 202 into an arbitrary number of wavelengths λ ₁ , ...,λ _n , each of which are directed to individual pixels on a focusing plane 203 located below the 3D scattering structure 201 , as shown in FIG. 2A . According to an embodiment of the present invention, the 3D scattering structure 201 may be a porous polymer cube, or may be a cluster of dielectric or semiconductor (eg, Si) particles embedded in a SiO2 matrix. According to a further embodiment of the present invention, the 3D scattering structure 201 may be a porous polymer cube, or may be a cluster of high refractive index particles embedded in a low refractive index matrix.

[027] It will be appreciated by those skilled in the art that, unlike the prior art image sensor 100 of FIG. 1A , the image sensor 200 of FIG. 2A does not function on an absorption basis and thus provides a substantial improvement in efficiency over existing solutions. will recognize that it provides This will be quantified later using exemplary embodiments of the present teachings. As will also be described in greater detail throughout the present invention, the disclosed devices and methods provide the following additional advantages over existing solutions.

도 2a의 3D 산란 구조물(201)은 알려져 있는 그리고 스케일러블한 리소그래피 프로세스들을 통해 제조될 수 있다.

The 3D scattering structure 201 of FIG. 2A may be fabricated via known and scalable lithographic processes.

도 2a의 3D 산란 구조물(201)은 적외선, 중적외선(mid-infrared) 등과 같은 임의의 스펙트럼 대역에 대한 스펙트럼 분할기로서 기능하도록 설계될 수 있다. 환언하면, 초분광 이미징과 함께, 열 이미징(thermal imaging)은 개시된 교시들의 또 다른 잠재적 응용이다.

The 3D scattering structure 201 of FIG. 2A may be designed to function as a spectral divider for any spectral band, such as infrared, mid-infrared, or the like. In other words, along with hyperspectral imaging, thermal imaging is another potential application of the disclosed teachings.

스펙트럼 분할 기능은 편광 분할과 같은 다른 원하는 기능들과 조합될 수 있다.

The spectral division function can be combined with other desired functions such as polarization division.

본 발명에 따른 실시예들은 또한, 엣지 검출을 위해 가버 필터링(Gabor filtering)과 같은 광학 이미지 프로세싱을 수행하도록 설계될 수도 있다.

Embodiments according to the present invention may also be designed to perform optical image processing such as Gabor filtering for edge detection.

[028] 2AA illustrates an image sensor 200' comprising an exemplary three-dimensional (3D) scattering structure 21 functioning as a spectral filter, in accordance with an embodiment of the present invention. Incident light 22 coming from above is scattered while passing through the 3D scattering structure 21 , consisting of four sub-pixels shown in red, blue, green (x-polarized light), and green (y-polarized light). It is sorted on the focusing surface 23 . Also, as shown in Fig. 2aa, the red (600 nm - 700 nm) and blue (400 nm - 500 nm) spectral bands are classified into opposite quadrants. Moreover, the green (500 nm - 600 nm) spectral band is further divided according to linear polarization. The red and blue quadrants may be polarization independent.

[029] According to embodiments of the present invention, the 3D scattering structure 21 can be designed using an adjoint variable method, which creates a structure that optimizes a particular objective function. For example, referring to FIG. 2AA , the objective function may be selected based on the focusing efficiency of incident light into one of four target regions according to frequency and polarization. Starting with an empty volume, full-wave finite-difference time-domain (FDTD) simulations are implemented to calculate the sensitivity of this figure of merit to perturbations of the refractive index. do. A defined scattering structure is formed and iteratively updated. In other words, an optimal design is generated through initial iterative updates to the geometry, improving performance at each step. The sensitivity can be calculated from only two simulations, allowing efficient optimization of 3D devices with appropriate resources. Sensitivity for multiple incident wavelengths across the visible spectrum can be calculated, so that each spectral band is in a different quadrant: red (600 nm - 700 nm) and green (500 nm - 600 nm) and blue (400 nm). - 500 nm). The spectral averaged sensitivity can then be used to update the refractive index of the device.

[030] 2B-2C show simulated incident light intensity within the 3D scattering structure 21 of FIG. 2AA. Intensity is analyzed along a diagonal cross section that intersects the red and blue quadrants of FIG. 2AA . Each wavelength undergoes multiple scattering before being focused on its respective target area. Figure 2c shows the intensity distribution of incident light in a diagonal cross section through green pixels for two orthogonal input polarizations. In both cases, a plane wave incident from above (λ = 550 nm) is preferentially routed to the pixel corresponding to its polarization. On the other hand, both polarizations are allocated the same region for the red and blue spectral bands, maintaining the mirror symmetry of the objective function.

[031] According to an embodiment of the present invention, the 3D scattering structure 21 of FIG. 2AA categorizes red, green, and blue light at 84%, 60%, and 87% efficiencies, respectively. Throughout the present invention, efficiency is defined as the proportion of total power incident on the device that reaches a target quadrant averaged over the spectrum for which the device is designed, i.e., the visible spectrum for the embodiment of Figure 2aa.

[032] 2A and 2A, those skilled in the art will appreciate that the disclosed concepts provide substantial flexibility in defining the target scattering function, with independent control over any incident polarization, angle, or frequency. will be. However, complex three-dimensional structures present significant challenges to their fabrication. Large-scale implementation of these devices in image sensors of visible wavelengths will require high manufacturing throughput with sub 100 nm resolution. This can be achieved by multilayer lithography, in which three-dimensional devices are constructed through repeated material deposition and patterning. Here, each layer consists of a series of patterned mesas composed of a high refractive index dielectric. The interstitial space is filled with a low refractive index dielectric to form a planar surface that serves as a substrate for subsequent layers.

[033] To further clarify the additive manufacturing approach described above, reference is made to FIGS. 3A and 3C , which illustrate the stacked 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 multiple layers 301 , ..., 305 of FIG. 3A on top of each other. The manufacturing process is CMOS-compatible, where manufacturing constraints can be incorporated directly into the design algorithm. Each of the layers 301 , ... , 305 may be created using lithography. The 3D scattering structure 31 may be made of TiO2 and SiO2, which are materials that are transparent at visible frequencies. The layers 301, ..., 305 may be 2 um x 2 um layers, each of which is 400 nm in height. Those skilled in the art will recognize that these are exemplary dimensions for purposes of illustration, and that embodiments in accordance with the present invention, and dimensions and numbers of layers other than those mentioned above, are possible. As shown in FIG. 3B , each layer may include a set of irregular TiO2 mesas surrounded by SiO2. Referring to FIG. 3B , the lithographic process may begin by growing a thin layer of dielectric (eg, TiO2) on top of a substrate (eg, SiO2). A pattern is transferred onto the layer by lithography, and the unprotected material is etched to create a two-dimensional dielectric structure. Finally, the surface is coated (deposited) with a low refractive index dielectric and mechanically polished (planarized). By repeating the same process for each layer and stacking the layers, the desired 3D structure is created. This lithography process provides flexibility in material design, and is compatible with industry-standard CMOS fabrication processes as described above.

Optimization Algorithms

Gradient descent

]에 의해 정의된다. 이는 확장된 설계 공간을, 복합적인 광학 다중-기능성을 광범위하게 표현하는 능력으로 나타낸다. 그러나 주어진 목표 기능에 대한 최적의 지수 분포를 식별하는 것은, 특히 강한 산란 디바이스들에 대해 난제시되는 역설계(inverse design) 문제점으로 남아 있다.[034] Referring again to Figures 2aa-3c, and as described above, three-dimensional dielectric structures optimized to perform a target optical scattering function are designed in accordance with the teachings of the present invention. 2aa-3c, this target scattering function consists in focusing the incident plane waves at different positions depending on frequency and polarization. Exemplary three-dimensional (3D) scattering structures 21 , 31 have a space-dependent refractive index distribution [

] is defined by This represents an expanded design space with the ability to broadly express complex optical multi-functionality. However, identifying the optimal exponential distribution for a given target function remains a daunting inverse design problem, especially for strong scattering devices.

[035] To overcome this challenge, in accordance with the teachings of the present invention, an iterative approach guided by gradient descent can be implemented, wherein, starting from an initial exponential distribution, calculating the sensitivity of the focusing efficiency to perturbations of the refractive index For this purpose, propagation simulations (FDTD) are used. The sensitivity can be calculated from only two simulations, allowing efficient optimization of three-dimensional devices with reasonable resources. To maximize performance while adhering to manufacturing constraints, the initial design is modified based on sensitivity. This update process is repeated until the optimized device can efficiently perform the target function.

]로 초기화되며[단계(81)], 여기서

및

은 굴절률의 최대값 및 최소값을 각각 나타낸다. 분포는 집속면[

]의 목표 위치에서 전자기 강도를 최대화하기 위해 지속적으로 업데이트된다. 이 목적 함수는 감도 계산을 단순화하면서 집속 효율성을 위한 프록시로서 작용한다. 감도[

]는 이하의 식에 따라 2개의 FDTD 시뮬레이션들(순방향 및 수반)[단계(72, 73)]에서 전자기장으로부터 연산된다[단계(74)].[036] To further clarify the foregoing, reference is made to FIG. 3D, which illustrates multiple steps of a gradient-based optimization algorithm according to an embodiment of the present invention. The algorithm is a uniform refractive index distribution[

] [step 81], where

and

denotes the maximum and minimum values of the refractive index, respectively. The distribution is the focal plane[

] is continuously updated to maximize the electromagnetic strength at the target location. This objective function acts as a proxy for focusing efficiency while simplifying sensitivity calculations. Sensitivity[

] is computed from the electromagnetic field in two FDTD simulations (forward and accompanying) (steps 72 and 73) according to the following equation (step 74).

(1)

(One)

는, 위로부터 평면파로 조명되었을 때[단계(72)] 입방체 내의 전기장이며,

는 목표 위치에서 아래로부터 포인트 소스(point source)로 조명되었을 때[단계(73)] 입방체 내의 전기장이다. 포인트 소스의 위상 및 진폭은 순방향 시뮬레이션에서 목표 위치의 전기장에 의해 주어진다. 감도는 가시 스펙트럼에 걸쳐 다중 입사 파장들 및 편광들에 대해 계산될 수 있어서, 각각의 스펙트럼 대역을 상이한 사분면에: 적색(600 nm - 700 nm), 녹색(500 nm - 600 nm), 및 청색(400 nm - 500 nm)에 할당한다. 그리고 스펙트럼 평균 감도는 아래의 식을 사용하여 디바이스의 굴절률을 업데이트하는 데 사용된다[단계(74)].here

is the electric field in the cube when illuminated with a plane wave from above (step 72),

is the electric field in the cube when illuminated with a point source from below at the target location (step 73). The phase and amplitude of the point source are given by the electric field of the target position in the forward simulation. Sensitivity can be calculated for multiple incident wavelengths and polarizations across the visible spectrum, placing each spectral band in a different quadrant: red (600 nm - 700 nm), green (500 nm - 600 nm), and blue ( 400 nm - 500 nm). And the spectral average sensitivity is used to update the refractive index of the device using the equation below (step 74).

(2)

(2)

The step size α can be fixed at a small fraction (eg α=0.001) to ensure that changes in refractive index can be treated as perturbations in the linear region. 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.

[037] 4A shows a 3D scattering structure 410 made of a dielectric, which includes a wire network 415 embedded inside the scattering structure 410 . The dielectric may be made of an oxide, such as SiO2, and the wire network 415 may be made of a metal, for example copper. As described above, voids may be formed in the 3D structure 410 by etching the wire network 415 initially fabricated within the 3D scattering structure 410 to create complex 3D scattering elements that perform the target function. can To do this, referring now to FIGS. 4A-4B , in accordance with further embodiments of the present invention, vias 420 are etched in the dielectric to the ends of the wires in the wire network 405 . access, and then etch the wires using a liquid etchant to obtain voids 415'.

[038] Throughout the present invention, the term “wire pitch” will be referred to as the minimum value at which two adjacent wires of a wire network within a 3D structure can be spaced apart from each other. A minimum wire feature size is also imposed by the constraints of the manufacturing process. Accordingly, when forming voids in a 3D structure by etching the wires, the minimum wire pitch sets the minimum dielectric feature size, and the minimum wire size sets the minimum void/air feature size. Exemplary steps of methods according to the teachings of the present invention for designing a 3D scattering structure 410 while taking into account manufacturing process constraints are described below.

free, continuous optimization

[039] Hereinafter, a 3D structure made of a dielectric in which pores are formed according to a target function will be described. The process can begin with a free optimization, as described in the previous sections with respect to Figs. 2a-3d, where the refractive index is continuously varied between air (n = 1.0) and the low refractive index material SiO2 (n = 1.5). it is allowed For example, a gradient descent algorithm that calculates the sensitivity of the objective function to the refractive index change at all points in the design domain may be used. Referring to the example of FIGS. 2A and 3C , the objective function to be optimized may be selected as the field strength at different focal points for different wavelength bands. This objective function can be used when the wavelength divider is designed. The design obtained by free and continuous optimization may not be consistent with the requirements imposed by constraints due to manufacturing. Throughout this document, the term "free optimization" refers to optimization methods in which no manufacturing constraints are imposed, and the term "continuous optimization" refers to an optimization method in which certain manufacturing constraints are lifted. represent them For example, in these optimization methods, the refractive index may take any value within a set range as well as extreme values. As detailed in the following paragraphs, the disclosed methods implement binarization of the refractive index and then address this problem by further optimization of the design, for example using a gradient descent approach while adhering to manufacturing constraints. solve it

Two-dimensional (2D) shape representation and binarization

[040] Throughout this document, the term “binarization” refers to a manufacturing constraint that does not allow a continuous exponential distribution as only a small number of substances can be selected. CMOS technology, for example, imposes these manufacturing constraints. Considering the example of a 2D shape, an explicit representation of such a shape could be a series of points in the 2D plane that define the boundary of this shape. In the case of a rectangle, its shape can be defined as four points in a plane. Another way to represent certain shapes or arbitrary shapes, such as rectangles, is to use an implicit representation. Throughout this document, the term “level set function” refers to a function that is an implicit representation of a geometric shape. For example, in the case of a two-dimensional shape, the level setting function may be defined as a function [f(x, y)] or, in short, a three-dimensional surface. A contour defined by f(x, y) = constant (eg, constant equals 0) defines the boundary of the shape in two dimensions.

[041] As will be described below in detail, in accordance with an embodiment of the present invention, a level setting function representing features having geometric shapes such as rectangles can be envisioned, instead of freeform shapes as allowed by free, continuous optimization algorithms. have. As discussed below, this approach allows for an optimized design while meeting the stringent requirements imposed by the manufacturing process. The slope information from the continuous optimization method can then be mapped to the perturbations of the level setting function so that the boundary of the shape moves in a way that improves the design. When features are simplified to, for example, a rectangular shape (or some other parameterizable shape), this boundary perturbation is a perturbation of the feature parameters, such as the center point and two widths, for example in the case of a rectangle. can be converted to In the following, examples of features having rectangular shapes will be used to illustrate the teachings of the present invention, with the mind that features having shapes other than rectangular may be envisioned.

Level set representation

[042] According to embodiments of the present invention, the design of the 3D structures described above is implemented in 2D while performing layering in the propagation direction of the input source. In other words, referring to, for example, rectangular shapes, the position and width of the features are parameters that are controlled. 5 depicts a flowchart 500 describing various steps of a design process, in accordance with embodiments of the present invention. As can be seen in flowchart 500, an initial optimized design is first provided based on free/continuous optimization (step 510). This design will essentially provide a distribution of refractive index along the horizontal directions of each layer, and no manufacturing constraints are imposed when creating this initial design. Then, for each layer, the following steps are taken.

1. The procedure proceeds to identify peaks in the void exponential distribution (step 520). The minimum values found in this way represent void regions that are not necessarily completely empty according to the free/continuous optimization described above. In other words, some regions may exhibit local minima.

2. The identified regions are then ranked based on how close they are to the void (step 530). This is done using the design result based on the free/continuous optimization algorithm described above. In other words, the void features are preferentially located in the position most likely to be desired in the free design.

3. In the progression from highest to lowest rank of void features, each void is replaced with a rectangle approximating the original exponential distribution (step 540). The dimensions of the rectangle are chosen to keep the volume-averaged refractive index equal to the original distribution, providing a binary-exponential replacement. This is illustrated in FIG. 6 , in which an exemplary graph showing an exponential distribution versus horizontal position is shown.

4. Manufacturing (eg, CMOS process) constraints are required to be met by each feature (steps 550-570). In other words, the width of each feature is required to meet the minimum width requirement set as the minimum manufacturable wire size as described above. The distances between the centers of adjacent features are required to meet manufacturing pitch requirements. Any feature that does not meet any of these requirements may be ignored.

5. Using the center/width of each feature as found in the previous steps, a level setting function is created and assigned to each feature (step 580). As described below, the generated level functions will be updated to improve the performance of the binarized design (step 580).

Improving the performance of binary designs

As described above, in accordance with embodiments of the present invention and to meet manufacturing constraints, 3D structures may be designed based on specific shapes, such as rectangular bars. As is typical for designs using free/continuous optimization, these designs already provide overall improved performance over existing solutions. However, designs based on free shapes may still perform better overall compared to those based on more specific features. In accordance with the teachings of the present invention, and starting from a binarized device, gradient information can be used to iteratively update the design to further improve overall performance. As illustrated by flowchart 500 (step 580 in FIG. 5 ), the gradient information from the free/continuous optimization method includes all rectangular features used in the binarized design (step 580 in FIG. 5 ). May be mapped to perturbations of width/center of parts. In other words, the slope of the objective function with respect to the surface distribution can be mapped to the perturbation of the boundaries via the Hamilton-Jacobi equation. This means that the boundaries (here, widths) can be updated using the same information used to optimize a continuous graded-exponential structure. We found that when adopting this approach and after several iterations, significant improvements were made to the already good performance of the binarized design, while simultaneously adhering to the constraints imposed by the manufacturing process (eg CMOS process). It was noted that it would be obtained. In the following, the performance of the described design approach will be demonstrated using exemplary embodiments of the present invention.

[043] 7A-7C show performance results associated with an exemplary 3D scattering structure optimized for single polarization and three color foci (eg, red, green, and blue). The 3D structure is fabricated from SiCOH (n = 1.3), where an air gap (n = 1) is formed using the methods described above. Using 8 layers (450 nm/layer), the 2D approach described above was used. Figure 7a shows the transmission spectra associated with a design based on free/continuous optimization. Graphs 701A, 702A, and 703A show plots of transmittance as a function of wavelength for colors (blue, green, red), respectively. Figure 7b shows the transmission spectra associated with the binarization design. Graphs 701B, 702B, and 703B show plots of transmittance as a function of wavelength for different focusing regions. In the case of free optimization, there is a performance degradation compared to the obtained results. Fig. 7c shows transmission spectra obtained after further optimization of the binarized design after the slope information from the free/continuous optimization method is mapped to the width/center perturbations of all rectangular features used in the binarized design; have. Graphs 701C, 702C, and 703C show plots of transmittance as a function of wavelength versus color (blue, green, red), respectively. A significant improvement can be seen compared to the performance of the binary design.

Claims (13)

A method for constructing a three-dimensional (3D) scattering structure, comprising:
forming a dielectric structure comprising a network of metal wires and a first dielectric, wherein the location, shape, and size of the metal wires are selected according to one or more target functions; and
etching away the metal wires from the dielectric structure to form a structure comprising voids and spaces filled with the first dielectric, the location, shape, and size of the voids being selected from the one or more According to target functions-
wherein the 3D light scattering structure so formed is configured to receive electromagnetic waves and to scatter the electromagnetic waves in accordance with the one or more target functions. According to claim 1,
filling the voids with a second dielectric different from the first dielectric to obtain a 3D light scattering structure made of two different dielectrics. 3. The method of claim 1 or 2,
wherein the etching is performed by creating vias in the 3D scattering structure. 4. The method according to any one of claims 1 to 3,
wherein the forming step is performed through a CMOS process. 3. The method of claim 2,
wherein the first dielectric material and the second dielectric material comprise SiCOH and TiO2, respectively. 6. The method according to any one of claims 1 to 5,
wherein the forming step is performed using stacked layers. 7. The method of claim 6,
wherein the location and size of the pores are provided using an optimization method based on gradient descent. 8. The method of claim 7,
wherein the voids in each layer have geometric shapes each represented by one or more parameters. 9. The method of claim 8,
wherein each geometric shape is rectangular, and wherein the one or more parameters include a center and two widths along horizontal directions. 10. The method of claim 9,
wherein the optimization method comprises providing an initial 3D pattern using a continuous optimization algorithm to generate a distribution of refractive index along horizontal directions within each layer. 11. The method of claim 10,
The optimization method is, for each layer:
identifying a minimum value of the refractive index distribution to provide a location for the voids;
ranking the voids to represent how each void is binarized based on the successive optimization algorithm;
proceeding from highest to lowest ranked void, setting the two widths and the center for each void;
checking each void against a set size and set pitch requirement to provide a set of acceptable voids; and
perturbing the two widths of voids in the set of allowable voids based on the successive optimization algorithm to further optimize and improve the overall performance of the 3D scattering structure.
A method for constructing a three-dimensional (3D) scattering structure comprising: 12. The method of claim 11,
wherein the size and pitch requirements established above are related to CMOS manufacturing constraints. 12. An image sensor built on the basis of the method according to any one of claims 1 to 11.

Images