# Optical Efficiency Enhancement of Nanojet-Based Dielectric Double-Material Color Splitters for Image Sensor Applications

Oksana Shramkova, Valter Drazic, Bobin Varghese, Laurent Blondé, Valerie Allié

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Oksana Shramkova, Valter Drazic, Bobin Varghese, Laurent Blondé, Valerie Allié. Optical Efficiency Enhancement of Nanojet-Based Dielectric Double-Material Color Splitters for Image Sensor Applications. Nanomaterials, 2021, 11 (11), pp.3036. 10.3390/nano11113036. hal-04447876

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Optical efficiency enhancement of nanojet-based dielectric double-material color splitters for image sensor applications

Oksana Shramkova *, Valter Drazic, Bobin Varghese, Laurent Blondé and Valerie Allié

InterDigital R&D France, 975 Avenue des Champs Blancs, 35576, Cesson Sévigné, France

* Correspondence: Oksana.Shramkova@interdigital.com

**Abstract:** We propose a new type of color splitter, which guides a selected bandwidth of incident light towards the proper photosensitive area of the image sensor by exploiting the nanojet (NJ) beam phenomenon. Such splitting can be performed as an alternative to filtering out part of the received light on each color subpixel. We propose to split the incoming light thanks to a new type of NJ-based near-field focusing double material element with an insert. To suppress crosstalk, we use a Deep-Trench-Isolation (DTI) structure. We demonstrate that the use of a dielectric insert block allows for reduction in the size of the color splitting element. By changing the position of the DTI, the functionality of separating blue, green and red light can be improved.

**Keywords:** Image sensor; color splitter; light diffraction; NJ beam deflection; double material element

1. Introduction

Image sensors are solid-state devices which are widely used in consumer electronic devices such as smartphones and various digital cameras. Depending on whether the sensor is CCD (Charge Coupled Devices) or CMOS (Complementary Metal-Oxide-Semiconductor), it will transfer information to the next stage as either a voltage or a digital signal. In the past decades we have observed significant improvement in the performance of CMOS image sensors [1-10]. Increasing the resolution of these sensors leads to the decrease of the pixel size. As a result of the size scaling each pixel gets decreased amount of light and increased spatial optical crosstalk. To address the existing problems and to improve pixel performance, diverse sensor structures were proposed. It was demonstrated that to increase the light collection efficiency and to improve optical performance we can use the image sensor with digital-microlenses [11], carefully designed periodic surface structures on crystalline silicon [8] and the front-inner lens located on the front side of the backside illuminated pixel [12]. We can also modify the shape and material of color filter [13-19]. To overcome the electrical and optical crosstalk problems, the DTI technology was proposed [8,13,20-22]. It was demonstrated that putting between pixels the deep tranches filled with lower refractive index materials compared to Si photodiodes, we can get a wall against electron diffusion preventing the interference between adjacent pixels.

For decades an absorptive Bayer color-filter array [23] has remained the dominant approach to achieve color imaging. To assess the colors, the color filters are integrated on

**Citation:** Lastname, F.; Lastname, F.²⁰

Lastname, F. Title. *Nanomaterials* 21

2021, 11, x. 22

https://doi.org/10.3390/xxxxx 23

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**Publisher's Note:** MDPI stay 29 neutral with regard to jurisdictional 30 claims in published maps and 31 institutional affiliations. 32

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the pixel array, below the microlenses. We must note that by using absorptive color filters
in image sensors, about two-thirds of the light entering a pixel is wasted by the filtering
process. Some sensor systems, such as the Foveon sensor [24], operate without absorp-
tive color filters or diffractive elements. In such systems, the pixel structure is threefold,
with three photodiodes being stacked vertically one on top of the other. The color selec-
tivity uses the fact that each color band will get absorbed after a different depth in the
silicon material. Blue radiation is absorbed in the first photodiode, and red in the last,
green being absorbed in between. Potential disadvantages of such systems include the
presence of color crosstalk as the absorption bands overlap somewhat. Moreover,
the Foveon sensor pixel size is about 7 µm which makes them less suitable for
smartphone or compact camera formats. Using the color splitters to enable light deflec-
tion at different angles for RGB wavelengths we can avoid the absorptive losses. Re-
cently, several solutions for color splitters based on new topologies were proposed. To
efficiently separate different spectral components of an optical beam it was proposed to
use symmetric and asymmetric deflectors having microscale plate-like structures com-
posed of a transparent medium with refractive index higher than the surrounding mate-
rial [25]. The proposed method has several weak points including a small aperture size of
the splitting component, a large aspect ratio between the dimensions of the color splitter
element and a high sensitivity of the proposed device to the direction of the incoming
light. Spatial splitting of incident light into RGB colors for pixel-scale color splitters based
on dielectric metasurfaces was demonstrated in [26]. A significant enhancement of the
amount of light detected by sensors was observed for the metasurface with dielectric
nanoposts. The dispersion-managed metasurface concept was used to create a RGB color
splitter. Low-index nanophotonic color splitters with the splitter element on the surface
of CMOS sensors was proposed in [27]. It was demonstrated that the created 2D and 3D
structures with as few as four layers can provide 4 times higher efficiency when com-
pared to filters alone.

Recently, we have proposed a new type of color splitters, which separate spectrally
and spatially the light reaching image sensors by exploiting the NJ beam phenomenon
[28,29]. The proposed method relies on light diffraction on the edges of constitutive parts
of the studied multi-material elements. It was observed that by combining two or more
dielectric materials with different refractive indexes we can design a NJ focusing com-
ponent capable of deviating the focused beam in the near zone [29]. Parameters of such
system control the deviation direction and the intensity of the generated NJ beam, which
must be considered as the result of recombination of the multiple NJ beams, originating
from different edges (associated with different blocks) of the microstructure. We have
demonstrated that the proposed topologies of multi-material microlenses [30] help to
reduce the size of the color splitting element as well as the optical crosstalk through the
dielectric layer.

In this work we propose a new topology of double material NJ-based color splitter
with DTI structures to suppress the crosstalk. We demonstrate that this solution im-
proves the quality of filtering and increases the sensitivity of a back-illuminated CMOS image sensor.

## 2. Materials and Methods

Figure 1a illustrates the general topology of the proposed color splitter. The cross-sectional view of the NJ-element on the top corresponds to a cuboid, cylinder or prism embedded in a homogeneous dielectric host media with a refractive index $n_1 < n_2$. The NJ-element has a dielectric insert block with a refractive index $n_3 < n_2$. We consider the electromagnetic wave incidence from the top of the elements. The topology is arranged in such a way that the NJ beams, originating from external and internal edges and having different intensities and angles of deviation, recombine and contribute to the formation of a spectrally-dependent NJ beam deflection, as illustrated in Figure 1b. The material and size of the insert block with refractive index $n_3$ can be selected based in part on the parameters of the outer block. The focal length of the NJ element with insert can be characterized as a function of the size (width or radius) and index ratio of the media inside and outside the microstructure.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** (a) Topology of a NJ-based dielectric color splitter for normal incidence; (b) Cross-section view of a color splitter with parameters of the system; (c) NJ generation by double-material elements for an inclined incidence of a plane wave.</figcaption></figure>

Let us present a set of equations to estimate the position of NJs generated by the system with $n_2>n_3>n_1$. The near-field pattern and position of NJ hot spots are determined by the form, size, position regarding the outer block and values of refractive index of the insert block. This effect is the result of an interference of, on one hand, the NJ beams as-
sociated with the top edge of the outer block of the NJ elements, and, on the other hand, the NJ beams associated with the top edge of the insert block (see Figure 1b). In this case, the intersection of NJs associated with the edges of different constitutive parts leads to the forming of hot spots located out of the axis of symmetry of the NJ element outer block. The total response of the inhomogeneous systems with dimensions larger than a few wavelengths of an incident wave represents the interplay between the NJ and Fresnel diffraction phenomena.

For the normal incidence of incident wave, the NJ beam radiation angle for constitutive parts of the NJ element can be determined as a function of the ratio between the refractive indexes of the surrounding media and material of the outer block of the lens (for the insert block, the “host medium” is the material of the outer block), and the base angle of the element. For the outer block part of the elements with refractive index n₂ and vertical edges, the NJ₁ beam radiation angle can be determined using the approximate formula:

$$ \theta_{B1} \approx \frac{90^{\circ}-\sin^{-1}\left(\frac{n_{1}}{n_{2}}\right)}{2} \qquad (1) $$

The cross point (hot spot) of the two identical and symmetrical NJ₁ generated by the external edges of the element (outer block) determines the focal length of the single material element. This focal length can be estimated as:

$$ F_{L} = \frac{W_{1}}{\tan \theta_{B1}}, \qquad (2) $$

where 2W₁ is the full width of the main part of the NJ element. Taking the height H₁ of the outer block approximately equal to the critical height [31] ($h_c \approx \lambda/(n_2 - n_1)$), we can generate the total NJ beam with maximal intensity. To determine the total width of the outer block, we take that $F_L > H_1$. So, we obtain: $W_1 > \lambda \tan \theta_{B1}/(n_2 - n_1)$.

To provide the color splitting functionality we need the input of several NJs with different angles of deviation and different intensity. To generate the NJ₂, we use an insert with refractive index n₃. In the case of a symmetrical inhomogeneous element with an insert for which n₃<n₂ and n₁<n₂, the two additional similar NJs (NJ₂) will be generated by the internal edges of the element with the insert. The NJ₂ beam radiation angle can be determined as:

$$ \theta_{B2} \approx \frac{90^{\circ}-\sin^{-1}\left(\frac{n_{2}}{n_{3}}\right)}{2} \qquad (3) $$

The proposed example ratio between the refractive indexes leads to a result in which $\theta_{B2} < \theta_{B1}$, and NJ₂ is less intensive than the NJ₁.

The size (width and height) of the insert may be selected based on parameters of the outer block and on the refractive index n₃. If n₂ ≤ 2, it is desirable for the generated NJ₂ not to cross the vertical edges of the main element to avoid the additional NJ refraction at the boundary between the material of outer block and host medium. So, parameters may be selected such that $AA' < 2W_1$ and $W_2 < 2(W_1 - H_1 \tan \theta_{B2})$. If n₂ > 2, NJ₂ will be reflected by the vertical wall due to the total internal reflection phenomenon. So, to get a maximal distance between NJ₁ and NJ₂ in the Si substrate, the width of the insert may be selected to provide favorable conditions to get AA' as close as possible to the full width of the outer block. The maximal input of NJ₁ may be observed when NJ₁ does not cross the insert. So, we get:

$$ H_2 < \frac{W_1 - \frac{W_2}{2}}{\tan \theta_{B1}}. \qquad (4) $$

For the chosen size of the outer block, we will observe at least two NJ hot spots (crossings of NJ₁ and NJ₂, see Figure 1b) symmetrically situated relative to the axis of symmetry inside the outer block. Outside the element there may be four NJs penetrating into the Si substrate. First two NJs (NJ₁) will cross the boundary between the element and substrate at points B and B'. The NJs of second type (NJ₂) will cross the boundary between the element and substrate at points A and A'. Inside Si, the radiation angles of all
these NJs will be reduced due to the refraction phenomenon, and the NJs of different types will be closer to each other.

For better separation of the NJs, we propose to use DTI. In an example, two symmetrically positioned (relative to the axis of symmetry of the single element) deep-trenches are located inside the substrate. To get the desirable color splitting function, each deep-trench should be placed between the NJs penetrating into the silicon substrate:

$$W_1 - H_1 \tan \theta_{B1} < \frac{W^*}{2} < \frac{W_2}{2} + H_1 \tan \theta_{B2}. \quad (5)$$

Here $W^*$ is the minimal distance between DTs as shown in Figure 1b.

Let us now consider the effect of the angle of plane wave incidence on the properties of generated NJ beam (see Figure 1c). In the case of plane wave oblique incidence on the outer block with refractive index $n_2$, two opposite vertical edges of this block will generate two NJs with nonequal beam radiation angles:

$$\theta'_{B1} \approx \frac{90^{\circ}-\sin^{-1}\left(\frac{n_1}{n_2}\right)}{2} + \frac{\alpha}{2}, \quad (6)$$

$$\theta''_{B1} \approx \frac{90^{\circ}-\sin^{-1}\left(\frac{n_1}{n_2}\right)}{2} - \frac{\alpha}{2}.$$

where $\alpha$ is the angle of electromagnetic wave incidence.

In a similar way, the NJ beam radiation angles for the insert can be determined as:

$$\theta'_{B2} \approx \frac{90^{\circ}-\sin^{-1}\left(\frac{n_3}{n_2}\right)}{2} + \frac{\alpha}{2}, \quad (7)$$

$$\theta''_{B2} \approx \frac{90^{\circ}-\sin^{-1}\left(\frac{n_3}{n_2}\right)}{2} - \frac{\alpha}{2}.$$

A system optimized for normal incidence may have poor splitting functionality in the case of inclined incidence. To improve the efficiency for a wider range of angles of incidence, the parameters of the system must be optimized taking into account that $\alpha>0$. Finally, for $\alpha>0$ Eq. (5) will take the form

$$W_1 - H_1 \tan \theta'_{B1} < \frac{W^*}{2} < \frac{W_2}{2} + H_1 \tan \theta''_{B2}. \quad (8)$$

Considering a periodic array of such elements with the inserts, inside the substrate and close to its surface we will observe periodic alternation of the hot spots for the NJs of the same type: NJs of first type will have their crossing points at the axis of symmetry of the elements; NJs of second type will provide hot spots at the boundaries of the pitches. Upon changing the pitch of this system, the intensity of the hot spot can be adjusted.

### 3. Results

To evaluate the EM response of the system, numerical simulations of a periodic array of 2D double-material elements with the inserts were performed using the COMSOL Multiphysics software. It was assumed that the system is illuminated by a linearly TM-polarized wave. To model wave propagation in a single unit cell of the array, on either side of the unit cell we use periodic boundary conditions with Floquet periodicity. To avoid non-physical reflection, we model the open boundaries using the perfectly matched layer domains. To measure the changing of the incident light transmittivity we scan the power density between the deep-trenches at some depth $d_{A,B}$ inside the Si layer (see Figure 1a).
In Figure 2 the color splitting functionality of a proposed system is illustrated using the power distribution for two wavelengths. It can be seen that for the red color band central wavelength (λ =700nm) main power is transmitted through Port A. In a case of wavelength corresponding to the green color band (centered on λ =500nm) the main part of the light will be transmitted through Port B.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Calculated power distribution in the unit cell for (a) λ =500nm, (b) λ =700nm</figcaption></figure>

The dependence of transmitted integral power density on the wavelength for 2 dif-
ferent positions of the ports (Port A and Port B) inside the Si layer (see Figure 1a) is pre-
sented in Figure 3. The simulations presented below correspond to such parameters of
the system selected for λ=620nm to provide red color splitting functionality. It is assumed
that the host medium has a refractive index n₁=1.0, system is periodic with d=1200nm.
Using the formula provided above and additional numerical optimization an embodi-
ment is selected using a system with n₂=2.0, n₃=1.4, H₁=600nm, H₂=400nm, W₁=380nm,
W₂=240nm. A layer of SiNₓ with a thickness of dARC=200nm and refractive index 2.04 as
an antireflection layer is adopted. The DTI layers are simulated with SiO₂ material with a
refractive index of 1.5; W*=440nm, dDT=100nm. It is possible to observe that at Port A we
can register the maximal transmitted power at wavelengths corresponding to the red
color, while other wavelengths are registered at Port B.

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<caption>**Figure 3.** Transmittivity for the full visible spectrum at normal incidence and different positions of the ports inside the silicon layer: (a) $d_A = d_B = 100$nm; (b) $d_A = d_B = 1500$nm. Red curves correspond to Port A, blue curves correspond to Port B.</caption>

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Our analysis of the effect of anti-reflection coating on the transmittivity of the inci-
dent light has demonstrated that increasing the thickness $d_{ARC}$ we can increase the por-
tion of light transmitted through the Port A at the red color wavelengths. Moreover,
uniformity of the distribution can be also improved.

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<caption>**Figure 4.** Total transmittivity measured for three different RGB colors at normal incidence and $d_{ARC}=200$nm, $d_{DT}=100$nm, $W*=440$nm for two different values of refractive index $n_3$: (a) $n_3=1.4$; (b) $n_3=n_2=2.0$</caption>

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Figure 4 shows the dependence of total transmittivity measured for two ports at different depths for three different RGB colors at normal incidence. We can also observe the effect of refractive index of the insert on the color splitting functionalities of the system. It can be seen, that for $n_3=1.4$ (see Figure 4a) Port A effectively registers red colored
light. Green and blue colored light can be registered at Port B. Placing the photodiodes or other photodetectors for green and blue colors at different depths we can improve the ability to differentiate between them. By increasing the refractive index of the insert, the angles for $N_{J2}$ are decreased. As a result, the position of point A (see Figure 1b for normal incidence) will be shifted. To observe the effect of an insert on the characteristics of the proposed NJ element, Figure 4b corresponds to the case of single material block with $n_{3}=n_{2}$. The simulations show that the power transmitted through Port A rises with the refractive index of the insert. Correspondingly, the portion of power for green and blue colors registered at Port B will be decreased. Finally, in the case of a single material block, the main part of the power for the three colors will be transmitted through Port A.

The thickness and position of DTIs also affect the color splitting functionality of the device, as shown in Figure 5. The high red color transmittivity through the Port A can primarily be observed starting from some critical distance between the deep-trenches. It was demonstrated that the value of the critical distance rises with the thickness of the deep-trenches. It also depends on the position of photodetectors. Increasing $W^*$ can significantly reduce the transmittivity through Port B corresponding to green and blue colors. The presented simulations were obtained for $d_A = d_B = 100$nm and $d_{DT}=100$nm. Rise of the DTI width ($d_{DT}$) leads to an additional decreasing of the green and blue colors' transmittivity through Port B. For example, at $W^*=440$nm and $d_{DT}=200$nm we get about 10% less of transmitted green and blue color light at Port B. It was demonstrated that increasing the distance $W^*$ up to 540nm for $d_A = d_B = 800$nm we get 50% of transmitted red color light at Port A, 35% of transmitted green color light and less then 10% for blue color at Port B.

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Total transmittivity measured for three different RGB colors as a function of the distance between the deep-tranches at normal incidence and $d_{ARC}=200$nm, $d_A= d_B=100$nm, $d_{DT}=100$nm.</figcaption></figure>

The numerical simulations presented in Figure 6 demonstrate the transmittivity of RGB colors for an inclined incidence. It is possible to observe that the portion of power transmitted through Port B and corresponding to the blue band dramatically drops with the angle of incidence. At $\alpha=15^\circ$ the main part of blue color will be transmitted through Port A. In the case of green color, for all three angles of incidence, the main part of the
power will be transmitted through Port B. As it was mentioned before, keeping the same parameters for the NJ elements while changing the position of the deep-trench structures can redistribute the portion of power transmitted through the ports due to the limitation of the NJ input. Finally, it dramatically affects the power redistribution in the case of inclined incidence. It was obtained that decreasing W* the green and blue color transmittivity through Port B will be improved, but red color transmittivity through Port A will be decreased. Upon increasing W* the efficiency of the proposed color splitter may be improved for the red color, but blue and green color performance will become worse.

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Total transmittivity measured for three different RGB colors as a function of the distance between the deep-tranches at normal incidence and $d_{ARC}=200nm$, $d_{DT}=100nm$, W*=440nm for inclined incidence $α=15°$</figcaption></figure>

## 4. Discussion

In this paper we have demonstrated that for some particular parameters the NJ-based double-material element can split incident colors. To split the colors, the proposed system uses a dielectric element with an insert, where the outer block of this element is a dielectric material with refractive index $n_2$, and $n_3$ is the refractive index of an insert (with $n_2>n_3>n_1$, where $n_1$ is the refractive of the host medium). The position of focal spot, angle of deviation, intensity and shape of NJ beam can be controlled by the variation of the refractive indexes and sizes of the constitutive parts/blocks. We proposed to combine the double-material elements with DTI structures to suppress crosstalk. Choosing the proper position of deep-tranches, we can enhance the optical efficiency of the proposed color splitter. We demonstrated that upon changing the parameters of constitutive parts of the elements and choosing the proper depth for the detection we can obtain so-called blue, green, and red separation functionality.

In contrast to the classical absorptive solutions proposed double-material elements with the inserts provides increased light intake. Such solution has one or more of the following benefits: simpler pixel architecture; relaxed need of a focusing lens on top of the photodiode in the pixel architecture, as the color splitter element provides focusing effect as well; reduced risk of crosstalk due to DTI technology; better optical efficiency
due to thinner optical stack (less losses) and DTI structure; better angular performance with regards to the angle of the incident light; and the ability to split three colors.

We must note that the proposed solution applies for TE and TM polarizations. But to get the maximal efficiency, the system should be optimized taking into account the polarization of an incident wave.

We also must mention that proposed multi-material design can provide less constrained fabrication process due to the lack of high aspect ratios and small feature sizes. On the other hand, the complexity of fabrication could be related to the sophisticated shape of the main block. In collaboration with the company *Vmicro* from France we have fabricated single-material u-shaped periodic structure described in [32]. Full u-shape element was fabricated by the e-beam lithography using the mask materials for the protection of the different areas at different fabrication steps. To fabricate the multi-material element, we may pattern the new mask and apply Plasma Enhanced Chemical Vapor Deposition technique for deposition of the second material.

**Author Contributions:** Conceptualization, O.S.; investigation, O.S., L.B., V.D., B.V.; writing—original draft preparation, O.S.; writing—review and editing, O.S., B.V., V.D., V.A.; project administration, V.A. All authors have read and agreed to the published version of the manuscript.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author

**Conflicts of Interest:** The authors declare no conflict of interest

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