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This paper deals with the integration of metallic and dielectric nanostructured planar lenses into a pixel from a silicon based CMOS image sensor, for a monochromatic application at 1.064 μm. The first is a Plasmonic Lens, based on the phase delay through nanoslits, which has been found to be hardly compatible with current CMOS technology and exhibits a notable metallic absorption. The second is a dielectric Phase-Fresnel Lens integrated at the top of a pixel, it exhibits an Optical Efficiency (OE) improved by a few percent and an angle of view of 50°. The third one is a metallic diffractive lens integrated inside a pixel, which shows a better OE and an angle of view of 24°. The last two lenses exhibit a compatibility with a spectral band close to 1.064 μm.
© 2016 Optical Society of America
1. Introduction
The interest of the Near Infrared (NIR) spectral band (800–1400 nm) in imaging applications is well established. Indeed, these waves are less scattered than visible light and there is a great potential of applications in the field of security and defence. For instance, NIR lasers are already involved on the modern battlefield in many applications, from detecting the range of an object to designating a target [1]. Image sensors dedicated to NIR detection are mostly made of III–V materials like indium gallium arsenide (InGaAs) thanks to a quantum efficiency superior to 75% in this spectral range [2]. However, there is a strong interest in using complementary metal oxide semiconductor (CMOS) silicon-based image sensors in order to drastically reduce manufacturing costs. This implies a shorter NIR wavelength window from 800 nm to 1100 nm due to the operational spectral band of silicon. Unfortunately, this spectral band being very close to the silicon wavelength cut-off, the absorption coefficient is less than 800 cm−1 from 900 nm up to longer wavelengths [3] (by comparison the absorption coefficient of InGaAs is superior to 104 cm−1). Thus Si-based photodiodes present a quantum efficiency of a few percent in NIR spectral band [4]. There is one notable exception concerning black silicon [5, 6], fabricated using advanced ultrafast laser processing technology, which allows to breakthrough silicon’s fundamental spectral limits up to 1200 nm: the absorption coefficient in NIR is superior to 3000 cm−1. Nevertheless, this material process is currently not mature enough to be integrated in CMOS foundries.
In a conventional pixel of a CMOS image sensor, as represented in Fig. 1, the circuit complexity is detrimental to optical propagation [7]: as the number of metallic interconnections increases above the photodiode, the light collection efficiency is reduced due to reflection and diffraction phenomena. Considerable efforts are made to optimize the pixel design but can become a complicated task for CMOS sensors with high electronic processing density [8]. That is why extensive research has been carried out to relax constraints on this compromise. For example, advanced light-guide [9] and backside illuminated (BSI) pixel technologies [10] have been developed in the past years. Although BSI CMOS sensors are used in the industry for visible detection, they have a limitation for NIR range. Indeed, the silicon region is a thin membrane with a thickness of a few microns (in particular to implement trough-silicon vias) whereas for NIR detection, it should be significantly thicker due to the absorption depth of silicon superior to 900 μm. Another solution is to integrate a light collector at the level of each pixel to enhance optical transmission leading to an enlarged photon flux on the photodetector. Therefore External Quantum Efficiency (EQE), which measures the fraction of the incident photon flux that contributes to the photocurrent in the pixel, increases. These light collectors also help to decrease the inter-pixel crosstalk, even for BSI CMOS sensors. Moreover, a small focus spot allows a reduction of the photodiode area in order to reduce dark current.
Fig. 1 CMOS image sensor without spectral filter and microlens: (a) 3D schematic [14] and (b) SEM picture cross-section
Standard light concentrators for CMOS image sensors are convex micro lenses, which have already been well investigated in the past years [11–14]. These lenses are established as a reference for CMOS image sensors for years but present some disadvantages. Lenses produced using the photoresist reflow method can have large deviations from their spherical properties [15, 16]. Another drawback is when pixel size scales below 2 μm, diffraction affects the optical performance of the pixel [17]. Metallic and dielectric diffractive planar lenses could be an interesting alternative as they can be fabricated by standard lithography process already managed by CMOS foundries. Such structures can be deposited at the top of passivation layers (“post-process”) or integrated during the process fabrication (“in-process”) inside the oxide stack. As an illustration of using patterned metal layers for an optical function, the integration of metallic gratings as color filters in a standard CMOS pixel was previously proposed [18–20].
One of the planar lenses widely explored in recent years is the Plasmonic Lens [21–23]: focalization is produced by modulating light phase through nano-slits of various width drilled in a metallic film. They were suggested as integrated micro-lenses to improve the efficiency of pixels in solid-state image sensors [24–26]. An alternative design was proposed as a single slit of sub-wavelength width surrounded by grooves in a metallic layer enhancing light collection [27]. The focalization performance has been well demonstrated but the complex combinations of nanoscale high aspect ratio structures is nowadays an important technological constraint for mass production. There is also the possibility to integrate planar diffractive amplitude lenses called Fresnel Zone Plates [28] or Huygens Lenses [29], and diffractive phase lenses called Phase Fresnel Lenses [30]. Integration of these lenses into CMOS process fabrication have been studied [31], showing a good compatibility with mature processes. However, specific attention is needed to figures of merit linking lens efficiency and detector performance leading to critical analysis. Furthermore, planar lenses have not been implemented into pixels of a CMOS image sensor.
In this paper, we study complete integration of a Plasmonic Lens, Huygens Lens and Phase Fresnel Lens for a CMOS image sensor dedicated to monochromatic near-infrared detection, at 1.064 μm. This wavelength is typical of this spectral band, exploited for Nd:YAG laser imaging applications, close to silicon gap cut-off. Flux and cartographies obtained by numerical simulations through Finite-Difference Time-Domain (FDTD) method using MEEP software [32] will be presented. In section 2, the figures of merit and modeling aspects are defined. We will then discuss the problem of light propagation in a pixel in section 3. In section 4, theory and two-dimensional (2D) simulations will describe physics and results of lens integration. In section 5 three-dimensional (3D) simulations will be dedicated to a Phase-Fresnel lens post-process integrated and section 6 to a Huygens lens in-process integrated. Section 7 will present conclusions and perspectives.
2. Simulations
2.1. Figures of merit
The EQE is the fraction of the incident photon flux contributing to the photocurrent in a pixel. In other words, it is the product of the internal Quantum Efficiency (QE) by the photon flux reaching the photosensitive area.
To properly evaluate this photon flux, the Optical Efficiency (OE) [12] is defined as the fraction of optical flux incident on the surface of each pixel that reaches the intended photodiode:
where n = (0, 0, 1), Ptot and Pinc respectively the total Poynting vector through the surface of the photodiode and the incident Poyting vector through the surface of the pixel.The Joule losses Q inside the metallic interconnections are calculated to highligh and compare the performances of each lens [20]:
where ω is the angular frequency, ε0 is the vacuum permittivity, ℑ(εr) is the imaginary part of the metal relative permittivity.In a photodetector, the Signal-to-Noise Ratio (SNR) is defined as the ratio of the photocurrent to the noise current. In a CMOS image sensor, there are multiple noise sources like photon noise from the incident photon flux, noise associated with operation of the photodiode, and noise coming from analog readout circuitries [33].
In this paper, only random generation of electrons and holes in the photodiode will be considered, which is proportionnal to the dark current thus varies as the square root of photodiode area. Other noise sources are uncorrelated with the light collection and thus not estimated in these simulations. And because QE is constant (only depends on material and wavelength), an approximated SNR is thus defined as:
All FDTD simulations have been performed with an incident plane wave at 1.064 μm. Simulation results will be also presented in the form of electric-field intensity cartographies to evaluate light focalization. Polarization is Transverse Magnetic (TM) for 2D simulations: since a lens has a revolution symmetry, TM corresponds to the polarization state along a transverse cross-section in 3D. In addition, TM polarization will allow us to compare the Plasmonic Lens performance with the pixel and other planar lenses. In 3D designs, the electric field is parallel to y-axis.2.2. Modeling aspects
2D simulations have been computed with a Yee grid size of 5 nm and a set of Perfectly Matched Layers (PML) are used along propagation axis z, to truncate the substrate (below silicon) and superstrate (air). Bloch conditions in x and y are set to consider the simulated structure inside a an array of pixels. The result is that a FDTD simulation takes 6 hours by Central Processing Unit (CPU). These FDTD parameters are obviously different for 3D simulations being bigger and more source intensive. Yee grid size becomes 50 nm so that the amount of time of simulations remains reasonable, 83 hours by CPU, with identical PML and Bloch condtions.
Convergence has been calculated through an energy balance [20] by adding reflection at the top of pixel, transmission at the silicon interface and Joule losses inside metallic interconnections (equivalent to absorption). When 100% is obtained for 2D simulations, this total energy is reduced to 97% in 3D simulations probably due to a larger mesh grid size.
3. Pixel: the problem of light propagation
A pixel from a CMOS image sensor in Fig. 1(a) contains a photodiode made of silicon and a readout circuitry with transistors transferring and extracting the electrical signal. Above the photosensitive area, a dielectric stack mostly made of SiO2 includes metallic “rails” made of Aluminium (using εr = −97.903 + 27.676 i) to perform interconnections between transistors.
Our diffractive planar lenses are planned to be integrated on pixels where color filters and light concentrators are missing, shown in Fig. 1(b). Indeed, the purpose of this work is to improve light collection by considering a monochromatic illumination, or light propagation just below an infrared filter.
Each 5×5 μm2 pixel has an oxide stack of 3.9 μm thick. 2D electromagnetic simulations demonstrate that the metallic interconnections disturb the light propagation up to the photo-diode shown in Figs. 2(a) and 2(b). The photodiode width is 4.3 μm. Numeral calculations indicate that 82% incident photons would reach the photosensitive area if there is only the oxide stack without any metal interconnexion. This value is close to the photodiode filling ratio (86%), which means the oxide stack exhibits a satisfying transmission. In the real pixel, OE is only 65%, mainly because of high reflection of metal layers. The Joule losses Q are 4% inside the three metallic interconnections.
Fig. 2 FDTD simulations results of a pixel without lens. (a)(b) 2D results of the electric-field intensity at 1.064 μm, when a TM plane wave (Hz = 0) is incident, with corresponding profile at the photodiode surface. (c)(d) 3D view and top view at photodiode interface. The red dashed rectangle represents the photodiode area.
This effect is even more visible with 3D simulations. The three-dimensional complex geometry of metallic interconnections perturbs even more the light propagation, shown in Figs. 2(c) and 2(d). The photodiode area is 3.44×4.3 μm2, corresponding to a filling ratio of 60%. The dielectric stack would transmit 56% incident photons into the photodiode, as expected slightly inferior to filling ratio. The pixel OE is only 48% and there is absolutely no flux uniformity at the photodiode interface. There is therefore a need to integrate a light collector to increase OE and so the sensor performance.
4. Two-dimensional integration of planar lenses: theory and results
In order to increase the Optical Efficiency, three different planar lenses have been tested. First of all, each lens is designed according to theory and simply integrated at the top pixel surface. Then optimization has been performed by slightly varying the dimensions parameters: position, width of slits/grooves and thickness. Because this optimization process has been done in 2D (invariance along x), the following lenses are considered cylindrical.
4.1. Plasmonic lens
A Plasmonic Lens (PL) is a metal nanoslit array (see Table 1), with a phase front curvature generated by the phase delay through individual slits so that each waves are in phase at the focal point. The physics involved in designing these planar lenses depends first on the fundamental mode of each slit, following the dispersion relationship [34]:
with β the propagation constant of the fundamental mode of each slit, k0 the free space propagation constant, εm the permittivity of the metal, and w the slit width. The phase delay introduced by a slit is given by βd, with d the film thickness. Each phase delay has to match with the required phase retardation ϕ as a function of distance y from the center of the lens, in order to produce a focalization at the desired focal distance f: where λ is the wavelength, nI is the refractive index of the material beneath the lens and m an integer. The optimum designed PL was integrated at the top of the pixel. The metal layer is Copper (using εr = −49.782 + 5.3505 i) with a thickness of 1400 nm, and the slit widths are from 10 nm to 100 nm. Despite a satisfying focalization performance shown in Figs. 3(c) and 3(d), this plasmonic light concentrator only transmits 26% of photons into the photosensitive area. This phenomena is mainly due to the absorption (almost 46%) inside the metallic parts of the lens, where the electric field is concentrated. The reflection of the Plasmonic Lens is 28%. The calculated Joule losses inside metallic interconnections are reduced to 0.3%.
Table 1. Schematics of planar lenses integrated in a CMOS pixel
Fig. 3 2D FDTD calculated results of the electric-field intensity at 1.064 μm, when a transverse magnetic plane wave (Hz = 0) is incident (a) for a pixel without lens, and when (c) a Plasmonic, (e) Huygens, and (g) Phase-Fresnel lens is integrated. These planar lenses are represented with black dashed lines. (b,d,f,h) are the related transverse profile at the photodiode surface respectively for structure shown in (a,c,e,g).
4.2. Huygens lens
The Huygens Lens (HL) consists in a central aperture engraved in a thin metallic layer, and surrounded by several identical single mode slits producing interferences at the desired focal point (see Table 1). The design will be performed thanks to both equations below [29]:
with D0 the width of the central aperture, Di the distance between the two identical slits forming the ith pair.The simulated Huygens Lens shown in Figs. 3(e) and 3(f) presents a central aperture of 2.4 μm and only one pair of 530 nm slits for a lens width not exceeding pixel dimensions. The metal layer is aluminium with a thickness of 100 nm. The calculated OE is 51% because of an important reflection near 43%, due to metallic filling ratio. Joule losses are 1.2% inside metallic interconnections.
4.3. Phase-Fresnel lens
The Phase Fresnel Lens (PFL) is constructed of a series of concentric dielectric ridges (see Table 1) which delay the phase of the transmitted optical beam to form a curved wavefront [30]. With a lens phase profile ϕ(y) strictly identical to the PL one (4), a thickness profile t(y) is defined as:
where nlens is the refractive index of lens material. This profile must be discretized to be compatible with CMOS process fabrication: a top structuration alternating open zones and others which retards the incident wave of π radians, combined with a constant dielectric step-height which also has a π retardation. We studied the effect of constant layer in the PFL, shown in Fig. 4. Actually it is quite possible to construct a Phase Fresnel Lens with only the structured top part, corresponding to a π retardation. However one of several process parameters that limits the diffraction efficiency η, defined as the ratio of optical power diffracted into a designated direction, is the variation of film thickness t [30]:That means η is maximum for a thickness tmax = λ/(nlens − 1) conform to a a 2π retardation.
Fig. 4 2D FDTD calculated results of the electric-field intensity at 1.064 μm, when a TM plane wave is incident for a PFL (a) with maximum thickness corresponding to π phase, and (c) maximum 2π phase. The black dashed lines represent PFL. (b,d) are the related transverse profile at the photodiode surface respectively for structure shown in (a,c).
Consequently, to binarize the thickness profile and to reduce phase discontinuities, the PFL consists of π and 2π zones.
4.4. Performance comparison
The design of Plasmonic Lens consists in a high aspect ratio of 140, between thickness and minimum slit width, which is detrimental nowadays to an integration into CMOS process. Thus PL is hardly compatible with current CMOS technology. In addition, this lens is not really competitive due to a notable metallic absorption inside each nanoslit.
Table 2. Performances and integration of planar lenses dedicated to a CMOS pixel
The Huygens lens could prove interesting performance if the ratio of the photodiode area to the whole pixel area, called the Fill Factor, was decreased as shown in Fig. 5. Some CMOS image sensors present a low Fill Factor for high speed application [8]. And because the metal thickness does not play an important role in its behaviour (just thick enough to be opaque), the idea is to implement the HL at the uppermost metallic level, near the top of the pixel, exploiting metallization process already present in CMOS process fabrication. Obviously, this metal layer must not be connected to any circuitry. For this reason, the 3D design of an integrated metallic lens “in-process” is presented in section 6 (see Table 2).
Fig. 5 2D calculated OE as a function of a virtual photodiode width whose center is at the middle of the pixel, at 1.064 μm, when a TM plane wave is incident.
The Phase-Fresnel made of silicon nitride exhibits the best performance of the three lenses presented in this paper, described in Figs. 3(g) and 3(h). Even if there are only three alternate zones, the calculated reflection is less than 5% when the OE reaches 88% and Joule losses are 1.4% Fig. 5 indicates a good OE for this lens whatever the Fill Factor. This lens will be implemented into an existing CMOS image sensor, at the surface of a pixel, following a “post-process” integration in section 5.
5. 3D post-process: phase-Fresnel lens integration
5.1. Monochromatic source
The aim is to design and integrate a dielectric PFL at the surface of a pixel from an existing CMOS image sensor. A first circular lens is designed according to the dimension parameters from 2D simulations (Section 4.3) at the top of a pixel without metallic interconnections. Optimization is then performed by varying position and dimension parameters to find the maximum OE. Finally, this PFL is implemented to a real pixel for further and final optimization.
A circular PFL was designed in Fig. 6(c) with a central aperture of 2.8 μm, and a outer diameter of 4.5 μm, not exceeding pixel dimensions. The structured top layer is made of silicon nitride with a thickness of 590 nm, and constant step of silica with a thickness of 800nm described in Fig. 6(e), to make future process fabrication easier.
Fig. 6 3D view and top view of FDTD calculated results of the electric-field intensity at 1.064 μm, (a)(b) for a pixel without lens, (c)(d) for a circular Phase-Fresnel lens “post-process” integrated where (e) is the thickness profile of this lens. The red dashed rectangle is the photodiode area. Plots (f) and (g) are respectively 3D calculated OE and SNR as a function of a virtual photodiode area whose center is at the middle of the pixel.
FDTD simulations show that PFL produces a focus spot well delimited in Fig. 6(d), whereas the Optical Efficiency has slightly been improved by a few percent in Fig. 6(f). This surprising result can be explained by the pixel dimensions. Indeed, this pixel is too small considering the wavelength, in order to have a PFL with several rings. However, this circular lens leads to better SNR as described in Fig. 6(g). Joule losses are reduced as well from 5.5% to 3.2% for this pixel with a PFL.
5.2. Angular tolerance analysis
Because CMOS image sensors are supposed to be mounted into a camera with an objective lens, the mean angle of incidence varies as a function of pixel’s position. So there is a clear need to know the angular tolerance of PFL. Electromagnetic simulations have been done with several angles of incidence as seen in Fig. 7. We demonstrate that a PFL is able to focalize into the photodiode for an angle of view of 50°. It is important to precise that there is no difficulty at all to adapt the PFL for a particular angle of incidence: either by a position shift or by a design modification by introducing a phase term in the phase profile.
Fig. 7 Top view of FDTD calculated results of the electric-field intensity at 1.064 μm with a particular angle of incidence for a circular PFL. The table compares OE of a pixel and with a lens. The red dashed rectangle represents the photodiode area.
5.3. Spectral analysis
FDTD simulations were performed with a polychromatic source from 0.8 μm to 1.1 μm, and OE calculations have been done for two photodiode areas in Fig. 8 : 4 μm2 and 15 μm2. Because the optical properties of materials depend on wavelength, the OE of a pixel without metallic interconnections will be plotted. And to evaluate the lens performance, the spectral behaviour of a pixel without lens is studied. Aluminium frequency dispersion is implemented according to the Lorentz-Drude model [35], and optical constants of dielectric materials and silicon [3] are specified for each wavelength to reduce an important amount of time for the computation. That means 100 plane-wave simulations have been performed for spectral analysis.
Fig. 8 Calculated OE as a function of wavelength for the oxide stack (pixel without metallic rails), for a pixel and with a circular PFL integrated. Simulations have been performed for an photodiode area of (a) 15 μm2 and (b) 4 μm2.
First of all, the oscillations of OE are due to interferences caused by reflections inside the dielectric stack. These standing waves are clearly present in the pixel without metallic interconnections. This effect is very perturbed in the pixel with metal. For a large photodiode of Fig. 8(a), by reason of a Fill Factor of 60%, the OE cannot exceed this value when there is only dielectric material inside the stack. As expected in the pixel, less photons reach the photodiode whatever the wavelength due to diffraction and reflection phenomena. The PFL exhibits a OE improvement for a spectral band near the wavelength optimization. The performance of PFL declines with wavelength far from our reference. For a smaller photodiode of Fig. 8(b), OE in a pixel is better than the same oxide stack without metal. Actually, one hypothesis is that the metallic rails around the photodiode diffract light into the photodiode. Therefore, this effect is taken into account for a small photosensitive area. The PFL shows an OE increased by at least 10% for this large spectral band.
6. 3D in-process: metallic lens integration
6.1. Monochromatic source
In section 2.3, we demonstrated that a metallic lens could be efficient for a CMOS pixel with a low Fill Factor. Thus we designed a HL inside the oxide stack of low Fill Factor pixel with a photodiode area of 2.3 μm2 describes in Figs. 9(a) and 9(b). The same optimization process explained in section 5 is applied here.
Fig. 9 3D view and top view of FDTD calculated results of the electric-field intensity at 1.064 μm, (a)(b) for a pixel without lens, (c)(d) for a circular metallic lens integrated “in-process”. The red dashed rectangle is the photodiode area.
Metallic “rails” are implemented at several levels inside the oxide stack, where level positions depend on fabrication process technology. The Huygens Lens, made of Aluminium, will be thus designed using the uppermost metal level because other metallic interconnections must interact as little as possible with light propagation. The calculated OE for this pixel is 21%. The focalization distance is 2.8 μm, which results to important impact on the design.
The central aperture of circular HL is 3.5 μm. The pixel dimensions do not allow to add slits in the lens design. Cartography results are shown in Figs. 9(c) and 9(d). The focus spot is degraded and not as uniform as 3D simulations of PFL. This effect is related to the combination of incident wavelength (1.064 μm) compared to focalization distance: the lens aperture should be smaller to properly produce an uniform central spot. But this configuration would be at the expense of number of transmitted photons. Therefore we designed a lens where the focalization point is deep inside the silicon instead of photodiode surface. Despite this disadvantageous configuration, the Optical Efficiency with HL has increased of around 5% in absolute terms. The reflection is 41% and is consistent with 2D simulations. Joule losses are reduced from 4.7% to 1.4% for this pixel with a HL.
6.2. Angular tolerance analysis
As in section 5.2, electromagnetic simulations were performed with different incident angle conditions for the circular metallic lens as seen in Fig. 10. HL is effective for an angle of view of 24°. This low value was expected because of a shortened focal distance and a photodiode area smaller than before. Despite all this, we collect more photons on the photosensitive area in this angle of view condition.
Fig. 10 Top view of FDTD calculated results of the electric-field intensity at 1.064 μm with a particular angle of incidence for a circular HL. The table compares OE of a pixel and with a lens. The red dashed rectangle is the photodiode area.
6.3. Spectral analysis
As previously, we studied the spectral behaviour of the circular HL with a polychromatic source in Fig. 11 from 0.8 μm to 1.1 μm. The Huygens Lens show a OE improvement by 5% in absolute terms especially between 0.9 μm and 1.15 μm. The maximum performance is still near λ = 1.064 μm.
Fig. 11 Calculated OE as a function of wavelength for the oxide stack (pixel without metallic rails), for a pixel and with a circular HL integrated.
7. Conclusion
In this paper, we investigated in the complete integration of three planar lenses: a Plasmonic Lens, Huygens Lens and Phase-Fresnel Lens for a CMOS image sensor dedicated to monochromatic near-infrared detection at 1.064 μm. We demonstrated by 2D electromagnetic simulations that the Plasmonic Lens exhibits high metallic absorption and is hardly compatible with CMOS specifications. Huygens Lens shows a better Optical Efficiency for pixels with low Fill Factor, whereas Phase-Fresnel Lens is competitive for any pixel configurations.
Electromagnetic simulations of a Phase Fresnel lens integrated at the top of a pixel exhibits an Optical Efficiency improved by a few percent for a large photodiode but leads to high SNR for low Fill Factor pixel. PFL exhibit an angular tolerance with a an angle of view of 50°, and a large-band source compatibility in NIR region. Finally, a Huygens lens integrated inside a pixel (on a metal level) was studied and showed a better OE of 5% in absolute terms, an angle of view of 24° and a compatibility with a spectral band close to 1.064 μm.
As a perspective, it is planned to fabricate and integrate these two planar lenses (HL and PFL) into CMOS image sensors in order to evaluate experimentally their performances. The conception of nanostructured planar lens with a filtering function will be also studied.
Acknowledgments
We thanks Direction Générale de l’Armement (DGA) for a financial support to this project. This work was granted access to the HPC resources of CALMIP supercomputing center under the allocation 2015-[P1441].
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